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Abstract
We consider the indirect exchange interaction between magnetic ions in semimagnetic semiconductors. Based on the band structure calculated by the empirical tight-binding method and the double summations over the first Brillouin zone carried out by the tetrahedron method, we show that the indirect exchange interaction is highly anisotropic and the [110] and equivalent directions are the strongest coupling directions with the longest interaction range. The indirect exchange interaction consists of two competing components, one ferromagnetic and one antiferromagnetic, mediated by electrons occupying different valence bands. The antiferromagnetic part coming from the higher valence bands dominates the ferromagnetic one for any nonzero interspin lattice vector. The interaction between the nearest-neighboring pair is the strongest and is responsible for the magnetic ordering of the materials observed. The calculated results are consistent with available experimental data.
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