Spin interactions of interstitial Mn ions in ferromagnetic GaMnAs

The recently reported Rutherford backscattering and particle-induced x-ray emission experiments have revealed that in low-temperature molecular beam epitaxy grown ${\mathrm{Ga}}_{1-x}{\mathrm{Mn}}_x\mathrm{As}$ a significant part of the incorporated Mn atoms occupies tetrahedral interstitial sites in the lattice. Here we study the magnetic properties of these interstitial $\left({\mathrm{Mn}}_{\mathrm{I}}\right)$ ions. We show that they do not participate in the hole-induced ferromagnetism. Moreover, ${\mathrm{Mn}}_{\mathrm{I}}$ double donors may form pairs with the nearest substitutional $\left({\mathrm{Mn}}_{\mathrm{Ga}}\right)$ acceptors—our calculations evidence that the spins in such pairs are antiferromagnetically coupled by the superexchange. We also show that for the Mn ion in another, hexagonal, interstitial position (which seems to be the case in the ${\mathrm{Ga}}_{1-x-y}{\mathrm{Mn}}_x{\mathrm{Be}}_y\mathrm{As}$ samples) the $p-d$ interactions with the holes, responsible for the ferromagnetism, are very much suppressed.