Self-Compensating Incorporation of Mn in Ga$\text{}_{1-x}$Mn$\text{}_{x}$As

We consider hypothetical Ga$\text{}_{7}$MnAs_8, Ga$\text{}_{16}$MnAs$\text{}_{16}$, and Ga$\text{}_{14}$Mn$\text{}_{3}$As$\text{}_{16}$ crystals with Mn in a substitutional, interstitial, and both positions. Spin-polarized full-potential linearized augmented plane wave calculations were used to obtain their electronic structure. We show that the interstitial Mn acts as a double donor and compensates the holes created by two Mn atoms in substitutional positions. This explains why the number of holes in Ga$\text{}_{1-x}$Mn$\text{}_{x}$As is much smaller than x. The presence of interstitial atoms may also be the reason for the lattice expansion with increasing content of Mn. The differences in electronic behavior of substitutional and interstitial Mn are discussed.