Statistical Mechanics and Origin of the Magnetoelectric Effect inCr2O3

Abstract

Expressions for the temperature dependence of the magnetoelectric susceptibility parallel and perpendicular to the trigonal axis in ${\mathrm{Cr}}_2$ ${\mathrm{O}}_3$ are presented. A two-sublattice model is used. The relation between the sublattice magnetization and the temperature is derived from experimental results for the parallel magnetic susceptibility. All statistical averages appearing in the expressions for the magnetoelectric susceptibilities are then evaluated using this susceptibility-derived result. Using this technique, quantitative agreement with the experimental results is obtained. For the parallel case, three mechanisms that have been previously proposed as contributing to the parallel magnetoelectric susceptibility are considered. It is concluded that the parallel effect is dominated at low temperatures by the electric-field-induced $g$ shift and at higher temperatures by the electric-field-induced shift in the intrasublattice exchange energy. For the perpendicular case, three mechanisms are also considered; two of them, an electric-field-induced antisymmetric exchange term and an electric-field-induced $g$ shift, have not previously been discussed. It is concluded that the perpendicular effect is dominated by the electric-field-induced shift in the single-ion anisotropy energy. Crystal-field aspects of the perpendicular effect are presented, and it is argued that the electric-field-induced $g$ shift is actually 1-2 orders of magnitude smaller than the crystal-field estimate.