The spontaneous, uniform orientation of atomic or molecular
magnetic moments to generate what is collo quially called a magnet
(more correctly, a ferromagnet) has been explored for more than
2,500 years. Barely a century ago, it was discovered that
spontaneous order ing of electric dipole moments can occur as
well1. This phenomenon was named ferroelectricity because of the
analogies to ferromagnetism, such as the hysteretic switching
between two stable states in an external field. Although the
technological merits of ferromagnetism and ferroelectricity are
quite different, attempts were made to combine them in the same
phase of a mat erial to create a socalled multiferroic material
(BOX 1). Multiferroic materials are interesting mainly for two
reasons. On the one hand, they make it possible to exploit the
functionalities of both orders; for example, a magnetic bit may be
complemented by an electric bit to establish a fourstate memory
element. On the other hand, a coupling between the ferromagnetic
and the ferro electric states might induce novel functionalities
not present in either state alone. The control of the magnetic
properties by electric fields instead of magnetic fields is an
example of the advantages that multiferroic materials can offer. In
the reading and writing of a magnetic bit, if a voltage pulse can
be used instead of a magneticfield generating electric current,
the waste heat and relatively long buildup time associated with
electric currents are avoided. Multiferroics may thus lead to
faster, smaller, more energyefficient datastorage
technologies.
The field of multiferroics covers aspects ranging from
technological applications to abstract problems of fundamental
research. In addition, the study of multi ferroics increasingly
influences neighbouring research
areas, such as complex magnetism and ferroelectric ity, oxide
heterostructures and interfaces, and also seemingly remote subjects
such as cosmology. In this Review, we give an overview of the
twists and turns in the development of the diverse field of
multiferroics, and we discuss the trends and challenges that will
define its future. Readers looking for a more comprehensive or more
technical coverage are referred to more extensive general
reviews2,3, or to reviews on particular aspects that are
highlighted in further sections.
We begin with a brief survey of the early days of multi ferroics.
The realization that in some important classes of materials,
magnetic and electric longrange order compete with each other4 may
be regarded as the mile stone separating historical from
contemporary research in this field. We continue with an overview
of mecha nisms permitting the coexistence of magnetic and ferro
electric order, and evaluate their potential for inducing
pronounced magneto electric coupling effects (BOX 1). We then
scrutinize heterostructures and, in particu lar, interfaces that
introduce additional functionalities, bringing multi ferroics
closer to device applications. Domains and domain walls are also
discussed: any type of coupling between magnetic and electric
longrange order in a multiferroic material has its roots in the
cou pling between the magnetic and electric domains. We then have
a closer look at the nonequilibrium dynam ics of multiferroic
materials, because, considering that the focus in multi ferroics is
on the manipulation of the magnetic order by electric fields, it is
very important to understand the processes and timescales governing
the magnetoelectric coupling. Important progress in the
understanding of the coupling of magnetic and electric
Department of Materials, ETH Zürich, Vladimir-Prelog-Weg 4, 8093
Zürich, Switzerland.
All authors contributed equally to this work. Correspondence to
M.F.
[email protected]
Article number: 16046 doi:10.1038/natrevmats.2016.46 Published
online 5 Jul 2016
The evolution of multiferroics Manfred Fiebig, Thomas Lottermoser,
Dennis Meier and Morgan Trassin
Abstract | Materials with a coexistence of magnetic and
ferroelectric order — multiferroics — provide an efficient route
for the control of magnetism by electric fields. The study of
multiferroics dates back to the 1950s, but in recent years, key
discoveries in theory, synthesis and characterization techniques
have led to a new surge of interest in these materials. Different
mechanisms, such as lone-pair, geometric, charge-ordering and
spin-driven effects, can support multiferroicity. The general focus
of the field is now shifting into neighbouring research areas, as
we discuss in this Review. Multiferroic thin-film heterostructures,
device architectures, and domain and interface effects are
explored. The violation of spatial and inversion symmetry in
multiferroic materials is a key feature because it determines their
properties. Other aspects, such as the non-equilibrium dynamics of
multiferroics, are underrated and should be included in the topics
that will define the future of the field.
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S i
S i
states has often been introduced by symmetry consider ations; for
this reason, we pay some attention to funda mental symmetry
properties of multiferroic materials. Many of the unusual
properties of these materials are linked to the unconventional
symmetry resulting from the simultaneous presence of magnetic and
electric long range order. In turn, there are compounds displaying
the symmetry of multiferroic materials, and the material properties
permitted by this symmetry, but no multifer roic order. These
systems are equally worth exploring, which we cover in the section
devoted to research areas that were significantly influenced by the
existence of multiferroics, even though multiferroicity in itself
has a minor role in them. Finally, we identify major questions and
challenges that will continue to influence research in
multiferroics. Fundamental aspects, as well as the efforts to
obtain working multiferroic devices, are covered in
this Review.
Seeding the field Efforts to combine magnetic and ferroelectric
order in a single compound were first undertaken in the former
Soviet Union. In 1958, Smolenskii and Ioffe5 suggested the
introduction of magnetic ions into ferroelectric perovskites to
create solid solutions hosting magnetic longrange order without
losing the ferroelectric order. However, the most intensely
investigated compounds were boracites, such as Ni3B7O13I, in which
a pro nounced linear magnetoelectric effect with hysteretic
switching of multiferroic domains by electric or mag netic fields
was observed6. The experimental, theoretical and applied
achievements of these early days of the field are summarized in
REFS 7,8.
Two precursurs of the present boom in multiferroics are noteworthy.
First, in 1978, Newnham and co workers9 reported that a
spirallike arrangement of magnetic moments in Cr2BeO4 breaks
spatial inversion
Box 1 | Important terms and definitions in the field of
multiferroics
Ferroic Ferroic materials display long-range order with respect to
at least one macroscopic property, and they develop domains that
can be switched by a conjugate field108,109, as shown in the
figure. Occasionally, the term primary ferroic167 is used to
indicate ferromagnetic, ferroelectric, ferroelastic and
ferrotoroidic order.
Magnetoelectric Originally, only materials in which a magnetic
(electric) field induces a proportional polarization
(magnetization) were referred to as linear magnetoelectrics, as
seen in the figure (the prefix linear, which is often omitted,
distinguishes this effect from higher-order effects with nonlinear
relations). Multiferroics with magnetic and electric order do not
necessarily permit the linear magnetoelectric effect (for example,
hexagonal YMnO3), and not all materials displaying the linear
magnetoelectric effect are multiferroic (for example, Cr2O3).
Nowadays, the term magnetoelectric usually refers nonspecifically
to any type of coupling between magnetic and electric
properties.
Multiferroic When introduced10, the term multiferroic referred to
materials with a coexistence of two or more primary ferroic orders
in the same phase. Its present use is different; it indicates a
coexistence of ferroelectric and ferro-, ferri- or
antiferromagnetic order in single- or even multiphase materials.
