Introduction to Multiferroics

Multiferroics: An Introduction

R.N.P. Choudhary and S. K. Patri

Department of Physics and Meteorology, Indian Institute ofTechnology Kharagpur - 721 302, India

Abstract. Multiferroics: the multifunctional materials exhibit the entwined nature between the two distinct phenomena of ferroelectricity and ferromagnetism, which allow them to utilize for novel device concepts that would not be attainable by either ferroelectric or ferromagnetic materials. Magnetic and ferroelectric materials are time-honoured research subjects which have led to new discoveries, both scientific and technological. Multiferroic compounds are the source of magnetoelectric (ME) effects that are strong enough to induce magnetic or electric phase transitions, thus exerting ME phase control. The giant response can be generated by the presence of exceptionally large magnetic and/or electric fields in matter, which are the result of the long-range ordering. In this sense the ME effect in multiferroics is 'large' if the ME contribution corresponding to the free energy of the system is large. Due to their interesting physical, chemical, and mechanical properties, these materials have been used to realize a vast number of devices ranging from giant devices like electrical transformers to tiny devices like sensors, used in integrated circuits or as storage devices. Furthermore, these materials are likely to offer new kinds of devices and functionality, because of their size-dependent physical and chemical properties, which have motivated a lot of current research activity in the area of ferroelectric and magnetic materials. In particular, advances in atomic and nanoscale growth and characterization techniques have led to the production of modern ferroelectromagnetic materials that reveal a range of fascinating phenomena. These phenomena derived from the fact that electrons have spin as well as charge, giving an extra level of complexity to the physics, and an extra degree of freedom in device design. Magnetoelectric coupling between electric and magnetic order parameters has been theoretically predicted, and there is intense interest in its implementation in device architectures taking advantage of these properties. Multiferroics may be in the form of single-phase, exhibit mulitferroicity generally at low temperatures and in a composite form as a product property of a composite phase consisting of a magnetostrictive and a piezoelectric material. Hence, the search continues for new single-phase and composite multiferroic materials that exhibit high ordering temperatures, high coupling constant, low dielectric loss and low leakage current.

Keywords: Magnetoacoustic effects. Transition-metal compounds. Composite materials, antiferromagnetics PACS: 72.55.+S, 72.80.Ga, 72.80.Tm, 75.50.Ee

INTRODUCTION

Multiferroics with multiple (charge, spin) order parameters; offer an exciting way of coupling between electronic and magnetic ordering [1]. In these materials, a weak magnetoelectric interaction can lead to spectacular cross-coupling effects when it induces electric polarization in a magnetically ordered state. Most of the work on these

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materials on control charges by applied magnetic fields and spins by apphed electric field, are useful to construct new type of multifunctional devices. It was proved to be a difficult problem towards bringing ferroelectricity and magnetism together; as these two contrasting order parameters turned out to be mutually exclusive [2-5]. Further, it was found that the simultaneous presence of electric and magnetic dipoles does not guarantee strong coupling between the two, as microscopic mechanisms of ferroelectricity and magnetism are quite different and do not strongly interfere with each other [6, 7]. Thus, there are very few materials which display the multiferroic properties [8-16]. The rareness of the ferroelectromagnets is ascribed to the fact that ferroelectricity and ferromagnetism are incompatible (e.g. ferromagnetic perovskites such as (La, Sr) MnOs and (La, Sr)Co03 are generally metalhc, while ferroelectric perovskites are insulator). The scarcity of multiferroics has resulted in the various obstacles for their utilization in multifaceted potential apphcations. Thus, some challenges developed in order to have multiferroic at moderate temperature with high coupling coefficient for potential device application. From the physical point of view multiferroics present an extremely interesting class of systems and problems. There are essentially two conditions for occurrence of this phenomenon: (i) microscopic condition, which determines the possibility to combine in one system both magnetic and ferroelectric properties, and (ii) the coupling between different degrees of freedom or order parameters. Different techniques can be adopted for the design of multiferroicity in materials; including doping of appropriate elements in a given host material which results in inducing the functional properties. In this paper, we discuss the origin and cause of multiferroicity, previous works on some well known family and some recent development on some multiferroics.

