Multiferroics are defined as materials that exhibit more than one of the primary ferroic properties in the same phase: ferromagnetism – a magnetisation that is switchable by an applied magnetic field ferroelectricity – an electric polarisation that is switchable by an applied electric field ferroelasticity – a deformation that is switchable by an applied stress While ferroelectric, ferroelastics, and ferromagnetics are formally multiferroics, these days the term is usually used to describe the magnetoelectric multiferroics that are simultaneously ferromagnetic and ferroelectric. Sometimes the definition is expanded to include nonprimary order parameters, such as antiferromagnetism or ferrimagnetism. In addition, other types of primary order, such as ferroic arrangements of magnetoelectric multipoles of which ferrotoroidicity is an example, were proposed.
Besides scientific interest in their physical properties, multiferroics have potential for applications as actuators, switches, magnetic field sensors and new types of electronic memory devices.
History
A Web of Science search for the term multiferroic yields the year 2000 paper "Why are there so few magnetic ferroelectrics?" from Nicola Spaldin (then Hill) as the earliest result. This work explained the origin of the contraindication between magnetism and ferroelectricity and proposed practical routes to circumvent it, and is widely credited with starting the modern explosion of interest in multiferroic materials. The availability of practical routes to creating multiferroic materials from 2000 stimulated intense activity. Particularly key early works were the discovery of large ferroelectric polarization in epitaxially grown thin films of magnetic BiFeO3, the observation that the non-collinear magnetic ordering in orthorhombic TbMnO3 and TbMn2O5 causes ferroelectricity, and the identification of unusual improper ferroelectricity that is compatible with the coexistence of magnetism in hexagonal manganite YMnO3. The graph to the right shows in red the number of papers on multiferroics from a Web of Science search until 2008; the exponential increase continues today.
Magnetoelectric materials
To place multiferroic materials in their appropriate historical context, one also needs to consider magnetoelectric materials, in which an electric field modifies the magnetic properties and vice versa. While magnetoelectric materials are not necessarily multiferroic, all ferromagnetic ferroelectric multiferroics are linear magnetoelectrics, with an applied electric field inducing a change in magnetization linearly proportional to its magnitude. Magnetoelectric materials and the corresponding magnetoelectric effect have a longer history than multiferroics, shown in blue in the graph to the right. The first known mention of magnetoelectricity is in the 1959 edition of Landau & Lifshitz' Electrodynamics of Continuous Media which has the following comment at the end of the section on piezoelectricity: One year later, Igor Dzyaloshinskii showed using symmetry arguments that the material Cr2O3 should have linear magnetoelectric behavior, and his prediction was rapidly verified by D. Astrov. Over the next decades, research on magnetoelectric materials continued steadily in a number of groups in Europe, in particular in the former Soviet Union and in the group of Hans Schmid at U. Geneva. A series of East-West conferences entitled Magnetoelectric Interaction Phenomena in Crystals (MEIPIC) was held between 1973 (in Seattle) and 2009 (in Santa Barbara),http://www.icmr.ucsb.edu/programs/MEIPIC6.html and indeed the term "multi-ferroic magnetoelectric" was first used by Schmid in the proceedings of the 1993 MEIPIC conference (in Ascona).
Mechanisms for combining ferroelectricity and magnetism To be defined as ferroelectric, a material must have a spontaneous electric polarization that is switchable by an applied electric field. Usually such an electric polarization arises via an inversion-symmetry-breaking structural distortion from a parent centrosymmetric phase. For example, in the prototypical ferroelectric barium titanate, BaTiO3, the parent phase is the ideal cubic ABO3 perovskite structure, with the B-site Ti4+ ion at the center of its oxygen coordination octahedron and no electric polarisation. In the ferroelectric phase the Ti4+ ion is shifted away from the center of the octahedron causing a polarization. Such a displacement only tends to be favourable when the B-site cation has an electron configuration with an empty d shell (a so-called d0 configuration), which favours energy-lowering covalent bond formation between the B-site cation and the neighbouring oxygen anions.
This "d0-ness" requirement is a clear obstacle for the formation of multiferroics, since the magnetism in most transition-metal oxides arises from the presence of partially filled transition metal d shells. As a result, in most multiferroics, the ferroelectricity has a different origin. The following describes the mechanisms that are known to circumvent this contraindication between ferromagnetism and ferroelectricity.
Lone-pair-active
In lone-pair-active multiferroics, the ferroelectric displacement is driven by the A-site cation, and the magnetism arises from a partially filled d shell on the B site. Examples include bismuth ferrite, BiFeO3, BiMnO3 (although this is believed to be anti-polar), and PbVO3. In these materials, the A-site cation (Bi3+, Pb2+) has a so-called stereochemically active 6s2 lone-pair of electrons, and off-centering of the A-site cation is favoured by an energy-lowering electron sharing between the formally empty A-site 6p orbitals and the filled O 2p orbitals.
