Experiments on (Ga,Mn)As in the low-doping insulating phase have shownevidence for the presence of an impurity band at 110 meV above the valenceband. The motivation of this paper is to investigate the role of the impurityband in determining the magnetic correlations in the low-doping regime of thedilute magnetic semiconductors. For this purpose, we present results on theHaldane-Anderson model of transition-metal impurities in a semiconductor host,which were obtained by using the Hirsch-Fye Quantum Monte Carlo (QMC)algorithm. In particular, we present results on the impurity-impurity andimpurity-host magnetic correlations in two and three-dimensional semiconductorswith quadratic band dispersions. In addition, we use the tight-bindingapproximation with experimentally-determined parameters to obtain the host bandstructure and the impurity-host hybridization for Mn impurities in GaAs. Whenthe chemical potential is located between the top of the valence band and theimpurity bound state (IBS), the impurities exhibit ferromagnetic (FM)correlations with the longest range. We show that these FM correlations aregenerated by the antiferromagnetic coupling of the host electronic spins to theimpurity magnetic moment. Finally, we obtain an IBS energy of 100 meV, which isconsistent with the experimental value of 110 meV, by combining the QMCtechnique with the tight-binding approach for a Mn impurity in GaAs.
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