Microscopic approach to the magnetoelectric coupling in RCrO3

A microscopic model is proposed to describing the multiferroic properties in [Formula: see text], where [Formula: see text] is the magnetic rare earth ion. Using the Green’s function theory, the weak ferromagnetism and the coercive field are calculated by a balance between the Dzyaloshinskii–Moriya interaction (DMI), the single-ion anisotropy and the exchange interaction. We have discussed the magnetic rotational spin-reorientation (SR) transition between [Formula: see text] and [Formula: see text] phases in [Formula: see text] and the abrupt one between [Formula: see text] and [Formula: see text] in [Formula: see text] calculating the energies in the corresponding phases. The type of the phase transition in [Formula: see text] is determined by the sign of the second magnetic anisotropy constant. In order to investigate the origin of the extraordinary ferroelectricity in [Formula: see text], we have studied the different contributions in the polarization due to the antisymmetric exchange DMI and the magnetostriction arising from the Cr-ordering. It is shown that the polarization is due to the interaction between the magnetic [Formula: see text]- and Cr-ions. The influence of a magnetic field on the polarization and of an electric field on the magnetization are also calculated as an evidence for a strong magnetoelectric coupling in [Formula: see text].