Role of Disorder in Mn:GaAs, Cr:GaAs, and Cr:GaN

We present calculations of magnetic exchange interactions and critical temperature T_c in Ga_1-xMn_xAs, Ga_1-xCr_xAs, and Ga_1-xCr_xN. 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. 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, while ordering the dopants on a lattice increases it. With all the factors taken into account, T_c is reasonably predicted by the local spin-density approximation in Mn:GaAs without the need to invoke compensation by donor impurities.