Superexchange in insulators and semiconductors: II. The range of the exchange interaction

Abstract

In this paper we discuss the range of exchange interactions in magnetic semiconductors. It is shown that the range depends strongly on the energy required to excite an electron from the fully occupied valence band to the empty magnetic d orbitals. The range of the exchange interaction and of the spin-density distribution is the same when this excitation energy is large. It is found that kinetic exchange and correlation exchange are the dominant contributions. The usual perturbation theory breaks down when the dp excitation energy becomes of the order of the band width. In this case one has to calculate the exchange interaction in a more rigorous way. This limit is discussed using two-particle Green functions. It is found that these results deviate strongly from the ones obtained using perturbation theory. We derive a path model from an analysis of the effective transfer between two magnetic orbitals. Such a model can explain the long-range exchange interactions reported in the last decades in a large number of magnetic semiconductors and semimagnetic semiconductors. This path model can explain the anisotropy of long-range spin-density distributions found in doped semiconductors.