  The recently reported Rutherford backscattering and particle-induced X-ray
emission experiments have revealed that in low-temperature MBE grown GaMnAs a
significant part of the incorporated Mn atoms occupies tetrahedral interstitial
sites in the lattice. Here we study the magnetic properties of these
interstitial ions. We show that they do not participate in the hole-induced
ferromagnetism. Moreover, Mn interstitial double donors may form pairs with the
nearest substitutional Mn 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 the other, hexagonal, interstitial position (which
seems to be the case in the GaMnBeAs samples) the p-d interactions with the
holes, responsible for the ferromagnetism, are very much suppressed.