The single-phase compounds are sometimes more specifically referred
to as magnetoelectric multiferroics in anticipation of a behaviour
as seen in the figure. If the magnetic and ferroelectric orders
occur independently, the multiferroic material is denoted as
type I. If the ferroelectric and magnetic transitions emerge
jointly, the multiferroic is of type II. The two types are
depicted in the figure. Note that the term multiferroic prevailed
from about the year 2000, whereas terms like ferroelectromagnetic
were in use before.
Magnetodielectric This term denominates a material in which the
dielectric function, ε, changes in a magnetic field. Because the
electrical capacitance, C, is proportional to ε, the term
magnetocapacitive is also used. In contrast to the linear
magnetoelectric effect, which parameterizes a well-defined relation
between magnetic and electric fields, the magnetodielectric effect
represents a response function for which this relation is
ambiguous.
Domains and domain walls Domains are regions with a uniform
orientation of the relevant order parameter: for example, the
polarization or the magnetization. At least two orientations of the
order parameter (domain states) are allowed for any ferroic
material; thus, a typical ferroic material consists of multiple
domains, each representing one of the allowed domain states. The
interfaces between domains are called domain walls. They can have a
width ranging from less than 1 nm to more than 100 nm. They denote
the region across which the order parameter reorients between
adjacent domains.
E, applied electric field; H, applied magnetic field; M,
magnetization; P, polarization; Si, spin at site i.
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symmetry, as does the electric polarization that is thereby
induced. In their analysis, the authors foreshadowed much of the
physics behind a new type of magnetically driven (improper)
ferroelectricity that, a generation later, would be exploited to
obtain multiferroics with strong magnetoelectric interactions.
Second, in 1993, many of the phenomena, systems and concepts at the
base of con temporary multiferroics research, including the inven
tion of the term multiferroic itself, were formulated at a
conference on magnetolelectric phenomena — even today, its
proceedings are a fascinating read10.
In 2000, Spaldin revisited the original idea of Smolenskii and
Ioffe and explained the reason why the ferroelectric and magnetic
orders obstruct each other in crystals with the versatile
perovskite structure that is technologically relevant4. In
perovskites, the ferro electric state emerges because the electron
clouds of neighbouring ions hybridize, which supports off centred
ions; this type of ferroelectricity is called dis placive
ferroelectricity and is particularly energetically favourable when
the 3d shell is empty. By contrast, magnetic transitionmetal
ordering requires partially filled 3d shells — the contradiction is
obvious. This realization triggered an intensive search for
materials in which ferro electricity is driven by other,
nondisplacive mechanisms that are compatible with magnetic order or
that do not have the perovskite structure. The first breakthrough
was the discovery of pronounced mag netoelectric interactions in
hexagonal (h) YMnO3 (REF. 11), orthorhombic (o) TbMnO3
(REF. 12) and TbMn2O5 (REF. 13). In these last two
materials, the magnetoelectric interaction originates from noncen
trosymmetric spin textures that induce a magnetically controllable
electric polarization. Contrary to the earlier work on Cr2BeO4
(REF. 9), these discoveries inspired the concerted action of
different communities — materials science, condensed matter physics
and materials theory — that resulted in an impressive expansion of
the field of multiferroics.
Mechanisms supporting multiferroicity Following the aforementioned
study on perovskite multi ferroic materials, the search for
ferroelectric materials of the nondisplacive type that permit the
coexistence of ferroelectric and magnetic order became the main
focus of the field. We distinguish four main classes of these
materials on the basis of the mechanisms inducing the
multiferroicity (FIG. 1). Other reviews present detailed
surveys of these classes14,15 and their distinction by diffraction
techniques16.
Ferroelectricity may be driven by electronic lone pairs, geometric
effects, charge order or magnetism. In the first three classes, the
magnetic and ferroelectric orders occur independently, and the
multiferroic material is denoted as type I. In the last class,
the ferro electric and magnetic transitions emerge jointly, in
which case the multiferroic material is type II
(BOX 1).
Lone-pair mechanism. The lonepair mechanism is based on the
spatial asymmetry created by the ani sotropic distribution of
unbonded valence electrons
around the host ion (FIG. 1a). This mechanism is respon sible
for the roomtemperature ferroelectricity observed in BiFeO3. In
this material, a pair of Bi3+ valence elec trons in the 6s orbital
is not involved in sp hybridiza tion and creates a local dipole,
yielding a spontaneous polarization17 of ~100 μC cm−2 below the
Curie temper ature18, TC = 1,103 K. A longrange periodic
antiferro magnetic structure arises below the Néel temperature19,
TN = 643 K. Among the lonepair systems, BiFeO3 is the only
roomtemperature singlephase multiferroic material. It has large
and robust electric polarization and pronounced magnetoelectric
coupling.
Geometric ferroelectricity. Spacefilling effects and geometric
constraints can cause structural instabilities in materials. If
such steric effects, rather than bond chem istry, lead to ionic
shifts that result in the formation of a polar state, the term
geometric ferroelectricity can be used (FIG. 1b). For example,
in hRMnO3 (R = Sc, Y, In or Dy–Lu), unitcell tripling drives the
emergence of a ferroelectric order20–22 at TC ≥ 1,200 K with a
polarization Ps = 5.6 μC cm−2 (REF. 23), followed by magnetic
ordering at TN ≤ 120 K (REF. 24). A similar behaviour is
observed in hLuFeO3 thin films, which exhibit a larger magnetic
moment and roomtemperature magnetic order25, but magnetoelectric
coupling remains to be demonstrated in this material. Another
example is BaNiF4, in which an asymmetry between Ba2+ and F− sites
leads to a spon taneous electric polarization26. Despite its small
value (~0.01 μC cm−2), this polarization is of interest because it
couples to a weak ferromagnetic moment, which can thus be reversed
along with the electric polarization27. Finally, a cooperation
between two nonpolar lattice modes drives a ferroelectric
polarization in Ca3Mn2O7; this polarization can interact with the
canted magnetic moments of the compound28.
Charge ordering. Valence electrons can be distributed nonuniformly
around their host ions in the crystal lat tice to form a periodic
superstructure. For example, it was suggested that the Fe atoms in
LuFe2O4 may form a superlattice with an alternating sequence of
Fe2+ and Fe3+ ions29. This kind of charge ordering might be the
source of an electric polarization and, hence, ferro electricity30
(FIG. 1c). LuFe2O4 is a prime candidate for
chargeorderdriven multiferroicity, but after a decade of research
the occurrence of ferroelectricity in this material is still
questioned29,31. Mixed manganites, such as Pr1 − xCaxMnO3, were
also taken into consideration32 but did not attract broader
attention. For now, charge orderdriven multiferroicity
essentially remains at the stage of an interesting concept.
