Substitutional cobalt in ZnO has a weak preference for antiferromagnetic ordering. Stabilization of ferromagnetism is achieved through $n$-type doping, which can be understood through a band coupling model. However, the description of the transition to a ferromagnetic ground state varies within different levels of band theory; issues arise due to the density functional theory underestimation of the band gap of ZnO, and the relative position of the nominally unfilled Co $t_{2d}$ states. We examine these limitations, including approaches to overcome them, and explain the contradictions in previous studies, which drastically overestimate the doping threshold for magnetic ordering.

• Received 4 March 2008

DOI:https://doi.org/10.1103/PhysRevLett.100.256401