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Multiferroics: Crystals and Thin Films Abstract Multiferroic materials have generated increasing interest in the scientific community over the past decade, because of the unique coexistence of ferroic properties and possible potential applications for new types of next generation novel devices. In this report, I present the analysis of the structure, properties, processing, characterization and potential applications of multiferroic crystals and thin films, covering structured FE properties (Polarization, leakage, switching), Magnetic properties (canted and excess magnetism), Domains in films (100/110/111 and switching), Probing Antiferromagnetism (with SHG, THz and XMLD), Coupling between FE and AFM, Coupling between FE, AFM and FM, Coupling in nanopillar heterostructures, research progresses, potential applications of Multiferroics and concluding with my suggestions. To present the overall view for the deeper understanding of multiferroics, I have covered right from the study of Materials, Electronic materials, Metal Oxides, Transition Metal oxides (TMO), properties of TMO, Thin film processing (PLD, CVD, Sputtering, MBE) and then I have proceeded with to the in depth analysis of Multiferroic Crystals and thin films right from its crystal chemistry using BiFeO3 as a model system.

Pradeep D Iyer UGR Advisor: Dr. Ramesh Ramamoorthy

Department of Materials Science & Engineering University of California, Berkeley, CA 94720, USA E-mail:pradeepdiyer@berkeley.edu

1.0 Introduction The continuous research, developments and discoveries in the field of Condensed-matter, especially in the sub fields of Material Physics and Material Chemistry in the 20th century, has made possible the massive technological progress in the fields of Microelectronics, optoelectronics, Bio-electronics, computing and data storage. The vertical integration of material science and engineering through thin film technology; has developed and produced more complex sensors, integrated circuits, displays, bio-electronic devices, data storage and recording devices. The quest for producing miniaturized and more powerful devices with less power consumption drives materials science and engineering to new limits and it has led to the increasing interest, of the researchers towards multiferroic materials, which are very promising candidates for the

development of the next generation novel devices.

2.0 Multiferroics Multiferroicity is the coupling between magnetic and (ferro) electric order, which originated from the magnetoelectric effect, discovered by Pierre Curie in 1894 (Fig-1) [1].

Fig-1, Magnetoelectric Effect [1]

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It is the magnetization by an electric field or the induction of electric polarization by a magnetic field. The study of the magnetic and ferroelectric materials has led to some of the most important technological advances to date. 2.10 Magnetoelectric (ME) effects. The coupling between magnetic and electric properties of a material is termed as magneto-electric effects. These effects can be expressed as the expansion of the free energy of a material as follows.

Where PS and MS denote the components of the spontaneous polarization and magnetization and εij and µij are the electric and magnetic susceptibilities, respectively. The tensor αij corresponds to the induction of polarization by a magnetic field or of magnetization by an electric field and is designated as the linear ME effect [4]. The linear magnetoelectric effect can be expressed as follows

Pi = αij Hj Mi = αji Ej

Where α is the magnetoelectric tensor, non-zero only in the absence of space and time- inversion [2]. The ME effects are limited by the following relation.

From this expression it is clear that in order to obtain the largest ME effects in single phase of a material, large dielectric constants and magnetic susceptibilities are important. The materials possessing these two properties are called multiferroics and are the best candidates to show strong ME effects. Magnetism and ferroelectricity are involved with local spins and off-center structural distortions, respectively. These two seemingly unrelated phenomena can coexist in certain unusual materials, termed "multiferroics"[1-6], and sometimes called "magnetoelectric multiferroics ", possess two or more switchable states such as polarization, magnetization or strain[3,4].

Fig-2 Ferroelectricity and Antiferromagnetism in BFO

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The term (magnetoelectric) multiferroics comprises not only ferroelectromagnetism but also Antiferromagnetism, Antiferroelectricity and ferroelasticity, eg- BFO in Fig-2 [7, 8 & 9]. 2.20 Requirements for Multiferroics The requirements for multiferroics are detailed in Fig-3.

Fig-3 – Requirements for Multiferroics [8, 9]

So, Multiferroics can be defined as materials which combine at least two “ferroic” properties in the same phase such as ferromagnetic order (spontaneous magnetic polarization that can be reversed by a magnetic field), ferroelectricity (spontaneous electric polarization that can be switched by an applied electric field) or ferroelasticity (change in electric polarization accompanied by a change in shape). Some materials not having ferromagnetic but antiferromagnetic(Parallel Magnetic field but opposing spins which varies with temperature), ferrimagnetic (Incomplete cancellation of antiferromagnetic arranged spins

giving a net magnetic moment), ferrotoroidic (spontaneous magnetic vortex), or helimagnetic ordering (Magnetic spin moments arrange themselves in a spiral or helical pattern due to exchange interaction between Ferromagnetic and Antiferromagnetic ordering) are also accepted as multiferroics (Fig-3). There are only a few materials that possess both ferroelectricity and magnetism, but their coupling effect is not large enough for industrial applications. The non-trivial spin-lattice coupling, in these multiferroics has been manifested through various forms, such as linear and bilinear magnetoelectric effects, polarization change through field-induced phase transition, magneto-dielectric effect, and dielectric anomalies at magnetic transition temperatures [4, 5, 6 & 7]. So, before going deep in to the investigation of multiferroics, I would like to briefly review about the Materials from its origin, engineering materials, Electronics material, Transition metal oxides- its structure and properties for better and deeper understanding about multiferroics from the fundamental view point.

3.0 Materials In general, materials are substances of which something is composed or made. Materials can be classified as Natural and Man made or value added. Man-made or Value added materials are termed as engineering materials (Fig-4) [13-16]. 3.10 Materials Science and Engineering (MSE) The understanding of the behavior of materials and their properties is only possible, with detailed understanding of materials from its atomic and electronic structure level. Quantum

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mechanics pioneered in explaining the atoms and then solids starting from 1930s. The combination of physics, chemistry, and the focus on the relationship between the properties of a material and its microstructure is the domain of Materials Science. The development of this science allowed the designing of materials and provided a strong knowledge base for engineering applications termed as Materials Engineering [13-16]. 3.20 Importance of MSE All engineering disciplines need to know about materials, even the most material-less, like software or system engineering depends on the development of new high performance material like Multiferroics, which in turn alter the economics, like software-hardware trade-offs, miniaturization and high performance. The knowledge of MSE enables Engineers, Chemists, Designers, Researchers, Scientists to select a material for a given use based on considerations of design to cost with high performance; also to understand the limits of materials and the change of their properties with use; and to create a new material that will have desirable properties. 3.30 Historical Perspective of Materials Materials are vital in the development of civilization and are used to name the period of civilization like Stone Age, Metal Age (Bronze Age, Iron Age and so on. From the origin of human life on Earth, the Stone Age people used only natural materials, like stone, clay, skins, and wood. The discovery of copper and its alloys was the cause for the birth of Bronze Age about 3000 BC. The use of iron and steel, a stronger material that gave advantage in wars started at about 1200 BC. The next big step was the discovery of a cheap process to make

steel in 1850, which enabled the railroads and the building of the modern infrastructure of the industrial world. Structural materials Used for construction purposes. Includes construction materials (steel beams, concrete, wood, bricks, glass etc.), materials for machines, cars, aircraft, ships, railways, roads, bridges, pipelines, containers etc. Functional materials Used for their special properties like electrical, magnetic, optical, thermal, chemical properties, that decides the performance of the system. Functional materials are called Electronic Materials [13-16]. 3.40 Classification of Electronic Materials The electronic materials are classified by application (Structural and Functional electronic materials) and by composition (Inorganic and Organic electronic materials) as detailed in Fig- 4 [13-16]. But Electrical / Computer Engineers like to classify materials based on electrical behavior (Insulating, Semi- insulating and Metals) and the Materials Engineers / Scientists like to classify materials based on bond types (Ionic, Covalent and Metallic / Van der Waals) or Structure (Crystalline, Polycrystalline and Amorphous materials). As far as multiferroics are concerned, the crystal chemistry of solids plays a vital role in understanding and investigating the Atomic Bonds and Band Structures and provides the strong knowledge base for designing and synthesizing new fascinating classes of multiferroics.

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Fig: 4 – Classification of Materials [10-16]

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4.0 Atomic Bonds and Band Structures The chemical bond arises from a redistribution of electronic charge when atoms are brought in close proximity. The bond in solids results from the superposition of charge densities of all atoms in the system. When an infinite number of atoms come together to form solids they would form bonding, non-bonding and antibonding molecular orbitals of different energies so close together that they blur into one another forming a band. These molecular orbitals are described by wave functions. The most important point to come out of the theory is that for N atomic orbitals in a molecule, N molecular orbitals are the outcome. 4.10 Atomic Structure and Bonding Atoms are composed of electrons, protons, and neutrons. Electrons and protons are negative and positive charges of the same magnitude,

The mass of the electron is negligible with respect to those of the proton and the neutron, which form the nucleus of the atom. The unit of mass is an atomic mass unit (amu) = 1.66 × 10-27 kg, and equals 1/12 the mass of a carbon atom. The Carbon nucleus has Z=6, and A=6, where Z is the number of protons, and A the number of neutron. Neutrons and protons have very similar masses, roughly equal to 1 amu. All neutral atoms have the same number of electrons and protons, Z.

A mole is the amount of matter that has a mass in grams equal to the atomic mass in amu of the atoms. Thus, a mole of carbon has a mass of 12 grams. The number of atoms in a mole is called the Avogadro number, Nav = 6.023 × 1023. Note that Nav = 1 gram/1 amu. Where, M is the atomic mass in amu (grams per mol). Most solids have atomic densities around 6 × 1022 atoms/cm3. The cube root of that number gives the number of atoms per cubic centimeter is about 39 million. The mean distance between atoms is the inverse of that, or 0.25 nm. This is an important number that gives the scale of atomic structures in solids (Fig- 5) [12].

Fig – 5 Shell model of an atom with electrons revolving

within shells and sub shells [17].

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4.20 Electrons in Atoms The forces in the atom are repulsions between electrons and attraction between electrons and protons. The neutrons play no significant role. Protons (Z) is what characterizes the atom, electrons form a cloud around the neutron, of radius of 0.05 to 2 nm. Electrons move in ‘fuzzy’ orbits called shells (Fig-5) [12]. According to quantum mechanics, the orbits are identified by a principal quantum number n, which is related to the size, n = 0 is the smallest; n = 1, 2 are larger. (They are "quantized" or discrete, being specified by integers). The angular momentum l is quantized, and the projection in a specific direction m. Two electrons can be placed in an orbit with opposite spins in a given n, l, m shell [12]. In 1925, Wolfgang Pauli explained the arrangement of electrons in an atom by his exclusion principle. His hypothesis was that only one electron can occupy a given quantum state. Each electron in an atom has a unique set of quantum numbers (the principle quantum number gives its energy level, the magnetic quantum number gives the direction of orbital angular momentum, and the spin quantum number gives the direction of its spin). In fact, we now know that that the Pauli Exclusion Principle holds for not just electrons but for any fermions (half-integer spin particles like electrons, protons, neutrons, muons.) 4.30 The Periodic Table Elements are categorized by placing them in the periodic table. Elements in a column share

similar properties. The noble gases have closed shells, and so they do not gain or lose electrons near another atom. Alkalis can easily lose an electron and become a closed shell; halogens can easily gain one to form a negative ion, again with a closed shell. The propensity to form closed shells occurs in molecules, when they share electrons to close a molecular shell. Examples are H2, N2, and NaCl. The ability to gain or lose electrons is termed electronegativity or electropositivity, an important factor in ionic bonds. The vertical columns in the periodic table of the chemical elements are referred to as groups (Fig-6). There are 18 groups in the standard periodic table. The modern explanation of the pattern of the periodic table is that the elements in a group have similar configurations of the outermost electron shells of their atoms, as most chemical properties are determined by the orbital location of the outermost electron. The international way of numbering the groups of the periodic table is using Hindu-Arabic numerals / Indian numerals. The type of orbital in which the atom's outermost electrons reside determines the "block" to which it belongs and the number of valence shell electrons determines the group. The total number of electron shells an atom has determines the period to which it belongs. Each shell is divided into different subshells and as atomic number increases, they are filled in roughly in this order (the Aufbau principle) as shown in Fig-6. Progressing through a group from the lightest element to heaviest element, the outer-shell electrons (those most readily accessible for participation in chemical reactions) are all in

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the same type of orbital, with a similar shape, but with increasingly higher energy and average distance from the nucleus [13].

Fig-6 shows the periodic table of elements with various labeling schemes.

Fig-6 the Periodic table

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For example, the outer-shell (or "valence") electrons of the first group, headed by hydrogen, all have one electron in an s orbital. In hydrogen, that s orbital is in the lowest possible energy state of any atom, the first-shell orbital (and represented by hydrogen's position in the first period of the table). In francium, the heaviest element of the group, the outer-shell electron is in the seventh-shell orbital, significantly further out on average from the nucleus than those electrons filling all the shells below it in energy. The increase in

the atomic number (i.e. charge on the atomic nucleus) leads to greater spin-orbit coupling between the nucleus and the electrons. Because of the importance of the outermost shell, the different regions of the periodic table are sometimes referred to as periodic table blocks, named according to the sub-shell in which the "last" electron resides, e.g. the s-block, the p-block, the d-block, etc (Fig-7). The elements Ununbium, ununtrium, ununquadium, etc., have been discovered, but so far have not been named [13].

Fig-7 the Periodic table based on electronic configuration

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4.40 Bonding Forces and Energies The Coulomb forces are simple: attractive between electrons and nuclei, repulsive between electrons and between nuclei. The net force between atoms is given by a sum of all the individual forces, and the fact that the electrons are located outside the atom and the nucleus in the center (Fig- 8) [12].

Fig- 8 Forces and distance between atoms [12]. When two atoms come very close, the force between them is always repulsive, because the electrons stay outside and the nuclei repel each other. Unless both atoms are ions of the same charge (e.g., both negative) the forces between atoms is always attractive at large internuclear distances r. Since the force is repulsive at small r, and attractive at small r, there is a distance at which the force is zero. This is the equilibrium distance at which the atoms prefer to stay (Fig- 9) [12]. The interaction energy is the potential energy between the atoms. It is negative if the atoms are bound and positive if they can move away

Fig- 9 Forces Vs Separation distance [12]. from each other. The interaction energy is the integral of the force over the separation distance, so these two quantities are directly related (Fig- 10) [12].

Fig- 10 Energy Vs Separation distance [12]. The interaction energy is the minimum at the equilibrium position. This value of the energy is called the bond energy, and is the energy needed to separate completely to infinity (the work that needs to be done to overcome the attractive force.) The strongest the bond energy, the hardest is to move the atoms, for instance the hardest it is to melt the solid, or to evaporate its atoms [12].

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4.50 Atomic Bonds Atomic Bonds are classified as primary and Secondary Atomic bonds. The primary atomic bonds are further classified as Ionic Bonds, Covalent Bonds, and Metallic Bonds. Ionic Bonding This is the bond when one of the atoms is negative (has an extra electron) and another is positive (has lost an electron). Then, there is a strong, direct Coulomb attraction. An example is NaCl. In the molecule, there are more electrons around Cl, forming Cl- and less around Na, forming Na+. Ionic bonds are the strongest bonds. In real solids, ionic bonding is usually combined with covalent bonding. In this case, the fractional ionic bonding is defined as %ionic = 100 × [1 – exp (-0.25 (XA – XB) 2], where XA and XB are the electronegativities of the two atoms A and B, forming the molecule (Fig-11) [17].

Fig-11 Ionic Bonding Covalent Bonding In covalent bonding, electrons are shared between the molecules, to saturate the valence. The simplest example is the H2 molecule,

where the electrons spend more time in between the nuclei than outside, thus producing bonding (Fig- 12).

Fig- 12 Covalent Bonding Metallic Bonding In metals, the atoms are ionized, loosing some electrons from the valence band. Those electrons form a electron sea, which binds the charged nuclei in place, in a similar way that the electrons in between the H atoms in the H2 molecule bind the protons. In metals, the atoms are ionized, loosing some electrons from the valence band known as metallic bonding. Those electrons form an electron sea, which binds the charged nuclei in place, in a similar way that the electrons in between the H atoms in the H2 molecule bind the protons (Fig- 13) [18].

Fig-13 Metallic Bonding

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Secondary Atomic Bond (Van der Waals) Secondary Atomic and Molecular Bonds are classified as Permanent Dipole Bonds and Fluctuating Dipole Bonds. Fluctuating Induced Dipole Bonds Since the electrons may be on one side of the atom or the other, a dipole is formed: the + nucleus at the center, and the electron outside. Since the electron moves, the dipole fluctuates.

Fig - 14 Van der Waals Bonds This fluctuation in atom A produces a fluctuating electric field that is felt by the electrons of an adjacent atom, B. Atom B then polarizes so that its outer electrons are on the side of the atom closest to the + side (or opposite to the – side) of the dipole in A. This bond is van der Waals bonding (Fig-14) [18]. Polar Molecule-Induced Dipole Bonds A polar molecule like H2O (Hs are partially +, O is partially –), will induce a dipole in a nearby atom, leading to induced dipole bonding.

Permanent Dipole Bonds This is the case of the hydrogen bond in ice. The H end of the molecule is positively charged and can bond to the negative side of another dipolar molecule, like the O side of the H2O dipole (Fig-15) [18].

Fig - 15 Permanent Dipole Bond in Ice 4.60 Chemical bonding Models Chemical bonding models are theoretical models used to explain atomic bonding structure, molecular geometry, properties, and reactivity of physical matter. Modern bonding theories such as VBT, LFT, and MO theory assume that bonds are formed by atoms sharing electrons in directional orbital [18]. The Major Models Valence Bond Theory (VBT), an early bonding theory that has developed into Modern valence bond theory. VBT views bonds as weakly coupled orbitals, with each atom sharing a valence electron in a manner governed by the octet or 18 electron rules. Lewis structures are a representation of VBT's most basic bonding while molecular geometry is derived from orbital hybridization [18].

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VSEPR Valence shell electron pair repulsion (VSEPR) theory describes molecular geometry through the repulsion of electron fields which include bonds and lone pairs and does not require any application of orbital shape [18]. Crystal Field Theory (CFT) CFT is an approximation that begins with the geometries of the d orbitals derived from quantum mechanics. Ligands (an atom, ion, or molecule) with their electron density are assumed to destabilize the metal d- orbitals and they interact with raising their energy while the remaining d-orbitals drop in energy to balance the overall change in energy [18]. Ligand Field Theory (LFT) LFT is a hybrid of CFT and MO Theory. It is a simple application of MO Theory to transition metal compounds [18]. Molecular Orbital (MO) Molecular Orbital (MO) theory is a current and often applied model of molecular bonding. MO Theory assumes that bonds are derived from a linear combination of atomic orbitals and each pair of atomic orbitals involved in bonding results in a bonding and anti-bonding orbital. The destabilized orbitals of CFT are now seen as anti-bonding component of orbitals that have overall been stabilized through bonding interactions [18]. 4.70 Electronic band structure The band structure of a material determines a number of characteristics such as electronic, optical properties etc. The band structure of a solid describes ranges of energy that an electron is limited to have due to the

diffraction of the quantum mechanical electron waves in the periodic crystal lattice [18]. When several atoms are brought together to form a molecule, their atomic orbitals split, as in a coupled oscillation. This produces a number of molecular orbitals proportional to the number of atoms. When a large number of atoms (of order 1020 or more) are brought together to form a solid, the number of orbitals becomes exceedingly large, and the difference in energy between them becomes very small, so the levels may be considered to form continuous bands of energy rather than the discrete energy levels of the atoms in isolation. However, some intervals of energy contain no orbitals forming band gaps [18]. This band gap is one of the most useful aspects of the band structure, as it strongly influences the electrical and optical properties of the material. Electrons can transfer from one band to the other by means of carrier generation and recombination process. The band gap and defect states created in the band gap by doping can be used to create semiconductor devices such as solar cells, diodes, transistors, laser diodes, and others [18]. Basic concepts Theoretically, a solid has a large number of bands but a few lie at energies so high that any electron that reaches those energies escapes from the solid. These bands are usually disregarded. Bands have different widths, based upon the properties of the atomic orbitals from which they arise. Allowed bands may overlap, producing a single large band. Metals contain a band that is partly empty and partly filled regardless of temperature;

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therefore, they have very high conductivity. The lowermost, almost fully occupied band in an insulator or semiconductor is called the valence band by the valence electrons of individual atoms. The uppermost, almost unoccupied band is called the conduction band because only when electrons are excited to the conduction band current flows in these materials. The difference between insulators and semiconductors is only that the forbidden band gap between the valence band and conduction band is larger in an insulator, so that fewer electrons are found there and the electrical conductivity is lower. Because one of the main mechanisms for electrons to be excited to the conduction band is due to thermal energy, the conductivity of semiconductors is strongly dependent on the temperature of the material. Band theory The electronic structure of solids can also be described by MO theory. A solid can be considered as a supermolecule. One mole of atoms (NA), each with X orbitals in the valence shell contributes X moles of atomic orbitals producing X moles of MO’s. (Consider qualitatively bonding between N metal atoms of ns1 configuration (Li, Na etc) arranged in a chain; N = 2, 4, NA. If X=1, then N ~ NA and they do not form bonds but they do form bands [18-26].

Fig- 16, ns1 chain configuration (Li, Na)

The band appearing in the bonding region is called valence band. The antibonding region is called conduction band. In the case of metals the valence and conduction bands are immediately adjacent (Fig-16). If an electrostatic potential is applied to a conductor, the energy levels will tend to change the electrons and they will be able to flow using empty adjacent conduction band (Fig-17) [18-26].

Fig-17 Intrinsic conductivity in semiconductors and insulators In the case of insulators and semiconductors, the energy gap between the valence and conduction bands is more or less significant; electrons cannot easily get into the conduction band and thermal or photo-energy is needed to bring some electrons to the conduction band (Fig-18) [18-26].

Fig- 18, Electronic band structure of metals, semiconductors, and insulators.

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Fig- 19, Elements with band gaps and conductivities. Some elements with their respective band gaps and conductivities are tabulated in Fig-19 [18-

26]. Crystal Orbital theory The band structure of a crystalline material of virtually any complexity can be found through the application of the Molecular Orbital (MO) theory for solid state materials (Crystal Orbital theory). One of the ways to model a real (finite size) crystal is by using cyclic boundary conditions by assuming that a chain of bound atoms forms a very large ring. It turns out that the energy levels in a cyclic molecule composed of N hydrogen atoms look as shown below in Fig-20 [18-26].

Fig-20 Energy levels N Molecular orbitals

Crystal orbitals (Bloch functions) If N hydrogen atoms with atomic wave functions (m = 1 … N) related by symmetry and spaced at distance a, we can get N MO’s (n = - N/2, …, 0, …, N/2) which are called Bloch functions. For the n-th crystal orbital, , we will have:

When n changes from 0 to N/2, variable k = 2πn / (aN)) (wave vector) changes from 0 to π/a and the type of the MO changes from the completely bonding to the completely antibonding as shown below in Fig-21, 22.

Fig-21 Bonding to antibonding

Fig-22 Energy levels of set of Molecular orbitals Energy levels of the resulting set of MO’s (band structure) can be described with help of

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continuous functions E and density of states (DOS) dn/dE [18-26]. Bonding in Crystalline Metals Crystal orbital theory can be used to rationalize the well known fact that the metals with highest melting points are those belonging to 6th and 7th groups as shown in Fig-23.

Fig-23 Crystal Orbital overlaps A common way to analyze bonding in solids is by calculating and analyzing the crystal orbital overlap population (COOP). COOP is defined in the same way as the bond order is defined in MO theory of molecules. For any two atoms i and j

COOP (i-j) = S2cicjSij (Sij is the overlap integral for two atomic wave functions; summation is performed for all pairs of overlapping orbitals of atoms i and j). A negative value of COOP means antibonding situation while a positive value is characteristic for bonding [18-26]. Cluster model Cluster Model takes into account the interaction of a metal atom with surrounding Ligand atoms (oxygen in the case of oxides).

Basically cluster calculations are molecular orbital calculations carried out on a cluster shown in Fig-24.

Fig- 24, Molecular orbital diagram for a octahedral MO6 Unit. The MO diagram of a transition metal ion octahedrally surrounded by 6 oxygen (Oh point group).The different orbitals arises from the combination of metal d orbitals and oxygen p orbitals [20].

5.0 Crystals A Crystal is defined as a solid composed of atoms arranged in a periodic pattern in three dimensions (3D) [19]. However, not all solids are crystalline; some solids do not possess a

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periodic arrangement and are called amorphous or “undercooled liquids”. 5.10 Crystal Lattice Structures Unit Cell Periodicity in crystals is generally represented by replacing the repeating unit by a point, the resulting array of such points in space is called lattice. In a space lattice the translation vectors, a, b, c in the crystallographic directions define a primitive cell. When a primitive cell or some other suitable combination is chosen as the repeating unit of the lattice, it is referred to as the unit cell (Fig- 6). A crystallographic unit cell is defined by three translation vectors a, b, and c; and three angles α, β and γ. The most common types of unit cells are the faced-centered cubic (FCC), the body-centered cubic (BCC) and the hexagonal close-packed (HCP). Other types exist, particularly among minerals.

Fig - 25 Three Dimensional Unit Cell

A simple, or primitive, unit cell (symbol P or R in the Fig-25), has only one lattice point per cell; a non-primitive unit cell has more than

one lattice point per cell. The number of lattice points is given by the following equation, where Ni is the number of interior points, Nf is the number of face centered points and Nc is the number of corner points:

The symbols ‘f’ and ‘i’ refers to face-centered and body-centered cells, respectively, while A, B, C base-centered cells, centered on one pair of opposite faces A, B, C (the A face is the face defined by b and c axes, etc.) [19-21]. Seven Crystal Systems The seven crystal systems are detailed in Fig -26 below.

Fig -26, Seven Crystal Systems and Bravais Lattices [18-

20].

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The Bravais Lattices In 1848 the French crystallographer Bravais demonstrated that there are fourteen possible lattice points by arranging the points in 3D. It was so arranged that each point has [statistically] identical surroundings [20]. The 14 Bravais lattices are detailed in Fig-27 below.

Fig -27, Bravais Lattices The 14 Bravais lattices are as follows: (1) triclinic P, (2) monoclinic P, (3) monoclinic C, (4) orthorhombic P, (5) orthorhombic C, (6) orthorhombic 1, (7) orthorhombic F, (8) tetragonal P, (9) tetragonal 1, (10) cubic P, (11) cubic 1, (12) cubic F, (13) hexagonal P, (14) trigonal R (Fig -28) [21]. There are only 14 Bravais lattices because of the unit cell selection is made based on the following criteria, o Highest symmetry

o Consistency with past convention to minimize unit cell volume

o Satisfaction of minimal symmetry

requirements Which limits the maximum of 14 lattices and several of these criteria are used to define the cell structure of a crystal.

Fig – 28, Fourteen Bravais Lattices [18-20]

A crystal's structure and symmetry play a role in determining many of its properties, such as cleavage, electronic band structure, and optical properties [20]. 5.20 Types of crystals based on bonding Based on bonding considerations five types of crystals can be defined, which are ionic,

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covalent, metallic, molecular and hydrogen bonded. Ionic Crystals These types of crystals are usually formed between highly electro-positive and highly electro-negative elements which favor electron transfer. The atoms themselves are ionized because the elements with higher electro-negativity obtain the valence electrons of the element with the low electro-negativity. The different types of atoms become oppositely charged and, are held together by electrostatic forces. Ionic crystals such as NaCl have relatively high melting points and are hard. The cohesive energy calculations can not be used to predict the structure of an ionic solid. Covalent Crystals These crystals have covalent bonding between all the atoms present in the crystal. These crystals generally have high melting points and are non-conductors. Diamond and zinc sulfide are examples of covalent crystals. Metallic Crystals In metallic crystals individual metal atoms sit on lattice sites, while the valence electrons from each atom flow freely around the lattice. Metallic crystals have high densities along with high melting points. Molecular Crystals In this type of crystal, molecules within the crystal are held together by secondary bonds such as van der Waals forces or hydrogen bonding (Eg- Sugar). Molecular crystals are generally soft and have low melting points.

Hydrogen Bonded Crystals Crystals with hydrogen bonds are a special type of dipole-dipole force that exists between an electronegative atom and a hydrogen atom bonded to another electronegative atom. This type of force always involves a hydrogen atom and the energy of this attraction is close to that of weak covalent bonds (155 KJ/mol). These attractions can occur between molecules (intermolecular), or within different parts of a single molecule (intramolecular). The hydrogen bond is a very strong fixed dipole-dipole van der Waals-Keesom force, but weaker than covalent, ionic and metallic bonds. In many Oxide Hydrates or Hydrogen oxides, hydrogen bonding contributes to the cohesive energy. 5.30 Defects in Crystals A perfect crystal, with every atom of the same type in the correct position, does not exist. All crystals have some defects. Defects contribute to the mechanical properties of metals. Defect is intentionally used to manipulate the mechanical properties of a material. Adding alloying elements to a metal is one ways of introducing a crystal defect. The basic classes of crystal defects are as follows:

Point defects are places where an atom is missing or irregularly placed in the lattice structure. Point defects include lattice vacancies, self-interstitial atoms, substitution impurity atoms, and interstitial impurity atoms.

Linear defects are groups of atoms in irregular positions. Linear defects are commonly called dislocations.

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Planar defects are interfaces between homogeneous regions of the material. Planar defects include grain boundaries, stacking faults and external surfaces.

Plastic deformation in a material occurs due to the movement of dislocations (linear defects).Any defect in the regular lattice structure disrupts the motion of dislocation, which makes slip or plastic deformation more difficult. The defects of Oxides are explained in detail in the Transition Metal Oxide section [20].

6.0 Metal Oxides Multiferroic materials are poly crystals, which belong to the family of “Transition Metal oxides”. Metal Oxides are formed when metals are oxidized by oxygen. Metal oxides can be classified into two classes Non Transition Metal Oxides and Transition Metal Oxides. 6.11 Non-Transition Metal oxides Oxides of non-transition metals, (Na2O, MgO, Al2O3, SiO2) consist of a filled valence band (derived from oxygen 2p) and an empty conduction band (derived from the outer shells of the metal atoms), separated by a large gap. Such oxides are therefore diamagnetic insulators under ordinary conditions. Since the intrinsic activation energy for electronic conduction is higher than the energy required for the creation and migration of point defects, ionic conduction predominates over electronic conduction in many of these oxides at moderately high temperatures [20-22]. 6.12 Transition metal oxides Transition metal oxides (TMO) are a series of compounds with a uniquely wide range of electronic properties from insulating (e.g. Cr2O3), semi-insulating (e.g.BaBiO3) and

metallic (e.g. TiO). Other properties, especially the "high-temperature" superconductivity of mixed oxides (cuprates) have been recently discovered. The typical examples of these complex oxides crystal structure for cubic and layered perovskites are given in Fig-29. In Transition Metals (TM) the valence electrons may be present in more than one shell, making most TM to have more than one oxidation state. The oxides of TM show a rich variety of electronic properties, ranging from insulating to metallic and even superconducting behavior. The same applies to their magnetic properties, where every- thing is found from Pauli paramagnetism to local moment behavior including the occurrence of ferromagnetism and antiferromagnetism.

Fig – 29, Crystal structure of functional oxides Additionally, these materials can often be tuned from one electronic or magnetic phase to

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another by varying the temperature, pressure, or by doping. Therefore, the transition metal oxides (TMO) have been the subject of intense experimental and theoretical studies for a long time. Especially d-band TMO are of interest because of their catalytic properties. Transition metal oxides are used in a wide variety of technologically important catalytic processes. For example, they are used in selective oxidation, selective reduction and dehydrogenation [20-22]. The transition metal oxides form a large, rich and still not well understood class of compounds. These materials can have unusual and useful electronic and magnetic properties. Many of these properties strongly depend on material defects like vacancies, dislocations, stacking faults and grain boundaries. The oxides of the early transition-metals (periodic groups 4, 5, 6 and 7) containing d0 and d1 electronic configurations are a special subclass, distinctly different from the other transition-metal oxides, showing several unique features. For example, crystal structures of d0 metal oxides consist of distorted metal oxygen (MO6) octahedra where the cation is displaced from the centre of the octahedron (Fig-30) [20-22]. Several of the interesting features of these oxides can be directly traced to this distortion. The occurrence of layered structures and distinct oxide hydrates for V2O5, MoO3 and Re2O7 is a direct consequence of the distortion. The high static relative permittivity and the consequent ferroelectric behavior, the presence of soft phonon modes and the ability to

accommodate oxygen-deficient non- stoichiometry (e.g. WO3−x, TiO2−x) without oxygen vacancies could all be traced to a soft M-O potential that is again a direct consequence of the out-of-centre distortion of MO6 octahedra in d0 metal oxides [26-27].

