Magnetic states at the Oxygen surfaces of ZnO and Co-doped ZnO

First principles calculations of the O surfaces of Co-ZnO show that substitutional Co ions develop large magnetic moments which long-range coupling depends on their mutual distance. The local spin polarization induced at the O atoms is three times larger at the surface than in the bulk, and the surface stability is considerably reinforced by Co. Moreover, a robust ferromagnetic state is predicted at the Oxygen (0001) surface even in the absence of magnetic atoms. The occurrence of surface magnetic moments correlates with the number of {\it p}-holes in the valence band of the oxide, and the distribution of the magnetic charge is, even in the absence of spin-orbit interaction, highly anisotropic.