  We study 1 or 2 neighboring Mn impurities, as well as complexes of 1 Mn and 1
or 2 Mg ions in a 64 atoms supercell of GaN by means of density functional
calculations. Taking into account the electron correlation in the local spin
density approximation with explicit correction of the Hubbard term (the LSDA+U
method) and full lattice relaxation we determine the nearest neighbor exchange
J for a pair of Mn impurities. We find J to be ferromagnetic and of the order
of about 18 meV in the Hamiltonian H=-2*J1*J2. That J is only weakly influenced
by the U parameter (varying between 2 and 8 eV) and by the lattice relaxation.
From a detailed analysis of the magnetization density distribution we get hints
for a ferromagnetic super-exchange mechanism. Also the Mn valence was found to
be 3+ without any doubt in the absence of co-doping with Mg. Co-doping with Mg
leads to a valence change to 4+ for 1 Mg and to 5+ for 2 Mg. We show that the
valence change can already be concluded from a careful analysis of the density
of states of GaN doped with Mn without any Mg.
