Role of Disorder in Mn:GaAs, Cr:GaAs, and Cr:GaN
  We present calculations of magnetic exchange interactions and critical temperature T_c in Mn:GaAs, Cr:GaAs and Cr:GaN. The local spin density approximation is combined with a linear-response technique to map the magnetic energy onto a Heisenberg hamiltonion, but no significant further approximations are made. Special quasi-random structures in large unit cells are used to accurately model the disorder. T_c is computed using both a spin-dynamics approach and the cluster variation method developed for the classical Heisenberg model.   We show the following: (i) configurational disorder results in large dispersions in the pairwise exchange interactions; (ii) the disorder strongly reduces T_c; (iii) clustering in the magnetic atoms, whose tendency is predicted from total-energy considerations, further reduces T_c. Additionally the exchange interactions J(R) are found to decay exponentially with distance R^3 on average; and the mean-field approximation is found to be a very poor predictor of T_c, particularly when J(R) decays rapidly. Finally the effect of spin-orbit coupling on T_c is considered. With all these factors taken into account, T_c is reasonably predicted by the local spin-density approximation in MnGaAs without the need to invoke compensation by donor impurities. 
J. L. Xu, M. van Schilfgaarde, G. D. Samolyuk