Fig - 30, Structures of do Oxides 6.2 Structures of Transition metal oxides Transition metal oxides can be classified into four basic structures based on crystallization which are Rock Salt, Rutile, Corundum and Perovskites. The basic structures are of three types AX- type, AmXp type and AmBnXp type (Fig-31) [20-22].

Fig - 31, Types of TMO Structures

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6.21 Rock Salt Rock salt crystal structure is highly ionically bonded. Large anions are arranged in cubic close packing and all the octahedral interstitial positions are filled with cations in this structure. This structure has an octahedral coordination (CN = 6). This type of coordination predicted from the radius ratio calculation of cation to anion should be 0.732-0.414.

Fig -32 Rock Salt Structure

Eg: The NaCl is anion ccp (fcc). Radius Na+ = 1.02Å, radius Cl- = 1.81Å; radius ratio = 0.563. So in the Na octahedral, each octahedral has one anion, thus 100% octahedral sites are filled. The coordination # Na = 6; coordination # Cl = 6. Therefore, there is an fcc arrangement of the Na cations and Cl anions. For an fcc lattice there are 4 lattice points per cell, the motif in this case is a Na cation and a Cl anion. Therefore the cell contents are 4 Na cations + 4 Cl anions (Fig -32) [28].

6.22 Rutile TiO2 (titanium dioxide) is a nominal rutile structure. It can be thought of as infinite columns of edge sharing TiO6 octahedra. In addition, it has its each edge-shared oxygen, corner-shared with an adjacent infinite chain. Each Ti is coordinated to 6 oxygen atoms (by definition for octahedral coordination) and each oxygen atom is coordinated to 3 titanium atoms, 2 within a column, and 1 within the adjacent column [28]. Titanium dioxide occurs naturally as the mineral Rutile. The ionic radius of the titanium (IV) ion is 0.745 Å and that of the oxide ion is 1.26 Å. The ratio of radii for the cation and anion is thus r+/r- = 0.745/1.26 = 0.591. With a radius ratio of 0.591, the cubic holes are too large (r hole/r = 0.732). The titanium ions will prefer to occupy octahedral holes in a close-packed structure. The oxide ions in rutile pack in a hexagonal close-packed structure. The images below depict the structure of Rutile. The red spheres represent the oxide ions and the blue spheres represent the titanium (IV) ions (Fig-33) [28].

Fig -33, Rutile Structure of Ti O2

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Rutile Derivative: ABO4, ordered and disordered Two different metals can replace Ti in the rutile structure giving a new formula of ABO4, keeping the metal-oxygen ratio. If the metals are disordered on the site, then the crystallographic description remains the same, with 50% of each metal on the Ti site. While this is most often the case, the metals can also be ordered. Fig-34 shows structure of CoReO4.

Fig-34, CoReO4 rutile structure

In a 1-2-6 ratio, the metal cations will have the same basic skeleton as rutile, but the cations will order is such a way as to triple the c-axis, i.e. the axis pointing along the infinite edge-sharing columns. FeTa2O6 is shown below as an example (Fig-35) [28].

Fig-35, FeTa2O6 tri-rutile structure

Skew-edge sharing, alpha PbO2 / columbite structures In some situations, the MO6 octahedra will share skew edges and the infinite edge-sharing columns become zigzagged instead of straight. However, the edge-shared oxygen atoms still share 1 corner with an adjacent chain and in that sense the structure is the same as rutile. In the Fig-36 below, FeWO4 is used as an example. In the upper left, only the FeO6 octahedra are shown. In the upper right, the WO6 octahedra are added, but the structure orientation is the same. Two simplified versions from the side are shown in the lower panels [28]. In the case of ABO4, the A and B cations are ordered on the two different sites typified by Fe and W. In the case of AO2, e.g. alpha-PbO2, the Fe and W sites are equivalent, and occupied by the same cation (Fig-36) [28].

Fig-36, FeTa2O6 tri-rutile structure

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6.23 Corundum The corundum structure is a general structure of a class of minerals consisting of hexagonal close packed O atoms with cations filling up 2/3 of the central octahedral sites. The cations occur two in a row and they skip a site. This pattern is staggered for adjacent rows. An example is given in Fig-37.

Fig- 37 Corundum Structure – Al2O3 Al2O3 has a space group of R-3c, Number: 167, Pearson symbol: hR10, Unit cell dimensions: a = 4.758 Å, c = 12.991 Å, 90° 90° 120°, Atomic positions: Al at (0, 0, 0.355), O at (0.303, 0, 1/4) [28]. 6.24 Pervoskite Structures Perovskites are a large family of crystalline ceramics that derive their name from a specific mineral known as perovskite. The parent material, perovskite, was first described in the 1830's by the geologist Gustav Rose, who named it after the famous Russian mineralogist Count Lev Aleksevich von Perovski. Number of isostructural ternary oxide families exhibit pervoskite, spinel, garnet, pyrochlore, K2NiF4, and other structures whose electrical and

magnetic properties have been extensively studied. Multiferroics are perovskites with general formulas of ABO3 and A2BBO6

8 with units of cubic cell type (eg-LaxTiO3), tetragonal type (eg-BaTiO3) and orthorhombic type (eg-GdFeO3) structures (Fig-38) [28].

Fig- 38 Perovskite Structure Many different types of distortions can occur from the ideal structure of perovskites. These include tilting of the octahedra, displacements of the cations out of the centers of their coordination polyhedra, and distortions of the octahedra driven by electronic factors (i.e. Jahn-Teller distortions). Multiferroic materials have a slightly deformed symmetry with the 3m point symmetry group instead of the ideal cubic symmetry m3m [28]. Many of the physical properties of perovskites depend crucially on the details of these distortions, particularly the electronic, magnetic and dielectric properties which are so important for many of the applications of

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perovskite materials. Some examples of Pervoskites are given and discussed below. Cubic Perovskite The principle perovskite structure found in ferroelectric materials is a simple cubic structure containing three different ions of the form ABO3. The A and B atoms represent +2 and +4 ions, respectively, while the O atom is the Oxygen-2 ion. This ABO3 structure is a face centered cubic (FCC) lattice with A-atoms at the corners and O atoms on the faces. The B atom completes the picture and is located at the center of the lattice. This A-atom is the largest of the atoms and consequently increases the overall size of the ABO3 (fcc) structure. As a result, there are minimum energy positions off centered from the original octahedron that can be occupied by the B atom. Shifting of this atom due to applied electric fields causes the structure to be altered, creating electric dipoles Eg SrTiO3 (Fig-39) [28].

Fig: - 39. SrTiO3 - Cubic Perovskites

This structure can be visualized in terms of the BO6 octahedra which share corners infinitely in all 3 dimensions, making a symmetric structure. The A cations occupy every hole which is created by 8BO6 octahedra, giving the A cation a 12-fold oxygen coordination, and the B-cation a 6-fold oxygen coordination. In (SrTiO3) the Sr atoms sit in the 12 coordinate A-site, while the Ti atoms occupy the 6 coordinate B site. There are many ABO3

compounds for which the ideal cubic structure is distorted to a lower symmetry (e.g. tetragonal, orthorhombic, etc.) [28].

Sr2FeMoO6 - Double Perovskites The double perovskite structure is named because the unit cell of it is twice that of the perovskite. It has the same architecture of 12 coordinate A- sites and 6 coordinate B sites, but two cations are ordered on the B site.

Fig: - 40, Sr2FeMoO6 - Double Perovskites

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The example shown here is Sr2FeMoO6. The Fe and Mo atoms have ordered in a 3D chessboard type fashion (Fig-40) [28]. Layered Perovskites Layered Perovskites can be identified as Ruddleson-Popper, Aurivillius and Dion-Jacobson phases. Layered perovskites consist of infinite 2D slabs of the ABO3 structure which are separated by some motif. The general formula for the layered perovskite is: A(n-1)B(n)O(3n+1). The differentiating characteristics for the layered perovskites are o The motif which separates the layers, and o The offsetting of the layers from each

other. In this formula, "n" indicates the size of the 2D slabs. n=1 means the slab is one BO6

octahedron thick. n=2 means two BO6 octahedra thick, etc. The clearest examples of this are the n=1 and n=2 Ruddleson-Popper phases Sr2RuO4 and Sr3Ru2O7 (Fig-41) [28].

Fig: - 41, Ruddleson-Popper phases Sr2RuO4 and Sr3Ru2O7

For these phases, Sr is the A cation, and Ru is the B cation. The separating motif is a layer of Sr2, and the perovskite slabs are offset by a (1/2, 1/2) translation. Ruddleson Popper phases has the general formula as A(n+1)BnO(3n+1), indicating that the outer A atoms are part of the 2D perovskite slabs.

Aurivillius phases The n=2 phase Bi3TiNbO9 is representative of the Aurivillius phases, for which the general formula is {Bi2O2}-{A (n-1) B2O7}. For this phase, Ti and Nb are statistically dispersed on the B site. The formula can be re-written as: {Bi2O2}-Bi (Ti, Nb) 2 O7. The separating motif for all Aurivillius phases is a rock-salt Bi2O2 layer. Bi is also the A cation, but that need not be the case. The displacement of the perovskite slabs is a (1/2, 1/2) translation (Fig-42) [28].

Fig: - 42. Aurivillius phases of Bi2O2

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Dion-Jacobson phases The Dion-Jacobson phases have the general formula M+1A(n-1)BnO(3n+1). They differ from the other layered phases by having a layer of alkali metal as the separating motif. Below is a picture of KLaNb2O7 and CsLaNb2O7. The displacement of the perovskite slabs is either (1/2, 0) or nothing at all depending upon which alkali metal is used as the separating motif. The crystal structures of d0 metal oxides consist of distorted metal–oxygen (MO6) octahedra where the cation is displaced from the centre of the octahedron, creating several of the interesting features of these oxides (Fig-43) [28].

Fig-43 Dion-Jacobson phases of KLaNb2O7 and CsLaNb2O7

Spinel structure Spinel structure oxides with the formula of AB2O4, are well-known magnetic materials. Ferrimagnetic CoCr2O4 has a conical spiral configuration. Some of the spinels (e.g., FeCr2O4) exhibit Jahn-Teller effect. Other oxides showing this effect are rare earth zircons (e.g., TbVO4, DyVO4) and PrAlO3. In

vandate spinels, AV23+O4, the d electrons are

localized when 2.88A < Rv-v< 2.97Α. Fe3O4 is an inverse spinel. The spinels Li1-xM2+xTi2O4 where (M=Mg, Mn) and Li1+xTi2O4 shows superconductivity. Some of these hydrogen bronzes, Di- and monophosphate tungsten bronzes of the type Ax(PO2)4(WO3)2m (A = Na, K, Rb, or Ba) possess hexagonal tunnels. The tunnels may be empty, as in the monophosphate bronze P4W8O32 (m=4), or occupied, as in the diphosphate tungsten bronzes. CsP8W9O40, has a unique anisotropic structure [20-28]. 6.241 Spinel (MgAl2O4) Spinel, MgAl2O4, is a rare gemstone that was used to imitate rubies. The structure has face-centered cubic symmetry and the general formula is AB2O4. The oxygen atoms form an fcc lattice. The A cations occupy tetrahedral holes, and the B cation occupy octahedral holes. It then follows that 1/8 of the tetrahedral holes, and 1/2 of the octahedral holes are occupied. The array of Al atoms sit on the corners of tetrahedra which share corners infinitely in 3 dimensions, an array known as a Kagome net.

Fig- 44 Spinel structure of MgAl2O4

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The image above shows Al atoms sitting on the corners of tetrahedral and the Mg atoms sitting in tetrahedral holes (Fig-44) [28]. 6.3 Properties of Transition Metal Oxide Physical properties of metal oxides arise as responses to external stimuli like mechanical stress, electrical field, magnetic field and temperature. The important properties TMO are Electronic, magnetic, dielectric, optical and catalytic properties. Also the metal to Non metal transition Phenomenon and Super conductivity is of notable importance [28]. 6.31 Electronic Properties of TM Oxides Transition metal oxides can be classified into two classes based on its electronic configuration those in which the metal ion has d0 electronic configuration (empty d shell) and those in which d shell is partially filled (Fig-45). The d0 class of oxides has a filled oxygen 2p valence band and an empty metal d conduction band; the energy gap is around 3-5eV. High purity oxides of this class exhibit intrinsic electronic conduction only at high temperatures. With the d0 cations at octahedral sites, the oxides exhibit spontaneous ferroelectric distortions (e.g., WO3). Many lose oxygen at high temperatures, becoming nonstoichiometric. Oxygen loss or insertion of electropositive metal atoms into these oxides promotes electrons to the conduction band. The nature of electronic conduction in these materials depends on the strength of electron-phonon coupling and the width of the conduction band derived from metal d states. When the coupling is large and the band is narrow, small polarons are formed and such materials (e.g., NaxV2O5) exhibit hopping

conduction. When the conduction band is broad, the material (e.g., NaxWO3) exhibits metallic properties. Transition metal oxides with partially filled d bands can be metallic or insulating. Some of them exhibit temperature-induced non metal-to-metal transitions. Magnetic properties vary anywhere from Curie-Weiss paramagnetism to Pauli paramagnetism (through spontaneous magnetism). Rare earth metal oxides containing localized 4fn electrons are generally insulators or hopping semiconductors and exhibit paramagnetism [28]. Transition metal oxides with the dn configuration exhibit metallic properties when the overlap between orbitals of the valence shells of constituent atoms is large. Two kinds of metallic behavior can be distinguished: one due to strong cation-cation interaction arising from a small cation-cation separation, and the other due to strong cation-anion-cation interaction arising from a large covalent mixing of oxygen 2p orbitals with cation d orbitals. Iso-structural series of transition metal oxides, possessing rock salt, corundum, rutile, and perovskite structures, exhibit systematic changes in electronic properties, wherein at least one member of the series shows properties of itinerant electrons while others exhibit properties due to localized electrons [20-

28]. d0 (Empty d shell) The d0 class of oxides has a filled oxygen 2p valence band and an empty metal d conduction band; the energy gap is around 3-5eV. High purity oxides of this class exhibit intrinsic electronic conduction only at high temperatures. With the d0 cations at octahedral sites, the oxides exhibit spontaneous

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ferroelectric distortions (e.g., WO3). Many lose oxygen at high temperatures, becoming nonstoichiometric. Oxygen loss or insertion of electropositive metal atoms into these oxides promotes electrons to the conduction band. The nature of electronic conduction in these materials depends on the strength of electron-phonon coupling and the width of the conduction band derived from metal d states. When the coupling is large and the band is narrow, small polarons are formed and such materials (e.g., NaxV2O5) exhibit hopping conduction. When the conduction band is broad, the material (e.g., NaxWO3) exhibits metallic properties [20-22]. dn (Partially Filled d shell) Transition metal oxides with partially filled d bands can be metallic or insulating. Some of them exhibit temperature-induced non metal-to-metal transitions. Magnetic properties vary anywhere from Curie-Weiss paramagnetism to Pauli paramagnetism (through spontaneous magnetism). Rare earth metal oxides containing localized 4fn electrons are generally insulators or hopping semiconductors and exhibit paramagnetism. Transition metal oxides with the dn configuration exhibit metallic properties when the overlap between orbitals of the valence shells of constituent atoms is large. Two kinds of metallic behavior can be distinguished: one due to strong cation-cation interaction arising from a small cation-cation separation, and the other due to strong cation-anion-cation interaction arising from a large covalent mixing of oxygen 2p orbitals with cation d orbitals.

Iso-structural series of transition metal oxides, possessing rock salt, corundum, rutile, and perovskite structures, exhibit systematic changes in electronic properties, whereas at least one member of the series shows properties of itinerant electrons while others exhibit properties due to localized electrons [20-

22].

Fig-45, Electronic and magnetic properties of binary transition metal oxides 6.32 Magnetic Properties Oxides with positive magnetic susceptibility are called Paramagnetic and those with negative magnetic susceptibility are called diamagnetic. Paramagnetic oxides generally follow the Curie’s Law.

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Where M is the magnetization, H is the magnetic field, XM the molar susceptibility and C is the Curie constant. Because of the interaction between atomic moments giving rise to an internal field in the oxide, the susceptibility is described by Curie- Weiss Law

Where θ depends on the nature of magnetic interaction (ordering) and can either be positive, negative or zero. Clearly when θ = 0 then the Curie-Weiss law equates to the Curie law. When θ is non-zero, there is an interaction between neighboring magnetic moments and the material is only paramagnetic above a certain transition temperature. If θ is positive, the material is ferromagnetic below the transition temperature and the value of θ corresponds to the transition temperature (Curie temperature, TC). If θ is negative, the material is antiferromagnetic below the transition temperature (Néel temperature, TN) and the value of θ does not relate to TN. This equation is only valid when the material is in a paramagnetic state. It is not valid for many metals as the electrons contributing to the magnetic moment are not localized. However, the law does apply to some metals, e.g. the rare-earths, where the 4f electrons, that create the magnetic moment, are closely bound. The Pauli model of paramagnetism is true for materials, where the

electrons are free and interact to form a conduction band, which is valid for most paramagnetic metals. In this model the conduction electrons are considered essentially to be free and under an applied field an imbalance between electrons with opposite spin is set up, leading to a low magnetization in the same direction as the applied field. The susceptibility is independent of temperature, although the electronic band structure may be affected, which will then have an effect on the susceptibility. The paramagnetism of transition metal compounds is different from that of rare earth compounds, because of the involvement of d electrons to varying degrees in crystal bonding. Ferrimagnetism is only observed in compounds, which have more complex crystal structures than pure elements. Ferrimagnetism is a phenomenon in which the magnetic moments of the atoms on different sub lattices are opposed and unequal; therefore, a spontaneous magnetization remains. This happens when two or more chemically different magnetic species, occupy two kinds of lattice sites producing two sub lattices A and B. The moments of ions in each sublattice are ferromagnetically coupled, but coupling between the moments of A and B is antiferromagnetic. Since the net moment of A and B are different, there is a resultant spontaneous magnetization. The temperature dependence of ferrimagnetism is similar to that of ferromagnetism except that the spontaneous magnetization decreases more rapidly with increase in temperature. Ferrimagnetism can be observed in Fe3O4 and Spinel ferrites [29-30].

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Fig- 46, Types of magnetism with details

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Types of Magnetism The magnetic behavior of a material can vary widely, depending on its structure, magnetic ordering, and electronic configuration. There are five major types of magnetism are Diamagnetism, Paramagnetism, Ferro-magnetism, Antiferromagnetism, and Ferrimagnetism as detailed in Fig-46 [29-30]. The fundamental properties of a magnetic material are characteristic of the material and are unaffected by the microstructure. These properties include the Curie temperature, saturation magnetization and magneto crystalline anisotropy. Saturation Magnetization The saturation magnetization (MS) is a measure of the maximum amount of field that can be generated by a material. It will depend on the strength of the dipole moments on the atoms that make up the material and how densely they are packed together. The atomic dipole moment will be affected by the nature of the atom and the overall electronic structure within the compound. The packing density of the atomic moments will be determined by the crystal structure (i.e. the spacing of the moments) and the presence of any non-magnetic elements within the structure. For ferromagnetic materials, at finite temperatures, MS will also depend on how well these moments are aligned, as thermal vibration of the atoms causes misalignment of the moments and a reduction in MS. For ferrimagnetic materials not all of the moments align parallel, even at zero Kelvin and hence, MS will depend on the relative alignment of the moments as well as the temperature. The saturation magnetization is also referred to as

the spontaneous magnetization, although this term is usually used to describe the magnetization within a single magnetic domain. (Fig-47) gives some examples of the saturation polarization (PS) and Curie temperature (TC) of materials commonly used in magnetic applications [30-31].

Fig-47, Saturation polarization (PS) and Curie temperature (TC) of a range of magnetic materials Magnetic Anisotropy Magnetic anisotropy is a phenomenon of aligning the magnetic moment in an easy axis in zero fields. Magnetic anisotropy is the direction dependence of a material's magnetic properties. A magnetically isotropic material has no preferential direction for its magnetic moment in zero fields, while a magnetically anisotropic material will align its moment to an easy axis. In a crystalline magnetic material the magnetic properties will vary depending on the crystallographic direction in which the

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magnetic dipoles are aligned. (Fig-48) demonstrates this effect for a single crystal of cobalt. The hexagonal crystal structure of Co can be magnetized easily in the [0001] direction (i.e. along the center-axis), but has hard directions of magnetization in the <1010> type directions, which lie in the basal plane (90° from the easy direction). A measure of the magneto crystalline anisotropy in the easy direction of magnetization is the anisotropy field, Ha (Fig- 48), which is the field required to rotate all the moments by 90° as one unit in a saturated single crystal. The anisotropy is caused by a coupling of the electron orbital to the lattice, and in the easy direction of magnetization this coupling is such that these orbital are in the lowest energy state.

Fig-48, Magneto crystalline anisotropy of cobalt The easy direction of magnetization for a permanent magnet, based on ferrite or the rare earth alloys, must be uniaxial, however, it is also possible to have materials with multiple easy axes or where the easy direction can lie anywhere on a certain plane or on the surface of a cone. The fact that a permanent magnet

has uniaxial anisotropy means that it is difficult to demagnetize as it is resistant to rotation of the direction of magnetization [29-31]. Magnetic Domains A magnetic domain describes a region within a material which has uniform magnetization. This means that the individual moments of the atoms are aligned with one another. The regions separating magnetic domains are called domain walls, where the magnetization rotates coherently from the direction in one domain to that in the next domain. The concept of magnetic domains was proposed by Weiss to explain that ferromagnetic materials with spontaneous magnetization could exist in the demagnetized state. The findings of his work revealed that within a domain large numbers of atomic moments are aligned typically 1012 to

1018, over a much larger volume than was previously suspected. The magnetization within the domain is saturated and will always lie in the easy direction of magnetization when there is no externally applied field. The direction of the domain alignment across a large volume of material is more or less random and hence the magnetization of a specimen can be zero. Magnetic domains exist in order to reduce the energy of the system. A uniformly magnetized specimen has a large magnetostatic energy associated with it (Fig- 49a). This is the result of the presence of magnetic free poles at the surface of the specimen generating a demagnetizing field, Hd. From the convention adopted for the definition of the magnetic moment for a magnetic dipole the magnetization within the specimen points from the South Pole to the North Pole, while the direction of the magnetic field points from north to south. Therefore, the demagnetizing

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field is in opposition to the magnetization of the specimen. The magnitude of Hd is dependent on the geometry and magnetization of the specimen. In general, if the sample has a high length to diameter ratio and is magnetized in the long axis, then the demagnetizing field and the magnetostatic energy will be low. The break up of the magnetization into two domains reduces the magnetostatic energy by half (Fig-49b). In fact, if the magnet breaks down into N domains then the magnetostatic energy is reduced by a factor of 1/N, hence Fig- 49(c) has a quarter of the magnetostatic energy of Fig-49(a). Fig- 49(d) shows a closure domain structure where the magnetostatic energy is zero, however, this is only possible for materials that do not have a strong uniaxial anisotropy, and the neighboring domains do not have to be at 180º to each other.

Fig-49, Schematic illustrations of the break up of magnetization into domains (a) single domain, (b) two domains, (c) four domains and (d) closure domains. The energy associated with a domain wall is proportional to its area. Within the domain wall, the dipole moments of the atoms are not pointing in the easy direction of magnetization and hence are in a higher energy state (Fig-50).

In addition, the atomic dipoles within the wall are not at 180º to each other and so the exchange energy is also raised within the wall.

Fig-50, Schematic representation of a 180º domain wall Therefore, the domain wall energy is an intrinsic property of a material depending on the degree of magneto crystalline anisotropy and the strength of the exchange interaction between neighboring atoms. The thickness of the wall will also vary in relation to these parameters, as strong magneto crystalline anisotropy will favor a narrow wall, whereas a strong exchange interaction will favor a wider wall. A minimum energy can be achieved with a specific number of domains within a specimen. This number of domains will depend on the size and shape of the sample, which will affect the magnetostatic energy and the intrinsic magnetic properties of the material, which will affect the magnetostatic energy and the domain wall energy [29-31].

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Magnetic Hysteresis Hysteresis is well known in ferromagnetic materials. When an external magnetic field is applied to a ferromagnet, the atomic dipoles align themselves with the external field. Even when the external field is removed, part of the atomic dipole alignment will be retained and the material will become magnetized. The relationship between magnetic field strength

(H) and magnetic flux density (B) is not linear in such materials. If the relationship between the two is plotted for increasing levels of field strength, it will follow a curve up to a point where further increases in magnetic field strength will result in no further change in flux density. This condition is called magnetic saturation.

Fig-51, Hysteresis loop for a ferro or ferrimagnetic material.

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If the magnetic field is now reduced linearly, the plotted relationship will follow a different curve back towards zero field strength at which point it will be offset from the original curve by an amount called the remnant flux density or remanence. If this relationship is plotted for all strengths of applied magnetic field the result is a sort of S- shaped loop. The 'thickness' of the middle bit of S describes the amount of hysteresis, related to the coercivity of the material. Ferromagnetic and ferrimagnetic materials have non-linear initial magnetization curves (dotted lines in Fig-51), as the changing magnetization with applied field is due to a change in the magnetic domain structure. These materials also show hysteresis and the magnetization do not return to zero after the application of a magnetic field. Fig- 51 shows a typical hysteresis loop; the two loops represent the same data, however, the red loop is the polarization (P = µoM = B - µoH) and the blue loop the induction, both plotted against the applied field. The first quadrant of the loop is the initial magnetization curve (dotted line), showing the increase in positive polarization (and induction) on the application of a field to a demagnetized sample, and are both in the same direction. The polarization increases initially by the growth of favorably oriented domains, which will be magnetized in the easy direction of the crystal. When the polarization can increase no further by the growth of domains, the direction of magnetization of the domains then rotates away from the easy axis to align with the field.

When all of the domains are fully aligned with the applied field, the saturation is reached and the polarization can increase no further. If the field is removed the polarization returns along the solid red line to the y-axis (i.e. H=0), and the domains will return to their easy direction of magnetization, resulting in a decrease in polarization. In Fig-51, the line from the saturation point to the y-axis is horizontal, which is representative of a well aligned material, where the domains are magnetized in the easy direction of the crystal at the saturation point. When the direction of applied field is reversed then the polarization will follow the red line into the second quadrant. The hysteresis means that the polarization lags behind the applied field and will not immediately switch direction into the third quadrant (negative polarization). The polarization will only decrease after a sufficiently high field is applied to nucleate and grow domains favorably oriented with respect to the applied field or rotate the direction of magnetization of the domains towards the applied field. After applying high enough field saturation, polarization will be achieved in the negative direction. If the applied field is then decreased and again applied in the positive direction then the full hysteresis loop is plotted. If the field is repeatedly switched from positive to negative directions and is of sufficient magnitude then the polarization and induction will cycle around the hysteresis loop in a counter-clockwise direction. The area contained within the loop indicates the amount of energy absorbed by the material during each cycle of the hysteresis loop [29-31].

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Magnetic parameters The hysteresis loop is used to measure the various parameters to characterize magnetic materials. The Saturation polarization, PS and Saturation magnetization, M S can be measured from the first quadrant. Most of the useful information is derived from the second quadrant of the loop [29-31]. Remanence The field that is produced by the magnet after the magnetizing field has been removed is called the remanence, Br or Pr

[29-31]. Inductive coercivity The reverse field required to bring the induction to zero is called the inductive coercivity, bHc, whereas the reverse field required to bring the magnetization to zero is called the intrinsic coercivity, MHc. The maximum value of the product of B and H is called the maximum energy product, (BH)MAX and is a measure of the maximum amount of useful work that can be performed by the magnet. (BH)MAX is used as a figure of merit for permanent magnet materials. In addition, the shape of the initial magnetization curve and the hysteresis loop can provide information about the magnetic domain behavior within the material. The squareness factor is a measure of how square the loop is and is a dimensionless quantity between 0 and 1, defined by the ratio of the reverse field required to reduce P by 10% from the remanence to Hcp. A squareness factor of one therefore corresponds to a perfectly square loop. There are several other methods to quantify the squareness of the loop, such as the ratio of Pr to Ps

[29-31].

Coercivity-mechanisms There are various methods of increasing or decreasing the coercivity of magnetic materials, all of which involve the controlling of the magnetic domains within the material. For a hard magnetic material it is desirable that the domains cannot easily rotate on its direction of magnetization and the domain walls do not move easily and nucleation of domains is difficult. However to prevent easy rotation of domains the material could have a strong uniaxial magneto crystalline anisotropy. If the size of a magnetic particle / grain decreases then there is a critical size below which the decrease in magnetostatic energy by splitting into two domains is less than the increase in energy due to the introduction of the domain wall. Particles that are below this critical size are known as “single domain particles”, and if they have sufficiently high anisotropy to prevent the easy rotation of the direction of magnetization then the particles will be permanently magnetic and difficult to demagnetize. This type of coercivity mechanism can be observed in melt-spun NdFeB magnets where the crystal size is ~50nm, compared to the critical size for single domain particles of ~300nm [29-31]. Magnetoelasticity Magnetoelasticity refers to the coupling of the magnetic and elastic fields in a material. Magnetostriction is the result of the magnetoelastic coupling and refers to the dimensional change undergone by a material in the presence of a magnetic field. Most ferromagnetic materials, such as iron and nickel, show some measurable shape change when subject to a magnetic field. The highest room temperature magnetostriction of a pure element is Co - 60 microstrains [29-31].

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However, alloying elements can produce much larger magnetostriction even under a small field; examples are: DyFe2, and TbFe2. There are two processes that contribute to magnetostriction on a macroscopic level. The one is migration of domain walls in the materials in response to the applied field and second is the rotation of the domains. These two mechanisms cause the dimensional change in the material which in turn raises the strain energy of the system (elastic properties of materials are discussed later). When strain energy increases the material tries to elongate in both horizontal and vertical directions when a field is applied, but this is not possible because ferromagnetic material usually possess triangular domains for closure and this orientation does not enable the material to elongate in both directions simultaneously (Fig- 52b).

