The magnetic properties of dilute magnetic semiconductors (DMSs) are calculated from first-principles by mapping the ab initio results on a classical Heisenberg model. By using the Korringa-Kohn-Rostoker coherent-potential approximation (KKR-CPA) method within the local-density approximation, the electronic structure of (Ga, Mn)N and (Ga, Mn)As is calculated. Effective exchange coupling constants J ij 's are determined by embedding two Mn impurities at sites i and j in the CPA medium and using the J ij formula of Liechtenstein et al. [J. Magn. Magn. Mater. 67, 65 (1987)]. It is found that the range of the exchange interaction in (Ga, Mn)N, being dominated by the double exchange mechanism, is very short ranged due to the exponential decay of the impurity wave function in the gap. On the other hand, in (Ga, Mn)As, where p-d exchange mechanism dominates, the interaction range is weaker but long ranged, because the extended valence hole states mediate the ferromagnetic interaction. Curie temperatures (T C 's) of DMSs are calculated by using the mean-field approximation (MFA), the random-phase approximation, and the, in principle exact, Monte Carlo method. It is found that the T C values of (Ga, Mn)N are very low since, due to the short-ranged interaction, percolation of the ferromagnetic coupling is difficult to achieve for small concentrations. The MFA strongly overestimates T C . Even in (Ga, Mn)As, where the exchange interaction is longer ranged, the percolation effect is still important and the MFA overestimates T C by about 50%-100%. Dilute magnetic semiconductors (DMSs), such as (In, Mn)As and (Ga, Mn)As discovered by Munekata et al. and Ohno et al., have been well investigated as hopeful materials for spintronics. 1 Curie temperatures (T C 's) of these DMSs are well established 1-3 and some prototypes of spintronics devices have been produced based on these DMSs. The magnetism in these DMSs are theoretically investigated and it is known that the ferromagnetism in these systems, as well as (Ga, Mn)Sb, can be well described by Zener's p-d exchange interaction, due to the fact that the majority of d states lies energetically in the lower part of the valence band.4 Dietl et al. 5 and MacDonald et al. 6 explained many physical properties of (Ga, Mn)As based on the p-d exchange model, and first-principles calculations by Sato et al. showed that the concentration dependence of T C in (Ga, Mn)As was well understood by the p-d exchange interaction if a correction to the local-density approximation (LDA) is simulated by the LDA+ U method with U = 4 eV. 4 While these p-d exchange systems, in which the d states of Mn impurities are practically localized, are well understood, there exist an even larger class of systems where the d levels lie in the gap exhibiting impurity bands for sufficiently large concentrations. To these impurity band systems belong (Ga, Mn)N, (Ga, Cr)N, (Ga, Cr)As, (Zn, Cr)Te, (Zn, Cr)Se, and many others, as shown by first-principles calculations.
7Most of these systems are controversially discussed ...