Geometric ferroelectricity In geometric ferroelectrics, the driving force for the structural phase transition leading to the polar ferroelectric state is a rotational distortion of the polyhedra rather than an electron-sharing covalent bond formation. Such rotational distortions occur in many transition-metal oxides; in the perovskites for example they are common when the A-site cation is small, so that the oxygen octahedra collapse around it. In perovskites, the three-dimensional connectivity of the polyhedra means that no net polarization results; if one octahedron rotates to the right, its connected neighbor rotates to the left and so on. In layered materials, however, such rotations can lead to a net polarization.
The prototypical geometric ferroelectrics are the layered barium transition metal fluorides, BaMF4, M=Mn, Fe, Co, Ni, Zn, which have a ferroelectric transition at around 1000K and a magnetic transition to an antiferromagnetic state at around 50K. Since the distortion is not driven by a hybridisation between the d-site cation and the anions, it is compatible with the existence of magnetism on the B site, thus allowing for multiferroic behavior.
A second example is provided by the family of hexagonal rare earth manganites (h-RMnO3 with R=Ho-Lu, Y), which have a structural phase transition at around 1300 K consisting primarily of a tilting of the MnO5 bipyramids. While the tilting itself has zero polarization, it couples to a polar corrugation of the R-ion layers which yields a polarisation of ~6 μC/cm2. Since the ferroelectricity is not the primary order parameter it is described as improper. The multiferroic phase is reached at ~100K when a triangular antiferromagnetic order due to spin frustration arises.
Charge ordering Charge ordering can occur in compounds containing ions of mixed valence when the electrons, which are delocalised at high temperature, localize in an ordered pattern on different cation sites so that the material becomes insulating. When the pattern of localized electrons is polar, the charge ordered state is ferroelectric. Usually the ions in such a case are magnetic and so the ferroelectric state is also multiferroic. The first proposed example of a charge ordered multiferroic was LuFe2O4, which charge orders at 330 K with an arrangement of Fe2+ and Fe3+ ions. Ferrimagnetic ordering occurs below 240 K. Whether or not the charge ordering is polar has recently been questioned, however. In addition, charge ordered ferroelectricity is suggested in magnetite, Fe3O4, below its Verwey transition, and .
Magnetically-driven ferroelectricity In magnetically driven multiferroics the macroscopic electric polarization is induced by long-range magnetic order which is non-centrosymmetric. Formally, the electric polarisation, , is given in terms of the magnetization, , by
.
Like the geometric ferroelectrics discussed above, the ferroelectricity is improper, because the polarisation is not the primary order parameter (in this case the primary order is the magnetisation) for the ferroic phase transition.
The prototypical example is the formation of the non-centrosymmetric magnetic spiral state, accompanied by a small ferroelectric polarization, below 28K in TbMnO3. In this case the polarization is small, 10−2 μC/cm2, because the mechanism coupling the non-centrosymmetric spin structure to the crystal lattice is the weak spin-orbit coupling. Larger polarizations occur when the non-centrosymmetric magnetic ordering is caused by the stronger superexchange interaction, such as in orthorhombic HoMnO3 and related materials. In both cases the magnetoelectric coupling is strong because the ferroelectricity is directly caused by the magnetic order.
f-electron magnetism While most magnetoelectric multiferroics developed to date have conventional transition-metal d-electron magnetism and a novel mechanism for the ferroelectricity, it is also possible to introduce a different type of magnetism into a conventional ferroelectric. The most obvious route is to use a rare-earth ion with a partially filled shell of f electrons on the A site. An example is EuTiO3 which, while not ferroelectric under ambient conditions, becomes so when strained a little bit, or when its lattice constant is expanded for example by substituting some barium on the A site.
Composites It remains a challenge to develop good single-phase multiferroics with large magnetization and polarization and strong coupling between them at room temperature. Therefore, composites combining magnetic materials, such as FeRh, with ferroelectric materials, such as PMN-PT, are an attractive and established route to achieving multiferroicity. Some examples include magnetic thin films on piezoelectric PMN-PT substrates and Metglass/PVDF/Metglass trilayer structures. Recently a layer-by-layer growth of an atomic-scale multiferroic composite has been demonstrated, consisting of individual layers of ferroelectric and antiferromagnetic LuFeO3 alternating with ferrimagnetic but non-polar LuFe2O4 in a superlattice.
A new promising approach are core-shell type ceramics where a magnetoelectric composite is formed in-situ during synthesis. In the system (BiFe0.9Co0.1O3)0.4-(Bi1/2K1/2TiO3)0.6 (BFC-BKT) very strong ME coupling has been observed on a microscopic scale using PFM under magnetic field. Furthermore, switching of magnetization via electric field has been observed using MFM. Here, the ME active core-shell grains consist of magnetic CoFe2O4 (CFO) cores and a (BiFeO3)0.6-(Bi1/2K1/2TiO3)0.4 (BFO-BKT) shell where core and shell have an epitaxial lattice structure. The mechanism of strong ME coupling is via magnetic exchange interaction between CFO and BFO across the core-shell interface, which results in an exceptionally high Neel-Temperature of 670 K of the BF-BKT phase.
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