Fig-52, (a) Domain Structure after strain energy and exchange energy compromise, (b) Triangular domain structure for most ferromagnetics, (c) elongation due to reorientation and rotation However, the strain energy is reduced by decreasing the volume of the domains, which means additional domain walls will be needed. This would in turn increase the exchange energy; therefore, the final domain structure is usually a compromise between the two, as

shown in Fig-52a. Furthermore, the reorientation of the domains due to the two mechanisms mentioned above is shown in Fig-53c. Ferroelasticity Ferroelasticity is a phenomenon in which a material may exhibit a spontaneous strain when a stress is applied. The applied stress will cause a phase change to occur in the material from one phase to an equally stable phase either of different crystal structure (e.g. cubic to tetragonal) or of different orientation (a 'twin' phase). The shape memory effect and super elasticity are manifestation of ferroelasticity. Nitinol (nickel titanium), a common ferroelastic alloy, can display either superelasticity or the shape-memory effect at room temperature, depending on the nickel/titanium ratio. Super elasticity Pseudoelasticity / Superelasticity, is an elastic (impermanent) response to relatively high stress caused by a phase transformation between the austenitic and martensitic phases of a crystal. It is exhibited in Shape memory alloys. Pseudoelasticity is from the reversible motion of domain boundaries during the phase transformation, rather than just bond stretching or the introduction of defects in the crystal lattice. Even if the domain boundaries do become pinned, they may be reversed through heating. Thus, a pseudoelastic material may return to its previous shape (hence, shape memory) after the removal of even relatively high applied strains. One special case of pseudoelasticity is called the Bain Correspondence. This involves the austenite/martensite phase transformation

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between a face centered crystal lattice and a body centered tetragonal crystal structure [32-

33]. Superelastic alloys belong to the larger family of shape memory alloys. When mechanically loaded, a superelastic alloy deforms reversibly to very high strains - up to 10% - by the creation of a stress-induced phase. When the load is removed, the new phase becomes unstable and the material regains its original shape. Unlike shape-memory alloys, no change in temperature is needed for the alloy to recover its initial shape. Superelastic devices take advantage of their large, reversible deformation and include antennas, eyeglass frames, and biomedical stents. Nickel Titanium is an example of an alloy exhibiting superelasticity [32-33]. Shape memory alloys Shape memory alloy (SMA) / smart alloy is an alloy that "remembers" its shape. After a sample of SMA has been deformed from its original crystallographic configuration, it regains its original geometry by itself during heating (one-way effect) or, at higher ambient temperatures, simply during unloading (pseudo-elasticity or superelasticity). These extraordinary properties are due to a temperature-dependent martensitic phase transformation from a low-symmetry to a highly symmetric crystallographic structure. Those crystal structures are known as martensite (at lower temperatures) and austenite (at higher temperatures) [34]. The three main types of SMA are the copper-zinc-aluminum-nickel, copper-aluminum-nickel, and nickel-titanium (NiTi) alloys. The Copper based and NiTi (Nickel and Titanium)

based shape memory alloys are considered to be engineering materials. These compositions can be manufactured to almost any shape and size. The yield strength of shape memory alloys is relatively low compared to conventional steel, but some compositions have a higher yield strength than plastic or aluminum. The yield stress for NiTi can reach 500 [MPa]. The high cost of the metal and the processing requirements make it difficult and expensive to implement SMA's into design. As a result, these materials are used in applications where the superelastic properties or the shape memory effect can be exploited. The range of applications for SMAs, are increasing in recent years in the fields of consumer/commercial applications, industrial applications, medical applications. Nitinol wire is also used in robotics, Aerospace to reduce aircraft Engine noise by Boeing, General Electric Aircraft Engines, Goodrich Corporation, NASA, and All Nippon Airways [35]. 6.33 Electrical Properties Electrical conductivity or specific conductivity is a measure of a material's ability to conduct an electric current. The conductivity σ is defined as the ratio of the current density to the electric field strength:

On the basis of the electrical properties solid materials can be classified into metals, semiconductors and insulators, where the charge carriers move in band states. In certain semiconductors and insulators, charge carriers are localized and their motion involves diffusive process. The expression for electrical conductivity σ of a metal is given by

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Where l is the mean free path and m is the effective mass of the electrons, n is the density of conduction electrons, e is the electron charge [20-21]. Intrinsic Semiconductors In intrinsic Semiconductors with both electrons and holes as charge carriers,

σ = ni e (un + up)

ni = (NcNv)1/2exp (-Eg / 2kT)

Where Nc and Nv are the effective density of states in the conduction and valence bands respectively. un and up are electron and hole mobility [20-21]. Extrinsic Semiconductors In the presence of donors and acceptors, the conduction is extrinsic at low temperatures. kT<< Eg and σ exp( - Ed / 2kT) If the donor concentration is higher than of the acceptor the conduction becomes intrinsic at high temperatures [20-21]. Thermoelectric effect The thermoelectric effect is the direct conversion of temperature differences to electric voltage and vice versa. The term thermoelectric effect or thermoelectricity encompasses three separately identified effects,

the Seebeck effect, the Peltier effect, and the Thomson effect. The Seebeck Coefficient α, is the constant of proportionality between the voltage and temperature gradient that causes it when there is no current flow. It is defined as ∆V/∆T as ∆T 0, where ∆V is the thermo – emf caused by the temperature gradient ∆T; It is related to the entropy transported per charge carrier. The expression for Seebeck Coefficient α for metals is as follows.

Metals are characterized by a small | α| with temperature [20-21]. Intrinsic Semiconductors In intrinsic semiconductors α is given by

Where S* is the entropy by charge carriers (S*/k < 10µ V/K in metal oxides and EF is the Fermi energy relative to the appropriate band edge. The sign of α is generally positive for hole conduction and negative for electron

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conduction. So the above equation can be expressed as follows. Extrinsic semiconductors In extrinsic semiconductors is α generally large (0.1 – 1 mV/K) and decreases with increasing temperature [20-21]. Hall Coefficient The Hall Effect refers to the potential difference (Hall voltage) on the opposite sides of an electrical conductor through which an electric current is flowing, created by a magnetic field applied perpendicular to the current. The ratio of the voltage created to the power of the product of the amount of current and the magnetic field (I*B), divided by the element thickness, is known as the Hall coefficient RH. For a simple metal where there is only one type of charge carrier (electrons) the Hall voltage VH is given by

Where I is the current across the plate length, B is the magnetic flux density, d is the depth of the plate, e is the electron charge, and n is the charge carrier density of the carrier electrons.

Where Cr ~ 1, e is the electron charge, and n is the charge carrier density of the carrier electrons.

Hall Effect in semiconductors When a current carrying semiconductor is kept in a magnetic field, the carriers of the semiconductor experience a force in a direction perpendicular to the magnetic field and current field, this is called Hall Effect in semiconductors.

Where Eh is the Hall field The simple formula for the Hall coefficient given above becomes more complex in semiconductors where the carriers are generally both electrons and holes which may be present in different concentrations and have different mobilities. For moderate magnetic fields the Hall coefficient is

where is the electron concentration, the hole concentration, the electron mobility ,

the hole mobility and the electronic charge. For large applied fields the simpler expression analogous to that for a single carrier type holds [20-21].

6.34 Superconductivity Superconductivity is a transition phenomenon occurring in certain materials at extremely low temperatures, characterized by exactly zero electrical resistance and the exclusion of the interior magnetic field (the Meissner effect).

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The electrical resistivity of a metallic conductor decreases gradually as the temperature is lowered. However, in ordinary conductors such as copper and silver, impurities and other defects impose a lower limit. Even near absolute zero a real sample of copper shows a non-zero resistance. The resistance of a superconductor, on the other hand, drops abruptly to zero when the material is cooled below its "critical temperature". The Meissner effect is the expulsion of a magnetic field from a superconductor and it is a fundamental property of the superconducting state. It is used as a means of detecting superconducting transitions. There are two kinds of superconductors depending on their magnetic behavior [20-21]. Type - 1 Superconductors Materials in which superconductivity is destroyed abruptly at a critical field Hc (function of temperature) called type-1 superconductors. Type - 2 Superconductors In type 2 superconductors the magnetic flux starts to penetrate the material at a field of Hc1 lower than the thermodynamic critical field Hc. The magnetization gradually decreases with increasing field strength until H = Hc2, the superconducting state is completely destroyed. Between Hc1 and Hc2 the material is in vortex state consisting of rod-shaped regions of normal conductivity within the superconducting bulk substance. Oxides are some of the most important superconducting materials showing the highest Tc values [20, 21-30].

6.35 Dielectric Properties Dielectric materials are substances that are poor conductors of electricity, but efficient supporters of electrostatic fields. If the flow of current between opposite electric charge poles is kept to a minimum while the electrostatic lines of flux are not impeded, an electrostatic field can store energy. This property is useful in capacitors, especially at radio frequencies. Dielectric materials are also used in the construction of radio-frequency transmission lines. Most dielectric materials are solids and some examples are ceramic, mica, glass, plastics, and the oxides of various metals. Some liquids and gases can serve as good dielectric materials. Dry air is an excellent dielectric, and is used in variable capacitors and some types of transmission lines. Distilled water is a fair dielectric. A vacuum is an exceptionally efficient dielectric. An important property of a dielectric is its ability to support an electrostatic field while dissipating minimal energy in the form of heat. The lower the dielectric loss (the proportion of energy lost as heat), the more effective is a dielectric material [20, 21, 26]. Capacitance When two parallel plates of area A, separated by a small distance l, are charged by +Q, –Q, an electric field develops between the plates can be expressed as follows

Where D = Q/A. e0 is called the vacuum permittivity and e the relative permittivity, or dielectric constant (e = 1 for vacuum). In terms of the voltage between the plates, V = E l,

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The constant C= Aee0/l is called the capacitance of the plates [20, 21]. Field Vectors and Polarization The dipole moment of a pair of positive and negative charges (+q and –q) separated at a distance d is p = qd. If an electric field is applied, the dipole tends to align the positive charge points in the field direction. Dipoles between the plates of a capacitor will produce an electric field that opposes the applied field. For a given applied voltage V, there will be an increase in the charge in the plates by an amount Q' so that the total charge becomes

Where, Q0 is the charge of a vacuum capacitor. With Q' = PA, the charge density becomes

Where the polarization is given as follows,

Types of Polarization Three types of polarization can be caused by an electric field are detailed below, o Electronic polarization→ the electrons in

atoms are displaced relative to the nucleus. o Ionic polarization→ cations and anions in

an ionic crystal are displaced with respect to each other.

o Orientation polarization→ permanent dipoles (like H2O) are aligned.

The molar polarization of a solid is given by the Clausius – Mossotti equation

Where εr, εv are the dielectric constant of the materials (relative to vacuum) and of vacuum respectively, M is the molecular weight, N0 is the Avogadro number and is the Polarizability. Frequency Dependence of the Dielectric Constant Electrons have much smaller mass than ions, so they respond more rapidly to a changing electric field. For electric field that oscillates at very high frequencies (such as light) only electronic polarization can occur. At smaller frequencies, the relative displacement of positive and negative ions can occur. Orientation of permanent dipoles, which require the rotation of a molecule can occur only if the oscillation is relatively slow (MHz

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range or slower). The time needed by the specific polarization to occur is called the relaxation time [20, 21 and 36]. Dielectric constant Another consideration is the dielectric constant, the extent to which a substance concentrates the electrostatic lines of flux. In Dielectric materials the randomizing effect of temperature is balanced by orienting effect of the internal field. The dielectric constant is derived as follows.

Where εr, is the dielectric constant of the

material( relative to vacuum), is the optical high frequency dielectric constant, C is the Curie constant, Tc is Curie temperature and T is Dissipation temperature of the Dielectric material. Substances with a low dielectric constant include a perfect vacuum, dry air, and most pure, dry gases such as helium and nitrogen. Materials with moderate dielectric constants include ceramics, distilled water, paper, mica, polyethylene, and glass. Metal oxides, in general, have high dielectric constants [20, 21]. The prime asset of high-dielectric-constant substances, such as aluminum oxide, is that they make possible the manufacture of high-value capacitors with small physical volume. But these materials are generally not able to withstand electrostatic fields as intense as low-dielectric-constant substances such as air. If the

voltage across a dielectric material becomes too great -- that is, if the electrostatic field becomes too intense -- the material will suddenly begin to conduct current. This phenomenon is called dielectric breakdown. Dielectric Strength Very high electric fields (>108 V/m) can free electrons from atoms, and accelerate them to such high energies that they can, in turn, free other electrons, in an avalanche process (or electrical discharge). This is called dielectric breakdown, and the field necessary to start the breakdown is called the dielectric strength or breakdown strength. In components that use gases or liquids as the dielectric medium, this condition reverses itself if the voltage decreases below the critical point. But in components containing solid dielectrics, dielectric breakdown usually results in permanent damage [20, 21]. Dielectric Materials Capacitors require dielectrics of high e that can function at high frequencies (small relaxation times). Many of the ceramics have these properties, like mica, glass, and porcelain). Polymers usually have lower ‘e’ [20, 21]. 6.36 Optical Properties Transitions between 3d-states are of great influence on the optical properties and often determine the color of the compounds. For example, the d-d transitions of the Cr3+ ions in Cr2O3 are responsible for the green color of this compound, used in ceramic glazing. The equivalent transitions at Cr3+, embedded in the different crystal-field of Al2O3, provide the beautiful red color of ruby and are used for the generation of laser light in the ruby [36, 37]. In

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addition, the energetic shift of these transitions due to the pressure dependence of the crystal-field splitting is used in sensors for very high pressures of up to more than 109 Pa. Electromagnetic Radiation & Light Interaction The optical behavior of a solid material is a function of its interactions with electromagnetic radiation [Fig-53] having wavelengths within the visible region of the spectrum. Possible interactive phenomena include refraction, reflection, absorption, and transmission of incident light [36, 37].

Fig-53 Nature of Light Atomic and Electronic Interactions The dielectric constant of a transparent oxide varies as a function of the frequency of the oscillating electric field in the non absorbing region of the electromagnetic spectrum. The refractive index similarly varies with the frequency, generally increasing with ω. Such dispersion behavior of materials is of importance in the choice of materials for

prisms and other purposes. Oxides absorb electromagnetic radiation by different modes depending on the nature of bonding. Tightly bound electrons and ions in oxides give rise to narrow resonance absorption, electrons in the ultraviolet region, and ions in the infrared region (restrahlen absorption). Absorption of radiation due to loosely bound electrons is generally attributable to inter-band transitions. Such absorption bands in semiconductors are broad and featureless, but with a sharp absorption edge. Transition metal ions give absorption bands because of the presence of d-d transitions which are Laporte-forbidden. Both donor and acceptor impurities in semiconducting materials give absorption bands owing to photo-ionization at energies lower than the gap energies. Excitons (electron-hole pairs) in insulators give characteristic bands with the energy depending on how tightly bound the electron-hole pair is. Electrons in metallic and semiconducting materials give raise to free carrier absorption, the absorption coefficient being proportional to square of the incident wavelength (hence high in the infrared region for most metals). The reflectivity of metals (e.g., ReO3, TiO) which is related to the plasma frequency is almost total up to high frequencies. Inelastic scattering in solids is typified by the Raman Effect. If a single phonon is involved, the scattering is referred to as first-order Raman Effect. In second-order Raman Effect, two phonons are involved. In Brillouin scattering, a special case of Raman scattering, the phonons involved are from the acoustic branch [20, 36, and 37].

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Refraction Light radiation experiences refraction in transparent materials and its velocity is retarded and the light beam is bent at the interface. Index of refraction is the ratio of the velocity of light in a vacuum to the velocity in a particular medium. The phenomenon of refraction is a consequence of electronic polarization of the atoms or ions, which is induced by the electric field component of the light wave. The optical coefficient is the index of refraction n. The index of refraction relates to the ratio of the velocity of propagation of an electromagnetic wave in vacuum c to the velocity v in a medium

------------- (1) The refractive index similarly varies with the frequency, generally increasing with ω (Frequency of incident light). Such dispersion behavior of materials is of importance in the choice of materials for prisms and other purposes [20, 36 and 37]. Whenever the index depends on the frequency of the incident light n = n (ω), the medium is said to be dispersive. In addition to a decrease in the propagation velocity, light in a medium may undergo absorption. The intensity a distance x in the medium from the boundary is given by

--------------- (2) Where I0 is the incident intensity and the absorption coefficient α is the fraction of power absorbed in the medium per unit length. The absorption coefficient is given by

---------------------- (3) Where κ is the extinction coefficient, The index of refraction n and the extinction coefficient κ represent the real and imaginary parts, respectively, of a single complex quantity, namely the complex index of refraction

------- (4) Knowledge of ˜n allows derivation of additional optical coefficients more useful in comparing with predictions from theoretical models, e.g., the complex dielectric constant or the complex optical conductivity. The complex dielectric constant obtained from Maxwell’s equations is related to by

----- (5) The complex optical conductivity

relates to giving

-------- (6) Here is defined by the relation of the electric displacement to the electric field, D

= . Conventionally represents the response of bound charges, though may in principle be redefined providing that Eq. (6) is maintained. Rearranging Eq. (6) gives the real σ1 and imaginary σ2 parts of the complex optical conductivity

----------- (7)

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--- (8) Equations (5), (7), and (8) provide relations between the complex index of refraction, optical conductivity and dielectric constant:

(absorption) and (screening) [20, 36]. Reflection When light radiation passes from one medium into another having a different index of refraction, some of the light is scattered at the interface between the two media even if both are transparent. The reflectivity R represents the fraction of the incident light that is reflected at the interface, or where I0 and IR are the intensities of the incident and reflected beams, respectively.

If the light is normal (or perpendicular) to the interface, then n1 and n2 are the indices of refraction of the two media.

If the incident light is not normal to the interface, R will depend on the angle of incidence. When light is transmitted from a vacuum or air into a solid s, then the index of refraction of air is very nearly unity.

The higher the index of refraction of the solid, the greater is the reflectivity. (Eg- Silicate glasses, the reflectivity ~0.05). The reflectivity varies with wavelength of the incident light. Reflection losses for lenses and other optical instruments are minimized by coating the reflecting surface with very thin layers of dielectric materials such as magnesium fluoride (MgF2). Absorption Nonmetallic materials are either intrinsically transparent or opaque. Opacity results in relatively narrow-band gap materials as a result of absorption whereby a photon’s energy is sufficient to promote valence band-conduction band electron transitions. Transparent nonmetals have band gaps greater than about 3 eV. Some light absorption occurs in even transparent materials as a consequence of electronic polarization [20, 36]. Optical Properties of Metals Metals appear opaque as a result of the absorption and then reemission of light radiation within a thin outer surface layer. Absorption occurs via the excitation of electrons from occupied energy states to unoccupied ones above the Fermi energy level. Reemission takes place by decay electron transitions in the reverse direction. The perceived color of a metal is determined by the spectral composition of the reflected light [20,

36].

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Opacity and Translucency in Insulators Normally transparent materials may be made translucent or even opaque if the incident light beam experiences interior reflection and/or refraction. Translucency and opacity as a result of internal scattering may occur, (1) in polycrystalline materials that have an anisotropic index of refraction, (2) in two-phase materials, (3) in materials containing small pores, and (4) in highly crystalline polymers [20, 36 and 37].

Fig-54 the spectrum of electromagnetic radiation, including wavelength ranges for the various colors in the visible spectrum Color For wide-band gap insulators that contain impurities, decay processes involving excited electrons to states within the band gap are possible with the emission of photons having energies less than the band gap energy. These materials appear colored, and the color depends on the distribution of wavelength

ranges in the transmitted beam [20, 36 and 37] (Fig-54). Optical phenomena Three other important optical phenomena are luminescence, photoconductivity, and light amplification by stimulated emission of radiation (lasers). Luminescence With luminescence, energy is absorbed as a consequence of electron excitations, which is reemitted as visible light. The electron-hole pair produced in photo-excitation processes reverts to the original state by releasing energy to the lattice through creation of phonons or radiative recombination, giving rise to luminescence. Such a de-excitation can be induced at impurity sites called activators. Absorption and emission processes in photoluminescence need not occur at the same impurity sites. For example, in Ca3 (PO4)

2 doped with Ce and Mn, absorption occurs at Ce sites (sensitizer) and recombination at Mn sites (activator). This process involves energy transfer between two centers, and the luminescence intensity therefore depends on the average distance between impurity centers. The cation Eu2+ in barium magnesium aluminate gives blue emission, while Eu3+ in Y2O3 gives red emission [20, 36 and 37]. Photoconductivity The electrical conductivity of some semiconductors may be enhanced by photo-induced electron transitions, whereby additional free electrons and holes are generated.

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Lasers Coherent and high-intensity light beams are produced in lasers by stimulated electron transitions. Laser (light amplification through stimulated emission of radiation) action is seen in materials such as ruby (0.01 atom%Cr3+ in Al2O3). This occurs because of population inversion, achieved by optical pumping to higher energy levels (4F1 and 4F2) from which de-excitation occurs through a non-radiative process to an intermediate level (2E), from which lasing occurs to the ground state (4A2), giving 6943 Ȧ radiation. The simulated laser light has the special property of coherence and it has the same phase and direction of propagation as the incident photon. When Nd3+ is doped in CaWO4, there is laser emission at 1.06 µm (4F 3/2 to 4I11/2) [20, 36]. The commonly employed Nd-YAG laser is Nd3+ in Y3Al5O12 (yttrium aluminum garnet). The polarization produced in a solid is generally proportional to the electric field of the radiation. Electric fields produced can be very high laser beams and nonlinear effects. Polarization would then contain multiples of frequencies. The number of photons with frequencies 2ω, 3ω …, will however be small. Generation of second and higher harmonics is accomplished by using non-centrosymmetric crystals such as KH2PO4, LiNbO3, and KTiOPO4

[20, 37]. 6.37 Electronic and Magnetic properties in relation to structure As explained in previous section 6.31, TMO exhibit electronic properties two ways one is due to the presence of itinerant electrons and

the other due to localized electrons. Further TMO based on oxygen bonding is discussed below. 6.371 Monoxides Monoxides of 3d transition metals, TiO to NiO, possess the rock salt structure and exhibit interesting properties (Fig-55). TiO and VO exhibit properties characteristic of itinerant d electrons. MnO, FeO, CoO, and NiO show localized electron properties.

Fig- 55, Transition metal mono-oxides with rock salt structure The properties can be understood in terms of cation-cation and cation-anion-cation interactions in the rock salt structure. Direct cation-cation interaction can occur through the

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overlap of cationic t2g orbitals across the face diagonal of the cubic structure. When such an interaction is strong (R < Rc and b > bc), cationic t2g orbitals are transformed into a cation sublattice t*

2g band; if this band is partially occupied, the material becomes metallic (e.g., TiO). VO is less metallic, and its magnetic susceptibility becomes temperature dependent at low temperatures because the increased nuclear charge contracts the radial extension of the 3d orbitals of vanadium, thereby decreasing the overlap of the t2g orbitals. The increasing nuclear charge across the TiO-NiO series has the effect of lowering the 3d manifold energy relative to the top of the anionic 20 states (fig-55) [20, 36 and 37]. 6.372 Dioxides Dioxides of many of the transition metals crystallize in the rutile structure, and their electronic properties are shown in (Fig-56). The rutile structure provides the possibility of 135o cation-anion-cation interaction between corner-shared octahedral and 90o cation-anion-cation interaction between edge-shared octahedral. A direct cation-cation interaction is possible along the direction c. The octahedral crystal field of the cation and the tetragonal structure provide an axial field, which splits the triply degenerate metal t2g orbital into a non degenerate t|| orbital and a

doubly degenerate t+ orbital. While t+ can form

π∗ bands with anion pπ orbitals, t|| forms cation sub lattice d bands of the cation-cation distance along the c-axis is less than Rc.

Fig-56, Transition metal Di-oxides with Rutile structure The rutile structure therefore enables the oxide to become metallic through cation-cation interaction and/or through cation-anion-cation interaction [20]. 6.373 Sesquioxides The important sesquioxides of the first row transition metals crystallizing in the corundum structure are Ti2O3, V2O3, Cr2O3, and α-Fe2O3. Cr2O3, and α-FeO3 are antiferromagnetic insulators. Ti2O3 and V2O3 exhibit semiconductor-metal transitions at 410K and 150K, respectively. The transition in Ti2O3 is broad, occurring over a large temperature interval. In V2O3, the transition is accomplished by antiferromagnetic ordering. These properties

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can be understood in terms of the cation-anion-cation interactions (135o and 90o) and cation-cation interactions (in the basal plane and along the hexagonal c-axis). The structure provides a trigonal component to the octahedral crystal field, which splits the t2g orbitals into a1g (directed along cH) and eg(π) directed in the basal plane. In Ti2O3, with one d electron per atom and a small hexagonal c/a ratio, both the cation-cation distances are smaller than the critical value (Rcc < Rbb < Rc). The a1g band is therefore filled and separated from the empty eg(π) band by a finite gap, accounting for the semiconducting behavior at low temperatures. In V2O3, with large c/a ratio and with two d electrons per vanadium, Rcc < Rbb < Rc; the eg (π) band is more stable than the a1g band. The metallic nature of rhombohedral V2O3 indicates that these bands overlap to some extent. In Cr2O3 and Fe2O3, the a1g and eg(π) orbitals are half-filled. In Cr2O3, the eg electrons are localized, but the a1g electrons are likely to be intermediate, since the interaction distance in the c direction is less than Rc. In Cr2O3, with no eg(σ) electrons. Accordingly, TN in Fe2O3 is higher (953 K) than in Cr2O3 (307 K). Fe2O3 exhibits weak, parasitic ferromagnetism in the range 253 < T < 953 K. In this temperature range, the atomic moments lie nearly in the basal plane. Anti-symmetric spin coupling is parallel to the c-axis, and the anisotropic super exchange cants spins in the basal plane to produce a net moment. Upon application of a strong magnetic field in the c direction, a field-induced first-order spin-flip transition (Morin transition) is observed around 260 K [20].

6.374 Properties of Pervoskites and Spinels The physical properties of perovskite include superconductivity, colossal magnetoresistance, ionic conductivity, and a multitude of dielectric properties, which are of great importance in microelectronics and telecommunication. The great flexibility inherent in the perovskite structure enables many different types of distortions, which can occur from the ideal structure. These include tilting of the octahedra, displacements of the cations out of the centers of their coordination polyhedra, and distortions of the octahedra driven by electronic factors (i.e. Jahn-Teller distortions). Many of the physical properties of perovskites depend crucially on the details of these distortions, particularly the electronic, magnetic and dielectric properties which are so important for many of the applications of perovskite materials. The perovskite structure is ideally suited for the study of 180o cation-anion-cation interaction of octahedral site cations. The possibility of cation-cation interaction is remote because of the large interaction distance along the face diagonal. Various properties of perovskites are shown with the examples: BaTiO3 is ferroelectric, SrRuO3 is ferromagnetic, LaFeO3 is weakly ferromagnetic, and BaPb1-xBixO3 is super-conducting, while LaCoO3 shows a nonmetal-to-metal transition. Several perovskite oxides exhibit metallic conductivity; some examples are ReO3, AxWO3, LaTiO3, AMoO3 (A = Ca, Sr, Ba), SrVO3, and LaNiO3. Metallic conductivity in perovskites is due to the strong cation-anion-cation interaction.

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6.375 Mixed Valence Many transition metal oxides contain cations in more than one oxidation state. Properties of these oxides are generally determined by the rate of electron transfer between the different oxidation states. A classification of such compounds has been made by Robin and Day on the basis of the valence delocalization coefficient (Fig-57).

Fig-57, Different classes of Mixed Valent Solids This type of mixed valence is different from that prevalent in rare earth and actinide materials, in which valence fluctuations, heavy fermion behavior, and superconductivity are found. Depending on the relative energies of the fn configuration and the Fermi level due to non-f electrons, three electronic regimes are distinguished: the magnetic regime, the Kondo regime, and the fluctuating valence regime. EuO and SmS exhibit valence fluctuations under pressure as a result of the promotion of an f electron to the conduction band [20].

6.376 Defects in Oxides Most crystalline materials are not perfect and their regular pattern of atomic arrangement is interrupted by crystal defects.

Fig- 58, Schematic illustration of defects in a compound solid, using GaAs as an example. In Fig-58, the defect notation in upper-case letters stand for atoms or vacancies (V) on a lattice site, and the subscripts for the lattice site in a perfect crystal. The subscript i→ stands for an interstitial site and the subscript S for a substitutional site. Thus e.g. Asi stands for a As atom on an interstitial site, VGa for a missing atom on the Ga sublattice, GaAs for a Ga antisite atom on the As sublattice, and BS for a B atom on a substitutional site. This notation is a variety of Kroger-Vink Notation for non-ionic solids A nonstoichiometric oxide can be defined as a crystalline oxide in equilibrium with its

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environment, behaving as a thermodynamically bivariant system. In stoichiometric oxides, vacancies order themselves to give rise to super structures or complexes [20]. o Roth clusters are complexes of the form

given by, VM – M3+

tet – VM where M is a transition metal, VM is the vacancy created by the absence of a metal atom, and the M3+ ion is tetragonally surrounded by oxygen atoms. The ratio of vacancies to tetrahedral M3+ ions in the Roth cluster is 2:1 = 2. o Another similar type of complex is the

Koch-Cohen cluster, which as a ratio of 3:4 = 3.25 in oxides of the form MO2+x or MO2-x, a defect cluster, known as the Bevan cluster which are tightly bound vacancies along a body diagonal, <III>.

o Another type of defect cluster, where two

vacancies, one interstitial of one kind and two interstitials of another kind, is known as the 2:1:2 Willis cluster.

In ionic solids, the common point defects are Schottky pairs (pairs of cation and anion vacancies) and Frenkel defects (cation or anion interstitial pairs plus a vacancy). When there is a large concentration of Schottky pairs, the measured pyknometric density of the solid is considerably lower than the density from the X-ray unit cell dimensions (e.g., VO) [20]. Creation of defects is generally an endothermic process. Thus, the formation energies of vacancies in ionic solids are generally 2eV or

more. The intrinsic defect concentration in these solids is therefore extremely small even at high temperatures. The intrinsic defect concentration in binary solids around 0.8Tm is ~10-5 [20]. Types of defects The various types of defects that occur in ionic solids are point, linear, planar and volumetric. Point defects Point defects arise from the absence of the constituent atoms on the lattice sites or their presence in interstitial positions. The presence of alien atoms constitutes another type of point defects. Point defects cause polarization of the surrounding region in the crystal and give rise to small displacements on neighboring atoms or ions. Thus a cation vacancy in an ionic solid will have an effective negative charge, causing displacements of neighboring anions. The energy of formation of point defect depends mainly on the atomic arrangement in the immediate neighborhood of the point defect. Linear defects Linear defects in crystals are dislocations, corresponding to rows of atoms that do not possess the right coordination. Planar defects Planner defects are boundaries between small crystallites (grain boundaries), stacking faults, crystallographic shear planes, twin boundaries and anti phase boundaries. Volumetric defects Segregation of point defects gives rise to 3D volumetric defects.

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Crystallographic shear One way by which anion-deficient nonstoichiometry is accommodated in some transition metal oxides is by eliminating point defects by crystallographic shear. This leads to the formation of isolated shear plane or a random array of shear planes, known as Wadsley defect. In close packed oxides, we also see stacking faults such as: tilt boundary (array of periodically spaced edge dislocations), twist boundary (array of screw dislocations), twin boundaries (a layer with mirror plane symmetry), and coincidence boundary (one part of a crystal rotated with respect to another) and antiphase boundaries (across which the sublattice occupation is interchanged) [20]. 6.377 Phase Transitions When temperature rises and pressure is held constant, a typical substance changes from solid to liquid and then to vapor. Transitions from solid to liquid, from liquid to vapor, from vapor to solid and vice versa are called phase transformations or transitions. Since some substances have several crystal forms, there can also be solid to another solid phase transformation. Phase transitions involve changes in atomic configuration, electronic or the spin configuration. During a phase transition, the free energy of the solid remains continuous, but thermodynamic quantities such as entropy, volume, and heat capacity exhibit discontinuous changes. Depending on which derivative of the Gibbs free energy, G, shows a discontinuous change at the transition. Phase transitions are generally classified as first order or second order. In a first-order transition,

where the G (P, T) surfaces of the parent and product phases intersect sharply, the entropy and the volume show singular behavior. In second-order transitions, on the other hand, the heat capacity, compressibility, or thermal expansivity shows singular behavior. Many physical properties diverge near Tc; that is, they show anomalously large values as Tc is approached from either side. An important aspect of phase transition in solids is the presence of two modes. Operationally, a soft mode is a collective excitation whose frequency decreases anomalously as the transition point is reached. In second-order transitions, the soft-mode frequency goes to zero at Tc, but in first-order transitions, the phase change occurs before the mode frequency goes to zero. It has been found convenient to classify phase transition in solids on the basis of the mechanism. Three important kinds of transition are as follows: nucleation and growth transitions, a typical example being the anatase-rutile transformation of TiO2; positional and orientational order-disorder transitions; and martensitic transitions. Orientational order-disorder is exhibited by many solids such as ammonium halides, plastic (orientationally disordered) crystals. A martensitic transition is a structural change caused by atomic displacements (and not by diffusion) corresponding to a homogenous deformation where the parent and product phases are related by a substitutional lattice correspondence, an irrational habit plane, and a precise orientational relationship [20, 21]. Structural phase transitions are also classified in the following manner:

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o Displacive: ferrodistortive, anti- ferrodistortive, and ferreoelastic transitions.

o Order-disorder: vacancy ordering Electronic: spin-state transitions.

Fig- 59 Magnetic phase diagram of RMnO3 The above Magnetic Mn Phase diagram (Fig-59) shows hexagonal and orthorhombically-distorted perovskite structures. Both differ on the FE and AF ordering temperatures. Open and closed triangles denote the Ne´el and lock-in transition temperatures respectively. Rare-earth manganites RMnO3 may be classified into those with hexagonal structure (where R = Ho to Lu) and those with orthorhombically distorted perovskite structures (where R= La, Gd and Dy). Fig-59 shows the magnetic phase diagram for RMnO3. The hexagonal RMnO3 (such as YMnO3 or LuMnO3) show both, ferroelectric and antiferromagnetic order, but the TFE ≈1000 K and TN ≈100 K differ by an order of magnitude which would not produce a feasible coupling between the two order parameters.

But, RMnO3 (with R = Gd, Tb, and Dy) possesses comparable transition temperatures for the magnetic and the ferroelectric ordering, indicating that there might be direct coupling between them. For instance, the switching of the electric polarization could be achieved by applying magnetic fields [20, 21].

7.0 Multiferroic Crystals Multiferroics are Poly crystals belonging to the family of Transition Metal Oxides that have coupled electric, magnetic, and structural order parameters that result in simultaneous ferroelectricity, ferromagnetism, and ferroelasticity. 7.10 Origin and History of Multiferroics The origin of multiferroics dates back to the discovery of magnetoelectric effect. Pierre Curie first postulated this effect in 1894.