Spin-driven mechanisms. Magnetic order can break inversion
symmetry. The interaction of spins and charges may transfer the
noncentrosymmetry from the magnetic to the electric lattice,
driving the formation of a polar state. These magnetically induced,
socalled improper ferroelectric materials represent the ultimate
shift away from displacive ferroelectrics, in which mag netic
ordering is inhibited, towards materials in which
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b Geometric ferroelectricity
c Charge ordering
Rare-earth ion Mn3+
the electric polarization is induced by the magnetic ordering. So
far, three main routes for the creation of this kind of
multiferroicity have been established (FIG. 1d), as discussed
in specific reviews on the topic33–35.
The most intensely discussed mechanism is the socalled inverse
Dzyaloshinskii–Moriya (DM) interaction. Whereas in the DM
interaction36 a non centrosymmetric crystallographic environment
pro motes an antisymmetric magnetic interaction, in the inverse DM
interaction an acentric spin structure drives a noncentrosymmetric
displacement of charges37,38. Spin–orbit coupling is crucial for
both the DM and inverse DM interaction. The polarization resulting
from the inverse DM interaction is essentially determined by the
optimization of the spin configuration from the point of view of
antisymmetric exchange, expressed by the antisymmetric product Si ×
Sj of neighbouring spins Si,j. It yields a onetoone correlation
between (antiferro)magnetic order and electric polarization.
Multiferroicity of this type was first found in Cr2BeO4
(REF. 9), oTbMnO3 (REF. 12) and CaMn7O12; this last
material arguably39 exhibits the highest polarization achieved so
far with this mechanism (0.3 μC cm−2)40.
In contrast to the DM interaction, the Heisenberglike exchange
striction describes an acentric displacement of charges derived
from the optimization of the symmet ric spin product Si · Sj
(REF. 41). Ferroelectricity gener ated by this kind of
displacement was first observed in TbMn2O5 (REF. 13). The
dominance of the nonrelativistic symmetric exchange over the
relativistic antisymmet ric mechanism (|Si · Sj| > |Si × Sj|)
is well represented in oTbMnO3, in which an orderofmagnitude
increase in the polarization is obtained when a cycloidal order
(parameterized by Si × Sj) transforms into a collinear
antiferromagnetic order (parameterized by Si · Sj) under
pressure42. In general, inversionsymmetryviolating magnetic order
may occur in several ways; thus, the existence of spin
distributions that could promote ferro electricity more
effectively than the currently known arrangements is
possible.
Figure 1 | Mechanisms promoting the coexistence of magnetic and
electric long-range order. a | Lone-pair ferroelectricity
in BiFeO3. Ferroelectricity originates from two Bi3+ electrons that
shift away from the Bi3+ ion and towards the FeO6 octahedra, giving
rise to a spontaneous polarization P along the [111] direction. The
lone pair is visualized by the isosurface (red) of the electron
localization function of ferroelectric BiFeO3.
b | Geometrically driven ferroelectricity in hexagonal
(h-) RMnO3 emerges from a tilt and deformation of MnO5 bipyramids,
which displace the rare-earth ions as indicated by the arrows,
leading to a spontaneous polarization along the [001] axis.
c | Charge ordering in LuFe2O3 creates alternating layers
with Fe2+/Fe3+ ratios of 2:1 and 1:2. This was argued to create a
spontaneous polarization between the two layers, which is oriented
parallel to the arrow. d | Mechanisms for spin-induced
ferroelectricity. Polar displacement is induced by antisymmetric
spin exchange interactions (inverse Dzyaloshinskii–Moriya
interaction; top panel) as observed, for example, in orthorhombic
(o-) RMnO3: the polarization vector is P ∝ eij × (Si × Sj), where
eij is the unit vector connecting neighbouring spins and Si,j are
the spins at neighbouring sites i and j. Ferroelectricity arises
from symmetric spin exchange in Ca3CoMnO6 (REF. 168) shown in
the middle panel, with P ∝ Rij(Si · Sj), where Rij denotes the
direction along which the magnetostriction occurs. Spin-driven
modulations of the chemical bond between magnetic 3d orbitals and
ligand 2p orbitals (indicated by grey clouds) yield a spontaneous
polarization along the bond direction in delafossites, such as
CuFeO2, as expressed by the relation P ∝ (Si · eij)
2eij (bottom panel). Part d is adapted with permission from
REF. 33, Institute of Physics, and from REF. 168,
American Physical Society.
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Pressure
Finally, in delafossite systems, such as CuMO2 (M = Fe or Cr), a
spontaneous polarization P ≤ 0.03 μC cm−2 is induced by a
screwlike spin structure with Si × Sj = 0. This polarization is
driven by a variation in the metal–ligand hybridization as a
function of spin–orbit coupling43.
Comparison between the different mechanisms. The polarization
values resulting from these four mech anisms are compared in
FIG. 2. So far, the lonepair mechanism has been the most
successful in yielding multiferroicity with the right
characteristics for device applications; however, BiFeO3 is the
only known mate rial to be multiferroic because of this mechanism.
In contrast, many spindriven multiferroic materials are being
discovered, and robust roomtemperature sys tems appear to be
within reach40,42,44. This hope is fuelled by the general nature of
the driving mechanism itself, which leaves ample room for
improvement, using chem ical doping, pressure effects and strain,
towards higher ordering temperatures or
polarization values.
Theory and experiment indicate that there are more mechanisms
resulting in multiferroicity than the ones dis cussed so far. For
example, ferroelectrically induced mag netic order was predicted
for LiNbO3type structures45. Here, a weak magnetization can occur
because a polar state breaks the inversion symmetry between
antiferro magnetically aligned spins. Some evidence for this kind
of multiferroicity was reported46 for FeTiO3, but it requires
additional verification, and the coupled magneto electric switching
still has to be demonstrated.
Composite multiferroics. So far, the focus has been on systems
permitting the coexistence of ferroelectric and magnetic order in a
single material. The alternatives are hybrid systems. A return to
the historical idea of alloy ing ferroelectrics with magnetic ions
led to the discovery of new multiferroic materials with a
magnetoelectric response at room temperature47, which can become
par ticularly pronounced near phase boundaries48. Another
possibility is to use composite multiferroic materials, in which a
ferromagnetic magnetostrictive and a ferro electric piezoelectric
constituent are merged in a granu lar or layered form. In
constituent 1, magnetostriction denotes the induction of strain by
a magnetic field; this strain is transferred via strain coupling
between the constituents to constituent 2, where it is converted
into a voltage via the piezoelectric effect49. The result ing
magneto electric coupling can be 108 times larger than that of
singlephase multiferroics50; however, it is observed only at
microwave frequencies and in a very limited range of operation
conditions. The other possible strategy is to use strain to change
the size and isotropy of unit cells to destabilize a
centrosymmetric structure in favour of a polar phase that emerges
independently of the magnetic order. Multiferroicity in Baalloyed
bulk SrMnO3 was obtained this way — the strain was exerted
chemically through the large size of Ba3+ ions51. However, precise
control of the strain value requires thinfilm architectures, which
are discussed below.