REQUIREMENTS FOR MULTIFERROICITY

By definition, for a material to be a magnetoelectric multiferroic; it must be simultaneously ferromagnetic and ferroelectric. Therefore, its allowed physical, structural and electronic properties are restricted to those which occur both in ferromagnetic and in ferroelectric materials. Basic requirement for the effect is the coexistence of magnetic and electric dipoles. The exceedingly rare occurrence of multiferroicity is due to the exclusiveness of partially filled atomic orbitals, for magnetic dipoles or moments and the occurrence of local electric dipoles, which are typically associated with the presence of either empty d-shells and/or an electron lone-pair configuration. In fact, the materials exhibiting the ME effect can be classified as: single phase and composites. Single phase materials will have an ordered structure. The ME effect arises in this class of materials due to the local interaction between the ordered magnetic and ferroelectric sublattices. The conditions for the occurrence of ferroelectricity and magnetic order in the same material often accompanied by ferroelasticity which implies (a) the presence of adequate structural building blocks permitting ferroelectric-type ionic movements, (b) magnetic interaction pathways, usually of the superexchange type, and (c) the fulfillment of symmetry conditions [17]. In composite materials, a suitable combination of two phases can yield the

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desirable properties such as a combination of piezomagnetic and piezoelectric phases or a combination of magnetostricitve and piezoelectric phases. The ME effect can also be reahzed by couphng the thermal interaction in pyroelectric-pyromagnetic composites. The ME coefficient of composites is more than a hundred times that of single-phase (ME) materials [18].

PREVIOUS WORK

To achieve rich functionality; one of the very promising approaches to create novel materials is to combine different physical properties in a single material. Two independent events mark the birth of the ME effect: (i) in 1888 R'ontgen discovered that a moving dielectric became magnetized when placed in an electric field [19], which was followed by observation of the reverse polarization effect of a moving dielectric in a magnetic field (17 years later) [20], and (ii) in 1894, Curie pointed out that it would be possible for an asymmetric molecular body to polarize directionally under the influence of a magnetic field [21]. The term 'magnetoelectric' was coined for the first time by Debye |̂ 22], a few years after the first (unsuccessful) attempt to demonstrate the static ME effect experimentally [23, 24]. In spite of Curie's early recognition of symmetry being a key issue in the search for ME behavior, many decades passed until it was realized that the ME response is only allowed in time-asymmetric media [25]. Such violation of time-reversal symmetry can extrinsically occur through application of an external magnetic field or movement as in the historic experiment conducted by R'ontgen, or intrinsically in the form of long-range magnetic ordering. Dzyaloshinskii [26] was the first to show violation of time-reversal symmetry explicitly for a particular system (antiferromagnetic Cr^O,), which was soon followed by experimental confirmation of an electric-field-induced magnetization [27] and a magnetic field- induced polarization [28, 29] in Cr^O,.

The search for ferromagnetism-ferroelectricity in the same material began in Russia in the 1950s, with the replacement of some of the d° B cations in ferroelectric perovskite oxides by magnetic d" cations [30, 31]. Later, Landau and Lifshitz [32] showed from symmetry considerations that a linear ME can occur in magnetically ordered crystals. Subsequently, Dzyaloshinskii [33], on the basis of theoretical analysis, predicted the existence of the ME effect in antiferromagnetic Cr203. This was confirmed by Astrov [34] by measuring the electric field induced magnetization and later by Rado and Folen [28, 35] by detection of the magnetic field-induced polarization. Smolenskii and Loffe [36] in 1958 synthesized the antiferromagnetic-ferroelectric perovskite ceramic Pb(Fei/2Nbi/2)03 (PEN). The first synthetic ferromagnetic ferroelectric material, (l-x)Pb(Fe2/3Wi/3)03 - x Pb(Mgi/2Wi/2)03, was produced in the early 1960s using this approach. Here the Mg^^ and W^̂ ions are diamagnetic and cause the ferroelectricity, and the formally d̂ Fe^^ ions are responsible for the magnetic ordering. Other examples include (a) B-site ordered Pb2(CoW)06 which is ferroelectric and ferromagnetic, (b) B-site disordered Pb2(FeTa)06 [37] which is ferroelectric and antiferromagnetic [38, 39]. Because of dilution of the magnetic ions, these materials have rather low Curie or N'eel

