Multiferroics
Multiferroics are defined as materials that exhibit more than one of the primary ferroic order parameters
in the same phase. While ferroelectric ferroelastics (with their associated piezoelectric and electrostrictive coupling) and ferromagnetic ferroelastics (with piezomagnetic and magnetomechanical coupling) 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.
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 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, in which an electric field induces a magnetisation that is linear in the applied field and vice versa, and the corresponding magnetoelectric effect have a longer history, shown in blue in the graph to the right. (Note that while magnetoelectric materials are not necessarily multiferroic, all ferromagnetic ferroelectric multiferroics are magneto electric.) 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 multiferroic was first used by H. Schmid in the proceedings of the 1993 MEIPIC conference (in Ascona).
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