Multiferroic phase transitions in manganites RMnO_3：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 RMnO 3 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.