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temperatures. The attempts to combine in one system both the (ferro)magnetic and ferroelectric (FE) properties started in 1960's, predominantly by two groups in then the Soviet Union: (i) the group of Smolenskii in St.Petersburg (then Leningrad) [40, 41] and (ii) by Venevtsev in Moscow [42]. Materials combining these different "ferroic" [43] properties were later on called "multiferroics" [44]. Since then the probability of new techniques has been reahzed for such novel materials for very promising applications in diverse fields. [45-48]. In composite materials, the ME effect is realized by using the concept of product properties introduced by Van Suchetelene [49]. In 1978, Boomgaard [50] outhned the conceptual points inherent to the ME effect in composites. These can be summarized as follows: (i) two individual phases should be in equilibrium, (ii) mismatching between grains should not be present, (iii) magnitude of the magnetostriction coefficient of piezomagnetic or magnetostrictive phase and magnitude of the piezoelectric coefficient of the piezoelectric phase must be greater, (iv) accumulated charge must not leak through the piezomagnetic or magnetostrictive phase and (v) deterministic strategy for poling of the composites. The basic ideas underlying composite electroceramics can be classified into three categories: (i) sum properties, (ii) product properties, (iii) combination properties [49-53]. On the basis of point group symmetry, Aizu have enlisted a number of possible species of ferroic crystals, their number of orientation states, and their relationships to ferromagnetism, ferroelctricity, and ferroelasticity [54]. In 1980, Ismailzade et al. [55] reported the presence of linear ME effect in BiFeOs, a compound of antiferromagnetic-feroelctric nature. Its combination with bismuth titanate and barium titanate forms a family with Aurrivilius structure (Bi4Bin,. sTisFcmjOsm+s) show coexistence of ferroelectric and magnetic nature up to high temperatures [56]. Schmid [57] has worked onboracites belonging to the large crystal structure family with a general formula M3B7O13X, where M stands for a bivalent cation of Mg^ ,̂ Cr̂ ,̂ Mn^ ,̂ Fe^^, Co^ ,̂ Ni^^, Cu^ ,̂ Zn^ ,̂ etc. and X stands for a monovalent anion like OH", F", CI', Br", I" or NO^'.

SOME RECENT WORKS

Since the discovery of multiferroic materials, several attempts were made to study the magnetoelectric effect in different compounds of many structural families. Unfortunately, because of some inherent properties (i.e., leakage current, small coupling coefficient, low temperature phase transition, structural distortion and stability), the industrial apphcations of these materials were very much limited, and hence not much attention was paid. The strucutural classification of magnetoelectrics include perovskies, hexagonal manganites, boracites, rare earth doped manganites, layered perovskites etc. Though the existence of weak magnetoelectric (i.e., coupling between magnetic and electric ordering in a monophase distorted structure) effects in Pb-based complex perovskites, Pb (Fei/2Nbi/2)03, were known for few decades, recent discovery of the effect in environmental friendly (i.e. free from Pb) rhombohedrally distorted BiFeOs (BFO) much above room temperature (i.e., TN = 650 K, Tc=IIOOK) has attracted much attention of researchers to design and develop new/modified

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magnetoelectric materials with high ME coefficients for multifunctional apphcations. In view of the above, we have also designed and developed (ceramics and composites) a few Pb/Bi based ferromagnetoelectrics for better understanding, and enhancement of the ferroelectric/ferromagnetic and couphng properties of materials for possible devices.

(a) Pb(Fei/2Nbi/2)03

Lead iron niobate Pb(Fei/2Nbi/2)03 [PFN] belongs to the series of complex perovskite compounds discovered at the end of the 1950s [58]. It was considered to be ferroelectrically and antiferromagnetically ordered below a certain temperature. Its (dielectric) Curie temperature is around 383 K and the antiferromagnetic order begins at about 143 K. In view of the importance of these materials, there have been intensive studies both on single crystals [59-63] and ceramics synthesized using different methods [64-72]. Due to their exceptionally high dielectric constant [73], PFN ceramics are one of the most attractive candidates for making multilayer capacitors. The presence of magnetic Fe^^ ions in octahedral (Bi) sites of (ABiBii)03 perovskite lattice makes PFN an interesting single-phase multiferroic material. Majumdar et. al [74] surprisingly have observed ferromagnetic ordering at room temperature in their sol-gel-derived PFN powders. It was assumed that any other segregated phase such as Fe304 is responsible for the observed room-temperature ferromagnetic ordering. In a disorder perovskite system such as PFN, no cation ordering is expected in between Fe^^ and Nb^^ cations. But again it was examined that Fe^^-0-Fe^^ spins are no longer collinear and was concluded that the room temperature behavior is not due to segregated phase, but as a result of small canting of spins to yield weak ferromagnetic behavior.