Thin films and heterostructures Oxide thin films can be grown layer
by layer with atomic scale precision, thus much more accurately
and control lably than bulk crystals. At first, the obvious goal
was the reproduction of multiferroic bulk phases in thin films and
their switching in electric fields — this was accomplished in
compounds such as oTbMnO3, hRMnO3 and BiFeO3
(REFS 17,52,53). An advantage of thin films is that battery
voltages applied across them can generate the electric fields
required for magnetoelectric phase control. New phases that are
specific to thin films and heterostructures were later explored.
For multiferroics, this approach was spectacularly successful in
the case of BiFeO3 thin films and heterostructures, which were
grown in a large range of structural configurations that are
inaccessible in bulk crystals. These structures have already been
reviewed in detail54–56; in this Review, we focus on a general
classifi cation of novel material phases and coupling effects that
may arise in heterostructures. In particular, the effects of
strain, heteroepitaxy and interfaces in thinfilm architec tures
open unprecedented opportunities for the develop ment of
multiferroic heterostructures and interface states with potential
for device applications. The interfaces between different phases
can either transfer the interac tion between the constituents of
the system or have an active role in determining the properties of
the material.
Ferromagnetic–multiferroic heterostructures. A major drawback of
almost all bulk multiferroics is their antiferro magnetic order. In
contrast to ferromagnets, the lack of a macroscopic magnetization
makes them techno logically difficult to exploit. However, this
shortcoming
Figure 2 | Types of single-phase multiferroic materials with their
maximum polarization values. Ferroelectricity may be driven by
electronic lone pairs, charge ordering, geometry and magnetism.
BiFeO3 displays the largest spontaneous polarization (relaxed, Ps ≈
100 μC cm−2; strained, Ps ≤ 150 μC cm−2)17. The polarization of
LuFe2O4 (25 μC cm−2)29 is still controversial. Hexagonal (h-) RMnO3
develops a polarization of about 5.6 μC cm−2 (REF. 23). Among
the spin-driven ferroelectrics, symmetric Heisenberg-like exchange
striction leads to a larger polarization than antisymmetric
Dzyaloshinskii–Moriya exchange. This is reflected by orthorhombic
(o-) TbMnO3, which experiences a transition from a spiral order (Ps
≤ 0.1 μC cm−2) to a collinear antiferromagnetic order (Ps ≈ 1 μC
cm−2) under pressure41. The largest spin-spiral-driven polarization
has been claimed for CaMn7O12 (Ps ≈ 0.3 μC cm−2)40.
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of the antiferromagnetic state may be overcome by cou pling it to
a ferromagnetic state. One possible solution is to exploit exchange
bias — the displacement and harden ing of a ferromagnetic
hysteresis induced by the presence of an adjacent antiferromagnet.
This is the mechanism used in the read–write heads of computer hard
disks. Connecting an electricallytuneable antiferromagnet with a
ferromagnetic layer could make it possible to manipulate the
magnetic exchange bias with an electric voltage and to electrically
shift the ferromagnetic hyster esis loop. This mechanism could
form the basis of low energy magnetoelectric memories57–59. An
important step in this direction was the lowtemperature demon
stration of electrically tuneable pinning of ferromagnetic domains,
which resulted in a voltagecontrolled modi fication of the
exchange bias in hYMnO3–Permalloy60. Following predictions of
magnetoelectric coupling61 (and possible weak magnetization) in
BiFeO3, a modification of the exchange bias, albeit irreversible,
was verified at room temperature in
BiFeO3–CoFe (REF. 62).
Another possible method to avoid the disadvantages of the
antiferromagnetic state is to transduce it into a ferro magnetic
state by establishing a rigid coupling between the
antiferromagnetic order parameter of the multi ferroic constituent
and the order parameter of an adjacent ferro magnetic constituent.
An important breakthrough was the observation of a voltageinduced
rotation of the magnetization in a microscopic BiFeO3–CoFe dot63,
which eventually led to the demonstration of repeatable
magnetization reversal by an electric field at room tem perature —
the holy grail of research on magnetoelectric
multiferroics64.
Aside from their technological appeal, these results are remarkable
because they trace the complex magneto electric switching
behaviour back to the formation of domains. Ultimately, domain
formation is the most signif icant factor for the response and
performance of devices. All recent experiments on lowenergy
magnetization reversal aim to establish a onetoone correlation
between domains in ferromagnetic and multiferroic
materials64,65.
Strain engineering. Another tool for the engineering of
multiferroic thin films is epitaxial strain. By selecting the right
substrate, a wide range of tensile and compressive strains can be
obtained. The associated modification of the lattice constant can
induce a transition to new mate rial phases or at least modify the
existing ones. By using a ferroelectric and, hence, piezoelectric
material as a sub strate, strain can even be reversibly tuned
postgrowth within a 0.1% window using an external voltage66.
The atomic arrangement and the strain provided by the crystal
lattice of the substrate can support the growth of otherwise
unstable multiferroic phases67; it is also used to pattern the
distribution of ferroelectric domains and domain states of
multiferroics59,68. Strain was used to demonstrate the correlation
between ferro electric and magnetic spiral order in BiFeO3
(REF. 69), a result that was sought after for a long time.
Strain can even induce ferroic order in otherwise nonferroic
compounds: polar order was induced in SrTiO3 (REF. 70) and,
coexisting with magnetic order, in EuTiO3 (REF. 71)
and SrMnO3 (REF. 72), whereas ferromagnetism was induced in
LuMnO3 (REF. 73). Strain also controls the density and
distribution of vacancies, which represent a powerful degree of
freedom for the modification of material properties72.
Finally, strain can be used to couple ferroelectric domains to
ferromagnetic domains across an inter face through
magnetostrictive and magnetoelectric coupling74,75 (FIG. 3b).
This effect was demonstrated in experiments on CoFe–BaTiO3, which
also revealed that the anisotropy and ordering temperature of
interfacial magnetism can be controlled by electric fields76. Note
that these experiments are different from experiments involving a
magnetoelectric response at microwave frequencies in
magnetostrictive–piezoelectric compos ites49. The first type of
experiment depends on epitaxal interfaces as a source of a
welldefined local interaction, whereas the second type involves
unspecified, rough interfaces that serve as strain mediators.
