DFT modeling of Mn charged states in Ga$_{1-x}$Mn$_x$As diluted ferromagnetic semiconductors: The cluster approach

Quantum chemical cluster modeling of the high-symmetry nanoclusters Ga$_{15}$MnAs$_{16}$H$_{36}$ and Ga$_{12}$MnAs$_{16}$H$_{36}$ simulating the bulk of a GaAs crystal with Mn paramagnetic impurity center is carried out within the Density Functional Theory. A Generalized Gradient Approximation method PBEPBE/LanL2DZ is used to study the neutral Mn$^0$ and ionized Mn$^-$ states of a Mn atom in the nanoclusters under consideration. The change of the charge state of the impurity center from Mn$^0$ to Mn$^-$ leads to a considerable relaxation of Mn–As bonds in the immediate surroundings of the Mn atom and to the "$p$-hole" recombination. It also affects the spin density localization. The components of the $g$-tensor for both the neutral Mn$^0$ and the ionized Mnstates are calculated by the Gauge-Independent Atomic Orbital (GIAO) method with the hybrid density-functional mPW1PW91. The resulting values of the $g$-factor are in good agreement with the experimental Electron Paramagnetic Resonance data. The results obtained confirm the applicability of the cluster approach for describing charge effects in dilute ferromagnetic semiconductors.