b) Ba Modified Pb(Fei/2Nbi/2)03

Due to the presence of Fe^^, O^" ion vacancies, PFN and related materials (ME) have high-leakage current which limits the materials for any meaningful devices with higher sensitivity [75-77]. In order to obtain suitable materials for devices, several attempts have been made to design and develop materials by substituting isovalent/nonisovalent elements/atoms at the B-site [78] or fabricating composites of 2-3 components/oxides. In view of the above, the effect of Ba substitution at the Pb-sites i.e., (i.e., (Pbi-xBax)(Fei/2Nbi/2)03 (PBFN) with x = 0, 0.05, 0.07) have been synthesized by high-energy ball milhng with particles of nanometer size. A decrease in phase transition temperature was observed in Ba modified PFN material in comparison to PFN, which may be due to intergranular stresses, ferroelectric domain sizes, compositional inhomogeneities, and Ba distribution at the Pb^^ site [79]. The phase transition behavior in PFN provides a signature of a normal transition of the paraelectric to the ferroelectric phase type. However on increasing Ba content to x = 70 wt%, a cross-over of phase transition from normal to relaxor ferroelectric was

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100 200 300 400 SCO eoo rut) BOO T(K)

100 150 JOO 250 300 350 400 450 500 550 T(K)

FIGURE 1. Temperature dependence of relative dielectric constantEjOf Pbi-jBa^fFeo.sNbosJOs with {a)x = 0, (b) X = 0.05, and (c) jc = 0.07 at frequencies 100 kHz (n), 250 kHz (o), 500 kHz (A), IMHz (+) [Ref 79].

fa) 3

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FIGURE 2. Variation of (a) magnetization vs. magnetic field at 300 K, (b) magnetization vs. temperature at 100 Oe, and (c) magnetization vs. magnetic field at 2K of Pbi-jBajfFeo.sNbo.sJOs {x = 0, j<: = 0.07)[Ref 79]

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observed (Fig.l). It is indeed an interesting and new observation on PFN [20]. A weak magnetization in PBFN (Fig. 2) is observed which may be largely related to structural distortion of the parent structure, since the magnetization is crucially dependent on the symmetry of the system [80, 81]. A stable antiferromagnetic G-type phase of PFN is related to ferroelectric tetragonal distortion with large shift of the Pb atom [79].

(d) BiFeOs

Recent discovery of ferromagnetoelectricity in BiFeOs (BFO) at high temperature (Tc = 1 lOOK and TN= 630K) has attracted much attention of researchers to design and develop (single crystals, thin films and ceramic structure) eco-friendly, toxic free modified BFO and/or the search of new materials with high magnetoelectric coefficient above room temperature useful for multifunctional devices. Although rhombohedral BFO has been studied extensively since 1960s, the electrical properties of the pure BFO R-phase have been rarely reported due to its high leakage current, which may be originated from uncertain oxygen stoichiometry, high defect density and poor sample quality [82-84]. BFO is reported to exhibit eight structural transitions and a weak ferromagnetic ordering [85-86]. However, it is an antiferromagnet with a spatially modulated spin structure [87], which does not allow net magnetization and also inhibits observation of the linear magnetoelectric effect. Spontaneous magnetization in BFO can be induced by the substitution of Fe^^ by other transition metal ions [88]. Again B-site ions substitution decreases magnetic ordering temperature drastically [89] thus hampering their apphcation at room temperature.

(e) La substituted BiFeOs

In order to solve few inherent problems of multiferroics in general, and BFO in particular, such as high leakage current, structural instability, formation of multiphase system during synthesis, etc. [90], and to increase the dielectric constant, reduce the leakage current, and hence to improve the ferroelectric polarization in BFO, some attempts have been made including a small doping at the Bi/Fe sites. There are also several reports on the synthesis of sohd solution of BFO with other perovskite structures (with different concentrations), which has enhanced electrical and magnetic properties of BFO. Several attempts have been made in recent years including (a) fabrication of composites, (b) use of different synthesis process, and (c) preparation of thin films and single crystals. Encouraging results have been obtained on substitution of La at the Bi-site and/or some isovalent elements at the Fe-site of BiFeOs [91-94]. It was observed that on La substitution at the Bi site (BFOL) ehminates the small impurity phase of BiFeOs and stabilized the crystal structure into hexagonal symmetry. However, the dielectric properties (Fig. 3 & 4) were not enhanced by La substitution, but systematic increase in both the ferroelectric and ferromagnetic properties (Fig.5) were achieved. With the increase in La concentration, the magnetic

269


parameters increase and this may be due to the doping, which increase the magnetic anisotropy and magnetization [95].