Interfaces. Multiferroic states can also be realized at the
interface between two constituents (FIG. 3c). At the inter
face, properties not found in the bulk can exist because of low
local symmetry, confinement effects, strain gra dients and
chemical anisotropy. Indeed, it was found that the interface
between a ferromagnetic material, Fe or Co, and a ferroelectric
material, BaTiO3, can be multi ferroic, and that the
multiferroicity is retained within several monolayers around the
interface77. The possible relevance for applications of these 2D
multi ferroic interface states still has to be elaborated. Note
that interfaces break space but not timeinversion sym metry. As
a consequence, the magnetization axis at the interface can be
reoriented by an electric field, but the direction along this axis
remains ambiguous unless a magnetic bias field is applied.
Another way of confining multiferroicity to an inter face might be
through domain walls; in this case, the interface is represented by
the multiferroic wall between different domains within a single
material that is in itself not multiferroic (FIG. 3d).
Domains and domain walls Domains and domain walls (BOX 1) are
crucial for the control of many material properties, such as
coercivity, resistance and/or fatigue. The magnetoelectric coupling
of a multiferroic material roots in the coupling between its
individual magnetic and ferroelectric domains.
Although advanced functionalities are often based on complex domain
architectures64, early investigations focused on symmetry
analysis10 and experiments on a sin gle domain state of a
singlecrystal multiferroic mat erial. An example is the study of
the reversal of the electric order parameter by a magnetic field
(or vice versa) via the linear magnetoelectric effect6. Domain
patterns were initially imaged by linear optics, and ferroelectric
domains were visualized after chemical surface etching or via
optical birefringence in materials with simulta neous elastic
deformation. Ferromagnetic domains were resolved by the
magnetooptical Faraday or Kerr effect10. Using these techniques,
domains were studied
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c Multiferroic interface d Multiferroic domain wall
FerroelectricMF
Ferromagnet
antiferromagnetic
M
in multiferroic boracites78, BiFeO3 (REF. 79) and hYMnO3
(REF. 80). The main limitations of the optical approach are
the insensitivity to antiferromagnetic order and the limited
resolution of, at most, 1 μm.
A seminal advance was the application of nonlinear optics to
multiferroics. In addition to providing access to antiferromagnetic
domain states, a technique such as second harmonic generation can
resolve electric and magnetic domains within the same experiment,
making spatial magnetoelectric coupling phenomena directly
visible81. This was crucial for resolving the pronounced coupling
between ferroelectric and antiferromagnetic domains in hYMnO3 and
to reveal that this coupling does not originate in the domains but
in the domain walls11. Similar studies on spinspiral
multiferroics, such as MnWO4 (REFS 82,83) or oTbMnO3
(REF. 84), revealed the dynamics of multiferroic domains in
external fields and on crossing phase transitions.
Scanningprobe and electronmicroscopy tech niques pushed the
resolution of domain imaging to the nanoscale, making even domain
walls accessible with atomicscale resolution. These advances were
extremely helpful for the understanding of the complex multiferroic
domain structures in BiFeO3 thin films85. The study of hRMnO3
revealed a particularly interesting example of
domain physics: the trimerizing lattice distortion leads to a
protected pattern of improper ferroelectric domains with unique
topological properties86,87.
More recently, attention is moving away from the domains and
towards their boundaries — the domain walls88. Whereas
heterointerfaces separate constituents in artificial multilayers,
domain walls can be regarded as natural homointerfaces occurring
within a material. At the walls, charge or spin phenomena similar
to the ones occurring at heterointerfaces can emerge but with the
advantage that domain walls can be created, moved and erased
postgrowth. As FIG. 4 shows, the domain walls in type I
and type II multiferroics are different. In type I
multiferroics, magnetic and electric walls can coincide but do not
have to because of the independence of magnetic and electric order.
In type II multiferroics, the magnetic order induces the
electric order; therefore, each ferroelectric domain wall is a
magnetic domain wall at the same time and, thus,
multiferroic.
The groundbreaking discovery that domain walls in BiFeO3 have a
larger conductance than the surrounding bulk89 triggered a broad
interest in domainwall engi neering90. Domain walls with
increased, attenuated or anisotropic conductance have been
investigated in many materials88. These investigations are mainly
targeted at
Figure 3 | Multiferroic thin-film architectures. a,b | In
3D transfer multiferroics, multiferroicity is a composite effect.
In panel a, the ferroelectric order, P, is coupled to the
antiferromagnetic order, m, within a non-composite multiferroic,
and the antiferromagnetic order, in turn, is coupled to the
ferromagnetic order, M, of an adjacent constituent via magnetic
exchange, J. In panel b, the magnetoelectric coupling between a
piezoelectric and magnetostrictive constituent is established via
strain, σ. c,d | In 2D confined multiferroics, only the
interface between two material phases is multiferroic. In panel c,
these phases are the permittivity, ε, and permeability, μ, states
of different compounds, and multiferroicity emerges as an interface
effect. In panel d, the interface is represented by the wall
separating different domains (that is, states A+ and A−,
represented by the block arrows) within a crystal. E, applied
electric field; MF, multiferroic.
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Crystal Crystal
M P
M P
M P
the ferroelectric state, and truly multiferroic domain walls
receive much less attention. Examples of the phe nomena observed
at the domain walls are the magne toelectric coupling or
spontaneous magnetization in the domain walls of multiferroic
manganites11,91,92. In spindriven ferroelectrics, examples are the
coupled Bloch or Néellike rotation of magnetic chirality and the
induced electric polarization83,93. In contrast to the
aforementioned multiferroicity emerging at the inter faces between
different nonmultiferroic compounds (FIG. 3c), multiferroicity
occurring at the domain walls within a single nonmultiferroic
compounds (FIG. 3d) has not yet been observed.
Non-equilibrium dynamics In the field of multiferroics, the strong
interest in the electricfield control of the magnetic state is
contrasted by the small number of investigations on the temporal
evolution of such magnetoelectric switching. However, understanding
the switching dynamics is essential for judging and improving the
speed, repeatability and control of voltageinduced magnetization
reversal. For example, the switching may be inherently faster or
slower than conventional magneticfield switching, a factor that
needs to be known before the design of a multiferroic memory
element can be envisaged.
Early work on nonequilibrium dynamics revealed a fundamentally
different temporal evolution for the polar and magnetic order94 in
multiferroic GaFeO3. Another study showed that optical excitation
of CuO induces a transition from commensurate to incom mensurate
magnetic order within picoseconds, which probably influences the
accompanying ferroelectric polarization95. LuFeO2 shows indications
of a dynamic correlation between the magnetic and an assumed polar
izationinducing charge order96. The resonant excitation of
spinspiral multiferroics was predicted to promote an alloptical
reversal of the multiferroic order parameters97;
related experiments on oTbMnO3, performed at acces sible
terahertz amplitudes, identified an ultrafast spin deflection98 of
~4%, far below a 180° reversal. Ultrafast optical pumpprobe
spectroscopy was used to reveal the coexistence and coupling of
antiferro magnetic or ferroelectric and ferromagnetic order in
strained oTbMnO3 films99. The ultrafast reversal of the multifer
roic order parameters by an electric field pulse in BiFeO3 is
debated100,101; electric field experiments on magneti cally driven
ferroelectrics even revealed that their order parameter reversal
can be inherently slow102. In a compos ite multiferroic, ultrafast
manipulation of the polarization via photoinduced magnetostriction
was observed103. As these results show, the field is still at the
stage of collecting disconnected bits of information on the
nonequilibrium dynamics of multiferroics, and a coherent
understanding of them has not yet been reached.
