Effect of orbital symmetry on the anisotropic superexchange interaction

Employing the microscopic superexchange model incorporating the effect of spin-orbit interaction, we have investigated the Dzyaloshinsky-Moriya (DM) interaction in perovskite transition-metal (TM) oxides and explored the interplay between the DM interaction and the TM-3d orbital symmetry. For d(3) and d(5) systems with isotropic orbital symmetry, the DM vectors are well described by a simple symmetry analysis considering only the bond geometry. In contrast, the DM interaction for d(4) systems with anisotropic orbital symmetry shows slightly different behavior, which does not obey simple symmetry analysis. The direction as well as the strength of the DM vector varies depending on the occupied orbital shape. We have understood this behavior based on the orbital symmetry induced by local crystal field variation.