  Mn doped semiconductors are extremely interesting systems due to their novel
magnetic properties suitable for the spintronics applications. It has been
shown recently by both theory and experiment that Mn doped GaN systems have a
very high Curie temperature compared to that of Mn doped GaAs systems. To
understand the electronic and magnetic properties, we have studied Mn doped GaN
system in detail by a first principles plane wave method. We show here the
effect of varying Mn concentration on the electronic and magnetic properties.
For dilute Mn concentration, $d$ states of Mn form an impurity band completely
separated from the valence band states of the host GaN. This is in contrast to
the Mn doped GaAs system where Mn $d$ states in the gap lie very close to the
valence band edge and hybridizes strongly with the delocalized valence band
states.
  To study the effects of electron correlation, LSDA+U calculations have been
performed.
  Calculated exchange interaction in (Mn,Ga)N is short ranged in contrary to
that in (Mn,Ga)As where the strength of the ferromagnetic coupling between Mn
spins is not decreased substantially for large Mn-Mn separation. Also, the
exchange interactions are anisotropic in different crystallographic directions
due to the presence or absence of connectivity between Mn atoms through As
bonds.
