Modeling and Physics of Multiferroic Perovskite Manganites

A new type of multiferroicity was experimentally discovered in 2003 in a perovskite manganite TbMnO$_3$ where its ferroelectricity is induced by cycloidally ordered Mn spins. Susequently, such spin-cycloid multiferroic phase was also discovered in $R$MnO$_3$ with other rare-earth ions $R$=Dy, Eu$_{1-x}$Y$_x$, Tb$_{1-x}$Gd$_x$, etc. In this class of materials, the magnetism and ferroelectricity are inseparably coupled, and resulting strong magnetoelectric coupling enables us to control/manipulate the electricity (magnetism) by magnetic (electric) fields. Moreover, many interesting magnetoelectric phenomena due to their cross correlation have been discovered. In this article, we discuss a microscopic theoretical model for $R$MnO$_3$ constructed by taking into account their precise electronic and lattice structures and overview the theoretical works based on this model which elucidated rich magnetoelectric phenomena of $R$MnO$_3$. The perovskite manganites are not only the first-discovered spin-spiral multiferroic materials but also a typical class of materials that exhibits most of the magnetoelectric phenomena manifested in many other multiferroics. Therefore, the comprehensive understanding of $R$MnO$_3$ directly leads to the clarification of universal physics of magnetoelectric phenomena in multiferroic materials.