Classifying multiferroics: Mechanisms and effects

Electricity and magnetism were combined into one common discipline in the 19th century, culminating in the Maxwell equations. But electric and magnetic ordering in solids are most often considered separately—and usually with good reason: the electric charges of electrons and ions are responsible for the charge effects, whereas electron spins govern magnetic properties There are, however, cases where these degrees of freedom couple strongly. For example, in the new, large field of spintronics, the effects of spins on the transport properties of solids (and vice versa) allow the possibility to control one by the other. The finding of a strong coupling of magnetic and electric degrees of freedom in insulators can be traced back to Pierre Curie, but the real beginning of this field started in 1959 with a short remark by Landau and Lifshitz in a volume of their Course of Theoretical Physics[1]: “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.” The situation changed soon thereafter, when Dzyaloshinskii predicted [2], and Astrov observed [3], this type of coupling, which is now known as the linear magnetoelectric effect. This was rapidly followed by the discovery of many other compounds of this class and by a rather complete classification of possible symmetry groups allowing for the effect. A new twist in this problem was the idea that not only can strong cross-coupling of responses exist in solids (i.e., the appearance of magnetization M in an electric field E, or the inverse effect of electric polarization P generated by the application of magnetic field H), but that there may exist systems in which two types of ordering—(ferro)magnetism, the spontaneous orderFIG. 1: Multiferroics combine the properties of ferroelectrics and magnets. In the ideal case, the magnetization of a ferromagnet in a magnetic field displays the usual hysteresis (blue), and ferroelectrics have a similar response to an electric field (yellow). If we manage to create multiferroics that are simultaneously ferromagnetic and ferroelectric (green), then there is a magnetic response to an electric field, or, vice versa, the modification of polarization by magnetic field. And, in principle we have here the basis for making a 4-state logic state: (P + M+), (+−), (−+), (−−). (Illustration: Alan Stonebraker)