Beyond Virtual Crystal and Molecular Field Approximations in Diluted Magnetic Semiconductors

The framework of the virtual crystal approximation and the molecular field approximation has been widely used in the description of the extended states affected by the presence of the p-d exchange interaction in diluted magnetic semiconductors. We review shortly the known examples of diluted magnetic semiconductors systems which are described beyond these approximations. The interesting case constitutes the nearly binding impurity potential in Cd$\text{}_{1-x}$Μn$\text{}_{x}$S. The lattice approaches developed earlier allowed to prove in this case the breakdown of the virtual crystal approximation for low concentrations of magnetic ions and to explain the apparent concentration dependence of the exchange integral. We take explicitly into account the substitutional disorder neglected in the lattice theories and we rederive these results within the dilute and the average t-matrix alloy approach. We generalize systematically this theory to include also the magnetic disorder of the dilute spin subsystem appearing at finite temperatures. When the off-diagonal exchange scattering terms are taken into account in our calculations, we get a good agreement with the experimental data on the asymmetric field dependent spin splitting and the zero-field concentration dependence of the energy gap.