Ferromagnetism in N doped ZnO and MgO

We investigate single and multiple dopings of N in ZnO$_{1-x}$N$_x$ and in MgO$_{1-x}$N$_x$ using a first principles density functional theory supercell method for x$<$ 10\%. We find evidence for ferromagnetism and propose a mechanism mediating the interaction. The magnetic coupling between the local moments on the N defects is studied as a function of the distance between N atoms and the role of hole and carrier co-doping is investigated. An RKKY-type interaction is found to mediate coupling, leading to both ferromagnetic and antiferromagnetic couplings for different doping configurations.