A mean-field model of ferromagnetism mediated by delocalized or weakly localized holes in zinc-blende and wurzite diluted magnetic semiconductors is presented. The model takes into account strong spin-orbit and ki p couplings in the valence band as well as the influence of strain upon the hole density of states. Possible effects of disorder and carrier-carrier interactions, particularly near the metal-to-insulator transition, are discussed. A quantitative comparison between experimental and theoretical results for ~Ga,Mn!As demonstrates that the theory describes the values of the Curie temperatures observed in the studied systems as well as explaining the directions of the easy axes and the magnitudes of the corresponding anisotropy fields as a function of biaxial strain. Furthermore, the model reproduces the unusual sign, magnitude, and temperature dependence of the magnetic circular dichroism in the spectral region of the fundamental absorption edge. Chemical trends and various suggestions concerning design of ferromagnetic semiconductor systems are described.
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