Microscopic model and phase diagrams of the multiferroic perovskite manganites

Orthorhombically distorted perovskite manganites, RMnO₃ 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 RMnO₃ 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 and the bc-plane spin cycloid with P. 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.