Role of disorder in Mn:GaAs, Cr:GaAs, and Cr:GaN.

We present calculations of magnetic exchange interactions and critical temperature T(c) in Ga1-xMnxAs, Ga1-xCrxAs, and Ga1-xCrxN. 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.