Ferromagnetism in Mn doped GaAs due to substitutional-interstitial complexes

While most calculations on the properties of the ferromagnetic semiconductor GaAs:Mn have focussed on isolated Mn substituting the Ga site (Mn$_{Ga}$), we investigate here whether alternate lattice sites are favored and what the magnetic consequences of this might be. Under As-rich (Ga-poor) conditions prevalent at growth, we find that the formation energies are lower for Mn$_{Ga}$ over interstitial Mn (Mn$_i$).As the Fermi energy is shifted towards the valence band maximum via external $p$-doping, the formation energy of Mn$_i$ is reduced relative to Mn$_{Ga}$. Furthermore, under epitaxial growth conditions, the solubility of both substitutional and interstitial Mn are strongly enhanced over what is possible under bulk growth conditions. The high concentration of Mn attained under epitaxial growth of p-type material opens the possibility of Mn atoms forming small clusters. We consider various types of clusters, including the Coulomb-stabilized clusters involving two Mn$_{Ga}$ and one Mn$_i$. While isolated Mn$_i$ are hole killers (donors), and therefore destroy ferromagnetism,complexes such as Mn$_{Ga}$-Mn$_i$-Mn$_{Ga}$) are found to be more stable than complexes involving Mn$_{Ga}$-Mn$_{Ga}$-Mn$_{Ga}$. The former complexes exhibit partial or total quenching of holes, yet Mn$_i$ in these complexes provide a channel for a ferromagnetic arrangement of the spins on the two Mn$_{Ga}$ within the complex. This suggests that ferromagnetism in Mn doped GaAs arises both from holes due to isolated Mn$_{Ga}$ as well as from strongly Coulomb stabilized Mn$_{Ga}$-Mn$_i$-Mn$_{Ga}$ clusters.