Mn doping in GaN results in the generation of deep acceptor levels in the band gap of GaN. In the absence of any extrinsic doping, these levels are partially occupied and result in a ferromagnetic state being stabilized. In this work we show that strongly p -type conditions generated by the presence of Ga vacancies can destroy the ferromagnetic state. This is because the shallow acceptor levels generated by the p -type conditions depopulate the Mn associated deep band gap impurity levels resulting in a reduction of the exchange splitting and, hence, destroy ferromagnetism. In addition we find a Hund's rule type of mechanism which makes the Ga vacancies favor spin polarized configurations. The exchange splittings are as large as 0.5-1 eV. As the host material is changed from GaN to GaP and GaAs, we find that the spin polarization of the vacancy level decreases. © 2006 The American Physical Society.