Fig- 60 Magnetoelectric Effects: Historical Survey Following the theoretical prediction by Dzyaloshinskii [38] in 1959 and the first

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experimental observation by Astrov [39] in 1960 and Folen in 1961 (Fig-60), the magneto electric effect was studied intensively in the 1960s and 1970s [40] attracted continuing interest for more than four decades. The history of multiferroics research dates back to 1958 from the work by Smolenskii and coworkers (Fig-60) [40]. Numerous multiferroics have been identified to date. Examples are some boracites (Ni3B7O13I, Co3B7O13I, etc.), some fluorides [BaMF4 (M = Mn, Fe, Co, and Ni)], magnetite Fe3O4, hexagonal manganites (YMnO3, HoMnO3, etc.), perovskites ABO3 having a Bi or Pb ion on the A site and transition metal(s) on the B site [e.g., PbFe 1−X NbxO3, BiFeO3 and BiMnO3], CdCr2S4, and hexagonal ferrites (e.g., LuFe2O4). Scientific communities around the world have made lot of contributions in publishing several reviews in the past years which led to the understanding of magnetoelectric effect, characterization of magnetoelectric multiferroics, according to the origin of their multiferroic nature [40].

Fig- 61 Multiferroic research progress and trend

7.20 Progress of researches in Multiferroics The field gained interest in the past decade (Fig-61) after the observation of gigantic ferroelectric polarization in one of the conventional multiferroics, BiFeO3 (Bismuth ferric Oxide) at room temperature [40], and the discovery of a new class of multiferroics showing a large magnetoelectric effect. In 2003, ferroelectric activity was found in rare-earth manganites with orthorhombically distorted perovskite structure, TbMnO3, which shows antiferromagnetic orders with long wavelength modulation as compared to their chemical unit cell, [44] owing to competing magnetic interactions. In this new multiferroic compound, a large magnetoelectric effect has been observed at the onset field of a metamagnetic transition. More recently, theoretical and experimental studies of the rare-earth manganites revealed that the ferroelectricity originates from a cycloidal spiral spin structure. These results indicate the emergence of a new class of ferroelectrics in which the origin of ferroelectricity is related to magnetic order and is different from known ferroelectrics. Magnetoelectric effects in materials provide a great opportunity to use an electric field to control ferromagnetism. Magnetoelectric coupling between electric and magnetic order parameters has been theoretically predicted, and there is intense interest in its implementation in device architectures to take advantage of these properties for applications in many fields, such as agile electromagnetics, optoelectronics or Spintronics [40]. 7.30 Constraints in most multiferroics The major constraint in most multiferroics is that, the temperature scale for ferroelectric

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order is much larger than for magnetic order, and the origins of these orders have no relation to each other, which leads to only weak coupling between magnetism and ferroelectricity. Single-phase multiferroics show spontaneous magnetization and polarization simultaneously at ambient conditions, remains elusive as most systems (Eg: manganites) exhibit multiferroicity only at low temperatures [40].

Fig-62 - RE MnO3 Vs Other Multiferroics The case of ferromagnetic and ferroelectric couplings within one phase is very difficult to be found in reality because ferromagnets tend to be metals and ferroelectrics need to be insulators. However one multiferroic material namely BiFeO3 (BFO), has played a key role in rejuvenating the field after a report of large ferroelectric polarization combined with interesting magnetic properties at room temperature in bulk BFO [41]. But numerous reports of Professor Ramesh Ramamoorthy and associate researchers on the

properties of BFO thin films, Nano structures and Nanopillar forms are quite promising and encouraging for further research to use the BFO thin films in industrial applications, especially in the new and novel device applications. 7.40 Structures of Multiferroics Multiferroics are perovskites with general formulas of ABO3 and A2BBO6

8 with units of cubic cell type (eg-LaxTiO3), tetragonal type (eg-BaTiO3) and orthorhombic type (eg-GdFeO3) structures. Many different types of distortions can occur from the ideal structure of perovskites. These include tilting of the octahedra, displacements of the cations out of the centers of their coordination polyhedra, and distortions of the octahedra driven by electronic factors (i.e. Jahn-Teller distortions). Multiferroic materials have a slightly deformed symmetry with the 3m point symmetry group instead of the ideal cubic symmetry m3m. 7.50 Mechanism of Multiferroics Normally, ferromagnetism and ferroelectricity exclude each other, but in multiferroic materials, researchers have reported magnetoelectric coupling in the same phase in materials like TbMnO3, DyMnO3, GdMnO3, and BFO. Several theories about mechanisms of multiferroics have been proposed to explain the origin of multiferroicity in the different materials that are discussed below [42-45]. 7.51 Paramagnetic doping. Coexistence of ferroelectric and ferromagnetic order parameters can be established when a transition metal ion is being replaced partially by a paramagnetic ion. The solid solution [PbFe2/3W1/3O3]1−x[PbMg0.5W0.5O3]x is the first

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system in which magnetic and electric ordering have been found to coexist. The Mg and W ions are diamagnetic and cause the ferroelectricity, and the d5 orbitals of Fe3+

ion are responsible for the magnetic ordering. Because of the mutually diluting properties, these systems possess low magnetic ordering temperatures [20, 42-45]. 7.52 Lone-pair asymmetry. The chemical compounds of BiRO3 (where R = Fe, Mn, Cr) exhibits multiferroicity when a lone pair of s2 (Bismuth ion) hybridizes with an empty p orbital of R-cation and causes a structural distortion by exhibiting ferroelectricity. Examples are: In Bi2FeCrO6 a spontaneous magnetization of 2µB and a spontaneous polarization of 80 µC cm−2

at room temperature are reported [41]. BiMnO3

possesses saturated magnetic moment with the magnitude of 3.6 µB at 10 K. For BiFeO3, bulk magnetization measurement shows 6.1 µC cm−2 [41]. 7.53 Electrostatic and size effects. The Electrostatic and size effects contributes a good coupling effect, for example in YMnO3. The hexagonal crystal structure consists of non-connected layers of MnO5 trigonal bipyramid corners linked by its in-plane oxygen ion (Op). In addition, an apical oxygen ion (OT) produces close-packed planes separated by a layer of Y 3+

ions. The trigonal bi-pyramids represent the MnO5 polyhedra and the spheres represent Y ions. There are two major atomic displacements in the crystal structure from the centro symmetric P63/mmc to the ferroelectric P63cm: Firstly, a buckling of MnO5 polyhedral structure results in a shorter c-axis and secondly the displacement is a vertical shift of the Y ions away from the

high temperature mirror plane, while keeping the distance to OT constant [45].

Fig- 63 Crystal structure of YMnO3 in the paraelectric and ferroelectric phases As a result of this buckling phenomenon, one of the two Y-Op bond lengths is reduced, and the other bond length is enlarged, leading to a net electric polarization. This asymmetric environment of the Y ions was recognized under neutron-powder-diffraction and X-ray diffraction studies. Since Y3+ or Mn3+ have no lone pair of electrons and the Mn ions remains close to the centre of their oxygen cages, the driving force for ferroelectricity in YMnO3 is entirely caused by the electrostatic and size effects (Fig-64). This is derived from the long range dipole-dipole interaction and the oxygen rotated in such way to make huge Y-Op off-centre displacements, which produces an electrical polarization and a stable ferroelectric state in YMnO3 structure. 7.54 Microscopy ME correlation Efremov, et.al mentioned that besides the well-known site-centered and bond centered charge ordering in doped manganites of the type R1-

XCax MnO3 (where R=La or Pr), But there is one intermediate situation among them which

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can produce multiferroics [46]. Charge ordering in the sites leads to a checker board ordering pattern as shown in Fig-64(a) and is known as Site-Centered ordering (SCO). When the charge ordering occurs in the bonds instead of in the sites, as depicted in Fig-64(b), it is called a Bond-Centered Ordering (BCO).

Fig- 64 Three types of charge ordering

For example, Pr1-XCaXMnO3 with x = 0.4. The intermediate state can be found in the doped Lanthanum-Calcium compounds at x ≥ 0.5 and in the Pr-Ca system at x = 0.3 as in Fig-64(c). The asymmetry on this intermediate phase leads to an ordered dipole moment and consequently produces ferroelectricity. 7.60 BFO Structure – as a model system As of today, several composite materials, consisting of separate piezoelectric and magnetic phases, have been reported to show magnetoelectric coupling at room temperature [47, 48], a requirement for device applications. However, the availability of room-temperature single-phase multiferroics is very limited.

Among the few room temperature single-phase magnetoelectric multiferroics reported so far, BiFeO3 shows the highest ferroelectric polarization, with a ferroelectric Curie temperature (TC) of ~1,100 K and an antiferromagnetic N´eel temperature (TN) of ~640 K. Both ferroelectricity and antiferromagnetism have long been known in BiFeO3 single crystals, and recent studies of BiFeO3 thin films have confirmed the existence of a large ferroelectric polarization, as well as a small magnetization, both of which are consistent with theoretical predictions. Although the possibility of coupling between the ferroelectric polarization and the weak ferromagnetism has been investigated using first-principles density functional theory [52, 53], there have been no previous investigations of the coupling between ferroelectricity and antiferromagnetism in this material. In addition to its fundamental interest, such a coupling would offer the intriguing possibility of electric field controllable ferromagnetism through exchange bias to an electrically controllable antiferromagnetic component [51-

53]. BFO structure can be characterized by two distorted perovskite unit cells (ar = 3.96 Å, αr = 0.6°) connected along their body diagonal, denoted by the pseudocubic <111>, to form a rhombohedral unit cell (Fig-65) [56, 57]. The large displacement of the Bi ions relative to the octahedral FeO6 induces ferroelectricity resulting in two important considerations. Firstly, the ferroelectric polarization lies along the pseudocubic <111> leading to the formation of eight possible polarization

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variants, corresponding to four structural variants [54, 57 and 58]. Secondly, the antiferromagnetic ordering of BFO is G-type, in which the Fe magnetic moments are aligned ferromagnetically within (111) and antiferromagnetically between adjacent (111). BFO is also known to exhibit a spin cycloid structure in the bulk [54] and the preferred orientation of the antiferromagnetically aligned spins is in the (111), perpendicular to the ferroelectric

polarization direction with six equivalent easy axes within that plane (Fig-65) [58, 60]. Therefore, it is obvious that there is a coupling between antiferromagnetism and ferroelectric polarization. Recent studies of BFO thin films have shown that canting of the antiferromagnetic sub lattice is the reason for the existence of a large ferroelectric polarization, as well as a small net magnetization of the Dzyaloshinskii–Moriya type [55, 60].

Fig.65 Schematic of the crystal structure of BFO and the ferroelectric polarization (arrow) and antiferromagnetic plane

(shaded planes).

8.0 Thin films Multiferroic thin films are thin films of materials consisting of two or more multiferroic properties. In general thin films is a field of the utmost importance in today's

microelectronics, materials science and engineering, electrical engineering, applied solid state physics and chemistry, bio-medical, telecommunications and so on, for both research and industrial applications.

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Advanced, high- performance computers, high-definition TV, digital camcorders, sensitive broadband imaging systems, flat-panel displays, robotic systems, and medical electronics and diagnostics are but a few examples of miniaturized device technologies that depend on the utilization of thin film materials [20, 53]. 8.10 History of Thin Films The first studies of thin films (magnetic films) of electronic material were conducted in 1884 by Professor August Kundt [61]. He fabricated thin films of iron, cobalt, and nickel, and was able to measure the rotation in the polarization of light transmitted through these films in a direction parallel to the film magnetization.

8.20 Materials for Thin Films Electronic materials are mainly used to fabricate or grow thin films and they can be classified in to insulating, semi-insulating and metallic. Thin films can be classified in to Ferro / Ferrimagnetic thin films, Ferro / Ferri electric thin films and Magnetoelectric / Multiferroic thin films. Most of the magnetoelectrics and multiferroics are insulating oxides, which are extensively used as thin films in electronics, microelectronics and research for advanced materials and for potential novel device applications as detailed in (Fig-66).

Fig-66 Material for Insulating Oxide Thin Films

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8.30 Thin-film deposition / Processing Thin-film deposition is a technique for depositing a thin film of material onto a substrate or onto previously deposited layers. Most deposition techniques allow layer thickness to be controlled within a few tens of nanometers and some allow single layers of atoms to be deposited at a time. General infrastructures for processing o PLD, CVD, Sputtering, solgel facilities for

thin film processing. o Laser MBE to process complex oxides like

crystalline oxides on Si o Clean room environment for

characterization and device processing. o Scanning force microscopy for

characterization like Piezoforce microscopy of FERAMS

o Nanoscale domain dynamics using AFM, MFM, TUNA.

o Switching dynamics using AFM for high speed measurements.

o Facilities for FE, transport, interface, pyroelectric studies

o Advanced Light Source for Insitu studies using synchrotron.

o NCEM for TEM studies 8.31 Classification of deposition processes Most of the thin film deposition processes and technologies originate from purely physical or purely chemical processes as detailed in Fig-67. All the available thin film processing techniques are based on liquid phase chemical processes, gas phase chemical processes, glow discharge processes and evaporation methods [62]. From the past couple of decades numerous novel processes that utilize a combination of different techniques have been developed and this combination allows a more defined control

and tailoring of the microstructure and properties of thin films.

Fig-67 Classification of the most common deposition processes General Characteristics of Thin Film Deposition � Deposition Rate � Film Uniformity

o Across wafer uniformity o Run-to-run uniformity

� Materials that can be deposited o Metal o Dielectric o Polymer

� Quality of Film – Physical and Chemical Properties o Stress o Adhesion o Stoichiometry o Film density, pinhole density o Grain size, boundaries and orientation o Breakdown voltage o Impurity level

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� Deposition Directionality o Directional: good for lift-off, trench

filling o Non-directional: good for step coverage

� Cost of ownership and operation Mass Deposition Rate per unit area of source surface Mass Deposition Rate (Rm) per unit area of source surface is given by Langmuire – Knudsen relation below [62, 63 and 64].

Maximum deposition rate reaches at high chamber vacuum (P ~ 0) (Fig-68).

Fig-68 Mass Deposition rate

Uniform Coating Uniform Coating for spherical surfaces with source on its edge (Fig-69) is given by

Fig-69 Uniform Coating for spherical surfaces Angle independent and uniform coating used to coat instruments with spherical surfaces. Uniformity on Flat Surfaces Uniform Coating for flat surfaces (Fig-70) is given as follows

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Fig-70 Uniform Coating for flat surface Uniformity requirement for Flat Surfaces Uniform Coating for flat surfaces (Fig-71) is given as follows

Fig-71 Graph showing Sample size Vs Source –Sample distance in Uniform Coating requirements for flat surface Thickness Deposition Rate vs. Source Vapor Pressure Rate of thickness deposition vs. Source Vapor Pressure is illustrated in the Fig-72.

Fig-72 Thickness Deposition Rate Vs Source Vapor Pressure

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Pe is function of source Temperature, So, higher the vapor pressure, the higher is the material’s deposition rate [62, 63 and 64]. Deposition Rate vs. Source Temperature Deposition Rate vs. Source Temperature is illustrated in the Fig-73 [62, 63 and 64].

Fig-73 Vapor Pressure Vs Temperature Classification of Processes Basically there are two types of Vapor depositions, which are Physical Vapor Deposition (PVD) and Chemical Vapor Deposition (CVD). Other thin film growth techniques from liquid and solution phase are also in practice. Physical Vapor Deposition Deposition happens because of a physical reaction.

Fig-74 Physical Vapor Deposition

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These processes create the solid thin films directly from the material without any chemical reaction. The deposited material is physically moved on to the substrate (Fig-74). Types of PVD o vacuum evaporation o sputtering o Molecular beam epitaxy (MBE) Chemical Vapor Deposition In CVD, the deposition happens because of a chemical reaction. This process creates the solid thin films directly from chemical reactions in gas and/or liquid compositions or with the substrate material. The solid material is usually not the only product formed by the reaction. By products can include gases, liquids and even other solids. Types of CVD o Atmospheric pressure chemical vapor

deposition (APCVD) o Low pressure chemical vapor deposition

(LPCVD) o Plasma assisted (enhanced) chemical vapor

deposition (PACVD, PECVD) o Photochemical vapor deposition (PCVD) o Laser chemical vapor deposition (LCVD) o Metal-organic chemical vapor deposition

(MOCVD) o chemical beam epitaxy (CBE) Other thin film growth techniques - from liquid and solution phase are: o spray coating o spin coating o electroplating o liquid phase epitaxy

8.32 Vacuum Systems Many prevalent deposition techniques used in modern thin film technology requires the creation of vacuum condition for the deposition to occur. The quality and consistency in quality of final products (thin film) depends on these vacuum systems [62]. Basic Vacuum Concept Vacuum is the absence of gases, moisture and particles which normally fill our environment. In a deposition system a container is provided and the majority of these elements are removed to create a vacuum. The vacuum condition is an important factor to get suitable vacuum environment to produce quality thin films. Vacuum condition, accelerates the mean free path for atoms by eliminating the presence of gases that could react with the materials to be deposited; It could reduce the vapor pressure and lower the evaporation temperature of the target material and provides the ultimate clean vacuum environment. Measure of vacuum In vacuum measurements, pressures are mostly measured in millimeters of mercury or torr. One torr is the pressure necessary to support a column of mercury with a height of one millimeter. 1 atmosphere = 101 KPa = 760 torr. Vacuum conditions are classified as low vacuum of pressure range 105 to 103 Pa (760- 25 torr), Medium vacuum 103 to 10-1 Pa (25 torr to 0.75 milli torr), High vacuum 10-1 to10-4 Pa (~ 10-3 to 10-7 torr) and Very high vacuum 10-4 to 10-7 Pa ( ~ 10-7 to 10-12 torr). Most practical deposition processes occur in the medium to high vacuum ranges [62].

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There are two pressure regimes in vacuum systems, and gases behave differently in each regime. o In the viscous flow regime, gas flows as a

fluid, where the mean free path of the gas molecules is much smaller than the dimensions of the apparatus.

o In the molecular flow regime, the mean free path is much longer than the characteristic dimensions of the apparatus. In this regime, gas molecules interact almost entirely with the walls of the chamber, acting independent of each other.

Gas flow in either regime is measured in torr liters per second, which is equivalent to mass per second. The conductance of a tube describes how much gas flows through the tube for a given pressure differential between the ends. The mass flow is given by

Where Q is the mass flow, P1 is the pressure at the input of the tube, and P2 is the pressure at the output and C is the conductance of the tube. Conductance in the viscous flow regime is proportional to the average pressure in the tube and is high, compared to the molecular-flow regime, because the gas molecules push each other along. In the molecular-flow regime, conductance through a tube is independent of pressure and is given by

Where D is the diameter of the tube in centimeters, and L is its length, also in centimeters. Pumping speed is expressed in liters per second. The amount of mass going through the Pump is given by

Where P is the pressure at the inlet of the pump, and Sp is the pump speed. The net speed of a pump connected to a vacuum chamber by a tube is

The time required to pump the system from an initial pressure of P0 down to P is

Where, V is the volume of the chamber. Vacuum Chambers Generally vacuum chambers are made out of stainless steel or glass chambers because they do not corrode, are easily cleaned, non magnetic and have good out-gassing characteristics. Stainless is used for large vacuum systems because of its relatively high strength, ease of welding and machinability. The vacuum system consists of a vacuum chamber, pumping system, deposition sources and monitoring equipment, as explained in Fig-75. Two basic configurations are (i) a glass or stainless steel enclosure sealed to a metal base or door by a gasket and (ii) a stainless steel chamber with several ports to connect depositions sources and measurement sensors.

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Fig-75 Typical Vacuum System

The bell jar vacuum system is less expensive to construct and maintain. The disadvantage is that the gaskets used to seal the bell and the base plate together create a large contact area with relatively high leakage rates. As a result bell jar systems normally cannot reach the low vacuum pressures that other stainless steel vessels can obtain [62,63]. 8.33 Pumping systems The valve-and-piston principle is still the most widely used way of extracting air in the viscous-flow regime. Modern mechanical pumps feature multiple stages, specialized low-vapor-pressure oil sealants, and electric motors. Mechanical pumps can attain base pressures of a few milli torr or a few tens of milli torr, though below about 100 milli torr the oil used in them will leak back into the chamber being pumped on. This is called back- streaming, which is undesirable. Back-streaming can be eliminated by placing a high-vacuum pump

between the mechanical pump and the chamber [62, 63 and 64]. Mechanical pumps are seldom operated below 100 milli torr, and for this reason they are called as roughing pumps. To achieve even a moderate vacuum of 10−2 torr or better, a different pump design must be employed. The most common and reliable high-vacuum pumps in use today are turbo-molecular pumps, or turbo pumps for short. These are basically just very high-speed fans, whose blades are moving at speeds comparable to the speeds of gas molecules. Turbo pumps are capable of sustaining very high compression ratios, the ratio of the gas pressure at the output to that at the input. Typical compression ratios are in the order of 107 for air, for an outlet pressure of 100mtorr. This low outlet pressure is maintained by a mechanical pump, which acts as both a roughing pump for the system and a backing pump for the turbo. One advantage of using a turbo pump in conjunction with a mechanical pump is that the turbo pump’s compression ratio depends strongly on the molecular weight of the gas being pumped. The log of the compression ratio is proportional to the square root of the molecular weight of the gas. Because the oils used in mechanical pumps typically have very high molecular weights, the compression ratio across the turbo pump for these oils is considerably higher than 107 and the turbo pump effectively blocks any back-streaming from the roughing pump. Speeds for turbo pumps are usually independent of the type of gas being pumped and they are specified by their speeds [62, 63 and 64].

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Contamination Contamination in the vacuum system is the result of leaks from the vacuum container and evaporation of moisture and other materials from the inside walls of the container known as out-gassing. The rate of out-gassing from a surface can be expressed as

Where Or is the rate of out-gassing, q is the specific out-gassing rate for the material and A is the surface area. The specific out-gassing rate is unique for a given material as in Fig-76. The types of materials used in vacuum system, the quality of seals (rubber seals, metallic seals etc) and the general clean environment can limit the maximum obtainable vacuum [62, 63].

Fig-76 Specific out-gassing rates for materials Some of the widely used processes like Pulsed Laser Deposition (PLD), Chemical Vapor

Deposition (CVD), Sputtering and Molecular Beam Epitaxy (MBE) are discussed below. 8.34 Pulsed Laser Deposition (PLD) Pulsed laser deposition (PLD) is an efficient method to produce thin films by utilizing a technique called laser ablation. PLD gained tremendous interest after T.Venketesan in 1987 first applied this method to create high temperature superconductive (HTSC) films. PLD is applicable to almost any material, in particular to compounds that are difficult to produce in thin-film form by other techniques. Examples of such materials include complex ceramic materials such as high-temperature superconductors and certain magnetic materials (e.g., yttrium iron garnet (YIG) and ferromagnetic shape-memory (FSM) alloy Ni-Mn-Ga. PLD is a very reliable technique and due to the short interaction times and the strong non equilibrium conditions, allows some unique applications o Synthesis of metastable materials that

cannot be produced by standard deposition techniques, (e.g. NbN, or Fe-Ag supersaturated solid solution).

o Formation of films from species that are generated only during PLD.

o Fabrication of nanocrystalline films. o Formation of composite films consisting of

different materials. Pulsed laser deposition is one of the newer techniques to deposit thin films, and uses the interaction between photons (laser beam) with material surfaces [67].

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Fig-77 PLD Process

The PLD process is shown in Fig-77 and the complete PLD system is shown in Fig-78. The pulses of a high power laser situated outside the vacuum deposition chamber are focused by optics onto the target surface, where they are absorbed.

Fig-78 Principal components of the vacuum system

The absorbed energy is converted into electronic excitations, followed by a transfer into thermal, chemical, and mechanical energy, which causes the ablation and exfoliation of the surface, which results in the plume formation. To produce the plume a minimum power density is needed, which will depend mainly on the target material, laser wavelength, and pulse duration. The plume consists of a mixture of energetic neutral atoms, molecules, ions, electrons, clusters, micron-sized particulates, and molten droplets. Gases, (i.e. O2, N2) can be introduced in the chamber to promote gas phase reactions, surface reaction, or to maintain the film stoichiometry. The plume expansion is followed by the re-condensation of the material on a substrate [62, 63 and 64]. The targets are mainly rods or cylinders. Rod-shaped targets have the advantage that the laser beam ablates always a new point suppressing surface roughening, structure formation, and surface enrichment in one element due to preferential sputtering or due to elemental enrichment in the molten phase (specially in multi-component targets). As a consequence, the density of particulates and changes in the plasma direction are minimized and when an additional gas pulse is used, it can be mounted closer to the rod geometry. The distance between target and substrate is typically 3-8 cm, while the thickness uniformity of the growing film is improved by rotation of the substrate. Excimer Lasers The term “excimer” is an abbreviation of “excited dimmer” which is a reminder of the

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excited Xe2 molecules used as laser gas in the first systems [64]. Modern excimer lasers use excited rare gas halogen molecules (exciplex) as active media due to the higher efficiency. The most common laser mixtures are: ArF (λ=193 nm), KrF (λ=248 nm), XeF (λ=351 nm), and XeCl (λ=308 nm) and recently a real excimer, i.e. F2 (157 nm) [63, 64]. KrF Excimer laser The light from an excimer laser is the result from a molecular gain medium in which the lasing takes place between a bound upper electronic state and a repulsive ground electronic state. Energy is pumped into the gas mixture by a fast avalanche electric discharge excitation (electric discharge strengths of 10-15 kV/cm). In contrast to most other laser types, the excitation of the active media of an excimer laser is performed by kinetic processes, involving a third body collision partner (i.e. buffer gas). This is necessary to absorb a part of the kinetic energy of the KrF collision. The most important reactions for a KrF laser are:

The collision of the Kr* and F- ion and the collision partner results in the formation of the

upper laser level, which is unstable and decays via spontaneous emission within ≈ 2.5 ns.

The formation rate of the ionic and excited precursors must be high enough to produce excimers at a rate of several 1023/cm3/s to allow lasing to occur [63, 64]. Mechanisms of PLD The principle of pulsed laser deposition is a very complex physical phenomenon. It involves the formation of plasma plume with high energetic species and even the transfer of the ablated material through the plasma plume onto the heated substrate surface [62, 63 and 64]. The thin film formation process in PLD can be divided into the following four stages. o Laser radiation interaction with the target. o Dynamics of the ablation materials. o Deposition of the ablation materials with

the substrate. o Nucleation and growth of a thin film on the

substrate surface

Each stage in PLD is critical to the formation of quality epitaxial crystalline, stoichiometric, uniform thin films with small surface roughness.

The main advantages of PLD: o Conceptually simple: a laser beam

vaporizes a target surface, producing a film with the same composition as the target.

o Versatile: many materials can be deposited in a wide variety of gases over a broad range of gas pressures.

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o Cost-effective: one laser can serve many vacuum systems.

o Fast: high quality samples can be grown reliably in 10 or 15 minutes.

o Scalable: as complex oxides move toward volume production [62, 63 and 64].

8.35 Sputtering Sputtering is a vacuum evaporation process which physically removes portions of a coating material called the target, and deposits a thin, firmly bonded film onto an adjacent surface called the substrate (Fig-79). The process occurs by bombarding the surface of the sputtering target with gaseous ions under high voltage acceleration. As these ions collide with the target, atoms or occasionally entire molecules of the target material are ejected and propelled against the substrate, where they form a very tight bond. The resulting coating is held firmly to the surface by mechanical forces, although, in some cases, and alloy or chemical bond may result [65, 66].

Fig- 79 Sputtering Vacuum Deposition Process

Sputtering has proven to be a successful method of coating a variety of substrates with thin films of electrically conductive or non-conductive materials. One of the most striking characteristics of sputtering is its universality. Since the coating material is passed into the vapor phase by a mechanical rather than a chemical or thermal process, virtually any material can be deposited. Direct current is used to sputter conductive materials, while radio frequency is used for non-conductive materials. The range of sputtering application is large. Current applications of great importance include thin films of: o Magnetic materials for data storage tapes.

Typical materials are Co-Ni, Tb-Fe and Co-Ni-Cr.

o Optical materials for lens characteristics. Typical materials are CeO2, MgO and MgF2.

o Lubricant materials for reducing friction. Typical materials are MoS2, WS2, and PTFE.

o Wear-resistant materials to lengthen cutting tool life. Typical materials are TiN, TiC, and ZrB2.

o Metallizing materials for microcircuits. Typical materials are Al, W-Ti, Al-Si and Al-Cu.

o Transparent conducting materials. The most typical material is xLn2O3 -ySnO2.

o Thin-film resistors. Typical materials are Ni-Cr, Cr-Si and Cr- SiO.

o Amorphous bubble memory devices. Typical materials are Gd-Co. Lu3Fe5O12, and Gd3Ga5O12.

o Microcircuit mask blanks. The most typical material is Cr.

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Additional applications include oxide microcircuit insulation layers, amorphous optical films for integrated optics devices, piezoelectric transducers, photoconductors, luminescent films for display devices, optically addressed memory devices, video discs, solid electrolytes and thin film lasers [65, 66]. Types of Sputtering The basic principle of sputtering is the same for all sputtering technologies. The differences typically relate to the manner in which the ion bombardment of the target is realized. Types of Sputtering are: o DC sputtering o DC Magnetron sputtering o RF sputtering DC Diode Sputtering Deposition Target (source) and substrate are placed on two parallel electrodes (diode) inside a chamber filled with inert gas (Ar).When a DC voltage (~ kV) is applied to the diode the free electrons in the chamber are accelerated by the e-field (Fig-80).

Fig- 80 Schematic of DC diode sputtering Vacuum

Deposition Process

These energetic free electrons in-elastically collide with Ar atoms and excitation of Ar occurs and the gas glows which induces the ionization of Ar forming Ar+ + 2nd electron. The 2nd electrons repeat the above process causing the gas to breakdown and the discharge to glow (plasma) (Fig-80) [65, 66]. Near the cathode, electrons move much faster than ions because of smaller mass and positive charge build up near the cathode, raising the potential of plasma. Fewer electrons collide with Ar and a few collisions with these high energetic electrons results in mostly ionization, rather than excitation forming a dark zone (Crookes Dark Space) (Fig-81).

Fig- 81 Self sustained discharge in DC diode sputtering

Vacuum Deposition Process Discharge causes voltage between the electrodes reduced from ~103 V to ~102V, mainly across the dark space and the electrical field in other areas is significantly reduced by the screening effect of the position charge in front of cathode. Positive ions entering the

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dark space are accelerated toward the cathode (target), bombarding (sputtering) the target. The atoms knocked out from the target transport to the substrate (momentum transfer, not evaporation!) and generate 2nd electrons that sustain the discharge (plasma) [65, 66]. Requirement for Self-Sustained Discharge If the cathode-anode space (L) is less than the dark space length, then the ionization occurs with a few excitations and cannot sustain discharges. On the other hand, if the Ar pressure in the chamber is too low then a large electron mean-free path is created and the 2nd electrons reach anode before colliding with Ar atoms and cannot sustain discharge either. Condition for Sustaining Plasma:

Where L is the electrode spacing and P is the chamber pressure For example: Typical target- substrate spacing: L ~ 10cm and P > 50 mtorr. Deposition Rate vs. Chamber Pressure Mean-free path of an atom in a gas ambient:

Sputtering deposition rate R:

High chamber pressure results in low deposition rate as shown in the example: L = 10 cm, P = 50 mtorr o λ~ 0.1 cm

o sputtered atoms have to go through hundreds of collisions before reaching the substrate

o significantly reduces deposition rate o also causes source to deposit on chamber

wall and re-deposit back to the target Large LP sustains plasma and small LP maintains good deposition rate and reduces random scattering. DC Magnetron Sputtering In DC Magnetron Sputtering low chamber pressure is used to maintain high deposition rate and a magnetic field is used to confine electrons near the target to sustain plasma as shown in Fig-82.

Fig- 82 Schematic of DC Magnetron sputtering

If a magnetic field parallel to the cathode surface is applied the electrons will be hopping (cycloid) near the surface (trapped). Impact of Magnetic Field on Ions The impact of Magnetic field on ions is explained in Fig -83 below.

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Fig- 83 Schematic of DC Magnetron sputtering showing

the impact of Magnetic field on ions. Hopping radius r:

Where, Vd is the voltage drop across the dark space (~ 100 V), B is the magnetic field (~ 100 G) for electron r ~ 0.3 cm and Ar+ ion the r ~ 81 cm. Then the current density (proportional to ionization rate) increases by 100 times and required discharge pressure drops 100 times and deposition rate increases 100 times~ as shown in Fig-84 [65, 66].

