Exchange interactions in diluted magnetic semiconductors

On the basis of ab initio calculations for Mn-doped GaN, GaP, GaAs and GaSb, we discuss the origin of ferromagnetism in diluted magnetic semiconductors. The calculations use the Korringa-Kohn-Rostoker method in connection with the coherent potential approximation to describe the substitutional and moment disorder. By mapping the total energy results onto a Heisenberg model, the Curie temperature T-C is estimated in the mean field approximation (MFA). If impurity bands are formed in the gap, as is the case for (Ga, Mn)N, double exchange dominates leading to a characteristic rootc dependence of T-C(MFA) as a function of the Mn concentration c. On the other hand, if the d states are localized, as in (Ga, Mn)Sb, Zener's p-d exchange prevails, resulting in a linear c dependence of T MFA. (Ga, Mn)As is an intermediate case, showing a rootc-like behaviour in the local density approximation (LDA), but a nearly linear c dependence, if the more accurate LDA + U method with U = 4 eV is used.