Multiferroic phase transitions in manganites RMnO₃: A two-orbital double exchange simulation

The semi-quantum two-orbital exchange model is used to investigate the effect of small rare-earth ion substitution on orthorhombic RMnO₃ with A-type antiferromagnetic order, using the Monte Carlo algorithm, exact diagonalization, and zero-temperature optimization approaches. It is revealed that the substitution results in a rich multiferroic phase diagram where the coexisting A-type antiferromagnetic phase and spiral spin phase, pure spiral spin phase, coexisting spiral spin phase, the E-type antiferromagnetic phase, and the pure E-type antiferromagnetic phase emerge in sequence. The multiferroic phase transitions modulate substantially the electric polarization, which is consistent qualitatively with recent experiments.