Microscopic model and phase diagrams of the multiferroic perovskite manganites

Abstract

Orthorhombically distorted perovskite manganites, $R\mathrm{Mn}{\mathrm{O}}_{3}$ with $R$ being a trivalent rare-earth ion, exhibit a variety of magnetic and electric phases including multiferroic (i.e., concurrently magnetic and ferroelectric) phases and fascinating magnetoelectric phenomena. We theoretically study the phase diagram of $R\mathrm{Mn}{\mathrm{O}}_{3}$ by constructing a microscopic spin model, which includes not only the superexchange interaction but also the single-ion anisotropy (SIA) and the Dzyaloshinsky-Moriya interaction (DMI). Analysis of this model using the Monte Carlo method reproduces the experimental phase diagrams as functions of the $R$-ion radius, which contain two different multiferroic states, i.e., the $ab$-plane spin cycloid with ferroelectric polarization $P\ensuremath{\parallel}a$ and the $bc$-plane spin cycloid with $P\ensuremath{\parallel}c$. The orthorhombic lattice distortion or the second-neighbor spin exchanges enhanced by this distortion exquisitely controls the keen competition between these two phases through tuning the SIA and DMI energies. This leads to a lattice-distortion-induced reorientation of $P$ from $a$ to $c$ in agreement with the experiments. We also discuss spin structures in the $A$-type antiferromagnetic state, those in the cycloidal spin states, origin and nature of the sinusoidal collinear spin state, and many other issues.