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FIGURE 3. Variation of dielectric constant with temperature of BFO and BFOL ceramics at 100 kHz and 1 MHz. [Ref 95]

FIGURE 4. Variation of loss tangent with temperature of BFO and BFOL ceramics at 100 kHz and 1 MHz. [Ref 95]

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270


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H (kOe) FIGURE 5. Magnetic hysteresis loops of BFO and BFOL samples. The insets show the details of the

loops for lower fields [Ref 95]

(g) Y Substituted BiFeOj

The orientation of magnetic moments, magnetic moment canting and the spiral spin structure attributed to weak magnetic characteristics of BFO [96]. Bi substitution by rare earth ions improves magnetic properties attributed to structural phase transition, resulting in the release of latent magnetization [97-98]. Mishra et al [99] have substituted Y at Bi site. Substitution of Y at the Bi site of BFO (BYFO) has caused compositionally driven structural change and facilitates single-phase formation of the material by suppressing the pyrochlore phase. This has led to a considerable change in ferroelectric and magnetic properties of BFO. Up to 10% Y substitution there is a significant reduction of low frequency dispersion in both permittivity and loss pattern, indicating a considerable control of dc conductivity thereby enhancing ferroelectric behavior. However, with Y substitution at the Bi site, a remarkable increase in macroscopic magnetization and the switching behavior in low fields which are the most interesting observation of the field dependence of magnetization of BYFO samples, which makes them different from rare-earth substituted BFO. This unique magnetic behavior along with the existence of ferroelectricity in these samples makes them probable candidates for obtaining better magnetoelectric coupling.

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(i) BiFe03-Bi4Ti30i2 Composites

Among the different ferroelectromagnetic compounds mentioned above, special classes of bismuth layered structure ferroelectromagnetic (BLSFEM) compounds, of Aurivillius family [100,101], are found to be interesting because of their crystallographic anisotropy. From the earlier reports, the three-layered compound Bi4Ti30i2 has monoclinic symmetry at room temperature with a ferroelectric transition at 675°C [102], while BiFeOs is ferroelectric and also antiferromagnet with rhombohedral symmetry at room temperature Combining Bi4Ti30i2 with n moles of BiFeOs (BFTO), where n = integer, perovskite compounds with four, five, six, seven, and eight layers (i.e. BisFeTisOis, Bi6Fe2Ti30i8, Bi7Fe3Ti302i, Bi8Fe4Ti3024 and Bi9Fe5Ti3027) can be synthesized [103]. Rare-earth (Gd^ ,̂ La^ ,̂ Sm^ ,̂ Dy^^) doping/substitution at the Bi site in these layered compounds have shown interesting magnetic and ME properties [104-106].

CONCLUSIONS

In reviewing the growth, development and properties of multiferroics, it is worth discussing the issues of creating new materials and understanding the origin of multiferroism in them. The mechanisms of the coupling between ferroelectric and magnetic orders are the most challenging aspects. Nowadays, multiferroic is a topic of great interest, both in science and technology, because of their interesting properties and dimensionality for novel advanced devices. Beginning with a brief summary of the history of the ME effect since its prediction in 1894 by Curie, the paper focuses on the approaches to ME effect, its chronological development and recent works with possible future applications. At present the multiferroic and its related phenomena are primarily interesting from the point of view of basic research rather than applications. The number of multiferroic compounds is still small, and a continued research is going on to know the fascinating intriguing features of these materials in different forms (single crystals, composites and thin films) and only very few multiferroics with ME behavior at room temperature are known yet. ME behavior in several multiferroics have been understood and precise criteria for the search of new multiferroics have been given and future research on their improvement and tuning of their ME performance should drive multiferroics much closer to practical apphcations in the near future. In addition, exploration of new classes of multiferroic materials is on progress in our ongoing research.

REFERENCES

1. S.W. Cheong and M. Mostovoy, Nat. materials 6, 13-20 (2007). 2. F. Jona and G. Shirane, Ferroelectric Crystals, Dover, New York, 1993. 3. H. Schmid, Ferroelectrics 162, 317-338 (1994). 4. N. A Hill, J. Phys. Chem. B 104, 6694-6709 (2000).

272


5. M. E. Lines and A. M. Glass, Principles and Applications of Ferroelectrics and Related Materials, Oxford Univ. Press, Oxford, 2001.

