  We propose a new mechanism of indirect exchange interaction, which can be
responsible for the ferromagnetic ordering in Mn-doped semiconductors (like
GaMnAs) at low carrier concentration. The mechanism is based on the interplay
of the hybridization of band states (conduction or valence) with localized
impurity (donor or acceptor) states and the direct exchange interaction between
localized spins and the band states. The indirect exchange coupling between two
impurities occurs when the wavefunctions of the corresponding localized donor
(acceptor) states overlap. This coupling is independent of the free carrier
concentration and therefore may be responsible for ferromagnetic transition at
low or vanishing carrier concentration.
