Theory of diluted magnetic semiconductors: A minimal model

In this article we review our recent theoretical studies on the carrier induced ferromagnetism of DMS. We propose a minimal model, which is composed of a single tight-binding band of carriers and magnetic impurities, which randomly substitute the host sites. Both of nonmagnetic attractive potentials due to impurities and the exchange interactions between carrier and impurity spins are taken into account. We apply the coherent potential approximation in studying this system. The obtained phase diagrams illustrate the characteristic features of the carrier induced ferromagnetism in DMS. The role of nonmagnetic interaction for the enhancement of the Curie temperature is clarified. The results suggest that the ferromagnetism in Ga1−xMnxAs is caused by a double-exchange-like mechanism mediated by valence band holes. We also report the results of numerical simulations of the model.