Fig- 84 DC Magnetron sputtering – Deposition rate Vs Chamber pressure

RF Sputtering The use of radio frequency, RF to sputter material was investigated in the 1960’s. Davidse and Maiseel used RF sputtering to produce dielectric films from a dielectric target in 1966. In 1968 Hohenstein co-sputtered glass using RF and metals (Al, Cu, Ni) with DC, to form cermet resistor films. RF sputter deposition is not used extensively for commercial PVD for several reasons. The major reasons are it is not economic to use large RF power supplies due to their high cost and the fact that you introduce high temperatures, due to the high self-bias voltage associated with RF power, into insulating materials. DC sputtering cannot be used for depositing dielectrics because the insulating cathode will cause charge build up during Ar+ bombarding, which reduces the voltage between electrodes and the discharge distinguishes. To eliminate this problem AC power was used, that developed the RF Sputtering technique.

Fig- 85 RF sputtering

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Using AC power at low frequency (<100 KHz) both electrons and ions can follow the switching of the voltage (Fig-85) [65, 66]. At high frequency (> 1 MHz) the heave ions can no longer follow the switching and the ions are accelerated by dark-space (sheath) voltage. The electron neutralizes the positive charge buildup on both electrodes however; there are two dark spaces which sputter both target and substrate at different cycles as shown in Fig-86.

Fig- 86 RF sputtering with AC voltage bias

Where VT is the voltage across the target sheath, Vs is the voltage across substrate sheath, AT is the area of target electrode and As is the area of substrate electrode. Larger dark-space voltage develops at the electrode with smaller area making the target electrode VT

small [65, 66]. Reactive sputtering In this process, a small amount of some non-noble gas such as oxygen or nitrogen is mixed with the plasma-forming gas. After the

material is sputtered from the target, it reacts with this gas, so that the deposited film is a different material, i.e. an oxide or nitride of the target material. Reactive sputtering Process Reactive gases like oxygen or nitrogen is added to the chamber during deposition (evaporation or sputtering). Chemical reactions take place on substrate and target. The target may get unwanted impurities if chemical reactions are faster than sputter rate. This can be avoided by adjusting the reactive gas flow to get good stoichiometry without incorporating excess gas into film [65, 66]. 8.36 Molecular Beam Epitaxy (MBE) MBE is a technique for epitaxial growth through the interaction of one or several molecular or atomic beams that occurs on a surface of a heated substrate (Fig-87).

Fig. 87 Schematic diagram of a MBE system

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The solid source materials are placed in evaporation cells to provide an angular distribution of atoms or molecules in a beam. The substrate is heated to the necessary temperature and, when needed, continuously rotated to improve the growth homogeneity [64,

66]. MBE operating conditions o The mean free path λ of the particles

should be larger than the geometrical size of the chamber. It is easily fulfilled if the total pressure does not exceed 10-5 Torr (Fig-88).

o The condition for growing a sufficiently

clean epilayer must be satisfied. (Eg: For the monolayer deposition times of the beams tb and the background residual vapor tres the relation is t res < 10-5 tb. This can be fulfilled by (UHV) ultra high vacuum).

Fig. 88 Graph showing Mean Free path

UHV is the essential environment for MBE. Therefore, the rate of gas evolution from the materials in the chamber has to be as low as possible. So pyrolytic boron nitride (PBN) is chosen for the crucibles which give low rate of gas evolution and chemical stability up to 1400oC, molybdenum and tantalum are widely used for the shutters, heaters and other components, and only ultra pure materials are used as source. To reach UHV, a bakeout of the whole chamber at approximately 200oC for 24 hours is required any time after having vented the system for maintenance. A cryogenic screening around the substrate minimizes spurious fluxes of atoms and molecules from the walls of the chamber. Despite this big technological problem, MBE systems permit the control of composition and doping of the growing structure at monolayer level by changing the nature of the incoming beam just by opening and closing the mechanical shutters. The operation time of a shutter of approximately 0.1s is normally much shorter than the time needed to grow one monolayer (typically 1-5s). Careful variation of the temperatures of the cells by PID controllers permits the control of the intensity of the flux of every component or dopant of better than 1 %.

Fig-89 RHEED Oscillations

The UHV environment of the system is also ideal for many insitu characterization tools,

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like the RHEED (Reflection High Energy Electron Diffraction). The oscillation of the RHEED signal exactly corresponds to the time needed to grow a monolayer and the diffraction pattern on the RHEED window gives direct indication over the state of the surface as can be seen in Fig-89 [64, 66]. Effusion Cells The effusion cells used in MBE systems exploit the evaporation process of condensed materials as molecular flux source in vacuum. In a closed enclosure, for pure substances, equilibrium is established between the gas and the condensed phase. Such systems have only one degree of freedom f, that means that the pressure peq is a function of the temperature T and can be approximately expressed by the Clapeyron equation.

Where, ∆H is the evaporation enthalpy and k B

the Boltzmann constant. Under this equilibrium condition, we observe that when the peq is very low, it is possible to treat the incoming and the outcoming flux independently. A close look to the fluxes of particles having a mass m on the condensed phase surface shows that the maximum value for the evaporated flux Γm is

This assumes that each molecule from the gas phase is always trapped by the surface and an equal opposite flux of material must leave the condensed phase to maintain the equilibrium pressure. Considering now that the impinging beam is partially reflected and only a fraction ‘a’ is

accommodated on the surface, the complete expression for the flux leaving the surface can be easily found as

The factor ‘a’ is dependent on the microscopic status of the surface and is strongly unpredictable. The Knudsen evaporating method overcomes this problem providing a molecular beam that is independent of ‘a’. An ideal Knudsen cell is composed of a large enclosure where the condensed material is in thermodynamic equilibrium with the gas phase and peq is not perturbed. The ideal Knudsen cell (as explained in in Section: ) exhibits an angular distribution of the evaporated particles that follows a cosine law, where the angle θ is referred to the normal to A.

The beam is usually bent through an angle of 270° in order to ensure that the gun filament is not directly exposed to the evaporant flux. Lower vapor pressure materials are deposited through this process because of the non uniformity in heating in this process. Typical deposition rates for electron beam evaporation ranges from 1 to 10 nanometers per second. In this process, slow streams of an element can be directed at the substrate, so that material deposits one atomic layer at a time.

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Compounds such as gallium arsenide are usually deposited by repeatedly applying a layer of one element (Ga), then a layer of the other (As), so that the process is chemical, as well as physical. The beam of material can be generated by either physical means (that is, by a furnace) or by a chemical reaction (chemical beam epitaxy) [64, 66]. A typical MBE chamber is shown in Fig-90 to visualize the actual equipment.

Fig. 90 MBE Growth chamber

Topotaxy In Topotaxy (heterotopotaxy / homotopotaxy), a specialized technique similar to epitaxy, thin film crystal growth occurs in three dimensions due to the crystal structure similarities between the substrate crystal and the growing thin film material [64-66]. Chemical deposition In this process, a fluid precursor (one of the compounds that participate in the chemical

reaction that produces another compound) undergoes a chemical change at a solid surface, leaving a solid layer on the surface with little regard to direction. Thin films from chemical deposition techniques tend to be conformal, rather than directional. Chemical deposition is further categorized by the phase of the precursor like liquid phase, Gas Phase [65, 66]. 8.37 Chemical vapor deposition (CVD) generally uses a gas-phase precursor, often a halide or hydride of the element to be deposited. In the case of MOCVD, an organometallic gas is used. Commercial techniques often use very low pressures of precursor gas. CVD Process Reactive precursor gases are introduced into the chamber and heat is applied to activate the decomposition of gases to form plasma. The gas is absorbed by the substrate surface and reactions takes place on substrate surface and the thin film is formed. Transport of volatile byproducts away form substrate takes place through Exhaust waste (Fig-91, 92) [65, 66].

Fig. 91 Schematic diagram of CVD Process

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Types of CVD reactions o Pyrolysis o Reduction o Oxidation o Compound Formation The types of reactions are explained in detail below. Pyrolysis (Thermal Decomposition)

Reduction (Lower temperature than Pyrolysis)

Oxidation

Compound Formation

CVD Deposition Condition Mass-Transport Limited Deposition o At high temperature such that the reaction

rate exceeds the gas delivering rate. o Gas delivering controls the film deposition

rate. o Film growth rate is insensitive to

temperature o Film uniformity depends on whether

reactant can be uniformly delivered across a wafer and wafer-to-wafer.

Reaction -Rate Limited Deposition o At low temperature or high vacuum such

that the reaction rate is below the gas arriving rate.

o Temperature controls film deposition rate. o Film uniformity depends on temperature

uniformity across a wafer and wafer-to-wafer.

Types of CVD o Low-Pressure CVD (LPCVD) o Plasma-Enhanced CVD (PECVD) o Atmosphere-Pressure CVD (APCVD) o Metal-Organic CVD (MOCVD)

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Low-Pressure CVD (LPCVD) Thermal energy for reaction activation o System works at vacuum (~ 0.1 –1.0 torr),

resulting in high diffusivity of reactants reaction-rate is limited.

o Wafer can stacked closely without lose uniformity as long as they have the same temperature

o Temperature is controlled around 600 -900ºC by “flat” temperature zone through using multiple heaters

o Low gas pressure reduce gas-phase reaction which causes particle cluster that contaminants the wafer and system

Fig. 92 Schematic diagram of PECVD

Plasma-Enhanced CVD (PECVD) Plasma enhanced CVD uses an ionized vapor, or plasma, as a precursor. Commercial PECVD, relies on electromagnetic means (electric current, microwave excitation), rather than a chemical reaction, to produce a plasma [65- 70]. Process stages of PECVD o Use RF-induced plasma (as in sputtering

case) to transfer energy into the reactant gases, forming radicals (decomposition)

o Low temperature process (< 300 ºC) For depositing film on metals and other

materials that cannot sustain high temperature

o Surface reaction limited deposition; substrate temperature control (typically cooling) is important to ensure uniformity)

Common CVD Reactants

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Fig-93 Comparison chart for various thin film deposition technologies

Technological comparison The comparison chart for typical thin film deposition technology is given above (Fig-93). Chemical Solution Deposition In (CSD) a liquid precursor, usually a solution of organometallic powders dissolved in an organic solvent is used. This is a relatively inexpensive, simple thin film process that is able to produce stoichiometrically accurate crystalline phases [65- 70]. Sol-Gel In the sol-gel process the precursor is dissolved in a solvent (forming a sol or gel

depending on the reactor conditions) and precipitates due to chemical reactions. The sol-gel process consists of 4 basic steps: Hydrolysis, Condensation, Polymerization of particles, growth of particles, agglomeration and formation of networks. The outcome of the process depends on several factors that influence the hydrolysis and condensation rates. Among them, there are few that are considered to have a greater impact: pH, nature and concentration of catalysts, H20/precursor molar ratio and temperature [65-

70].

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Doping Process The pure semiconductor is basically neutral. It contains no free electrons in its conduction bands. Even with the application of thermal energy, only a few covalent bonds are broken, yielding a relatively small current flow. A much more efficient method of increasing current flow in semiconductors is by adding very small amounts of selected additives to them, generally no more than a few parts per million. These additives are called impurities and the process of adding them to crystals is referred to as Doping (Fig-94).

Fig- 94 Doping a Semi conductor The purpose of semiconductor doping is to increase the number of free charges that can be moved by an external applied voltage. When an impurity increases the number of free electrons, the doped semiconductor is NEGATIVE or N TYPE, and the impurity that is added is known as an N-type impurity. However, an impurity that reduces the number of free electrons, causing more holes, creates a POSITIVE or P-TYPE semiconductor, and the impurity that was added to it is known as a P-

type impurity. Semiconductors which are doped in this manner with either ‘N’ or ‘P’ type impurities are referred to as EXTRINSIC semiconductors. N-Type Semiconductor The N-type impurity loses its extra valence electron easily when added to a semiconductor material, and in doing so, increases the conductivity of the material by contributing a free electron. This type of impurity has 5 valence electrons and is called a PENTAVALENT impurity. Arsenic, antimony, bismuth, and phosphorous are pentavalent impurities. Because these materials give or donate one electron to the doped material, they are also called DONOR impurities. Pure germanium may be converted into an N-type semiconductor by "doping" it with any donor impurity having 5 valence electrons in its outer shell. Since this type of semiconductor (N-type) has a surplus of electrons, the electrons are considered MAJORITY carriers, while the holes, being few in number, are the MINORITY carriers. P-Type Semiconductor The second type of impurity, when added to a semiconductor material, tends to compensate for its deficiency of 1 valence electron by acquiring an electron from its neighbor. Impurities of this type have only 3 valence electrons and are called TRIVALENT impurities. Aluminum, indium, gallium, and boron are trivalent impurities. Because these materials accept 1 electron from the doped material, they are also called ACCEPTOR impurities.

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Methods of doping The methods of doping are Diffusion, Ion implantation and doping during growth which are explained below. Diffusion In this method, the semiconducting material to be doped is placed in a furnace wherein the furnace contains an atmosphere of a carrier gas and a dopant containing gas. The doping containing gas is greater than about 0.1 volume percent of the total volume in the furnace chamber. The pressure of the composite gas is greater than about 0.1 Torr. The composite gas has an oxidizing agent concentration of less than about 1 part per million (Fig-95) [68-70].

Fig- 95 Doping a Semi conductor by diffusion method This method permits the direct doping of a silicon surface to form a shallow n-doped region having a high peak concentration by a diffusion process thereby eliminating damage to the silicon surface from ion implantation which is the commonly used method to achieve these high doping concentrations. Since the method is non directional trench sidewalls can be doped at high concentrations.

Ion implantation The introduction of dopants in a semiconductor is the most common application of ion implantation. Dopant ions such as boron, phosphorus or arsenic are generally created from a gas source, so that the purity of the source can be very high. These gases tend to be very hazardous. When implanted in a semiconductor, each dopant atom creates a charge carrier in the semiconductor (hole or electron, depending on if it is a p-type or n-type dopant), thus modifying the conductivity of the semiconductor in its vicinity (Fig-96) [68-70].

Fig- 96 Doping a Semi conductor by Ion implantation Doping during growth In this method the dopant is injected into the plasma and are based on the interactions of plasma or neutral gas with the surfaces of substrate at different temperatures and varying electric potentials (co-sputtering, dc-sputtering, thermally activated injection to the neutral gas, plasma-assisted transport) (Fig-97) [68-70].

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Fig- 97 Doping a Semi conductor during growth Procedure Sample preparation for Solid -Solid Reaction Method The samples can be prepared for standard solid - solid reaction by using appropriate quantities of precursors (Eg. ZnO of 99.99% purity) and (Eg.MnO2 of 99.99% purity) can be mixed and ground properly in order to obtain sub-micron size precursors. The mixture should then be calcined at 400oC for 8 hrs in air or appropriate atmosphere of Oxygen, Nitrogen, or hydrogen. The calcined powder obtained should be pressed to form dense pellets and sintered at or above transition temperature but below the melting temperature according to the materials to be calcined (eg 12 hrs at temperatures ranging from 500oC to 900oC in suitable atmospheres mentioned above for the Mixture of ZnO and MnO2). The pellets thus obtained have to be characterized for physical as well as magnetic properties and can be used as a source material to make thin films using PLD [62- 64].

8.40 Characterization Techniques The description of the structure of a solid requires the determination of the crystal system, space group, unit cell dimensions, atomic coordinates and electron density distribution around the atoms by means of diffraction involving X-rays, electrons or neutrons called characterization. 8.41 X-Ray diffraction X-Ray diffraction (XRD) is used to identify and characterize solids. Synchrotron X-radiation of continuously variable wavelength has made X-ray diffraction a powerful structural tool for the study of solids. A technique of great utility in determining the structures of oxides is the Rietveld treatment of powder X-ray diffraction. X-diffraction can be utilized for phase identification, quantitative analysis of mixtures of phases, particle size analysis, and characterization of physical imperfections and in situ studies of reactions. Variable temperature X-ray diffraction of crystalline materials is used to study phase transitions, thermal expansion, and thermal vibrational amplitude of atoms on solids [20]. Advanced developments of XRD Soft X-ray spectroscopies, X-ray absorption (XAS), X-ray emission (XES), and Resonant inelastic X-ray scattering (RIXS) spectroscopies are advanced developments of XRD [20]. 8.42 Magnetic Dichroism Spectroscopy The term dichroism is used more generally to reflect the dependence of photon absorption of a material on polarization. In fact, it is derived from Optics which means changes in the

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absorption of polarized light on passing through a material in two different directions called dichroism. The origin of the dichroism effect can be anisotropies in the charge or the spin in the material known as magnetic dichroism. The principles and applications of magnetic dichroism techniques in the x-ray region, the X-Ray Magnetic Circular Dichroism (XMCD) and X-Ray Magnetic Linear Dichroism (XMLD) techniques are discussed below [71]. 8.43 X-ray absorption spectroscopy (XAS) X-ray absorption spectroscopy (XAS) utilizes the energy dependent absorption of x-rays to obtain information about the elemental composition of the sample, as shown in Fig-98.

Fig- 98 X-ray absorption spectra of a wedge sample, revealing the composition at various points along the wedge The Fe signal increases from bottom to top because of the increasing Fe layer thickness and the Ni signal decreases because of the limited electron escape depth of the total electron yield signal used to record the spectra.

The Cu signal is constant, reflecting its constant 1nm thickness (Fig-99). It also gives information on the chemical environment of the atoms and their magnetic state. Core electrons are excited in the absorption process into empty states above the Fermi energy and thereby probe the electronic and magnetic properties of the empty valence levels. The magnetic properties of 3d transition metal elements Fe, Co and Ni are largely determined by the 3d valence electrons. Since X-ray absorption spectra are governed by dipole selection rules the d-shell properties are best probed by L-edge absorption studies (2p to 3d transitions). The L-edge X-ray absorption spectra of the transition metals and oxides are dominated by two main peaks separated by about 15 eV as shown in Fig-99 [71, 72].

Fig- 99 L - edge x-ray absorption spectra of Fe, Co and Ni in the form of the elemental metals and as oxides. The two main structures are called the L3 (lower energy) and L2 absorption edges The two main peaks in the spectra arise from the spin orbit interaction of the 2p core shell and the total intensity of the peaks is proportional to the number of empty 3d valence states. The metal spectra show two broad peaks, reflecting the width of the empty

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d-bands. The oxide spectra exhibit considerable fine structure, called multiple structure. The empty oxide states are more localized than metal states and their energies are determined by crystal field and multiple effects. Multiple effects arise from the spin and orbital momentum coupling of different 3d valence holes (or electrons) in the electronic ground state, and from coupled states formed after x-ray absorption between the 3d valence holes and the 2p core hole [71, 72]. The metals are usually ferromagnetic and their magnetic properties are best studied with X-Ray Magnetic Circular Dichroism (XMCD) spectroscopy, while the oxides are usually antiferromagnetic and are studied with X-Ray Magnetic Linear Dichroism (XMLD) spectroscopy. 8.44 X-Ray Magnetic Circular Dichroism (XMCD) The concepts of XMCD spectroscopy, was pioneered by Gisela Schütz et al. in 1987. The first X-ray absorption sum rule links the total intensity of the L3 and L2 resonances with the number N of empty d states (holes) (Fig-100). The d valence shell can hold up to 10 electrons which are filled into band states up to the Fermi level and the number of filled states is therefore 10 -N. For a magnetic material the d shell has a spin moment which is given by the imbalance of spin-up and spin-down electrons or equivalently (except for the sign) by the imbalance of spin-up and spin-down holes. The XMLD effect is large only in cases where the absorption edge exhibits multiple structures shown in (Fig-100) [71, 72].

Fig- 100 Size of magnetic dichroism effects. To measure the difference in the number of d holes with up and down spin, the x-ray absorption process is made spin dependent. This is done by use of right or left circularly polarized photons which transfer their angular momentum to the excited photoelectron. The photoelectron carries the transferred angular momentum as a spin or an angular momentum, or both (Stohr & Wu). If the photoelectron originates from a spin-orbit split level, e.g. the p3/2 level (L3 edge), the angular momentum of the photon can be transferred in part to the spin through the spin-orbit coupling. Right circular photons (RCP) transfer the opposite momentum to the electron as left circular photons (LCP) photons, and hence photoelectrons with opposite spins are created in the two cases. Since the p3/2 (L3) and p1/2 (L2) levels have opposite spin-orbit coupling, the spin polarization will be opposite at the two edges. In the absorption process, "spin-up" and "spin-down" are defined relative to the photon helicity or photon spin [71, 72].

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In Fig-101 the transitions occur from the spin-orbit split 2p core shell to empty conduction band states. In conventional X-ray absorption the total transition intensity of the two peaks is proportional to the number of d holes (first sum rule). By use of circularly polarized X-rays the spin moment (b) and orbital moment (c) can be determined from linear combinations of the dichroic difference intensities A and B, according to other sum rules [71, 72]. Since spin flips are forbidden in electric dipole transitions, spin-up (spin-down) photoelectrons from the p core shell can only be excited into spin-up (spin-down) d hole states.

Fig-101 Electronic transitions in conventional L-edge x-ray absorption (a) X-ray magnetic circular dichroism (b, c) one-electron model. Hence the spin-split valence shell acts as a detector for the spin of the excited photoelectron and the transition intensity is simply proportional to the number of empty d states of a given spin. The quantization axis of the valence shell "detector" is given by the magnetization direction. The size of the dichroism effect scales like cos θ, where θ is

the angle between the photon spin and the magnetization direction. The maximum dichroism effect (20%) is observed if the photon spin direction and the magnetization directions are parallel and anti-parallel as shown on the left side of Fig-102. When the photon spin and the magnetization directions are perpendicular the resonance intensities at the L3 and L2 edges lie between those obtained for parallel and anti-parallel alignments [71, 72]. The L3 and L2 resonance intensities and their differences for parallel and anti-parallel orientation of photon spin and magnetization directions are quantitatively related by sum rules to the number of d holes and the size of the spin and orbital magnetic moments. Angle dependent measurements in external magnetic fields give the anisotropies of the spin density and orbital moment [71, 72]. 8.45 X-Ray Magnetic Linear Dichroism (XMLD) XMLD spectroscopy was pioneered by Gerrit van der Laan et al. in 1986. The electric field vector E of linearly polarized X-rays acts as a search light for the number of valence holes in different directions of the atomic volume. The anisotropy of the charge in the atomic volume is caused by anisotropy in the bonding, i.e. by the electrostatic potential. In the absence of spin order, linear dichroism NEXAFS spectroscopy can only determine charge order in systems where the absorbing atom has lower than cubic symmetry. However, in the presence of spin order the spin-orbit coupling leads to preferential charge order relative to the spin direction even in

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cubic systems. This effect is the basis for the determination of the spin axis in ferromagnetic and especially antiferromagnetic systems by means of x-ray magnetic linear dichroism (XMLD) spectroscopy [71, 72]. Since the electric field vector oscillates in time along an axis and the radiation may be absorbed at any time, linearly polarized x-rays are only sensitive to axial not directional properties. The orientation of the antiferromagnetic or ferromagnetic axis, but the spin direction itself cannot be determined. Fig-102 shows the origin of the XMLD effect in NiO.

Fig-102 Origin of XMLD for NiO In Fig-102 the electronic configurations involved in the x-ray absorption process is shown in the Left. In the ground state there are two d holes (d2 hole configuration) and their energy levels are determined by multiple and crystal field effects. In the final state, a 2p hole is created by x-ray absorption and one d hole is filled by the excited electron.

The resulting pd hole configuration again gives rise to multiple splitting and the XAS spectrum reflects the multiple structure. In the paramagnetic state the absorption spectrum of NiO does not exhibit polarization dependence because of cubic symmetry. In the antiferromagnetic state the spin-orbit coupling leads to a distortion of the charge density and an XMLD effect is observed [71, 72]. Because of the cubic symmetry of the NiO lattice the charge distribution around the atoms is nearly spherical and no linear dichroism effect exists above the Néel temperature (520 K), where NiO is paramagnetic. At room temperature, NiO is antiferromagnetic and the Ni spins are oriented in the (1, 1, 1) plane along three possible directions in the fcc lattice. There is no net magnetic moment because an equal number of spins point into opposite directions, so only a preferential magnetic axis exists. The alignment of the local atomic spins along this axis breaks the cubic symmetry of the charge through the spin orbit coupling. As a consequence the charge exhibits a small anisotropy in the unit cell, i.e. it is no longer spherical but shows an ellipse-like distortion about the magnetic direction. This charge anisotropy leads to an asymmetry of the x-ray absorption signal through the search light effect [71, 72]. The maximum XMLD difference is obtained for E parallel versus E perpendicular to the magnetic axis, as shown in Fig-103. In contrast to the XMCD effect the XMLD effect has a cos 2θ dependence, where θ is the angle between E and the magnetic axis.

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In general, the XMLD effect is small in 3d metals owing to the small size of the spin orbit interaction and the large band width, resulting in small charge anisotropy when the d states are summed over the Brillouin zone. However, a sizeable XMLD effect (of order 10-30%) may be observed in the presence of multiplet splitting. At a particular multiplet energy only selected d valence states are probed through matrix element effects that enhance the XMLD effect. Each multiplet is a strongly coupled spin-orbit state whose spatial extent is non-spherical, giving rise to the large XMLD effect. In Fig-102 the XMLD effect is especially visible at the Ni L2-edge where a sizeable difference is observed for E parallel (green) versus perpendicular (red) to the magnetic axis. Since x-ray linear dichroism can arise from electric and magnetic asymmetry s, magnetic order effects can be distinguished from Ligand field effects through temperature dependent measurements. Circularly polarized x-rays have directionality and they can detect the direction of the spin and orbital moments which is utilized in XMCD microscopy of ferromagnets. The dependence of the XMLD intensity on the relative orientation of the electric field vector and the magnetic axis can be used for XMLD imaging for antiferromagnets [71, 72]. Electron diffraction Electron diffraction is a valuable technique for studies in solids. The differences entail the small wavelength of electrons and the charge carried by them. The smaller wavelength makes it possible to record extensive sections

of the reciprocal lattice directly with a small stationary crystal. Because of the charge, interaction of electrons with atoms is considerably stronger than that of X-rays, thus making it possible to record electron diffraction patterns almost simultaneously. One can investigate defect ordering, superstructures, and fine particle samples [20, 72,

and 73]. Neutron diffraction Thermal neutrons with a velocity of about 4000 m/s associated with a wavelength of ~ 1.0 Ǻ are used in neutron diffraction experiments. Neutron diffraction is particularly useful in locating light atoms such as hydrogen in crystals. Neutron diffraction provides an experimental means whereby the different magnetic structures can be determined. Inelastic neutron scattering by crystals is used in the study of quantized vibrational modes (phonons) and dynamics in solids [20, 72, and 73]. 8.46 Piezoresponse force microscopy Piezoresponse Force Microscopy (PFM) is a scanning probe microscopy (SPM) technique based on the reverse piezoelectric effect, where a (piezoelectric) material expands or contracts upon applying to it an electric field [20, 72, 73]. PFM is an Imaging Technique classified under Derivative Imaging Modes. It is a derivative of the Primary Imaging Mode called Contact Mode AFM. In PFM, the AFM probes a sample’s mechanical response to an applied electric field. The AFM tip used in PFM is usually made of, or is coated with, a conductive material, as this conductivity

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enhances the electrical contact between the tip and the sample.

Fig- 103 Piezoresponse Force Microscopy Setup

An AC modulation with an optional DC offset bias is applied to the tip, which is in contact with the sample surface, and the piezoresponse of the sample is measured from the deflection of the AFM cantilever [20, 72, and 73]. This measurement uses a lock-in amplifier (Fig-103). The frequency of the applied ac voltage is typically far from (below) the fundamental resonance frequency of the AFM cantilever so as to avoid driving the cantilever into resonant oscillations [71, 72]. The Utility of PFM PFM is one of the most important tools that enables measurements and characterization of piezoelectric behavior of materials on the nanometer, and sub-nanometer scale. There is no other tool currently available that can routinely and with the same ease measure the electromechanical response of a material on the level of individual nanometer-scale grains. The PFM has been shown to delineate regions of different piezoresponse with subnanometer lateral resolution.

In Fig-104, the PFM image (phase signal, right image) shows contrast that delineates regions of differing piezoresponse on the surface of a Lithium Niobate sample, whose topography (left image) reveals no features corresponding to those in the piezoresponse image. The PFM signal in this image is recorded from the vertical movement of the AFM tip, but similarly, the lateral movement of the tip may be recorded (as in Lateral Force Microscopy) to construct a map that is descriptive of in-plane polarization of the various regions on the sample surface.

Fig- 104 comparison AFM and PFM images

PFM is very useful in investigating the nanometer-scale piezoelectric properties of ferroelectrics. Ferroelectric thin films are the subject of intense research and development for their optoelectronic, sensor, and high-density memory applications. The lateral resolution of PFM provides highly localized information about the electromechanical behavior of thin ferroelectric films. The PFM can be used to interrogate a given nanometer-scale domain in an island for its piezoelectric response; if there is a piezo response, this implies ferroelectricity.

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PFM Spectroscopy is a non-imaging technique that compliments PFM imaging. In PFM Spectroscopy, the piezoresponse of a given location on the sample can be mapped versus the dc bias. This technique can also be used to study hysteretic characteristics of the piezoresponse [72-75]. 8.47 Transmission Electron Microscopy The electron microscope is the most versatile instrument available to study the ultrastructure of materials, to identify new or known phases, and to simultaneously yield information on composition. Usually electron diffraction and imaging are employed together in transmission electron microscopy (TEM). These capabilities are further enhanced in a scanning transmission electron microscope (STEM). TEM generally produces a projected image wherein all depths of thin specimens are in focus at the same time, making it difficult to interpret surface features of specimens to operate at different temperatures, in different atmospheres [20, 72-75]. 8.48 Scanning Electron Microscopy In scanning electron microscopy (SEM), a finely focused electron beam probe moves from one point on the specimen to the next to form a faster pattern, similar to television imaging. The most important aspect of electron microscopy in the study of metal oxide is its ability to elucidate problems that are beyond the capability of X-ray or neutron crystallography. High resolution electron microscope (HREM) images show local structures of crystal in great detail. Many other techniques are employed for the study of metal oxides. Some of the important ones are extended absorption fine structure (EXAFS) spectroscopy, solid state NMR spectroscopy,

electron spin resonance (ESR) spectroscopy, and scanning tunneling microscopy (STM) [20,

72-75]. 8.50 Classification of Thin Films Thin Film are classified based on their properties as follows o Magnetic Thin Films o Ferro / Ferri Electric Thin Films o Multiferroic thin films

o Magnetoelectric thin films o Magnetoelastic thin Films o Piezoelectric thin films

They can be of varying thickness from 10µm to 1nm based on its application requirements. 8.51 Magnetic thin films Thin magnetic films originated from the studies of their effects on light, today, they are being layered to make complex structures with unique magnetic properties. Devices based on these structures are revolutionizing electronic data storage, due to growing applications in magnetic sensors and in magnetic storage media like computer disks and random-access memories. Magnetic random-access memories (MRAMs) based on structures of magnetic metallic films interspersed with nonmagnetic metallic or insulating interlayer could be the next generation in magnetic-storage technology, replacing the semiconductor-based dynamic random-access memories (DRAMs) that are now the standard [76]. Advantages of MRAMs, o Non-volatility (they retain information

when the computer is switched off). o High storage density. o Low energy consumption. o MRAM devices would be smaller. o Faster. o Cheaper.

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o More robust in extreme conditions such as high temperature, or high-level radiation or interference.

Thin magnetic films was suggested as a replacement for core as early as 1955, and the first research results were presented in 1959, but problems with reliability of film-based MRAMs led to the adoption of DRAMs. Unlike conventional RAM chip technologies, in MRAM data is not stored as electric charge or current flows, but by magnetic storage elements. The elements are formed from two ferromagnetic plates, each of which can hold a magnetic field, separated by a thin insulating layer. One of the two plates is a permanent magnet set to a particular polarity; the other's field will change to match that of an external field. A memory device is built from a grid of such "cells", but the device power consumption was high [77]. The study of the physical properties of ferromagnetic thin film structures and the discovery of new techniques for fabricating these entities make up the field of layered magnetic structures. Ferromagnetic films can be combined with all kinds of other layers with different magnetic and electronic properties to obtain interesting and practical devices. Giant magnetoresistance (GMR), tunneling magnetoresistance (TMR) and interlayer coupling all involve the transfer of spin-polarized electrons from one ferromagnetic layer across an interface to another, and studies of such processes are giving rise to whole new fields of study, including spintronics and magnetoelectronics [75-78].

Fig- 105 Data storage applications Now MRAMs are in wide spread application in the data storage industries as illustrated in (Fig-105) [76, 78].

