Theory of spin-phonon coupling in multiferroic manganese perovskites RMnO₃

Magnetoelectric phase diagrams of the rare-earth (R) Mn perovskites RMnO₃ are theoretically studied by focusing on crucial roles of the symmetric magnetostriction or the Peierls-type spin-phonon coupling through extending our previous work. We first construct a microscopic classical Heisenberg model for RMnO₃ including the frustrated spin exchanges, single-ion anisotropy, and Dzyaloshinskii-Moriya interaction. We also incorporate the lattice degree of freedom coupled to the Mn spins via the Peierls-type magnetostriction. By analyzing this model using the replica-exchange Monte Carlo technique, we reproduce the entire phase diagram of RMnO₃ in the plane of temperature and magnitude of the orthorhombic lattice distortion. Surprisingly it is found that in the ab-plane spiral spin phase, the (S•S)-type magnetostriction plays an important role for the ferroelectric order with polarization P a whose contribution is comparable to or larger than the contribution from the (S×S)-type magnetostriction, whereas in the bc-plane spiral phase, the ferroelectric order with P c is purely of (S×S) origin. This explains much larger P in the ab-plane spiral phase than the bc-plane spiral phase as observed experimentally and gives a clue how to enhance the magnetoelectric coupling in the spin-spiral-based multiferroics. We also predict a noncollinear deformation of the E-type spin structure resulting in the finite (S×S) contribution to the ferroelectric order with P a, and a wide coexisting regime of the commensurate E and incommensurate spiral states, which resolve several experimental puzzles.