First-principles study of the origin and nature of ferromagnetism inGa1−xMnxAs

The properties of diluted ${\mathrm{Ga}}_{1-x}{\mathrm{Mn}}_x\mathrm{As}$ are calculated for a wide range of Mn concentrations within the local-spin-density approximation of density-functional theory. Mülliken population analyses and orbital-resolved densities of states show that the configuration of Mn in GaAs is compatible with either ${3d}^5$ or ${3d}^6;$ however, the occupation is not integer due to the large p-d hybridization between the Mn d states and the valence band of GaAs. The spin splitting of the conduction band of GaAs has a mean-field-like linear variation with the Mn concentration, and indicates ferromagnetic coupling with the Mn ions. In contrast, the valence band is antiferromagnetically coupled with the Mn impurities, and the spin splitting is not linearly dependent on the Mn concentration. This suggests that the mean-field approximation breaks down in the case of Mn-doped GaAs, and corrections due to multiple scattering must be considered. We calculate these corrections within a simple free-electron model, and find good agreement with our ab initio results if a large exchange constant $(N\beta =-4.5\mathrm{eV})$ is assumed.