8.52 Spintronics Spintronics is an emerging technology which exploits the quantum spin states of electrons as well as making use of their charge state. The electron spin itself is manifested as a two state magnetic energy system. The discovery of giant magnetoresistance in 1988 by Albert Fert et al. and Peter Grünberg et al. independently is considered as the birth of Spintronics. Generally, all conventional electronic devices depend on the transport of electrical charge carriers (electrons) in a semiconductor such as silicon. The information processing is done by utilizing circuits using transistors that work by transfer of electrons [79]. A Field-Effect-Transistor (MOSFET) consists of a source and a drain, two highly conducting

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n-type semiconductor regions, which are isolated from the p-type substrate by reversed-biased p-n diodes. A metal (or poly-crystalline) gate covers the region between source and drain and the flow of electrons from the source to the drain is controlled by the voltage applied to the gate and the gate voltage changes electron density (Fig-106).

Fig- 106 Metal oxide field effect transistor

With the advancement in technology, the devices are diminishing in size and increasing in speed. The number of transistors on an IC chip doubles every 12 months-following the Moore’s law [80, 81]. Moore’s law will subsequently lose momentum as the size of individual bit approaches dimensions of an atom. For this reason and to provide multifunctionality to the devices, investigators are trying to combine both, charge and spin degrees of freedom of electrons, to create a remarkable new generation of devices which will be smaller, more versatile and more robust than those currently making up silicon chips and circuit elements. Thus emerges a new field of electronics called spin electronics or Spintronics [81, 82].

Spintronics describes technology that makes use of the spin state of electrons. Electrons exhibit the basic properties of spin, charge, and mass. When the intrinsic spin of an electron is measured, it is found in one of two spin states, known as spin up and spin down. The Pauli Exclusion Principle states that the quantum-mechanical wave function of two paired fermions must be antisymmetric, no two electrons can occupy the same quantum state, implying that an entangled pair of electrons cannot have the same spin.

The advantage of spin over charge is that spin can be easily manipulated by externally applied magnetic fields, a property already in use in magnetic storage technology. Another significant property of spin is its long coherence, or relaxation time (nanoseconds, compared to tens of femtoseconds during which electron momentum decays), when created, it tends to stay that way for a long time, unlike charge states, which are easily destroyed by scattering or collision with defects, impurities or recombination [81].

These characteristics open the possibility of developing devices that could be much smaller, consume less power and will be more powerful for certain types of computations which is not possible with electron-charge-based systems. It is widely expected that new functionalities for electronics and photonics can be derived if injection, transfer and detection of carrier spin can be controlled at room temperature [80].

Spintronic devices Spintronic devices came into action after the discovery of powerful effect called “Giant magnetoresistance (GMR)” in 1988 by French

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and German physicists [84]. It results from subtle electron-spin effects in ultra-thin 'multilayers' of magnetic materials, which cause huge changes in their electrical resistance when a magnetic field is applied. It is a sandwich structure with alternating layers of magnetic and nonmagnetic metal (Fig-107).

Fig- 107 Typical GMR sandwich structure

Depending upon the relative orientations of the magnetizations in the magnetic layers, the electrical resistance changes from small (parallel magnetizations) to large (antiparallel magnetizations). The magnitude of this change is twice the order of magnitude larger than is possible with conventional materials, hence the name “giant magnetoresistance” [81]. To make a spintronic device, the primary requirement is to have a system that can generate a current of spin polarized electrons, and a system that is sensitive to the spin polarization of the electrons. Most devices also have a unit in between that change the current of electrons depending on the spin states. The simplest method of generating a spin-polarized current is to inject the current through a ferromagnetic material. The most common application of this effect is a giant magnetoresistance (GMR) device. Unlike traditional IC’s in which signals are determined by the charge of electrons, Spintronics devices utilize both the spin and

the charge of electrons for increased functionality. Potential benefits of using spin currents include increased speed of devices and decreased power consumption. IBM identified that the read heads incorporating GMR materials would be able to sense much smaller magnetic fields, allowing the storage capacity of a hard disk to increase from 1 to 20 gigabits [85]. In 1997, IBM launched GMR read heads, into the market. Researchers have found further possibilities of spin valves which can be made to act as switches by flipping the magnetization in one of the layers. This allows information to be stored as 0s and 1s (magnetizations of the layers parallel or antiparallel) as in a conventional transistor memory device. Another application is a magnetic version of a random access memory (MRAM) device used in computers [86]. MRAM is rapidly developing as a technology because it can allow quantum computing by use of spin of individual particles to process information, is known as a quantum bit or qubit. It is amazing to know that only 34 qubits are required to represent the total amount of information stored in a 10 Gb hard rive [80]. With the exception of MRAM, none of the spintronic devices such as spin based light emitting diodes (spin LEDs), resonant tunneling diodes (spin RTDs), field effect transistors (spin FETs), and spin based single electron devices based on quantum dot arrays can be fabricated without the ability to generate, maintain, and propagate long lived spins in a semiconductor [80]. All spintronic or more specifically semiconductor spintronic devices act according to the simple scheme: (1)information is stored (written) into spins as a particular spin orientation (up or down), (2) the spins, being attached to mobile electrons,

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carry the information along a wire, and (3) the information is read at a terminal [87].

Fig- 108 Application of Spintronics

The long coherence time of spin makes spintronic devices particularly attractive for memory storage and magnetic sensor applications, and, potentially for quantum computing where electron spin would represent a bit (called qubit) of information [79].

The basic idea behind semiconductor based spintronics is to add the characteristics of magnetic devices to existing devices such as light-emitting diodes and field effect transistors [81]. This would lead to technologies such as memory and microprocessor functions

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integrated on the same chip, magnetic devices with gain and integrated sensors with on-chip signal processing and off-chip optical communications. A technology tree which summarizes the spin-based devices is shown is shown in Fig-108. Recent Progress in Spintronics In the past few years, a new set of magnetoelectric multiferroics such as TbMnO3 and Ni3V2O8 has been discovered and it is under intense research in the field of spintronics for the potential novel applications as discussed below [40]. Researchers are now trying to use non-equilibrium thin film growth techniques to develop new materials for Spintronics applications and to perform detailed characterization to understand the correlation between the structural, magnetic, and electronic properties of materials such as complex oxides and diluted magnetic semiconductors. The complex oxides (e.g. perovskites) have received renewed interest due to their novel magnetic, electronic, and optical properties, including colossal magnetoresistance and predictions that they are half-metallic (i.e. possess a complete spin polarization of the carriers). These properties are particularly useful for sensor applications and the development of devices based on the transfer of spin currents. Moreover, sophisticated multi-functional sensors can be built by using the coupling between layers with different properties (e.g. ferromagnetism, magnetostriction, and piezoelectricity). Considerable research is being done to study the interactions between layers with different ferroic properties and to explore the existence of new phenomena at surfaces and interfaces

not found in the constituent materials. The ferroelectric order by magnetic phase transition in TbMnO3 in the absence of magnetic fields is discussed below [40]. 8.521 Magnetoelectric multiferroic Thin Films -TbMnO 3 and Ni3V2O8 In these magnetoelectric multiferroics, ferroelectric order develops upon a magnetic phase transition into a spiral magnetic ordered phase. In addition, these systems show large magnetoelectric effects accompanied by metamagnetic transitions. Non-collinear spiral magnetism is the key to understand the magnetoelectric properties in these systems. The reported studies [40] presented here indicate that spiral magnets are promising candidates for magnetoelectrics showing large magneto electric effects at low magnetic fields. Magnetic and ferroelectric properties of TbMnO 3 TbMnO3 is an example of magnetoelectric multiferroics that exhibit large magnetoelectric response [88].

Fig- 109 Structure of TbMnO3

The crystal structure of TbMnO3 is the orthorhombically distorted perovskite structure (the space group Pbnm and crystal symmetry mmm) at room temperature, as illustrated in

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(Fig-109). The crystal symmetry has an inversion center, and the system is nonpolar at room temperature, but at lower temperatures, the system shows successive magnetic phase transitions.

Fig- 110 (a) and (b) Nonpolar behavior of TbMnO3 at room temperature Temperature profiles of magnetization M at a magnetic field of 0.5 T, specific heat divided by temperature, and electric polarization along the c axis for a single crystal of TbMnO3 is shown in Fig-110a and 110b. The First anomaly o According to neutron diffraction studies

the Mn moments in TbMnO3 undergo an antiferromagnetic transition at TN ~ 41 K. This ordering corresponds to the anomaly in magnetization and specific heat at ~41 K {Fig- 110 (a) and (b)}.

For the magnetic structure below TN, the Mn moments are aligned along the b axis and show sinusoidal order with a propagation wave vector (0, kMn, 1) in the Pbnm orthorhombic unit cell (Fig-111). The kMn (~0.29) is insufficient at TN and decreases with decreasing temperature [89, 90].

Fig- 111 Collinear sinusoidal spin structure in paraelectric phase The second anomaly o The second anomaly is observed in

magnetization and specific heat at TC ~ 28 K (Fig-110a). Below TC, kMn ~ 0.28 shows little temperature dependence. In TbMnO3, ferroelectric order with spontaneous polarization along the c axis develops at TC ~ 28 K (Fig-110b).

Third anomaly o Upon further decreases in temperature, the

temperature dependence of the specific heat shows the third anomaly at ~7 K, where the Tb3+ moments show long-range ordering with a propagation vector (0, ~0.42, 1) different from that of Mn moments. At approximately this

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temperature, the electric polarization also exhibits a small anomaly.

These results suggest an intimate connection between magnetism and ferroelectricity in TbMnO3. At the lowest temperature, the magnitude of electric polarization is ~ 6 to 8 × 10−4C m−2. The spontaneous polarization of TbMnO3 is rather small as compared with that of conventional perovskite ferroelectrics.

Fig- 112 Non collinear spin structure in ferroelectric phase The sinusoidally modulated magnetic structure model was proposed by Quezel et al. [89] for both the antiferromagnetic paraelectric phase (TC ≤ T ≤ TN) and antiferromagnetic ferroelectric phase (T ≤ TC). However, a recent neutron diffraction measurement by Kenzelmann et al. [91] suggests that the magnetic structure below TC is not the sinusoidal structure rather, is a transversely modulated spiral magnetic

structure or elliptically modulated cycloidal spiral magnetic structure (Fig-112). This spiral spin structure has also been confirmed in a similar rare-earth manganite, Tb1−x DyxMnO3, for which the commensurate propagation wave vector (kMn = 1/3) is observed at ferroelectric phase by a model-free analysis via the use of single-crystal neutron diffraction data. The major difference between the antiferromagnetic paraelectric phase (TC ≤ T ≤ TN) and antiferromagnetic ferroelectric phase (T ≤ TC) is the existence of magnetic moments along the c axis in the ferroelectric phase (Fig- 112), which does not exist in the paraelectric phase (Fig- 111), which means that all Mn moments are aligned along the b axis in the paraelectric phase making the magnetic structure collinear when the system is paraelectric. In contrast, the magnetic structure in the ferroelectric phase shows an elliptically modulated non-collinear spiral spin structure. This appearance of the spiral spin structure accompanied by ferroelectric phase transition is the ‘origin of ferroelectricity in TbMnO3’, which is discussed below. Magnetic Control of Electric Polarization and Dielectric Constant The magnitude of electric polarization P in TbMnO3 is much smaller than that in conventional perovskite ferroelectrics and the ferroelectricity of TbMnO3 can be controlled by a magnetic field H [88, 92]. It has been reported that by applying magnetic fields along the b-axis the magnetic-field dependence of

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electric polarization along the c-axis (Pc) and the a-axis (Pa) is at 9 K and 15 K for a TbMnO3 single crystal Fig- 113a and 113b.

Fig- 113 Switching of the direction of electric

polarization by the application of Magnetic field Through the application of a magnetic field of 4 to 8T, Pc is suppressed, whereas Pa is induced. These results show that the spontaneous polarization is switched (or “flopped”) from the direction along the c-axis to that of the a-axis which means that the

direction of the spontaneous polarization in ferroelectric TbMnO3 can be switched by 90◦ by tuning the magnitude of magnetic field (electric polarization flop) [92]. As displayed in Fig-114, the electric polarization flop is attributed to a metamagnetic transition. In addition, the magnetic-field effect on electric polarization varies sensitively with the direction of a magnetic field relative to the crystallographic axes. Fig-114 shows the isothermal magnetization and Pc as a function of magnetic fields at selected temperatures. Single or double metamagnetic transitions can be seen in M–H curves, depending on the orientation of magnetic fields. With the application of a magnetic field along the a-axis, a double metamagnetic transition has been observed (Fig-114a). The first transition shows a distinct jump of M at ~1.7 T, and the second transition exhibits only a small change in M at ~10 T (Fig-114a). The application of a magnetic field along the b axis also gives rise to double transitions at ~1 T and ~4.5 T at 4K (Fig-114b).With increasing temperatures, the steps in the M–H curves become indistinct. In both configurations (H // ‘a’ and H // b), Pc is suppressed at the second metamagnetic transition field. This suppression of Pc is attributed to the electric polarization flop from P // c to P // a. According to recent in-field neutron and X-ray diffraction measurements [93,94], the electric polarization flop coincides with a first-order transition to a commensurate but still long-wavelength magnetic modulated phase with propagation vector of (0, 1/4, 1). For the in-field P // a phase, there are several proposed magnetic structure models, including spiral and non-spiral spin structures [93, 94].

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Fig- 114 Magnetization and (d–f) magnetic-field-induced changes in electric polarization along the c axis for TbMnO3

crystals

The application of a magnetic field along the c axis causes a single metamagnetic transition above 5 T, as shown in Fig-114c. Comparison of the M–H curves with the P–H curves (Fig-114f) reveals that the metamagnetic transition gives rise to the suppression of Pc. The observed feature in the H // c configuration is similar to that in H // ‘a’ and H // b, the effect of magnetic fields along the c axis is distinct from that along the ‘a’ and ‘b’ axes. The electric polarization vanishes for all crystallographic directions by the application of a high magnetic field along the c axis. This means thatTbMnO3 loses its ferroelectricity by

the application of sufficiently large magnetic fields along the c axis. A recent neutron diffraction measurement revealed that the suppression of ferroelectricity in a magnetic field along the c axis is related to the disappearance of the incommensurate antiferromagnetic ordering of Mn spins and the appearance of a simple commensurate antiferromagnetic ordering with the (0, 1, 0) magnetic Bragg reflection. These results clearly demonstrate the strong interplay between long-wavelength magnetic order and ferroelectricity in TbMnO3. The possible

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mechanism of the magnetic-field effect on ferroelectric properties is discussed in more detail below. When the Tb site in TbMnO3 is replaced by other trivalent rare-earth ions having similar ionic radius to Tb (e.g., Gd, Dy, and Eu1−xYx), similar ferroelectric properties related to magnetic order and its magnetic-field effect can be observed [95]. In DyMnO3, which shows ferroelectricity below TC ~19 K, a relatively large spontaneous polarization appears along the c axis (~2 × 10−3 C m−2) (Fig-115a ). In addition, the electric polarization flops from P // c to P // a by the application of magnetic fields along the ‘a’ and c axes, as observed in TbMnO3

[95].

These results show that the magnetic-field-induced polarization flop phenomenon (Fig-115c) leads to a gigantic magneto-capacitive effect with a change of dielectric constant up to ε(H)/ε(0) ~ 500% (Fig-115d ) in DyMnO3. When the media include a nonlinear dielectric such as Ba1−xSrxTiO3, applying an electric field changes its dielectric constant [40]. The materials showing this effect can be considered electric-field-tunable elements for high-frequency devices. Similarly, using magnetoelectric multiferroic materials, we can achieve the dielectric constant to be tuned by a magnetic field instead of an electric field.

Fig- 115 Giant magnetoelectric and magneto-capacitive effects

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ELECTRIC POLARIZATION INDUCED IN SPIRAL MAGNETS Spiral Configurations The appearance of a spiral magnetic structure accompanied by ferroelectric order presented in the above section helps in understanding the origin of the ferroelectricity in TbMnO3. The term spiral means that the spin vectors lie within a plane such that the components of the spin along two axes at right angles in the plane have a periodic variation along some arbitrary direction in the crystal as per Cox et al. [96].

Types of Spiral structures Fig-116 shows the (a) collinear sinusoidal and (b–e) various non-collinear spiral magnetic structures on a one-dimensional array of magnetic moments S. Here, eij is the unit vector connecting the neighboring i and j sites and is along the propagation vector q of the spiral structure. (Si × Sj) is parallel to the spin rotation axis. If the spin rotation axis is parallel to the propagation vector, the arrangement yields a screw spiral structure (Fig-116b).

Fig- 116 Schematic illustrations of types of magnetic structure with a long wavelength

If the spin rotation axis is perpendicular to the propagation vector of spiral, the resulting arrangement is termed a cycloidal spiral structure (Fig-116c). A rather more complicated system is conical spiral, in which a ferromagnetic component coexists with a

screw (Fig-116d) or cycloidal (Fig-116e) component. These conical structures are generally obtained by the application of weak magnetic fields to screw or cycloidal spiral structures [40].

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Magnetoelectric Effect in Screw Spin System In the 1980s, Siratori and colleagues [97, 98] discussed the magnetoelectric effect of a screw spiral magnet (Fig- 116b). In screw spiral magnets, there are two domains in terms of the handedness of screw: left-handed and right-handed as shown in Fig-117. These two-domain structures are converted into each other by space inversion operation. However, these two structures never coincide with each other. This can occur only if space inversion is not a symmetry operation. Inversion symmetry is

broken in screw spiral magnets, which is also applicable to any spiral magnetic structure with spin helicity. By contrast, time reversal plus half-period translation along the propagation vector of screw are a symmetry operation in the screw spiral. Therefore, the first-order magnetoelectric

effect where αij is the magnetoelectric coefficient), which requires breaking of both space inversion and time reversal, is not allowed in screw spiral magnets.

Fig-117 Propagation vector of the screw structure

In contrast, a second-order magnetoelectric effect is allowed. When a weak magnetic field is applied along the propagation vector in the screw spiral, the magnetic structure becomes conical, as illustrated in Fig- 116d. Then, time reversal is also broken, and the first-order magnetoelectric effect can appear. In spiral

magnets, the sign of the magnetoelectric coefficient, i.e., the direction of H-induced electric polarization can be reversed by changing the handedness of the spiral. Thus, the interaction between two neighboring magnetic moments (vectors Si and Sj) has to be antisymmetric for the moment exchange.

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Siratori and colleagues [97, 98] pointed out that the lowest-order antisymmetric spin coupling, i.e., Dzyaloshinskii-Moriya (DM) interaction plays an important role in the magnetoelectric effect of spiral magnets.

Ferroelectricity Induced by Cycloidal Spiral Magnetic Order Recent theoretical studies successfully explain the mechanism of ferroelectricity in a new class of magnetoelectric multiferroics such as TbMnO3 by means of both microscopic and phenomenological approaches. A key factor in the ferroelectricity of these materials lies in their non-collinear spiral magnetic structures with a cycloidal component. Katsura et al first proposed a microscopic mechanism of the ferroelectricity in these systems, that spin current (or vector spin chirality’s; Si × Sj), induced between non-collinearly coupled spins because of the Aharonov-Casher effect [99], leads to the electric polarization. This can be regarded as an inversed effect of the DM interaction in which two non-collinearly coupled magnetic moments displace the oxygen sandwiched by the two moments through the electron-lattice interaction. Fig-118 depicts the relationships among non-collinearly coupled magnetic moments, oxygen displacement, and resultant change of local electric polarization. As shown in Fig- 118a, when the magnetic moments are aligned in a cycloidal spiral manner, the direction of local electric polarization induced by the inversed DM effect is uniform in the system, and the total electric polarization can be finite. Because the exchange of two

moments reverses the sign of the effect in the asymmetric DM interaction, the sign of the induced electric polarization can be switched by a reversal of spin helicity (Fig-118b). This effect may exist locally in normal canted antiferromagnetic systems, as shown in Fig- 118c. However, in configurations in which the canting angle of the moments aligns alternately (CW-CCW-CW-CCW . . ., where CW and CCW denote clockwise and counterclockwise, respectively), the effect is canceled out macroscopically.

Fig- 118 Schematic drawings of the change of local electric polarization induced by spin canting These recent theoretical studies have deduced the general relation between the electric polarization and the magnetic moments in a system with spiral magnetic structures from symmetry considerations, as described in the following equation.

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Where γ is the constant, which is proportional to the spin-orbit coupling and superexchange interactions. In this equation, vector eij is along the propagation vector of a spiral structure, and vectors Si × Sj is parallel to the spin rotation axis. The above equation indicates that a finite electric polarization can appear when adjacent magnetic moments are coupled non-collinearly in a spiral manner and when the spin rotation axis is not parallel to the propagation vector. For example, the cycloidal spiral magnetic structure shown in Fig-119c meets these requirements. In addition, the direction of induced electric polarization is perpendicular to the spin rotation axis and the propagation vector of the spiral and can be reversed by the change in the helicity of the spiral. The ferroelectricity (at zero magnetic fields) of TbMnO3, in which ferroelectric order exists only in the cycloidal spiral phase and the electric polarization, appears in the direction along the c axis, which is perpendicular to both the spin rotation axis (//a axis) and the propagation vector of the spiral (//b axis). In addition, the suppression of ferroelectricity by the application of a magnetic field along the c axis can be explained by the disappearance of the cycloidal spiral structure. As for the mechanism of the electric polarization flop induced by external magnetic fields along the ‘a’ and b axes, two possibilities have been considered. o The first possibility is that the field-

induced phase with P along the ‘a’ axis is also a cycloidal spiral but that the spin

rotation axis changes from the a axis to the c axis by the application of magnetic fields.

o The second possibility involves the

ferroelectricity attributed to a symmetric interaction, so-called exchange striction (~ vector SI × vector Sj). In this scenario, the field-induced phase is a non-spiral magnetic structure with a commensurate propagation vector (0, kMn = 14, 1) and possesses a periodic modulation of vector Si · vector Sj. The modulation induces the lattice distortion with a nonzero wave vector (0, 2kMn, 0) through exchange striction and leads to ferroelectricity.

However, further detailed investigations of the crystallographic and magnetic structures in magnetic fields are needed to confirm the origin of ferroelectricity with P // ‘a’ at magnetic fields along the ‘a’ and ‘b’ axes. The analysis and review of the report confirms that in spiral magnets, inversion symmetry is broken owing to magnetic order, and some spiral-ordered structures such as a cycloidal make the system polar. This means that the system becomes ferroelectric when magnetic order develops. The ferroelectricity in a new class of magnetoelectric multiferroics such as TbMnO3

and Ni3V2O8 can be explained in terms of this scheme. Because spiral order often arises from the competition between nearest-neighbor and further-neighbor magnetic interactions, systems containing competing magnetic interactions (spin frustration) are promising candidates for magnetoelectric multiferroics.

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Thus, it is no longer so difficult to find new magnetoelectric multiferroics. Indeed, on the basis of this strategy several new magnetoelectric multiferroics related to spiral magnetic orders have been discovered in the past few years. The magnetically induced electric polarization in these systems can be controlled by fine tuning of the subtle balance of competing magnetic interactions, for example by magnetic fields and by chemical substitution [40]. Thus, large magnetoelectric effect accompanied by a metamagnetic transition is realized by relatively low magnetic fields in these systems. Through the use of these magnetoelectric multiferroics, ferroelectric order can be either induced or suppressed by the application of a magnetic field. Furthermore, the direction of the ferroelectric polarization vector by 90◦ and 180◦ can be switched or even turned full circle by the use of magnetic fields. The intimate relationship between magnetism and ferroelectricity in non-collinear spiral magnets presented in this article also suggests that the investigation of electric properties such as dielectric constant and electric polarization can be a new tool with which to study nontrivial magnetic properties in frustrated spin systems that often favor non- collinear magnetic structures [40]. 8.53 Diluted magnetic semiconductors (DMS) DMS have recently attracted huge research attention because of their potential application for spintronics devices [100, 101]. In the modern computer age, devices continue to diminish in size to achieve higher speeds. As this

shrinkage occurs, the design parameters are impacted in such a way that the materials in current use are pushed to their limits [102]. Several long-term alternative concepts are being investigated that would reduce the device size, power consumption, and exploit multifunctional properties of materials. One of the hot topics today is to use the spin of electrons, holes, nuclei, or ions to gain new functionalities in both analog and digital electronics as discussed in the above section-3.2. The charge, mass and spin of electrons form the foundation of present information technology. The integrated circuits and the high frequency devices made of semiconductors, used for information processing, use only the charge of electrons while the storage of information is done by magnetic recording using spin of electrons in a ferromagnetic metal [103, 104]. But tomorrow's information technology may see magnetism (spin), and semiconductivity (charge) combined in one device that exploits both charge and 'spin' to process and stores the information. We may then be able to use the capability of mass storage and processing of information in the same device. Such a device will be called as “Spintronic device” [105]. This could not be realized so far because the semiconductors currently used in integrated circuits, transistors and lasers, such as silicon and gallium arsenide are nonmagnetic. Moreover, in order to have a useful difference in the energy between the two possible electron spin orientations (up and down), the magnetic fields that would have to be applied are too high for everyday use [102]. There are semiconductors, which have a periodic array of magnetic elements eg. Europium,

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chalcogenides and semiconducting spinels but their crystal structure is quite different from that of Si and GaAs. Also their crystal growth is very difficult. Hence they are not ideal for spintronic applications [102]. One of the approaches to drive a semiconductor ferromagnetic is to introduce magnetic ions like Mn, Cr, Co and Fe into non-magnetic semiconductors. In these ferromagnetic semiconductors, a part of the lattice is made up of substitutional magnetic atoms. Hence they are called diluted magnetic semiconductors (DMS) [105]. In recent years there has been an extensive research towards introducing ferromagnetic property at room temperature in semiconductors to realize new class of spintronic devices such as spin valves, transistors, spin light emitting diodes, magnetic sensors, non-volatile memory, logic devices, optical isolators and ultra-fast optical switches. The potential advantages of spintronic devices will be higher speed, greater efficiency, and better stability, in addition to the low energy required to flip a spin [105]. Most of the past work on DMS has focused on (Ga,Mn)As and (In,Mn)As. But the highest reported Curie Temperature (Tc) in the single phase samples grown by MBE range from ~ 35 to 172 K [108, 109]. This search for a room temperature ferromagnetic Semiconductor, gained momentum, following a theoretical prediction by Dietl et al., that ZnO and GaN would exhibit ferromagnetism above room temperature on doping with Mn, provided that the hole density is sufficiently high [110].

Several researchers have since then reported observation of room temperature ferromagnetism in doped semiconductors. A considerable attention has been paid to semiconductors doped with ferromagnetic metals (Co, Fe, and Ni). In these types of systems, the fundamental issue of much concern is that the ferromagnetic ordering could be a result of metal precipitates e.g., Co in Co doped TiO2 and Co doped ZnO [111, 112,

113]. Moreover, a definite picture regarding the actual mechanism of ferromagnetic ordering in these systems has not been established. A ZnO based DMS would be very promising because of its widespread applications in electronic devices, such as transparent conductors, gas sensors, varistors, surface acoustic wave devices, optical wave guides, acousto-optic modulators/deflectors, ultra violet laser source, and detectors [114]. Out of all the transition metals (TM), the doping of Mn in ZnO is most favorable because Mn has the highest possible magnetic moment [115] and also the first half of the d-band is full, creating a stable fully polarized state. The theoretical studies on Mn doped ZnO also proved its novelties in the fabrication of room temperature spintronic devices. A Tc higher than 300 K for p-type ZnO has been predicted theoretically, but this has not been experimented. Moreover, Mn is known to be antiferromagnetic [116], which makes this system more clean in terms of metal precipitate induced ferromagnetism, which is the subject of great controversies in DMS. Despite uncertainty in the mechanism of ferromagnetism in doped semiconductors, and

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the fact that the obtained magnetization is lower than the theoretically predicted value in most of the reports, the results reported so far provide a pathway for exploring the Mn doped DMS. It is however, imperative to understand the phenomenon and the factors affecting the magnetization value in order to realize commercially applicable devices. History of DMS The study of dilute magnetic semiconductors started in late 1960s [118, 119] resulted in various exciting findings. Among the most extensively studied ferromagnetic semiconductors were Eu-Chalcogenides (e.g., EuSe, EuS, EuO) and Cr-Chalcogenide spinels (e.g., CdCr2Se4, CdCr2S4). In these magnetic semiconductors exchange interactions between the electrons in the semiconducting band and the localized electrons at the magnetic ions led to a number of interesting properties like red-shift of band gap when ferromagnetism sets in. In spite of the numerous studies carried out on these materials, no practical applications have been realized. A low Curie temperature hampered the application and extreme difficulty in growing these crystals hindered further studies on these materials [119]. The next generation of DMS began in early 1980s with the appearance of dilute magnetic semiconductors based on II-VI compounds together with those based on IV-VI compounds [118]. The materials of the type (e.g. CdVIxIIxBMnA−1VIB1-x Mn xTe, Cd1-x Mnx Se, Hg1-xMnxTe) were of much interest because of several distinct reasons. Their ternary nature gave the possibility of tuning the lattice constant and band parameters by varying the composition of the material, thus making it possible to engineer their band gap

[107]. The substitutional Mn atoms in A2B6 lattice are also characterized by highly efficient electroluminescence, which makes alloys important in the context of optical flat panel display applications. Furthermore, the strong exchange interactions between sp band electrons and d electrons associated with Mnx2xMnA−1++ resulted in interesting optical and electrical properties like giant Faraday rotation and magnetic and field induced metal-insulator transition [107]. In these materials the valence of cations matches that of common magnetic ions like Mn. This phenomenon makes this type of DMS relatively easy to make in bulk and thin epitaxial layers. Many fundamental studies were done on these systems but not much application could be realized except for optical isolators [118]. The magnetic interactions in these DMS is dominated by antiferromagnetic coupling of Mn spins, which results in paramagnetic, antiferromagnetic or spin glass behavior [118]. A ferromagnetic DMS based on II-VI materials could not be realized until recently by A. Hauri et al. (Tc~2K) [120]. Moreover, II-VI based DMS have been difficult to dope to create p-and n-type, which made it difficult to study their transport properties and hence makes it less attractive for applications [119]. Another group of materials, IV-VI materials (such as PbMnTe, nMnTe and GeMnTe) also attracted attention because of free carrier induced magnetism. Unlike II-VI DMS, these materials can be grown with higher concentration of free band carriers. Their magnetic properties can be controlled by modifying the carrier concentration through control of native defects. Story et al.

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demonstrated for the first time, effect of carrier concentration on magnetic properties of PbSnMnTe [121]. They reported a ferromagnetic ordering in this material up till 4 K and the Tc could be increased by increasing the carrier concentration. However, giant moment often talked about in certain metallic alloys of transition metals cannot be formed in IV-VI alloys because of the diamagnetism of the host crystal. Recently ferromagnetic transition temperature as high as 100 K was reported in Fe doped GeTe films [122]. The other class of semiconductors that is III-V semiconductors like GaAs and InAs had major markets in IR LEDs and lasers and magnetic sensors respectively [104]. Magnetism, especially ferromagnetism, has not been a part of activity in these semiconductors because of the lack of material technologies that would allow introduction of magnetic cooperative phenomena into III-V heterostructures [120]. The equilibrium solubility of transition metal atoms into these semiconductors is very low ~1018cm-3 [123] or less. Beyond a certain doping level, the surface segregation, and in extreme cases phase separation would occur and impede further incorporation of high concentration of magnetic ions into the crystals. Therefore, preparation of ternary alloys to form DMS of III-V semiconductors is an extremely difficult task. No DMS based on these materials was formed until Ohno et al. reported ferromagnetism in epitaxial films of InMnAs grown by Molecular Beam Epitaxy (MBE) in 1992 and GaMnAs (Tc~110 K) in 1996 [124, 125]. The low temperature used to grow a crystal by MBE prevents formation of a secondary phase. Since then both these systems have been investigated extensively in

an attempt to increase the ferromagnetic transition temperature to more practical limits. Till date the highest reported Curie temperature in Mn δ-doped GaMnAs heterostructures is ~172 K by Nazmul et al. [109]. Besides II-VI, IV-VI and III-V semiconductors based DMS; room temperature ferromagnetism was reported in II-IV-V2 type chalcopyrite compound CdGeP2 doped with Mn. [118]. It is easier to achieve p-type doping in ternary semiconductors with chalcopyrite type structure. Also II-IV-V2 semiconductors are reported to have higher carrier mobility, which is important for device applications [118]. Another important discovery was a group IV ferromagnetic semiconductor Mn

xGe

1-x by

Park et al. in 2002 [126]. It followed a prediction based on mean field solution of Zener model that ferromagnetic (FM) order can be stabilized in group-IV semiconductors like Si, Ge and Si

1-xGe

x. The single crystal Mn

xGe

1-x films on

Ge and GaAs (001) substrates have Curie temperatures varying linearly with the Mn concentration from 25 K to 116 K. Process of doping DMS DMS are semiconductors which have been doped with a few percent of a magnetic impurity. These materials allow for the linking of magnetic and electronic devices on a single microelectronic platform. Two important requirements for spintronic applications include the ability to control the spin properties of these materials through external means such as an applied voltage and to attain room temperature magnetism. Predictions that moderate dopant levels of 5% result in room temperature magnetism in ZnO and GaN has spurred significant work in doping a wide variety of oxides and nitrides. However, the

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results to date remain highly controversial with widely varying reports and uncertainty about the origin of the magnetism observed in these films. Recent work on spintronics focuses on achieving practical magnetic ordering temperatures in technologically useful semiconductors. While the progress in synthesizing and controlling magnetic properties of III-arsenide semiconductors has been astounding, the reported Curie temperatures are too low (~172 K) [109] to have a significant practical impact. A key development that focused on wide band gap semiconductors as being the most promising for achieving high Curie temperatures was the work of Dietl et al. They employed Zener model of ferromagnetism to predict Tc values for several materials. The schematic showing the predicted Tc values is given below [106].

