  The mechanism for the ferromagnetic order of (Ga,Mn)As and (Ga,Mn)N is
extensively studied over a vast range of Mn concentrations. We calculate the
electronic structures of these materials using density functional theory in
both the local spin density approximation and the LDA+U scheme, that we have
now implemented in the code SIESTA.
  For (Ga,Mn)As, the LDA+U approach leads to a hole mediated picture of the
ferromagnetism, with an exchange constant $N\beta$ =~ -2.8 eV. This is smaller
than that obtained with LSDA, which overestimates the exchange coupling between
Mn ions and the As $p$ holes.
  In contrast, the ferromagnetism in wurtzite (Ga,Mn)N is caused by the
double-exchange mechanism, since a hole of strong $d$ character is found at the
Fermi level in both the LSDA and the LDA+U approaches. In this case the
coupling between the Mn ions decays rapidly with the Mn-Mn separation. This
suggests a two phases picture of the ferromagnetic order in (Ga,Mn)N, with a
robust ferromagnetic phase at large Mn concentration coexisting with a diluted
weak ferromagnetic phase.
