Spin-Dependent Interaction of a Band Electron with Paramagnetic Impurities

A band electron interacting with N electrons in a d-shell of a paramagnetic impurity in zinc-blende type semiconductors was considered. The hybridization of band and d-states in the crystal field and the nonorthogonality mechanisms of interaction were examined in addition to the standard direct exchange. The Heisenberg-type form was derived for the interaction between a Γ$\text{}_{8}$-electron and an impurity with a half-filled d-shell. The domination of the hybridization mechanism explains the observed sign of the effective exchange constant for Γ$\text{}_{8}$ electrons in diluted magnetic semiconductors (DMS) and the difference in magnitude of this constant for Mn$\text{}^{2+}$ and Fe$\text{}^{3+}$ ions in HgSe.