Fig-119 Tc for Various doped semiconductors

The Tc exceeding room temperature for semiconductors such as GaN and ZnO containing 5% Mn and a high hole

concentration (3.5 x 1020

cm-3

) initiated intense research to realize a room temperature DMS based on wide band gap semiconductors. Tremendous progress has been made in the realization of high quality epitaxial layers of DMS films and in the theory of ferromagnetism in these dilute magnetic semiconductors. 8.54 Mechanisms of ferromagnetism It is an important challenge of materials science to understand the ferromagnetism in magnetic semiconductors and to develop functional semiconductor systems with the Curie temperatures Tc exceeding comfortably the room temperature. The fact that the DMS are ferromagnetic and independent of their weakly metallic or strongly insulating nature implies a robust character for the underlying mechanism leading to the long range magnetic order in these systems. Clearly the ferromagnetic mechanism should not depend crucially on the carrier system being “free” valence band holes since the strongly insulating DMS systems do not have any free holes. The currently accepted picture for DMS ferromagnetism is that it is the local antiferromagnetic coupling between the carriers (i.e., holes in GaMnAs) and the Mn magnetic moments that leads to long range ferromagnetic ordering of Mn local moments. The carrier system also becomes spin-polarized in the process with the carrier magnetic moment directed against the Mn magnetic ordering by virtue of the antiferromagnetic hole-Mn coupling, but the total magnetic moment of the spin polarized carriers is extremely small since nc<<ni and |S| > |s|

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where S is the Mn, s the hole spin, nc and ni are carrier and local moment densities respectively. The relevant DMS effective magnetic Hamiltonian can be written as [127].

Where S(r) and s(r) are respectively the Mn and hole spin densities. The coupling J(r) between Mn local moments and hole spins can, in principle, be ferromagnetic (J < 0) or antiferromagnetic (J > 0), but the effective interaction between the Mn local moments mediated by the holes (through HM) is always ferromagnetic. The magnitude of J must come from a first principles band structure calculation or from experiments. Oxide based DMS Compared to non-oxide semiconductors, the oxide semiconductors have many advantages. Their wide band gap makes them transparent and also suitable for applications with short wavelength. They can be easily grown at low temperature even on a plastic substrate and are ecologically safe and durable besides being low in cost. In addition, strong electronegativity of oxygen is expected to produce strong p-d exchange coupling between band carriers and localized spins, a prerequisite for DMS [128]. Summarized below are some of the reports on oxide semiconductor based DMS. TiO2 based DMS TiO2 has been widely studied for its unique physical and chemical properties like high refractive index, optical transmittance in the visible and near-infrared region, high dielectric constant and photo catalysis for water

cleavage. TiO2 are wide band gap semiconductors that exist in three kinds of crystal structures rutile, anatase, and brookite. Anatase TiO2 has high mobility of n-type charge carriers when doped with several percents of Co are ferromagnetic at room temperature as shown by Matsumoto et al. [129]. SnO2 based DMS SnO2 is ‘n-type’ semiconductor with a wide band gap of ~3.6 eV which has its application as a transparent conducting electrode in solar cells [129] and gas sensors. It has a rutile structure with octahedral coordination similar to anatase TiO2. Large n-type carrier concentration up to 1021 cm-3 can be achieved by antimony doping. The effective electron mass is quite large ~0.3me. These characteristics are important for strong magnetic exchange interactions in terms of carrier induced magnetism. Epitaxial films of Mn doped rutile-SnO2 were fabricated by PLD. Co doped ZnO ZnO based DMS have wide band (3.3eV) gap, and large excitation energy (60meV) [131, 132]. It is a well-known piezoelectric and electro-optic material, and can be easily deposited in thin film form. It has wide applications in electronic devices such as transparent conductors, thin film gas sensors, varistors, surface acoustic wave (SAW) devices, optical wave-guides, acousto-optic modulators / deflectors, ultraviolet LASER sources, and ultraviolet detectors [113]. It is n-type semiconductor with the room temperature hall mobility in ZnO single crystals in the order of 200cm2V-1s-1. Electron doping via defects originates from Zn interstitials in the ZnO lattice. The intrinsic

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defect levels that lead to n-type doping lie approximately at 0.05eV below the conduction band. There is also interest in developing the use of ion implantation of ZnO for device doping, and isolation, as well as investigating the effectiveness of different transition metals for magnetic doping. Mn doped ZnO Theoretical predictions of researchers revealed that, FM ordering in TM doped ZnO can be achieved without using any additional carriers with V, Cr, Fe, Co and Ni [133], whereas with Mn doping additional p-type doping is needed [109]. Despite this Mn remains the primary dopant of interest because solubility of Mn in ZnO is larger than 10 mol% and the electron mass is as large as ~0.3m

e, where m

e is the free

electron mass. In fact, Fukumura et al. showed that Mn atoms could be doped into ZnO up to 35 % by PLD technique without phase segregation [131]. Therefore, the amount of injected spin in the host material can be very large with Mn doping. Moreover, Mn is known to be antiferromagnetic, which makes this system more clean in terms of metal precipitate induced ferromagnetism, which is the subject of great controversies in DMS (eg in Co doped TiO

2, Co doped ZnO)

The model by Dietl et al predicts that the transition temperature in dilute magnetic semiconductors (DMS) will scale with a reduction in the atomic mass of the constituent elements due to an increase in p – d hybridization and a reduction in spin–orbit coupling. The theory predicts a T

C greater than

300 K for p-type ZnO doped with Mn mediated by heavy p-type doping, with T

C

dependent on the concentration of magnetic ions and holes [109]. In view of these findings one can say that carrier concentration is not the only parameter that influences the magnetic properties of Mn: ZnO. This is consistent with work by Theodoropoulou et al. who found that FM in ZnO films deposited by reactive magnetron sputtering was strongly dependent on parameters such as growth temperature, O

2

partial pressure, and type of substrate (only films deposited on Al

2O

3 substrates were FM).

Non-optimized growth conditions produced weakly paramagnetic behavior [134]. Spin valve The most successful Spintronics device to date is the spin valve, due to their widespread application in hard disk read/write heads. This device utilizes a layered structure of thin films of magnetic materials, which changes electrical resistance depending on applied magnetic field direction. In a spin valve, one of the ferromagnetic layers is "pinned" so its magnetization direction remains fixed and the other ferromagnetic layer is "free" to rotate with the application of a magnetic field. Future applications Future applications may include a spin-based transistor which requires the development of magnetic semiconductors exhibiting room temperature ferromagnetism. One possible material candidate is manganese doped gallium arsenide GaMnAs. The operation of MRAM or magnetic random access memory is also based on spintronic principles. Spintronics-based non-volatile 3D optical data storage has also been proposed.

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8.60 Ferroelectric Thin Films Introduction With an ever-expanding demand for data storage, transducers, and microelectro-mechanical (MEMS) systems applications, materials with superior ferroelectric and piezoelectric responses are of great interest. The lead zirconate titanate (PZT) family of materials has served as the basis for such applications until now. Applications of the piezoelectric effect have expanded into many fields since Curie brothers discovered this effect in 1880-1881. Since then, based on the type of piezoelectric materials, four stages of historical developments may be identified. The first material was single crystal quartz, the second was single-crystal Rochelle salt, the third was barium titanate ceramics, and the fourth was lead-zirconate-titanate (PZT) ceramics [135]. Quartz crystals were first used for underwater transducers during World War I, and then for quartz crystal oscillators. Rochelle salt was used for underwater transducers and phonograph pickups. Barium titanate ceramics were discovered at the end of World War II and were first used for underwater transducers, communication devices, and dielectric components such as capacitors. PZT ceramics were discovered in 1954 and replaced barium titanate ceramics in all fields of piezoelectric applications. At present, single-crystal quartz is still the most important piezoelectric material. Of the ceramic materials, PZT ceramics are the most widely used because of their high electromechanical coupling factor, good frequency-temperature characteristics, and suitable quality factor.

The History and origination of PZT The origin of PZT dates back from the study of Barium Titanate (BaTiO3). BaTiO3 ceramics were discovered by E. Wainer and N. Salomon [136] in the USA in 1942, by T. Ogawa [137] in Japan in 1944, and by B. M. Vul [138] in the Soviet Union also in 1944. All discoveries were made independently with no communication between the researchers because of World War II. At first, the discoverers suggested that barium titanate ceramics were typical ferroelectric materials and had no specific piezoelectric advantages. However, in 1947, S. Roberts [139] of the USA discovered the piezoelectric properties of the material resulting from poling the material with a high DC voltage. This prompted W. P. Mason [140] and others to study the piezoelectric properties of the material. By the early 1950s, piezoelectric transducers based on barium titanate ceramics were becoming well established in a number of consumer and military applications. Piezoelectric barium titanate ceramics were good materials for electro-mechanical transducers because of their non water solubility, high coupling coefficient, and ease of production. However, this material had serious weak points as described below. o Poor temperature coefficient of resonance

frequency caused by the second phase transition of crystal [135] just below room temperature.

o The second problem was excessive aging because of the material’s low Curie point.

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Many researchers tried to improve the temperature characteristics by shifting the second phase transition. One method was to add other materials such as Ca or Pb. Especially, the addition of Pb had a drastic effect in shifting the Curie point to a temperature >120◦C and the second phase transition to <-20◦C. Study of the phase transition in lead titanate and lead zirconate led to the discovery of PZT ceramics, which had much better temperature and aging characteristics than barium titanate [135]. Emergence of ferroelectric thin-film Until very recently, ferroelectrics have been used in the form of bulk ceramics and, where available, as single crystals. These materials have proved to be robust and reliable solution for producing thin layers. Since the 1980s, various methods have been developed [141] to fabricate ferroelectrics in the form of thin films. The availability of thin-film ferroelectrics has encouraged the re-examination of previously unrealizable designs, resulting in the integration of ferroelectrics with semiconductor circuits, and architectures combining the excellent properties of ferroelectrics with micromachined silicon. Ferroelectricity Ferroelectricity is a physical property of a material whereby it exhibits the spontaneous polarization (Charge), by either Mechanical / Thermal / electrical field as listed below [142,

143]. o Piezoelectrics: Charge generation by

mechanical fields

o Pyroelectrics: Charge generation by thermal fields

o Ferroelectrics: Charge generation by electrical fields

Crystal Symmetry The lattice structure described by the Bravais unit cell of the crystal governs the crystal symmetry and they all can be grouped together into 230 microscopic symmetry types or space groups based on the symmetry elements [13, 14]. In the physical properties of crystals, only the orientations of the symmetry elements and not their relative positions are important. Hence, if only the orientations of the symmetry elements are taken into account, then the macroscopic symmetry elements in crystals reduce to a center of symmetry, mirror plane, 1-, 2-, 3-, 4- or 6- fold rotation axes and 1-, 2-, 3-, 4- or 6- fold inversion axes. A combination of these symmetry elements gives us the macroscopic symmetry also called as point groups. It can be shown by the inspection of the 230 space groups that there are just 32 point groups. The seven crystal systems can be divided into point groups according to the point group symmetry they possess (Fig-120)

[142, 143].

Fig-120 Symmetry based Phenomenon of Ferroelectric material

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The thirty-two point groups can be further classified into o Crystals having a center of symmetry and o Crystals which do not possess a center of

symmetry. Crystals with a center of symmetry include the 11 point groups labeled as centrosymmetric and these point groups do not show polarity. The remaining 21 point groups do not have a center of symmetry (i.e. non-centrosymmetric) which possesses one or more crystallographically unique directional axes. All non-centrosymmetric point groups, except the 432 point group, show piezoelectric effect along unique directional axes. The symmetry based Phenomenon of Ferroelectricity is shown in Fig-120 [142, 143]. Structure of Ferroelectric Materials The feature of all ferroelectrics is the presence of a field re-orientable spontaneous polarization. Many ferroelectrics are characterized by structures incorporating oxygen polyhedra and the most important of these is the perovskite structure A2+B4+O3 (Fig-121) [142,].

Fig-121 Crystal structure of Ferroelectric material

This polarization appears as a result of the small, highly charged B cation being displaced into a noncentrosymmetric position as the structure is cooled below the Curie temperature (TC) [142, 143]. The physical significance of this spontaneous polarization is that it confers the largest relative permittivity of any type of capacitor dielectric, and as well as a field-orientable polarization, which has been exploited in the manufacture of a range of piezoelectric and pyroelectric products. Ferroelectric Properties 8.61 Piezoelectrics It is the ability of certain crystalline materials to develop an electrical charge proportional to a mechanical stress. All ferroelectrics are piezoelectric. Piezoelectric materials also show a converse effect, where a geometric strain (deformation) is produced on the application of a voltage. The direct and converse piezoelectric effects can be expressed in tensor notation as follows [142, 143].

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8.62 Pyroelectrics

8.63 Ferroelectrics

Major ferroelectric oxides o Pb-based materials - Pb(Zr,Ti)O3 o Layered perovskites – SrBi2Ta2O9,

Bi4Ti3O12 o BaTiO3-based materials – (Ba,Sr)TiO3 Material Properties for Piezoelectrics - PZT Direct piezoelectric effect:

Converse piezoelectric effect:

Where D is the charge density, deff – effective piezoelectric coefficient, X is stress, is strain. Electrostrictive effect – Quadratic effect, present for all materials

Piezoelectric coefficient

Where dijk is the third-rank tensor. Relation between piezoelectric coefficient and polarization as illustrated in (Fig-122) [142, 143]

Where, εεεε - dielectric permittivity, m - index in the matrix notation.

Fig- 122 Relationship between dzz and Pz

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For particular case of tetragonal symmetry:

d33=2ε33Q33P3

d31=2ε33Q13P3

d15=2ε11Q44P3

Where D is the charge density, deff – effective piezoelectric coefficient, X is stress, is strain and d33 is the amount of polarization developed along the direction of applied force, per unit applied force [142, 143]. For Rhombohedral symmetry, as illustrated in (Fig-123)

Fig- 123 Rhombohedral PZT Comparison between PZT and BaTiO3 The relationship between piezoelectric coefficient (d ZZ) and Polarization (PZ) are detailed in Fig-124 [142- 147].

Fig- 124 Relationship between dzz and Pz of PZT and

BaTiO3

For polycrystalline materials Piezoelectric coefficient (d ZZ) and Polarization (PZ) depends on the sample symmetry.

d – Actuator figure of merit g – Sensor figure of merit Electromechanical coupling factor k is given by k2 = Stored mechanical/(electrical) energy/Stored electrical (mechanical) energy,

s – Elastic stiffness

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Ferroelectric materials for piezoelectric applications Maximum d in systems with morphotropic phase boundary (MPB) - Pb(Zr,Ti)O3 as shown in Fig- 125

Fig- 125 Morphotropic phase boundary (MPB) - Pb(Zr,Ti)O3

Monoclinic phase at MPB

Fig- 126 Monoclinic phase at MPB

The monoclinic phase of PZT clearly exhibits the formation of MPB as illustrated in Fig-126 with the following characteristics [148-150]. o Not a sharp boundary between tetragonal

and rhombohedral phases o An additional monoclinic phase might exist o There are three different phases with

similar free energies and the polarization can rotate easily among different directions

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Current Demerits A critical drawback of this material, however, is the presence of lead and the recent concerns about the toxicity of lead-containing devices for the statutory compliance of RoHS (Restriction of Hazardous Substances). Researchers are trying with Lead Free material (K0.5Na0.5)1-xLi x (Nb1-yTay)O3 to comply with RoHS, the related properties are illustrated in Fig- 127. Recently, the lead-free ferroelectric BiFeO3 (BFO) has attracted a great deal of attention because of its superior thin-film ferroelectric properties, which are comparable to those of

the tetragonal, Ti-rich PZT system; therefore, BFO provides an alternate choice as a “green” ferro/piezoelectric material. Another advantage of BFO is its high ferroelectric Curie temperature (Tc = 850 °C in single crystals), which enables it to be used reliably at high temperatures. The ferroelectric domain structure of epitaxial BFO films are typically discussed in the context of the crystallographic model of Kubel and Schmid; however, by suppressing other structural variants in BFO, we can obtain periodic domain structures that may open additional application opportunities for this material [151].

Fig-127 Lead Free Piezoelectric materials

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Pyroelectrics Pyroelectric Coefficient Vs Relative Dielectric Constant is illustrated in Fig-128. The relation between Pyroelectric Coefficient Vs Relative Dielectric constant can be expressed as follows.

Figure of Merit

Fig-128 Pyroelectric Coefficient Vs Relative Dielectric Constant {Substitutions by: Zr (PZT), La (PLT) and Ca (PCT)} Application of Pyroelectric thin films o Intruder alarm o Linear pyroelectric arrays o Application in infrared gas spectroscopy o thin film focal plane array for thermal

imaging [145]

Materials for ferroelectric memories Charge by switching, is shown in Fig-129

Fig-129 Charge by Switching in FE Memories Intrinsic requirements[143-145]

Polarization ↑

Switching speed ↑

Coercive Field ↓

Retention ↓

Fatigue ↓

Imprint ↓ Extrinsic requirements

Processing temperature ↓

CMOS compatibility ↑

Availability ↑

Cost ↓

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Applications of ferroelectric thin films Ferroelectric devices are of vast ranges and many new designs have been proposed and developed based on the unique properties of ferroelectric films as shown in Fig-130

Fig- 130 Areas of application of Ferroelectric thin films o The advent of ferroelectric thin films

provides a practical method of realizing a new generation of integrated solid state devices. While memory storage devices represent the largest potential market, thin-film pyroelectric, piezoelectric and frequency agile devices will appear in a commercial form within the next few years [145].

8.7 Magnetoelectric Thin Films Magnetoelectric thin film materials are a class of multiferroics in which charge polarization and magnetization coexist and are coupled together. This property has crucial importance in the construction of actuators and sensors with high sensitivity. The Magnetoelectric effect has also been observed in layered composites such as (Pb,Zr)TiO3 (PZT)–Tb0.3Dy0.7Fe1.92 (Terfenol-D), PZT-NiFeO4, polyvinylidenefluoride–Terfenol-D and laminate Pb(Mg1/3Nb2/3)O3– PbTiO3–Terfenol-

D. These composite materials provide fundamental advantages when fabricated as thin films instead of bulk materials by constructing alternating piezoelectric and piezomagnetic layers for the fabrication of compact thin-film magnetoelectric devices as detailed under Spintronics – TbMnO3, and BFO model system [147].

8.8 Magnetoelastic Thin Films Magnetostrictive or Magnetoelastic thin films have drawn significant interest in sensor and actuator applications. The thin films applications are based on a cantilever, consisting of a magnetostrictive film deposited onto a non-magnetic substrate. Amorphous Fe-based thin films are currently being considered for this purpose as Fe-based metallic glasses show high values of the saturation magnetostriction, λs = 10-5. However, for thin films the magnetostrictive and magnetic behavior is dependent on several parameters such as the deposition conditions, mechanical behavior of the substrate and substrate thickness. The development of micro sensors based on magnetoelastic response requires highly magnetostrictive thin films with flexible substrates. The behavior of Fe80B20 is being examined by depositing (using magnetron sputtering) thin films of the material on different substrates for this reason [148, 152]. Magnetostriction measurements indicate the strong dependence of the saturation magnetostriction with the substrate. Samples on flexible substrates exhibit a better performance than samples deposited onto glass substrates.

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8.9 Piezoelectric Thin Films Piezoelectric thin films of materials such as lead zirconate titanate (PZT) are detailed in the piezoelectric section-8.61. o Piezoelectric thin films also have vast

applications in MEMS devices incorporating piezoelectric thin films. There are two ways to evaluate piezoelectric thin film[147].

o One is to use the direct piezoelectric effect such as normal loading method which gives the information prior to the high field poling process.

o The other is to employ the converse piezoelectric effect like interferometer, which by itself leads considerable domain reorientation in the ‘As’ deposited film when applying voltage for poling.

Some common piezoelectrics used are listed in the table below with their K values [145].

9.0 Multiferroic BFO Thin Films – as a model system The intense interest towards this fascinating multiferroic material has been discussed under the section of Multiferroic crystals in sec. 7.10 In brief BiFeO3 (BFO) is a room temperature single-phase magnetoelectric multiferroics reported so far, which shows the highest

ferroelectric polarization, with a ferroelectric Curie temperature (TC) of ~1,100 K and an antiferromagnetic N´eel temperature (TN) of ~640K. Both ferroelectricity and anti-ferromagnetism have long been known in BiFeO3 single crystals, and recent studies of BiFeO3 thin films have confirmed the existence of a large ferroelectric polarization, as well as a small magnetization, both of which are consistent with theoretical predictions [153,

154]. 9.11 Structure and properties of BFO The structure of BiFeO3 is characterized by two distorted perovskite unit cells (ar = 3.96 Å, αr = 0.6°) connected along their body diagonal, denoted by the pseudocubic <111>, to form a rhombohedral unit cell (Fig-131) [56, 57].

Fig-131 Schematic of the crystal structure of BFO and

the ferroelectric polarization (arrow) and antiferromagnetic plane (shaded planes).

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Ferroelectric (FE) Properties in Bulk The large displacement of the Bi ions relative to the octahedral FeO6 induces ferroelectricity resulting in two important considerations. o The ferroelectric polarization lies along the

pseudocubic <111> leading to the formation of eight possible polarization variants, corresponding to four structural variants [54, 57 and 58].

o The antiferromagnetic ordering of BFO is G-type, in which the Fe magnetic moments are aligned ferromagnetically within {111} and antiferromagnetically between adjacent (111).

BFO is also known to exhibit a spin cycloid structure in the bulk [54] and the preferred orientation of the antiferromagnetically aligned spins is in the (111), perpendicular to the ferroelectric polarization direction with six equivalent easy axes within that plane (Fig.131) [58, 60].Therefore, it is obvious that there is a coupling between antiferromagnetism and ferroelectric polarization. In the past, the ferroelectric nature of BFO was unclear, since early reports indicated a rather low spontaneous polarization in bulk [159]. But, recent studies of BFO thin films have shown that canting of the antiferromagnetic sub lattice is the reason for the existence of a large ferroelectric polarization, as well as a small net magnetization of the Dzyaloshinskii–Moriya type [55, 60]. 9.12 Ferroelectric Properties in thin films Polarization Recent investigations of ferroelectric and magnetic properties of BFO epitaxial thin films reveal, the importance of the individual order

parameters and the coupling between the order parameters showing the existence of a large ferroelectric polarization [160]. Researchers have also demonstrated based on theoretical calculations and through experimental studies of BFO films on substrates with various orientations (Fig-132) that the spontaneous polarization in BFO films is along <111> with a magnitude of 90–95 µC/cm2 [155]. The large polarization in thin films could be the result of a change in the switching mechanism in thin films compared with the bulk [156], as well as to epitaxial strain [157].

Fig.-132 Ferroelectric polarization loops measured on epitaxial BFO films with different crystallographic orientations. At the same time, two limiting factors are trouble with high leakage currents and difficulty in making electrical contacts remain to be solved. Leakage Ideal ferroelectric behavior has been demonstrated by recent work with BFO films

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grown on DyScO3 (DSO) substrates and sharp ferroelectric loops is obtained even at low frequencies (Fig-132) and measurements indicate low leakage levels [156-158]. Researchers are intensely investigating to solve this leakage problem in BFO heteroepitaxial thin films. 9.13 Electrical control of Magnetic Properties (AFM) Switching Switching is the reorientation of the polarization to a stable state that remains after the field is removed. Electrical control of multiferroic behavior in BFO films relies on controlling the ferroelectric switching. The recent report states that the researchers have observed a coupling between ferroelectricity and antiferromagnetism in BiFeO3 thin films, which can be understood to result from the coupling of both antiferromagnetic and ferroelectric domains to the underlying ferroelastic domain structure. Such a coupling is a crucial first step in the exploration of approaches to control and switch magnetic properties using an electric field [155]. The analysis of their experimental report is detailed below. Piezoelectric force microscopy (PFM) is used to characterize and determine the ferroelectric domain structure of BFO thin films grown on STO substrate with SRO bottom electrode [39,

40]. In PFM technique, a conductive cantilever with an ac signal induces an alternating electrical field between the tip and the SrRuO3 (SRO) bottom electrode. It has been reported that local converse piezoelectric vibrations

induced by the ac field produce displacements of the film. Using a locking technique enables the detection and recording of the sign and phase of the piezoelectric vibration, which can be used in conjunction with crystallographic information to determine the polarization direction in the films. Domains with up and down polarizations give rise to opposite contrast in out-of-plane (OP)-PFM images and differences in in-plane components of polarization produced a torque on the atomic force microscope (AFM) cantilever creating a contrast in the in-plane (IP)-PFM images. However, domains with polarization vectors along the scanning cantilever’s long axis do not give rise to any IP-PFM contrast. On the contrary, domains with polarization pointing to the right with respect to the cantilever’s long axis produce an opposite tone to domains with a polarization pointing to the left. This is caused by the anti-phase IP-piezo-response (PR) signals produced by these domains. By combining the OP- and IP-PFM images, the polarization direction of each domain (Fig-133b) was identified, showing an IP-PFM image of a BFO film grown on a (001) SrTiO3 (STO) substrate. The three contrast levels observed in the IP-PFM images acquired along the two orthogonal <110> directions, together with the uniform OP-PFM contrast indicate that the domain structure of the BFO films is characterized by four polarization variants (Fig- 133a). Fig-133b shows the ferroelectric domain structure for BFO films grown on STO (110) substrates (imaged with the cantilever along [110]. The films exhibit two ferroelectric variants with net polarization pointing ‘down’ over

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large areas (Fig- 133a). BFO films grown on STO (111) substrates exhibit one contrast in the OP-PFM image and no contrast in the IP-PFM image (Fig-133b), suggesting that the

polarization direction of the films on STO (111) is perpendicular to the substrate (Fig-133a).

Fig.-133 IP- PFM images of BFO thin film domains

Such domain structures agree well with phase-field models [42] in which the spatial distribution of the polarization field and its evolution is described by time-dependent Ginzburg–Landau equations [43].

It has been reported that to switch the films locally, a dc bias is applied to a conducting AFM tip while scanning over the desired area. By analyzing the OP and IP contrast changes

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following this electrical poling, all three possible switching mechanisms (71°, 109°, and 180°) have been observed (Fig-134) [43]. The red circles indicate the ferroelastic (71° and

109°) switching events, while the remainder of the domains is ferroelectric in nature.

Fig-134 OP- and IP-PFM images of (001) BFO/SRO/STO films after switching with schematics showing the three

possible switching mechanisms.

In ferroelectric domains with white contrast in OP and IP-PFM images, 180° switching events are observed as a reversal in both OP and IP-PFM image contrasts (changes to black in both cases). For 71° switching events, only a change in contrast in the OP image is observed (black contrast in OP and white contrast in IP). For 109° switching events, we observe the reverse change in an OP-PFM image (black contrast) but no response from IP-PFM (gray scale).

The antiferromagnetic domain structure of BFO can be studied using Photo Emission Electron Microscopy (PEEM) based on X-ray magnetic linear dichroism (XMLD) (Fig-135) [39-42]. Linear dichroism can arise from any anisotropy from charge distribution in a material. In non-ferroelectric antiferromagnets, asymmetry of the electronic charge distribution arising from magnetic order causes a difference in the optical absorption between

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orthogonal linear polarizations of light [39–43]. This is manifested as dichroism in the X-ray absorption, which can be used to distinguish different orientations of antiferromagnetic domains. Nonmagnetic ferroelectrics should also show linear dichroism because their polar nature causes an asymmetric electronic charge distribution. Therefore, in BFO, both antiferromagnetic and ferroelectric order should contribute to the dichroism. These two contributions can be separated by the temperature dependence of the XMLD or angle and polarization-dependent measurements. From their work, it is found that antiferromagnetic and ferroelectric domains are intimately related and match up spatially. The combination of PFM and PEEM, as well as the latter’s versatility, is useful for the further study of multiferroics.

Fig-135 PEEM allows the study of antiferromagnetism in BFO. Images taken based on XMLD show that the antiferromagnetic domain structure of BFO exactly matches the ferroelectric domain structure. In summary, we have observed a coupling between ferroelectricity and antiferromagnetism in BiFeO3 thin films, which can be understood to result from the coupling of both antiferromagnetic and

ferroelectric domains to the underlying ferroelastic domain structure. Such a coupling is a crucial first step in the exploration of approaches to control and switch magnetic properties using an electric field. 9.14 Magnetic properties of Thin Films The origination and magnitude of magnetism in BFO thin films is still under intense research, but some of the recent findings with possible origins of magnetism are explained in Fig-136 and promising results are discussed below.

Fig-136 Possible origins of Magnetism Wang et al. reported higher magnetization values for thin films of thickness less than ~ 100 nm, which is higher than the previously reported magnetization values in the bulk material [157]. o The measurements of magnetic moment

measured by higher resolution ‘Superconducting Quantum Interference Device’ (SQUID) is about 70 to 80 electromagnetic units (emu)/cm3, which is higher than their previous measurements

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made using vibrating sample magnetometer (VSM) as shown in Fig-137b.

o The measurements reported corresponds to a magnetization of about 0.5 µB/formula

unit, which progressively decreases as the film thickness is increased to above 120 nm.

Fig- 137 Magnetization measurements

o Detailed transmission electron microscopy studies of both planar and cross sections of the samples of thickness from 30nm, 90nm, 100nm and 120nm of BFO thin films grown on 001 STO substrates, did not reveal any second phases.

o Piezo imaging with an atomic force

microscope (AFM) has clearly shown the existence of piezoelectricity down to at least 30-nm thickness, although the degree of leakage goes up with decreasing thickness.

o X-ray diffraction studies have revealed no

secondary phases. o They have used Rutherford backscattering

and energy dispersive x-ray spectroscopy

to analyze the cation composition and see a Bi:Fe ratio of 1:1 in the films.

However, the oxygen stoichiometry is difficult to determine exactly so they have assumed the nominal oxygen composition to describe the film (ie- BiFeO3). Such notation does not imply that the films are free of point defects, including vacancies, interstitials, or anti-site defects. They have been using X-ray absorption spectroscopy (XAS) and X-ray magnetic circular dichroism (XMCD) to understand the origin of higher moments in the thin films. The measurements shown in Fig-138(a) was derived with a magnetic field of 800 Oe. XMCD results from the same series of films that were used to obtain the structural and

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magnetic data above. The signal magnitude, normalized to the total XAS signal, is a measure of the magnetic moment in the sample. o The data clearly shows that the 30nm thick

film has a distinct magnetic signal, which progressively decreases as the film thickness is increased.

o The position of the three peaks also reveals the mixed oxidation state of the sample by comparison with a known sample (Fe3O4).