6. T. Katsufuji, S. Mori, M. Masaki, Y. Moritomo, N.Yamamoto and H. Takagi, Phys. Rev. B 64, 104419/1-104419/6(2001).

7. T. Kimura, S. Ishihara, H. Shintani, T. Arima, K.T. Takahashi, K. Ishizakaand Y.Tokura, Phys. Rev. B 68, 060403/1-060403/4 (2003).

8. W. Prelher, M.P. Singh and P. Murugavel, J. Phys., Condens. Matter 17, R803-R832 (2005). 9. T. Lottermoser, T. Lonkai, U. Amann, D. Hohlwein, J. Ihringer and M. Fiebig, Nature 430, 541-544

(2004). 10. M. Fiebig, Th. Lottermoser, D. Frhlich, A.V. Goltsev and R.V. Pisarev, Nature 419, 818-820

(2002). 11. T. Kimura, S. Kawamoto, I. Yamada, M. Azuma, M. Takano and Y. Tokura, Phys. Rev., B 67,

180401-4(2003). 12. G.A. Smolenskii, V.A. Bokov, V.A. Isupov, V.N. Krainik and G.H. Nedlin, Helv. Phys. Acta 41,

1187-1198(1968). 13. T. Kimura, T. Goto, K. Thizaka, T. Arima and Y. Tokura, Nature 426, 55-58 (2003). 14. B.B. van Aken, T.T.M. Palstra, A. Filippetti and N.A. Spaldin, Nat. Mater. 3, 164-170 (2004). 15. N.A. Hill and K.M. Rabe, Phys. Rev., B 59, 8759-8769 (1999). 16. R. Seshadri and N.A. Hill, Chem. Mater. 13, 2892-2899 (2001). 17. H. Schmid, Ferroelectrics 161, 1-28 (1994). 18. J. Ryu, S. Priya and K. Uchino and H. Kim, J. Electroceram. 8, 107-119 (2002). 19. W C. Rontgen, Ann. Phys. 35, 264-270 (1888). 20. H. A. Wilson, Phil. Trans. R. Soc. A204, 129-136 (1905). 21. P.Curie, J. Physique 3c series, 393-415 (1894). 22. P. Debye, Z. Phys. 36, 300-301 (1926). 23. A. Perrier and A.J. Staring, Arch. Sci. Phys. Nat 4, 373-382 (1922). 24. A. Perrier and A.J. Staring, Arch. Sci. Phys. Nat 5, 333-360 (1923). 25. L.D. Landau and E.M. Lifshitz, Electrodynamics of Continuous Media, Oxford: Pergamon, 1960. 26.1. E. Dzyaloshinskii, Sov. Phys.-JETP, 10, 628-629 (1959). 27. D.N. Astrov, Sov. Phys.-JETP, 11, 708-709 (1960). 28. G.T. Rado, V.J. Folen, Phys. Rev. Lett. 7, 310-311 (1961). 29. V.J. Folen, G.T. Rado, E.W. Stalder, Phys. Rev. Lett.6, 607-608 (1961). 30. G.A. Smolenskii and A.I. Agranovuskaya, Sov. Phys. Solid State 1, 1429-1437 (1959). 31. G.A. Smolenskii, V.A. Isupov, N.N. Krainik, A.I. Agranovskaya, Isvest. Akad.

NaukSSSR, Ser. Fiz 25, 1333-1339 (1961). 32. L.D.Landau and E.Lifshitz, Electrodynamics of Continuous Media, Addison-Wesley Transition,

1958. 33. I.E. Dzyaloshinskii, Sov.Phys.- JETP, 37, 628-629 (1960). 34. V.A. Bokov, I.E. Myl'nikova and G.A. Smolenkii. Sov. Phys. JETP 15 (1962), 447- 452. 35. G.T.Rado, Phys. Rev. Lett. 13, 335-337 (1964). 36. G.Smolenskii, V.A.loffe, CoUoque International du Magnetisme, Communication No. 71, 394-424

(1958). 37. W. Brixel, J.-P. Rivera, A. Steiner and H. Schmid, Ferroelectrics 79, 201-204 (1988). 38. D.N. Astrov, B.I. Al'shin, Y.Y. Tomashpol'skii and Y.N. Venevtsev, Sov. Phys. JETP 28, 1123-

1128(1969). 39. L.A. Drobyshev, B.I. Al'shin, Y.Y. Tomashpol'skii, Y.N. Venevtsev, Sov. Phys. Ciyst. 14, 634-638

(1970). 40. G.A.Smolenskii., "Segnetoelectrics and antisegnetoelectrics", Nauka Publ., Leningrad, 1971 41. Y. Tokura, J. Magn. Mag. Mater. 310, 1145-1150 (2007). 42. Y.N.Venevtsev and V.V.Gagulin, Ferroelectrics 162, 23-31 (1994). 43. K.Aizu, Phys.Rev.B 2, 754-772 (1970). 44. H.Schmid, Ferroelectrics, 162, 317-338 (1994). 45. T.Kimura, Nature 426, 55-58 (2003).

