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.
The magnetism and conductance of two-dimensional Heisenberg spin lattices are investigated by using Monte Carlo simulations to qualitatively understand a fascinating magnetoresistance effect observed in magnetic materials and their artificial multilayers. Various magnetic profiles, including a pure ferromagnetic, a pure antiferromagnetic, two phase com-petitive cases, and an artificial sandwich junction, are simulated, and their conductances are calculated based on an extended resistor-network model. Magnetoresistance is observed in some lattices, which is prominent when the system is near phase boundaries. Compared with real manganites, the absence of colossal magnetoresistance in our simulation implies the es- sential role of charge ordered phase which is not included in our pure spin model. However, our model provides an intuitive understanding of the spin-dependent conductance in large scale.
