Microscopic mechanisms of spin-dependent electric polarization in 3d oxides

We address a systematic microscopic theory of spin-dependent electric polarization in 3d oxides starting with a generic three-site two-hole cluster. A perturbation scheme realistic for 3d oxides is applied which implies the quenching of orbital moments by low-symmetry crystal field, strong intra-atomic correlations, the dp-transfer effects, and rather small spin-orbital coupling. An effective spin operator of the electric-dipole moment is deduced incorporating both nonrelativistic proportional to((s) over cap (1)center dot(s) over cap (2)) and relativistic proportional to[s(1)xs(2)] terms. The nonrelativistic electronic polarization mechanism related to the effects of the redistribution of the local on-site charge density due to pd covalency and exchange coupling is believed to govern the multiferroic behavior in 3d oxides. The relativistic exchange-dipole moment is mainly stems from the nonrelativistic one due to the perturbation effect of Dzyaloshinsky-Moriya coupling and is estimated to be a weak contributor to the electric polarization observed in the most of 3d multiferroics.