Interstitial Mn in (Ga,Mn)As: Binding energy and exchange coupling

We present ab initio calculations of total energies of Mn atoms in various interstitial positions. The calculations are performed by the full-potential linearized plane-wave method. The minimum energy is found for tetrahedral $\mathrm{T}\left({\mathrm{As}}_4\right)$ position, but the energy of the $\mathrm{T}\left({\mathrm{Ga}}_4\right)$ site differs by only a few meV. The $\mathrm{T}\left({\mathrm{Ga}}_4\right)$ position becomes preferable in the p-type materials. In samples with one substitutional and one interstitial Mn, the Mn atoms tend to form a close pair with antiparallel magnetic moments. We also use the spin splitting of the valence band to estimate the exchange coupling $J_{\mathrm{pd}}$ for various positions of Mn. The exchange parameter is the same for the substitutional and for the $\mathrm{T}\left({\mathrm{As}}_4\right)$ position, and it is somewhat smaller in the case of the $\mathrm{T}\left({\mathrm{Ga}}_4\right)$ position.