Note that these experiments on switching are dis tinct from those
in which ultrafast processes in multi ferroics are investigated,
but not in connection with the multiferroic order — photostrain
effects in BiFeO3 are one example104.
Violation of inversion symmetry The Neumann principle relates the
physical properties of a material to its structural symmetry,
stating that the symmetry displayed by the material properties
includes the symmetry elements characterizing the structural
arrangement of its charges and spins. Many of the remarkable
physical properties of multiferroics arise from the breaking of
space and timeinversion symme try caused by the simultaneous
presence of magnetic and electric longrange order — the linear
magnetoelectric effect is a prototypical example.
The increasing understanding of the role of symme try led to the
realization that some phenomena origi nally associated with the
coexistence of magnetic and electric order are actually a
consequence of this twofold
Figure 4 | Domains and domain walls in type I and type II
multiferroics. a | In type I multiferroic materials,
magnetic and electric order emerge independently; thus, the
respective domain patterns do not have to coincide and domain walls
are either magnetic (blue) or electric (red) in nature. If the
domain patterns coincide, a multiferroic domain wall is formed
(orange). The formation of multiferroic domain walls points to a
coupling between magnetic and electric order which, however, is not
required by symmetry. b | In type II multiferroics,
the magnetic order induces the electric order; thus,
ferroelectricity emerges jointly with a magnetic phase transition.
Because of the interdependence of the electric and magnetic order
parameter, all ferroelectric domain walls are also magnetic domain
walls and, therefore, multiferroic. FE, ferroelectric; FM,
ferromagnetic; M, magnetic order; MF, multiferroic; P,
ferroelectric order.
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S i
r i
S i
symmetry violation and can therefore occur in non multi ferroics
as well. This could considerably expand the range of host systems
in which these phenomena are observed. A prime example is Cr2O3, a
nonmultiferroic material with broken space and timeinversion
symme try, which displays many of the effects discussed in this
Review, such as static and optical magnetoelectric effects,
ferrotoroidicity and magnetic quasimonopoles3,105–107.
Ferrotoroidicity. For a long time, the magnetoelectric coupling in
multiferroics has been associated with a viola tion of
timereversal symmetry by the magnetic order and a violation of
spatial inversion symmetry by the electric order. This vision
changed with the discovery that in spin driven ferroelectrics, it
is the magnetic order that breaks inversion symmetry, a realization
that intensified the search for a primary ferroic order violating
both space and timeinversion symmetry. The discovery of such a
state would symmetrize and complete the known forms of primary
ferroic order, which at the moment include states violating spatial
inversion symmetry (ferro electricity), temporal inversion symmetry
(ferromagnetism) or neither of the two
(ferroelasticity)108,109.
The multipole expansion of the electrodynamic vec tor potential
A(r) includes a space–timeantisymmetric term, a socalled
anapole110 or toroidal moment111. The spontaneous, uniform
alignment of toroidal moments would then establish a ferrotoroidic
state, with domains that could be hysteretically switched by an
adjunct toroi dal (that is, space–timeantisymmetric) external
field. Most investigations consider toroidal spin arrangements in
the unit cell where the toroidal moment, T = ∑i ri × Si, represents
a magnetic whirl (ri is the position of spin Si, FIG. 5a)112.
By contrast, the existence of atomic toroidal moments remains
debated113.
Compounds exhibiting a toroidal magnetic struc ture have been
identified; however, this does not mean that these compounds are
ferrotoroidic. Ferrotoroidicity requires the presence of domains
(FIG. 5b) and their pol ing in a toroidal field. Both
conditions were realized114,115 in LiCoPO4, in which the coupling
to the toroidal field was established with perpendicular magnetic
and electric fields. The direct generation of a toroidal field
remains an open challenge. Finally, ferrotoroidic structures can
also be regarded as antiferromagnetic, and ferrotoroidicity is a
reasonable concept only if the toroidal moment can act as the
driving (proper) order parameter. This latter criterion was
exemplified116 in the case of LiFeSi2O6.
Magnetic monopoles. Magnetic monopoles are a con cept closely
related to toroidal moments. Magnetic monopoles are the counterpart
of the electric (charge) monopoles, but they are not allowed in
free space, as expressed by the Maxwell equation, ∇B = 0. However,
in condensedmatter systems, magnetic quasimonopoles with ∇H ≠ 0
or ∇M ≠ 0 can exist in both an excited form (such as spin ice117)
or as the ground state. The ground state monopole is derived as
the secondorder term in the multipole expansion of the
magnetization density, μ(r), in which the magnetic monopole appears
along with the toroidal moment and the magnetic quadrupole
in space–timeinversionsymmetry violating systems107. These three
terms are associated to three qualitatively different contributions
to the linear magnetoelectric effect107,111. Note that the relation
between the deriva tions of the toroidal moment from μ(r) and A(r)
still needs to be established.
Magnetic monopoles, as toroidal moments, can be studied at the
level of atoms or unit cells. The first case is theoretically
discussed for the LiMPO4 system107 (M = Mn–Ni). A spin arrangement
that may be interpreted as a magnetic monopole is sketched in
FIG. 5c and was observed in the P63/cm phase of the hRMnO3
system118. The existence of a ferromonopolar state is debated107,
but it would depend on the existence of a conjugate sca lar
monopolar field. A solitary magnetic monopole may be conveniently
generated by placing a point charge in front of a magnetoelectric
medium, which would con vert the electric monopole into a
submergedimage mag netic monopole. Until now, this possibility
has only been explored for topological insulators exposed to a
magnetic field119, but a much stronger response can be expected for
conventional bulk magnetoelectrics.
Figure 5 | Magnetic toroidal moments and monopoles in crystals.
a | Hypothetical unit cell with six spins, Si, at
positions ri defining a toroidal moment, T = ∑i Si × ri, per unit
cell. The spin arrangements of opposite toroidal moments are shown
in the two sketches. b | Ferrotoroidic domain structure
with uniform arrangements of toroidal moments (represented by the
arrows). c | Hypothetical unit cell with a
magnetic-monopole-like arrangement of six spins. Spin arrangements
of opposite monopole moments are shown in the two sketches.
