  A microscopic Hamiltonian for interacting manganese impurities in diluted
magnetic semiconductors (DMS) is derived. It is shown that in p -type III-V DMS
the indirect exchange between Mn impurities has similarities with the Zener
mechanism in transition metal oxides. Here the mobile holes and localized
states near the top of the valence band play the role of unoccupied oxygen
orbitals which induce ferromagnetism. The Curie temperature estimated from the
proposed kinematic exchange agrees with recent experiments on GaAs:Mn. The
model is also applicable to the GaP:Mn system.