273


46. N.Hur, Nature 429, 392-395 (2004). 47. G. Lawes, A.B. Harris, T. Kimura, N. Rogodo, R.J. Cava, A. Aharony, O. E. Wohlman, T. Yildirim,

M. Kenzelmann, C. Broholm, and A.P. Ramirez, Phys. Rev. Lett.95, 087205/1-087205/4 (2005). 48. T.Kimura, G.Lawes and A.P.Ramirez, Phys. Rev. Lett. 94, 137201/1-137201/4 (2005). 49. J.Van Suchtelen, Phillips Res. Rep., 27, 28-37 (1972). 50. J.V.Boomgaard and R.A.J. Bom, J. Mater. Sci., 13, 1538-1548 (1978). 51. D.N. Astrov, Sov. Phys.-JETP, 13, 729-733 (1961). 52. R.E. Newnham. Ferroelectrics, 68, 1-32 (1986). 53. K.Uchino, Ferroelectric Devices, Marcel Dekker, New york, 2000. 54. K.Aizu, Phys. Rev. B. 2, 754-772 (1970). 55.1.H.Ismailzade, V.I. Nestemko, F.A.Mirishil and P.G.Rustamov, Phys, Status Sohdi. 57, 99-103

(1980). 56. R.S.Singh, T. Bhimasankaram, G.S.Kumar andS.V.Suryanarayana, Solid State

Commun., 91, 567-569 (1994). 57. H.Schmid, Bull. Mater. Sci. 17, 1411-1414 (1994). 58. V.A. Bokov, I.E. Myl'nikov and G.A. Smolensikii, Sov. Phys., Usp.42, 643-646 (1962). 59.1.H. Brunskill, P. Tissot and H. Schmid, Thermochim. Acta 49, 351 (1981). 60.1.H. Brunskill, R. Boutellier, W. Depmeier and H. Schmid, J. Ciyst. Growth 56, 541-546 (1982). 61.1.H. Brunskill, H. Schmid and P. Tissot, Ferroelectrics 37, 547-550 (1981). 62. T. Watanabe and K. Kohn, Phase Transit. 15, 57-68 (1989). 63. V. Bonny, M. Bonin and P. Sciau, Solid State Commun. 102, 347-352 (1997). 64. M.H. Lee and W.K. Choo, J. Appl. Phys. 52, 5767-5773 (1981). 65. S.A. Mabud, Phase Transit. 4, 183-200 (1984). 66. M. Yokosuka, Jpn. J. Appl. Phys. 32, 1142-1146 (1993). 67. Y. Ikeuchi, S. Kojma and T. Yamamoto, Jpn. J. Appl. Phys. 35, 2985-2988 (1997). 68. X.S. Gao, X.Y. Chen, J. Yin, J. Wu and Z.G. Liu, J. Mater. Sci. 35, 5421-5425 (2000). 69. S. Ananta, N. Thomas, J. Eur. Ceram. Soc. 19, 155-163 (1999). 70. Y. Yoshikawa, J. Eur. Ceram. Soc. 19, 1037-1041 (1999). 71. S. Ananta, N. Thomas, J. Eur. Ceram. Soc. 19, 1873-1881 (1999). 72. S. Ananta and N. Thomas, J. Eur. Ceram. Soc. 19, 2917-2930 (1999). 73. D. Mohan, R. Prasad and S. Banerjee, J. Am. Ceram. Soc. 84, 2126-2128 (2001). 74. S. B. Majumder, S. Bhattacharyya, R. S. Katiyar, A. Manivannan, P. Dutta and M. S. Seehra, J.

Appl. Phys., 99, 024108-1-024108-9 (2006).