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b
d
a
y
z
y
z
y
z
y
z
c
From a technological point of view, toroidal and monopolar systems
are interesting because of the inher ent linear magnetoelectric
effect they display107. This effect may be substantially enhanced
by combining a space–timeantisymmetric ferrotoroidic state with a
ferroelectric and/or ferromagnetic state, similar to how the
combination of space–timeantisymmetric magnetic order with
ferroelectric order in spindriven multiferroics can be the source
of giant magnetoelectric effects.
Effects at finite frequencies. The violation of space and
timeinversion symmetries is not a static phenome non; it is also
realized at finite frequencies. This fact is exploited in
composites in which a ferromagnetic mag netostrictive and a
ferroelectric piezoelectric constituent are mixed, so that an
oscillating magnetic field induces an oscillating electric
polarization via strain coupling49.
In singlephase multiferroics, attention is focused on two dynamic
effects: electromagnons, a magnetoelec tric excitation, and
nonreciprocal directional dichro ism, a groundstate optical
response. Both phenomena are manifestations of the twofold
symmetry violation rather than of the multiferroic state. As a
consequence, they are also observed in nonmultiferroics.
Electromagnons. An electromagnon is a magnetic resonance that
breaks inversion symmetry, giving rise to an oscillating electric
polarization (FIG. 6). Electromagnons were first reported in
the multi ferroics oTbMnO3 and oGdMnO3 (REF. 120), in which
a dielectric resonance influenced by magnetic order and magnetic
fields was observed. In oGdMnO3, this resonance appeared outside
the multiferroic phase, which showed from the start that
electromagnons are a consequence of the system symmetry rather than
of multiferroicity. Initially, in oTbMnO3, a spinwave excitation
was observed that induces a polarization oscillation via the
(symmetric) Heisenberg exchange121 (FIG. 6b). This is
remarkable, because the static polari zation of oTbMnO3 is driven
by the (antisymmetric) inverse DM interaction (FIG. 6c,d).
Later, oTbMnO3 also revealed a polarization oscillation mediated
by the inverse DM interaction122.
Electromagnons have been identified in various compounds, including
type I multiferroics123, high temperature multiferroics124
and nonmultiferroics125,126.
Nonreciprocal directional dichroism. Identical light waves
travelling in opposite directions through a mat erial in which
space and timeinversion symmetry are broken are transmitted with
different intensity and polarization, an effect called
nonreciprocal directional dichroism (NDD). The reversal of this
directional dependence by a magnetic field goes under the name of
the optical magnetoelectric effect127,128. Spontaneous NDD induced
by multiferroic order has been first stud ied in GaFeO3, a
material exhibiting relative absorp tion differences Δα/α of up to
1.6 × 10−3 (REFS 129,130). Giant NDD with Δα/α = 1 was
reported for multiferroic Ba2CoGe2O7 in the terahertz regime131.
The requirement of space–time antisymmetry means that NDD is not
lim ited to multi ferroics132; in fact, the observation of the
anti ferromagnetic analogue of the Kerr and Faraday effect in
Cr2O3 constitutes the earliest example of NDD105,133,134. The
strongest possible manifestation of NDD — transmission of light
through a material in one direc tion only — was also observed in a
nonmultiferroic. Experiments on CuB2O4 in magnetic fields of up to
53 T showed that such unidirectional propagation would develop at
about 75 T (REF. 135).
As discussed, space and timeinversion symmetry are violated
separately in the two constituents of a composite multiferroic.
Another way to acquire such spatially sepa rated symmetry breaking
is to grow trilayer superlattices formed by two dielectrics and one
magnetically ordered constituent136. Other systems are patterned
media, such as magnetic photonic crystals and toroidal or chiral
meta materials137,138. Experimentally, patterned media are
more
Figure 6 | Electromagnons in cycloidal spin structures. Grey arrows
represent the spins, Si, and their collective movement, and circles
indicate the corresponding magnetic easy plane — that is, the plane
in which the spins lie. The long-range modulated spin structure
induces a polarization along the z axis according to the relation P
∝ eij × (Si × Sj), where eij is the unit vector connecting
neighbouring spins and Si,j are the spins at neighbouring sites i
and j. a | The spin excitation indicated by the red
arrows does not induce a polarization change, because the vector
product remains constant. This excitation represents a magnon.
b | Excitation leading to a variation in the
antisymmetric and also the symmetric spin exchange. It leads to a
spatial modulation of the polarization amplitude. c | For
excitations that involve a rotation of the magnetic easy plane
around the y axis, the polarization also rotates around this axis,
yet retaining its amplitude. d | If the magnetic easy
plane rotates around the z axis, the cycloidal spin arrangement is
transformed into helical order. This leads to a spatially uniform
modulation of the polarization amplitude. The excitations in parts
a–c represent electromagnons. All the spin deflections shown in
parts a–d oscillate with time, and so does the associated
modulation of polarization. Figure is adapted with permission from
REF. 169, American Physical Society.
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successful in demonstrating NDD than other compos ite structures:
for example, interfaces139 and magnetized chevrons140 or
gratings141.
Other ways to obtain pronounced NDD are based on the resonant
excitation of magnetoelectrically active states such as magnons142,
electromagnons143 or skyrmions144.
Impact on other research fields The field of multiferroics is
experiencing a migration into other research disciplines, in which
multiferroic materials are studied for properties that are, at
best, indirectly related to their multiferroic nature. This trend
was already apparent in the discussion on space and timeinversion
symmetry violation in the previous section.
Multiferroics had a major impact on the field of ferroelectrics.
Research in multiferroics restored an awareness of the wealth of
mechanisms, in addition to the displacive mechanism, that can
promote spon taneous polar order. In particular, the importance of
improper ferro electric materials was recognized, because they
allow the formation of domains and domain walls with properties and
functionalities that do not occur if the polarization is the
primary order parameter83,88,145.
An increasing interest in oxide electronics146, in which
multiferroic materials and their magnetoelec tric interactions are
an important topic, stimulated impressive progress in the epitaxial
growth of oxide films and hetero structures. This opened a path to
var ious multiferroic functionalities. It allows coupling of the
antiferromagnetic state of a multiferroic material to the
ferromagnetic state of an adjacent material, a multi ferroic state
to be induced in the first place, and the creation of a
magnetoelectric coupling at or across interfaces. Heterostructures
also facilitate connection of the multi ferroic system to
electronic circuitry.
Research in multiferroics motivated the improvement of many
characterization techniques. For example, Xray diffraction
experiments were improved to detect atomic shifts at the femtometre
scale147; pyroelectric measure ments were refined to measure
spontaneous polariza tions down to 0.1 nC cm−2; nonlinear laser
spectroscopy was developed into a tool for imaging the coexistence
and interaction of magnetic and ferroelectric domains11,82; and
terahertz spectroscopy was advanced to study
electromagnons120.
