Statistical Theory of Magnetoelectric Effects in Antiferromagnetics

Abstract

It is shown on the basis of a statistical mechanical calculation involving the molecular field approximation and the free energy that the spin-orbit mechanism previously proposed by the author leads not only to the electrically induced but also to the magnetically induced magnetoelectric effect. In addition, this mechanism is found to lead to a magnetoelectric contribution to the electric susceptibility. For a two-sublattice antiferromagnet, the temperature dependence of the magnetoelectric susceptibilities is shown to be quantitatively different from but qualitatively similar to that predicted in the previous work on a phenomenological basis. Although even purely magnetic data indicate that a two-sublattice model is not strictly applicable to ${\mathrm{Cr}}_2$ ${\mathrm{O}}_3$, a comparison of the present theory with experiments suggests (with the help of data on the electric field splitting of certain paramagnetic resonance lines in ruby) that the spin-orbit mechanism accounts for a significant part of the magnetoelectric effects observed in ${\mathrm{Cr}}_2$ ${\mathrm{O}}_3$. The Appendix contains a revised derivation of some known thermodynamic relations relevant to magnetoelectric effects. It also contains a proposal, based on thermodynamic and symmetry considerations, that "piezomagnetoelectric" and "gyroelectric" effects may exist.