  We investigate the electronic and magnetic properties of (Ga,Mn)N
nanocrystals using the density functional theory. We study both wurtzite and
zinc-blende structures doped with one or two substitutional Mn impurities. For
a single Mn dopant placed close to surface, the behavior of the empty
Mn-induced state, hereafter referred to as "Mn hole", is different from bulk
(Ga,Mn)N. The energy level corresponding to this off-center Mn hole lies within
the nanocrystal gap near the conduction edge. For two Mn dopants, the most
stable magnetic configuration is antiferromagnetic, and this was unexpected
since (Ga,Mn)N bulk shows ferromagnetism in the ground state. The surprising
antiferromagnetic alignment of two Mn spins is ascribed also to the holes
linked to the Mn impurities located close to surface. Unlike Mn holes in
(Ga,Mn)N bulk, these Mn holes in confined (Ga,Mn)N nanostructures do not
contribute to the ferromagnetic alignment of the two Mn spins.