The field of multiferroics has also entered the realm of
highenergy physics. Materials with specific mag netic and
electric properties may allow the detection of a permanent electric
dipole moment of the electron with unparalleled accuracy. The
required properties can be obtained by replacing Eu in multiferroic
EuTiO3 with Ba until the magnetic order is suppressed148. The
multiferroic hRMnO3 compounds are used to scruti nize scaling
laws related to string formation in the post BigBang
universe86,87 — upon cooling, both systems undergo topologically
similar phase transitions. This similarity is used to relate the
distribution of the alleged cosmological strings to the
distribution of the lines along which ferroelectric domains meet in
hRMnO3.
Multiferroic materials are a part of these research areas because
of their predisposition to host ferroelectric states of uncommon
origin or topology.
Trends and challenges Despite the advances in the field of
multiferroics, some of the current goals are still the same as in
the 1960s, and it is safe to assume that they will continue to keep
research ers busy for a while. These objectives include the quest
for new materials with a strong coupling of magnetic and electric
properties, which could raise the very limited number149 of known
roomtemperature multiferroics. In particular, a roomtemperature
multi ferroic with pro nounced and strongly coupled spontaneous
magnetiza tion and polarization is not yet known. Novel mechanisms
driving multiferroicity may be discovered, but the existing ones
are far from being fully exploited. For example, there can be many
ways to obtain a magnetic order that can stabilize an improper
ferroelectric state. This may lead to inherently higher ordering
temperatures and polari zations compared with those of the
existing spindriven ferroelectrics — predictions and preliminary
discoveries are promising42,44. Other, underrepresented classes of
materials that may host multiferroic states are nonoxide
compounds150 and organic materials151.
A multiferroic device in which the magnetization is controlled by
an electric field, preferably at low voltages, at room temperature
and with ultrafast switching, remains a prime goal152–155. Major
accomplishments obtained so far are the repeatable,
roomtemperature magnetization reversal by an electric field
demonstrated in BiFeO3–CoFe heterostructures64 and the realization
of a multiferroic fourstate memory operated at low
temperatures156. These are important steps towards the integration
of multi ferroics into devices, but crucial aspects such as the
dynamics, reliability and fatigue of these device concepts still
have to be optimized in order to develop a competitive technology.
In addition to this, alternative routes for the control of
magnetism that use spin torque157 or spinorbit torque158,159
exerted by a spinpolarized electric current have been presented,
and any multiferroic device will need to compete with their
functionality and performance.
Multiferroic thin films and heterostructures hold the greatest
potential for device applications59. First, they may lead to new
types of systems combining magnetic and electric longrange order.
Multiferroicity may origi nate under strain, confinement or
gradient effects within one material, as well as at or across the
interface between different materials. All of these possibilities
represent degrees of freedom that so far have been only marginally
explored. Second, heterostructures with strongly cou pled
ferroelectric and ferromagnetic layers may be used to build a
magnetoelectric memristor. In this kind of device, an electric
field sets the ferroelectric layer polari zation state, which is
then transferred to the magnetic layer, where it defines the
memristive state through cou pling to an adjacent ferromagnetic
reference layer. Third, multilayer heterostructures with an
integral symmetry that is different from the symmetry of their
individual constituents may be assembled. This integral symmetry
may even be switchable by, for example, reversing the
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order parameter of only one of the layers constituting the
heterostructure. This was conceptually demonstrated160 by
layerselective polarization orientation of trilayer
heterostructures such as PbZr0.2Ti0.8O3–La0.7Sr0.3MnO3–
PbZr0.2Ti0.8O3. By setting the relative polarization of the outer
layers, the integral spaceinversion symmetry of the trilayer
structure is activated and deactivated on demand. Accordingly,
magneticfield poling of outer magnetically ordered layers could
switch time reversal symmetry on or off. These symmetrytunable
multilayer assemblies constitute a powerful option to increase the
number of systems with interesting and controllable magnetoelectric
coupling effects. Fourth, the focus on domain walls will grow
stronger, because it is an advantage to work with oxide interfaces
that can be created, shifted and annihilated postgrowth (in
contrast to conventional interfaces that, once grown, cannot be
modified). Controllable domain walls could be the key to
electricfieldcontrolled racetrack memo ries161. An electric
field may act on the magnetic domain wall and move it, exploiting
the magnetoelectric effect. Alternatively, if the domain wall is
multiferroic, the elec tric field may act directly on the wall
polarization. As in the bulk compounds, these concepts may be
extended to nonoxide thin films.
Another element that might have an important role for future
applications of multiferroic materials is skyr mions — magnetic
whirls that were first observed in halfmetallic systems162 and
that were detected in multi ferroic insulators163. In multiferroic
insulators, skyrmions are localized and electric currents — the
usual tool to manipulate them — cannot flow, but the coexistence
with ferroic order and the possibility of establishing
magnetoelectric control of the skyrmions are worth further
exploration. For example, skyrmions in systems with acentric
spinspiral order (instead of an acentric crystal structure) may
provide a route to giant, locally controllable magnetoelectric
interactions.
The field of multiferroics also has a prominent role in promoting
cooperation between formerly disjoint research disciplines —
systems with strong
magnetoelectric interactions are appealing for different fields.
Moreover, bringing together two types of order in one material is
an inherently interdisciplinary effort. For example, it is no
longer sufficient to track the thick ness of a thin film during
growth; continuous control of its emerging multiple ferroic
properties is also required. The combination of deposition
techniques with in situ electro and magnetooptical spectroscopy
could be very effective to this end.
In multiferroic research, dynamical phenomena are still a highly
underrated topic. With magnetoelec tric switching as one of the
declared goals of the field, more attention must be paid to the
temporal evolution of these reorientations. One important aspect is
the speed of the reversal of the order parameter, which has to
occur within picoseconds if memory applications are envisaged. In
this respect, alloptical control164 of a multi ferroic state may
be a particularly reward ing goal. On the other hand, the reversal
needs to be highly reproducible at the level of individual domains
if magneto electric switches, sensors or transducers are
considered. Apart from establishing a onetoone association
between the orientation of a magnetic order parameter and the
orientation of an electric field, more complex types of
magnetoelectric control may be taken into consideration. If, for
example, a multiferroic state is characterized by three or more
order parame ters, it might be possible to invert an entire
distribu tion of magnetic domains; the domain pattern remains
unchanged but in each individual domain the order parameter is
reversed. The inversion of an inhomoge neous physical state has a
great technological relevance; for example, it is at the basis of
the spinecho effect in nuclear magnetic resonance tomography165
and of active noise reduction166.
In conclusion, even though the field of multiferroics has reached
some maturity after more than 50 years of research, it is
still far from being full grown. Its twists and turns continuously
lead to the exploration of new systems and effects, and it is
possible that the most exciting results and discoveries have not
yet been realized.
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