The magnetic properties of dilute magnetic semiconductors (DMS) are calculated from first-principles by mapping the ab initio results on a classical Heisenberg model. It is found that the range of the exchange interaction in (Ga, Mn)N is very short ranged due to the exponential decay of the impurity wave function in the gap. Curie temperatures (Tc) of DMS are calculated by using the Monte Carlo method. It is found that the Tc 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.
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