75. V. R Palkar, J. Johnand and R. Pinto, Appl. Phys. Lett. 80, 1628-1630 (2002). 76. S.H. Yoon and H. Kim, J. Eur. Ceram. Soc. 22, 689-696 (2002). 77. S.H. Hong, S. Troher-McKinstry and G.L. Messing, J. Mater. Sci. Lett. 19, 1661-1664 (2000). 78. M.P. Singh, W. Prellier, C. Simon and B. Raveau, Appl. Phys. Lett. 87, 022505/1- 022505/3

(2005). 79. D. Varshney, R.N.P. Choudhary, C. Rinaldi and R.S. Katiyar, Appl. Phys. A 89, 793-798 (2007). 80. S.M. Pilgrims, A.E. Sutherand S.R. Winzer, J. Am. Ceram. Soc. 73, 3122-3125 (1990). 81. C. EdererandN.A. Spaldin, Phys. Rev. B 95, 257601-1-257601-4 (2005). 82. J.R. Teague, R. Gerson and W.J. James, Solid State Commun. 8, 1073-1074 (1970). 83. K.-Y. Yun, M. Noda and M. Okuyama, J. Korean Phys. Soc. 42, SI 153-S1156 (2003). 84. V.R. Palkar, J. John and R. Pinto, Appl. Phys. Lett. 80, 1628-1630 (2002). 85. N.N. Krainik, N.P. Khuchua, V.V. Zhdanova and V.A. Evseev, Sov. Phys.-Solid State 8, 654-658

(1966). 86. M. Polomska, W. Kaczmarek, and Z. Pajak, Phys. Status Solidi a23, 567-574 (1974). 87.1. Sosnowska, T. Peterlin-Neumaier and E. Steichele, J. Phys. C 15, 4835-4846 (1982). 88. V.A. Khomchenko, D.A. Kiselev, E.K. Selezneva, J.M. Vieira, A.M.L. Lopes, Y.G.Pogorelov, J.P.

Araujo and A.L. Kholkin, Mat. Lett. 62, 1927-1929 (2008). 89. M. Azuma, K. Takata, T. Saito, S. Ishiwata, Y. Shimakawa and M. Takano, J. Am.Chem. Soc.127,

8889-8892 (2005).

274


90. M.M. Kumar, A. Srinivas and S.V. Suryanarayana, J. Appl. Phys. 87, 855-862 (2000). 91. S. Lokovlev, C.H. Solterbeck, M. Kuhnke and M. Es-Souni, J. Appl. Phys. 97, 094901/1-094901/6

(2005). 92. H. Zheng, J. Wang, S.E. Lofland, Z. Ma and L. Mohades Ardabilo, Science 303, 661-663 (2004). 93. V.R. Palkar, C. D. Kundaliya and S.K. Malik, J. Appl. Phys. 93, 4337-4339 (2003). 94. Y. K. Jun, W.T. Moon, C. M. Chang, H. S. Kim, H. S. Ryu, J. W. Kim, K. H. Kim, and S. H. Hong,

Solid State Comm. 135, 133-137 (2005). 95. S. R. Das, R. N. P. Choudhary, P. Bhattacharya, and R. S. Katiyar, P. Dutta, A. Manivannan and M.

S. Seehra, J. Appl. Phys. 101, 034104-1-034104-7 (2007).

96. C. Ederer andN.A. Spaldin, Phys. Rev. B 71, 224103-1-224103-9 (2005). 97. A.V. Zalesskii, A.A. Frolov, T.A. Khimich and A.A. Bush, Phys. Solid State 45, 141-145 (2003). 98. S.T. Zhang, L.H. Pang, Y.Zhang, M.H. Lu and Y.F. Chen, J. Appl. Phys. 100, 114108/1-114108/6

(2005). 99. R.K.Mishra, Dillip K. Pradhan, R .N. P Choudhary and A Banerjee, J. Phys.: Condens. Matter 20,

045218-1-6(2008). 100. B. Aurivillius, Arki. Kemi. 1, 463-480 (1949). 101. S. K. Patri, R. N. P. Choudhary and B. K. Samantaray, J Electroceram, 20, 119-126 (2008). 102. E.C. SubbaRao, Phys. Rev. 122, 804-807 (1961). 103. A. Srinivas, M. Mahesh Kumar, T. Bhimasankaram and S.V. Suryanarayana, Mater. Res. Bull. 34,

989-996 (1999). 104. A.R. James, G.S. Kumar, T. Bhimasankaram and S.V. Suryanarayana, Ferroelectrics, 189, 81-90

(1996). 105. A.R. James, G.S. Kumar, M. Mahesh Kumar, S.V. Suryanarayana, T. Bhimasankaram, Mod. Phys.

Lett. B 11, 633-644 (1997). 106. A.R. James, G.S. Kumar, S.V. Suryanarayana, T. Bhimasankaram, Ferroelectrics, 216, 11-26

(1998).

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