Multiferroics

Multiferroics are defined as materials that exhibit more than one of the primary ferroic properties: Multiferroics are defined as materials that exhibit more than one of the primary ferroic properties: in the same phase. While ferroelectric ferroelastics and ferromagnetic ferroelastics 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 non-primary order parameters, such as antiferromagnetism or ferrimagnetism. In addition other types of primary order, such as ferroic arrangements of magneotelectric multipoles of which ferrotoroidicity is an example, have also been recently proposed. Besides scientific interest in their physical properties, multiferroics have potential for applications as actuators, switches, magnetic field sensors or new types of electronic memory devices. A Web of Science search for the term 'multiferroic*' yields the year 2000 paper Why are there so few magnetic ferroelectrics? from N. A. 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. (An article on how Spaldin arrived at the question is here). 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. 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: “Let us point out two more phenomena, which, in principle, could exist. One is piezomagnetism, which consists of linear coupling between a magnetic field in a solid and a deformation (analogous to piezoelectricity). The other is a linear coupling between magnetic and electric fields in a media, which would cause, for example, a magnetization proportional to an electric field. Both these phenomena could exist for certain classes of magnetocrystalline symmetry. We will not however discuss these phenomena in more detail because it seems that till present, presumably, they have not been observed in any substance.” One year later, I. E. 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 H. 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), and indeed the term 'multi-ferroic magnetoelectric' was first used by H. Schmid in the proceedings of the 1993 MEIPIC conference (in Ascona). 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. 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.