Fig-138 Probing of Origin of Magnetism through XMCD In Fig-138(b), the normalized XMCD spectrum of the 30-nm BFO film to that of a Fe3O4 film is compared and several key points that emerge from this comparison are discussed below. o First, using the Fe3O4 spectrum as a

fingerprint, it is clearly identified that the peak at 709.5 eV as the Fe2+ peak, is consistent with our X-ray photoelectron spectroscopy results.

o Second, this peak progressively vanishes as the thickness is increased (Fig-138a).

o Third, the total intensity of the spectrum from the 30nm BFO film is approximately 15% of the Fe3O4 film, which suggests that

the total moment is also approximately 15% of Fe3O4.

o Finally, the ratio of the three peaks in Fig -138(b) is not the same as that in Fe3O4, for which detailed studies have revealed a ratio for BFO as, Fe2+(oct):Fe3+(tet):Fe3+(oct) = 1:1:1

The noticeable part is that the +2 state vanishes at thicknesses higher than ~100 nm, associated with the magnetism decreasing to the level of 8 to 10 emu/cm3. The researchers [115] have concluded that the most likely origin of Fe2+ in the thin films is the presence of oxygen vacancies, which are typically quite common in perovskites. In fact the sample films were grown under relatively reducing conditions and thus favored the formation of Fe2+. In the absence of Fe2+, their observations (that is, at thicknesses >120 nm) and theoretical analysis [120] suggest that the magnetization should be 8 to 10 emu/cm3, consistent with the observations of Eerenstein et al [163]. The presence of Fe2+ in the films suggests the origination as discussed below One possibility is a ferrimagnetic arrangement in which the moments of the Fe2+ ions are aligned oppositely to those of the Fe3+ ions, leading to a net magnetic moment. Eerenstein et al. [163] suggest that an oxygen count of 2.75 (instead of 3) would be required to produce our experimentally observed moment of 0.5µB/Fe. This would be the case for high-spin Fe2+, but the oxygen deficiency required to produce the observed moment would be much lower if low-spin Fe2+ were present. But on the contrary, Wang et al suggests that such a ferrimagnetic arrangement may be

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unlikely; even if Fe2+ and Fe3+ were to couple ferrimagnetically locally, they would need to also have long-range ordering or the moments from locally ferrimagnetic regions would cancel out. An alternative possible mechanism is a gradual increase in the canting angle as the thickness is reduced, which could be driven by increasing distortions resulting from epitaxial strain, oxygen vacancies, or both. Clearly, this aspect is scientifically very interesting and requires further experimental and theoretical study.

9.15 Thin Film Thickness dependence The ferroelectric and magnetic properties of BiFeO3 (BFO) epitaxial thin films was reported by Wang et al. [157], they have reported that they have demonstrated the thickness dependence of these properties, and suggested that monoclinic distortion, relaxing gradually is a likely explanation of these effects. The heteroepitaxial strain induced a increasing thickness as explained in Fig-139. Detailed X-ray studies [157] have shown evidence for such a monoclinic structure, as well as no evidence for secondary phases.

Fig-139 Thin Film Thickness dependence

The out-of-plane lattice parameter for the BFO layer progressively increases as the thickness is decreased, consistent with the expected effect of epitaxial constraint. In contrast to all their

prior studies, the recently grown epitaxial BFO thin films showed a large spontaneous polarization.

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o They suggested the hypothesis that this change could be directly attributed to the epitaxially induced change in structure.

o Possibility that the large polarization in thin films could be the result of a change in the switching mechanism in thin films compared with the bulk [156], a change that could be related to other differences as well as to epitaxial strain.

o Another possibility, originally suggested by Teague et al [160], is that the high leakage in the bulk samples, was reduced in the films, could have prevented prior researchers (over the past four decades) from observing the large value of spontaneous polarization of BFO.

These latter proposals are consistent with various subsequent measurements of high polarization of BFO in thin film form [164-166]. 9.16 Magnetoelectric (ME) coupling: FE-AFM Researchers have demonstrated that there is a ME coupling in BFO thin films [155] and the direction of the polarization can be changed by ferroelectric (180°) and ferroelastic switching events (71° and 109°). At the same time, magnetic moments on the Fe ions couple ferromagnetically within the pseudocubic {111} and antiferromagnetically between adjacent planes. Coupling between the ferroelectric and antiferromagnetic order in BFO is accomplished by the rigid alignment of the antiferromagnetic axis perpendicular to the polarization direction. Thus, certain types of 71° and 109° rotation of the polarization from <111> axis to one of a specific set of three

other <111> axes can result in changes in the magnetic configuration. Through a combination of PFM and PEEM, it has been demonstrated that the coupling exists between antiferromagnetic and ferroelectric domains during different ferroelectric switching events [155]. 9.17 FE-AFM-FM Coupling The demonstration of room temperature magnetoelectric coupling presents the potential for ultimately controlling magnetism with an applied electric field as explained below.

Fig-140, an approach for the electrical control of ferromagnetism

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To use such functionality for device applications, scalable control of antiferromagnetism and ferromagnetism is essential. So, to achieve such a goal, the researchers have proposed an approach based on the presence of two coupling mechanisms (Fig-140a). o The first is the coupling between

ferroelectricity and antiferromagnetism in BFO as discussed earlier.

o The second coupling mechanism of interest

is based on a classic exchange coupling interaction [167] that arises at the interface between a ferromagnet and an antiferromagnet (Fig- 140b).

Researchers have used such heterostructures to tune the properties of ferromagnets for over five decades. With the addition of a multiferroic antiferromagnet, we can control the state of the antiferromagnet electrically and thereby indirectly control the state of the ferromagnet by completing the bottom leg of the coupling triangle in (Fig-140a). Thus the combination of magnetoelectric coupling in a multiferroic and exchange coupling between magnetic materials offers a new approach for the electrical control of magnetism. 9.18 Epitaxial Strain - RSM Epitaxial Strain induces modification of various physical properties in BFO thin films, when compared to the bulk. Recently Wang et al. [157] reported an enhancement of the room-temperature spontaneous polarization in epitaxially compressed strained thin films of the ferroelectric compound BiFeO3. The crystal structure of these films was found to be monoclinic, in contrast to that of the bulk material which is rhombohedral. The effect of

a small monoclinic distortion arising from strain in BFO leads to a break in the magnetic symmetry and the formation of a preferred antiferromagnetic axis [42]. This occurrence is important because it will make the antiferromagnetic axis to rotate by 90° only for those ferroelectric switching events that have a 90° rotation of the in-plane component of the polarization. This indicates the added level of control exists in the magnetoelectric coupling. Recent report of experimental work carried out by the researchers to explore the multiferroic nature of epitaxially strained BFO thin films are discussed below. High-quality epitaxial BFO films have been prepared by pulsed laser deposition (PLD) [168, 169], radiofrequency sputtering [160] metal-organic chemical vapor deposition [160], and chemical solution deposition on various substrates [167], including STO, DSO, and LaAlO3, with various conducting-oxide electrodes such as SRO, (La, Sr) MnO3, and LaNiO3. Transmission electron microscopy (TEM) was used to identify the presence of a highly coherent and smooth interface between BFO and the electrode layer and the relevant TEM image is shown in Fig-141(a). Substrate and film thickness can be varied to study epitaxial strain effects in BFO. The out-of-plane lattice parameter is shown in Fig-141(b) as a function of BFO film thickness on both STO and DSO substrates. It has been observed that because of the lattice mismatch between BFO and STO, the BFO lattice is compressed in the in-plane direction and elongated in the out-of-plane direction; this strain gradually decreases with increasing film thickness. Films thinner than ~30 nm, the

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out of plane lattice parameters reach a maximum value implying that a fully epitaxial and maximally strained film has been created and the close lattice match between BFO and

DSO means that the out-of-plane lattice parameter remains close to the bulk value.

Fig-141 Analysis of TEM images

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The effect of strain on the structure of epitaxial BFO films was measured using high-resolution X-ray diffraction (HRXRD). Reciprocal space mapping (RSM) RSM was used to identify the crystal structure of the BFO films [172]. The BFO lattice is isotropically compressed in the plane of the film because of the lattice mismatch between STO and BFO. Such an effect can lead to the formation of a mono clinically distorted structure for BFO films on STO (001) and (110) substrates. The structural variants of a BFO thin film was characterized by detailed RSM measurements [172]. Fig-141c shows a typical RSM for BFO thin films (<60 nm). The in-plane positions of the 203PC BFO peaks remain almost identical to that of the substrate indicating that the films are fully strained. The splitting between the two peaks reveals the monoclinic angle to be ~0.7° with the distortion direction along [152]. Thicker films of thickness greater than 100 nm exhibited peak splitting, which indicates a lower symmetry than the tetragonal structure. The in-plane (H-direction) position of the 203PC peaks deviates from the centerline toward smaller values, while the out-of-plane (L-direction) position becomes larger than the thinner films. This means that the structure of the film becomes more like the bulk through strain relaxation. It is apparent that the growth of epitaxially constrained thin films of BFO results in the formation of a slightly distorted structure. In the mono clinically distorted

rhombohedral structure, the polarization direction will likely be close to <111>. It has been reported that they have identified three different contrasts in these images (Fig-142). o For all BFO films, the out-of-plane and in-

plane PFM images can be explained within the confines of the mono clinically distorted rhombohedral structure with the polarization along <111>.

o Using the PFM tip as the top electrode,

they probed the piezoelectric hysteresis of the films locally, down to a thickness of 2 nm, and found that five BFO unit cells are switchable [172] .

Fig-142 PFM images of 9 nm (001) BFO/SRO/DSO films

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The antiferromagnetic properties of epitaxial BFO have also been investigated by researchers and reported that magnetic measurements prove that the cycloidal structure has been broken, which leads to a weak ferromagnetic moment arising from canting of the antiferromagnetic moments in the system [172]. Furthermore, neutron diffraction has been used to obtain insights into the microscopic magnetic structure, confirming the absence of any bulk-like cycloidal modulation in BFO thin films [172]. Finally, using PEEM, a break in the magnetic symmetry, leading to the formation of a preferred antiferromagnetic axis, has been proposed which is consistent with theoretical predictions [171]. 9.19 Temperature dependence of Thin Films Researchers have recently reported that they have demonstrated at room temperature, the magnetic and ferroelectric components of BFO thin films are roughly of equal strength and have the same sign [155]. Their reported demonstration has been discussed below. Temperature-dependent measurements using XLD was made from room temperature to 800K on five samples; numbers 1–3 were recorded during heating, whereas 4 and 5 were recorded during cooling as shown in Fig-143. On heating, the antiferromagnetic contribution to the dichroism must reduce to zero at the N´eel temperature (~640 K), whereas the ferroelectric contribution can persist up to the ferroelectric Curie temperature (~1,100 K). In all cases the PEEM images were captured from the same area of the BiFeO3 film after waiting 30 min at each temperature to allow

thermal equilibrium. The data in sample 2 were recorded on an electrically switched area, whereas the others were recorded on un-switched areas. We see that in all cases the linear dichroism signal drops rapidly on heating above room temperature, with only ~50% of the room temperature XLD value remaining at the N´eel temperature; this reduction is recovered on cooling. The XLD scales with the thermal average (M2) of the antiferromagnetic order parameter as shown in Fig-49. The XLD data in Fig. 49 closely follows this curve up to the N´eel temperature. The XLD signal does not change significantly between the N´eel temperature and 800 K

Fig-143 Temperature dependence of normalized order parameters of BFO It is known in bulk BFO that the order parameter for ferroelectricity does not change much below its Curie temperature (~1,100 K), which is illustrated by the plots of Fe and Bi ionic displacements in Fig. 143. To investigate the ferroelectric order parameter in the 600nm BFO film, we also plot the temperature-

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dependent out-of-plane lattice parameter obtained from X-ray diffraction, and the ferroelectric polarization obtained using high-frequency ferroelectric pulse measurements. Similar to bulk BFO, the 600nm BFO film shows very little change in the ferroelectric order parameter from room temperature to 800 K and the order parameter change correlates with the high temperature XLD signal. A PFM measurement also confirmed the existence of stable ferroelectricity in the BFO film up to 800 K. The bulk-like behavior of the order parameter is consistent with earlier first-principles computations and with the fact that minimal lattice strain is expected in the 600nm. Therefore the researchers have concluded that the high-temperature XLD signal results from

the ferroelectric ordering, and the signal below TN from the sum of the antiferromagnetic and ferroelectric contributions. So, at room temperature, the magnetic and ferroelectric components are of roughly equal strength and have the same sign [155]. 9.20 Controlling domain structure and switching The ferroelectric nature of BFO could dominate the magnetic nature of the system because of the relative robustness of the ferroelectric order parameter at normal operating temperatures for devices. Therefore, controlling the ferroelectric domain structure becomes a critical issue for device functionality.

Fig-144 Schematic of vicinal STO substrates and the corresponding BFO domain structure and polarization variants

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Vicinal STO substrates Vicinal STO substrates are used to break the symmetry of complicated domain structure of BFO thin films. In order to simplify the domain structure of BFO films, a break in symmetry for the ferroelectric variants should be induced. One way of accomplishing this is through the use of vicinal STO substrates (Fig-144a) [172]. The researchers have used vicinal substrates miscut along the [010] and (110) directions. The substrates with maximum vicinal angle along [010] correspond to (110) substrates, while those with maximum vicinal angle along [110] correspond to (111) substrates. By using a substrate with a vicinal angle along the [010], the domain structure of BFO films can be limited to exhibit two polarization variants. Stripe patterns, created by two polarization variants 71° apart, with polarization vectors pointing into the substrate, have been observed (Fig-144b). Similarly, by using a substrate with the miscut along the [110], the formation of one dominant ferroelectric variant can be induced. The same approach can be applied to BFO films grown on STO (110). The two-domain architecture in BFO (110) films can likewise be controlled and evolved into a single domain film on the STO (110) surface. To verify the polarization variants, RSM with line scanning has been used to confirm the domain architecture in these samples (Fig. 144c). This, in conjunction with the fact that epitaxial films on (111) STO with an SRO bottom electrode also exhibit single domain behavior, provides us with a set of model thin-film systems to explore the magnetoelectric properties further, as well as the interactions with other layers.

Additionally, multiferroic materials with electrically controllable periodic domain structures (Fig-144b) could be of great interest for applications in photonic devices. In recent work, an approach to create a one-dimensional periodic domain structure in epitaxial BFO films has been demonstrated [173]. A schematic of the constraints imposed by heteroepitaxy to create long-range order in the domain structure of BFO is shown in Fig-144d. To achieve this, they have taken the DSO lattice which very closely matches the lattice of BFO and SRO. Further, the small structural anisotropy in DSO is used to pin the structure of the SRO layer such that a single domain variant of SRO is formed under the appropriate growth conditions. This structurally simplified SRO film can then be used to provide an anisotropic strain that excludes two of the four possible ferroelectric polarization variants and induces a one-dimensional periodic domain structure in BFO films (Fig-144e). Optical diffraction patterns (ODP) obtained from these PFM images (Fig-144f); yield an average stripe-domain width of ~200 nm. After gaining the control of the underlying domain structure, the next step is to control the nature of the ferroelectric switching events in BFO. A combination of phase-field modeling and scanning force microscopy of carefully controlled, epitaxial [110] BFO films with a simplified domain structure reveals that the polarization state can be switched by all three primary switching events through selection of the direction and magnitude of the applied voltage [172, 173]. Moreover, the instability of certain ferroelastic switching processes and

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domains can be dramatically altered through proper selection of neighboring domain walls.

Fig-145 Schematic of a planar electrode PFM setup. For eventual device applications, the use of coplanar epitaxial electrode geometry has been proposed to aid in the control of multiferroic switching in BFO (Fig-145) [173]. PFM has been used to detect and manipulate the striped ferroelectric domain structure of a multiferroic BFO thin film grown on a DSO substrate. Time-resolved imaging reveals ferroelastic switching of domains in a needle like region growing from one electrode toward the other. Purely ferroelectric switching is suppressed by the geometry of the electrodes. Such results demonstrate the ability to control the multiferroic order in BFO films by exerting precise control over the ferroelectric order parameter. 9.210 The future for multiferroics Exploring the coupling between ferromagnetic layers and BFO as shown in Fig-146 will be the future focus of researchers.

Fig- 146 Interaction between a multiferroic BFO and a ferromagnetic layer It has been reported that o Epitaxial BFO/La2/3Sr1/3MnO3 (LSMO)

magnetic tunnel junction heterostructures have been grown without suppressing the ferroelectric order in BFO [174, 175].

o Sizeable tunneling magnetoresistance and exchange-bias effects have been reported on epitaxial BFO/LSMO, BFO/CoFeB [176], and NiFe/BFO [177].

It is essential to further investigate the nature of the coupling mechanism in such heterostructures and it has been suggested that PEEM-based measurements can be made in order to probe this interaction [178]. Promising research along this direction is under way and exciting possibilities are waiting for potential industrial applications.

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9.30 Nanotechnology Nanotechnology involves ‘research and technological development at the atomic, molecular, or macromolecular levels, in the length scale of approximately 1 to 100 nm range, to provide a fundamental understanding of phenomena and materials at the nanoscale and to create and use structures, devices, and systems that have novel properties and functions because of their small and/or intermediate size’ per the official definition of the US National Nanotechnology Initiative [179]. 10.1 BFO Heteroepitaxial nano-structures Here we focus on multifunctional materials that have attracted increasing interest in recent years because of their potential applications in novel technological devices [180-181]. BiFeO3–CoFe2O4 is a multifunctional system, with ferroelectricity (BiFeO3) and ferrimagnetism (CoFe2O4) that couple with each other through a stress mediation. Haimei Zheng, et.al. [197,198] has recently demonstrated that BiFeO3–CoFe2O4 self-assembles into nanostructures with CoFe2O4 nanopillars heteroepitaxially embedded in a BiFeO3 matrix on (001) SrTiO3 substrates, which show considerable magnetoelectric coupling [182] in which the substrate orientation can be used to control the morphology of two phase nanostructures by inverting from an arrangement of spinel nanopillars in a perovskite matrix to perovskite nanopillars in a spinel matrix. The reported details of their research work are discussed below. The ferroelectric and magnetic properties as well as the degree of the coupling are critically dependent on the morphology of the nanostructures, including domain patterns and

shapes as well as the interfaces. In order to pursue the enhanced multifunctionality, significant effort has been made by researchers on understanding the growth mechanism and controlling the morphology of the nanostructures. The fundamental issue of heteroepitaxy is the morphology adopted by a crystalline material during nucleation on a substrate surface. Based on the surface energy terms, i.e., substrate surface energy , interface energy , and

surface energy of the crystalline phase, the equilibrium shape of a crystalline nucleus on a substrate can be determined using the Winterbottom construction [183]. The expected configuration of the crystalline nucleus on the substrate is a Wulff shape that has been cut off by the substrate, translated by

the signed distance from the origin where

is the wetting strength, which is the energy difference obtained by replacing the substrate surface with an interface and is expressed as,

In the BiFeO3–CoFe2O4 system, BiFeO3 has a distorted perovskite structure (R3c) [184] and CoFe2O4 has a cubic spinel structure (Fd3m). CoFe2O4 is characterized by the lowest surface energy of {111} surfaces, which is reflected in an equilibrium shape of an octahedron bounded by eight {111} facets [185, 186]. In contrast, most perovskite phases have the lowest energy surfaces of {001} surfaces and a corresponding equilibrium shape of a cube

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dominated by six {100} facets [187–190]. Because of the difference in the surface energy anisotropy in BiFeO3 and CoFe2O4 the two phases can display different growth modes on a substrate surface. They have estimated the morphology of the BiFeO3-CoFe2O4 nanostructures grown on a substrate surface using the Winterbottom construction. Fig-147 is the Winterbottom

construction of the BiFeO3 and CoFe2O4 phases nucleating on single crystal substrates as a function of the substrate orientation. They assumed a wetting strength of Dc = c2 for both phases. On a (001) oriented substrate, BiFeO3 wets the substrate completely and follows a layer-by-layer growth; in contrast, CoFe2O4 partially wets the substrate and forms islands bonded by four {111} surfaces.

Fig-147 Schematics of perovskite-spinel nanostructures on (100) and (111) surfaces

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In the consequent growth, each phase grows on top of its own phase, which leads to CoFe2O4 pillars embedded in a BiFeO3 matrix. On a (111) oriented substrate, CoFe2O4 displays layer-by-layer growth and BiFeO3 forms islands characterized with three {100} surfaces. At a later growth stage, BiFeO3 grows into pillars embedded in a CoFe2O4 matrix. When the substrate orientation is not parallel to the lowest energy surface of either phase, both BiFeO3 and CoFe2O4 phases could have comparable wetting configuration with similar nucleation barriers. In this case, both phases have island growth modes, for example, on a (110) oriented substrate. As a consequence of the competing wetting conditions, the film can form a maze pattern in which neither phase can be identified as the matrix or pillars. Based on the above inference, they have explored the growth of the BiFeO3 – CoFe2O4 nanostructures on SrTiO3 substrates with (001), (111), or (110) orientations. On each substrate, they have studied the effects of changing the volume fraction of the two phases (65:35, 1:1, and 33:67 of BiFeO3/ CoFe2O4) on the nanostructures. Because the morphologies of the BiFeO3 – CoFe2O4 nanostructures are critically dependent on the growth conditions, the growth kinetics of the nanostructures have also been studied. The magnetic and ferroelectric properties as well as the coupling of the BiFeO3 – CoFe2O4 nanostructures that depends on the morphologies of the nanostructures are also reported. The morphologies of the BiFeO3 – CoFe2O4 nanostructures (volume fraction of 1:1) grown on (001)-, (111)-, and (011)-oriented SrTiO3 substrates are shown in Fig-148. On the (001) SrTiO3 substrate, CoFe2O4 forms nanopillars embedded in a BiFeO3 matrix (Fig-148a–d).

Rectangular shaped CoFe2O4 nanopillars and {110}-type interfaces with the matrix was observed in Fig-148a). CoFe2O4 nanopillars change their shape across the film thickness, which is shown in the cross-sectional transmission electron microscopy (TEM) images and the schematic of a pillar (Fig- 148b–d). Within a 100 nm film thickness, the width of the CoFe2O4 pillar increases, resulting in an inverted cone shape at the substrate interface. The rest of the pillar maintains roughly the same lateral dimensions within the BiFeO3 matrix. There are sharp interfaces between the two phases as well as between the substrate and the two phases. No obvious interdiffusion was observed across the interface from energy dispersive spectroscopy (EDS) studies. On the top of the film, the CoFe2O4 pillar forms an island with characteristic facets. The facet planes are 54.7° with respect to the (001) plane indicating {111}-type facets. The structure of the matrix phase and the pillar phase is inverted in the nanostructures grown on a (111) SrTiO3 substrate. BiFeO3 forms triangular shaped nanopillars embedded in a CoFe2O4 matrix (Fig-148e–h). All the BiFeO3 nanopillars have the same crystallographic orientation and have {112} interfaces with the CoFe2O4 matrix. Similar inverted cone shaped BiFeO3 pillars at the substrate interface were observed. Fig-148f is a cross-sectional TEM image of a single BiFeO3 pillar from a 100 nm thick film. The lateral dimensions of the BiFeO3 pillar continuously increase from the substrate interface and reach a constant value at a certain film thickness. A high-resolution TEM image of the interface between a BiFeO3 pillar and matrix shows the change of the slope

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(Fig-148g). BiFeO3 pillars form islands with {100} facets on the top of the film. As it was predicted from the above Winterbottom construction, a maze pattern with entangled BiFeO3 and CoFe2O4 phases was observed on a (011)-oriented SrTiO3

substrate (Fig-148i–k). Fig-148i is a plan-view

TEM image showing the morphology of the nanostructures. The corresponding electron diffraction pattern shows only BiFeO3 and CoFe2O4 phases that are epitaxial to the substrate (Fig-148j). A cross-sectional TEM image shows that both phases grew from the substrate surface to the top of the film (Fig-148g).

Fig-148 Morphologies of BiFeO3 - CoFe2O4 nanostructures

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Unlike the nanostructures grown on (001) and (111) substrates, the two phases on the (110) substrate keep a relatively constant volume fraction across the film thickness. The “columnar” shape of both phases in the cross section suggests that a similar morphological pattern is maintained in the film close to the substrate interface and on the top of the film. The distinct different morphologies of the BiFeO3–CoFe2O4 nanostructures on (001), (110), and (111) oriented substrates are consistent with the Winterbottom construction in Fig- 147. The large difference in the surface energy anisotropy of the BiFeO3 and CoFe2O4 phases results in the different nucleation modes of the two phases on a substrate. On both the (100) and (111) oriented substrates, the wetting phase covers a large area of the substrate and the partially wetting phase forms islands at the initial nucleation stage. They have observed the early stage morphologies of the nanostructures in 5 nm film thickness, which shows the relatively small dimensions of the islands. The subsequent growth establishes the area fraction of the two phases close to the volume fraction of the two phases. The facets of the pillars close to the substrate interface prefer the lowest energy interfaces of the two phases. We have also observed that the facet is the (111) surface of the CoFe2O4 phase in Fig-148c. However, different facets have also been observed in other pillars. For the nanostructures grown on (110) substrates, because the two phases have similar wetting conditions (and similar island growth modes), the area fraction of the two phases is established at an early stage and there is no distinct change in their area fraction within the

film thickness. The atomic force microscopy (AFM) phase-contrast images and their schematics show the topographic facets of BiFeO3–CoFe2O4 nanostructures with a 1:1 volume fraction grown on (001), (111), and (110) oriented SrTiO3 substrates (Fig-149).

Fig-149AFM images of BiFeO3 -CoFe2O4 nanostructures The facets and interfaces of islands have been identified based on both AFM and TEM studies. On the (001) oriented substrate, CoFe2O4 forms islands and BiFeO3 is flat at the film surface. CoFe2O4 islands have (001) end facets and (111), (11), ( 1) and ( 11) side facets. The interfaces with the BiFeO3 matrix are {110} planes. The aspect ratio of the islands, h/a (defined in Fig-149a), is

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dependent on the growth temperature (T) and growth rate (v). On the (111) substrate, BiFeO3 forms islands and CoFe2O4 has a flat surface. BiFeO3 islands have a (111) end facet (with a negligible area fraction) and (001), (010), and (100) side facets. The interfaces with the CoFe2O4 matrix are {112} planes. On the (110)-oriented substrate, both BiFeO3 and CoFe2O4 phases form facets. BiFeO3 mostly forms hut-shaped islands with the (110) end facet and the (001), (010), (00), and (100) side facets. The facets of the CoFe2O4 phase are {111} type; however, they are not clearly identified from Fig-149c. BiFeO3 has a higher geometry than CoFe2O4, which is probably because of the slight difference in their wetting properties on the (110) substrate. The observed topographic

shape and facets of the BiFeO3–CoFe2O4 nanostructures agree very well with the Winterbottom construction based on the surface energy isotropy. It is further found that the volume fraction of the two phases did not introduce distinct changes in the morphologies of the BiFeO3–CoFe2O4 nanostructures. For example, irrespective of the volume fraction, CoFe2O4 forms nanopillars in a BiFeO3 matrix on a (001)-oriented substrate, BiFeO3 forms nanopillars in a CoFe2O4 matrix on a (111)-oriented substrate, and BiFeO3 and CoFe2O4 form a maze pattern on a (110)-oriented substrate (Fig-150). So, it is clear that differences in anisotropic strain, surface stress, and surface diffusivity [192] can result in differences in the morphologies of the nanostructures with different compositions.

Fig-150 AFM images of BiFeO3 -CoFe2O4 nanostructures

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Size and Spacing of nanostructures The size and spacing of nanostructures are controlled by their growth kinetics (e.g., growth rate, temperature), which will be discussed below. From Fig-150 the differences in the details of the morphologies are observed in the nanostructures with different volume fractions. The fact that the volume fraction of the two phases does not change their growth modes there by validating the growth model based on surface energy anisotropy using the Winterbottom construction. At growth temperatures in the range of 550–700°C and growth rates of 0.5–8 nm / min, the dimensions of the BiFeO3–CoFe2O4 nano-structural features increase as the growth temperature increases and decrease as the growth rate increases. A lower growth temperature and/or a higher growth rate induce supersaturated perovskite type phases which are metastable. These trends are applicable to all BiFeO3–CoFe2O4 nanostructures with different volume fractions on differently oriented substrates. We focus on the kinetics of BiFeO3–CoFe2O4 nanostructures with a volume fraction of 1:1 grown on (001) substrates. At a constant growth rate of 4 nm min–1, the lateral size of the CoFe2O4 pillars versus the growth temperatures is plotted in Fig-151a. The lateral size of the pillars (ln(d)) decreases as the growth , which can be fitted into a linear plot, ln(d) ∞ 1/T. For comparison, we also plotted the temperature dependence of

CoFe2O4 nanopillar size from a BaTiO3– CoFe2O4 system. [193]

Fig-151 Temperature dependence of BiFeO3 - CoFe2O4 It is interesting that a similar trend and fitting has been observed in both cases. Fig-151b plots the lateral size of the CoFe2O4 pillars versus the growth rates at a constant growth temperature of 700 °C. The lateral size of the pillars (d) decreases as the growth rate increases, which can be fitted into a second order plot, d2∞1/v. Diffusion process model The growth of the BiFeO3–CoFe2O4 nanostructures can be modeled as a diffusion process. In a steady-state growth of the nanostructures, the multi-component species come to the film surface and phase-separate

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into nanostructures. The nanostructures are formed at the film surface and subsequently incorporated into the bulk film. Transport is limited to the advancing solid–vapor interface, and diffusion within the bulk film is negligible. This has been confirmed by the result that no obvious changes were observed after the nanostructures were annealed at the film growth temperatures for 10 hours. For the 2D diffusion, we simply use the standard equation

This analysis based on diffusion agrees well with the experimental observations in Fig-151. The temperature dependence of the CoFe2O4

nanopillars for the BiFeO3– CoFe2O4 system gives activation energy of 0.83 eV, yielding activation energy for diffusion of 1.66 eV. Such activation energy for diffusion is close to the value (1.56 eV) calculated for the BaTiO3– CoFe2O4 nanostructures. They further calculated the activation energy from the temperature dependence of the size of the BiFeO3 nanopillars (also a linear plot) in the BiFeO3–CoFe2O4 nanostructures grown on (111) substrates. A smaller activation energy value (0.58 eV) for diffusion was been obtained. The calculated activation energy corresponds to the diffusion barrier for the formation of nanopillars. For example, the relatively high volatility of Bi may induce lower activation energy of the BiFeO3 nanopillars. Step growth is unlikely to be the limiting factor for the growth of BiFeO3–CoFe2O4 nanostructures. This is based on the fact that the activation energy for CoFe2O4 nanopillars are similar for both BiFeO3–CoFe2O4 and BaTiO3–CoFe2O4 nanostructures but the facets of the CoFe2O4 nanopillars are very different (CoFe2O4 islands are in a dome shape in BaTiO3–CoFe2O4 nanostructures[191-193] and they have distinct {111} facets in BiFeO3–CoFe2O4 nanostructures). A similar diffusion mechanism was used to understand the phase separation in Al–Ge films by Atzmon and co-workers, [194, 195] from which the calculated activation energy is consistent with the surface diffusion barrier of Al and Ge. The activation energies for CoFe2O4 were relatively high (above 1 eV) and only a slight difference was observed in the

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values for BaTiO3– CoFe2O4 and BiFeO3–CoFe2O4 nanostructures, although there is about 200 °C difference in the growth temperature. For the growth of nanostructures with different structures and multiple components, the surface steps, exchange mechanisms, [196] and other factors may have to be considered as diffusion barriers. In summary, they have reported that the BiFeO3– CoFe2O4 nanostructures with volume fractions of 65:35, 1:1, and 33:67 grown on SrTiO3 substrates with (100), (111), and (110) orientations. Unique morphologies, obtained irrespective of the volume fraction, was observed on each substrate. The dependence of the morphologies of the BiFeO3–CoFe2O4 nanostructures on the substrate orientations is attributed to the different growth modes of the two phases. They also studied the growth kinetics of the BiFeO3–CoFe2O4 nanostructures. A higher growth temperature and/or a slower growth rate induce larger-sized nanopillars. The BiFeO3–CoFe2O4 is a model system for the growth and control of two-phase nanostructures. The BiFeO3–CoFe2O4 nanostructures are ideal for the future study on the morphological dependence of magnetoelectric coupling.

Conclusion Multiferroic material offers a great prospect for the development of next generation multifunctional devices to meet the growing demand of Microelectronics and Nanotechnology. The contributions of scientific communities positively ascertain the industrial application of Multiferroic BFO thin films in the very near future by the following findings. o Heteroepitaxial growth of these materials

in to thin films allows, controlling and engineering the properties and functionalities.

o Growth and investigation of vertical nanostructures confirm the strong epitaxy mediated coupling, but emphasizes the need to break time reversal symmetry to switch magnetism.

o Strong exchange coupled heterostructures have been created.

o Promising indication for the possibility of controlling ferromagnetism with an electric field using BFO thin films through switching and reduction of leakage currents.

o BiFeO3 is a green material (lead-free) ferroelectric / piezoelectric, very promising for memory / piezo / multifunctional applications, and a potential candidate to replace the hazardous PZT.

o Role of defects has to be investigated further to understand their contribution.

Acknowledgement It is indeed a great pleasure in thanking professor Ramesh Ramamoorthy for guiding me to this valuable gold mine of knowledge about Multiferroics and its allied subjects.

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