A first-principles approach to magnetic properties of diluted magnetic semiconductors (DMS) is presented that is based on the local spin-density approximation (LSDA) as implemented in the framework of the tight-binding linear muffin-tin orbital method, while the effect of randomness is described by the coherent potential approximation. Application of a real-space Greenfunction formalism yields the exchange pair interactions between distant magnetic atoms that are needed for quantitative studies of magnetic excitations including the Curie temperatures. We have found that the pair exchange interactions exhibit a strong directional dependence and are exponentially damped with increasing distance between magnetic atoms due to disorder and the half-metallic character of the DMS. As a case study we consider (Ga, Mn) As, (Ga, Mn)N, and (Zn, Cr)Te alloys. The calculations demonstrate that inclusion of disorder and, in particular, realistic distances among magnetic impurities, are needed to obtain critical temperatures which are in good agreement with available experiments.
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