Magnetic Interactions of Cr-Cr and Co-Co Impurity Pairs in ZnO within a Band-Gap Corrected Density-Functional Approach

The well-known "band-gap" problem in approximate density functionals is manifested mainly in an overly low energy of the conduction band (CB). As a consequence, the localized gap states of 3d impurities states in wide-gap oxides such as ZnO occur often incorrectly as resonances inside the CB, leading to a spurious transfer of electrons from the impurity state into the CB of the host, and to a physically misleading description of the magnetic 3d-3d interactions. A correct description requires that the magnetic coupling of the impurity pairs be self-consistently determined in the presence of a correctly positioned CB (with respect to the 3d states), which we achieve here through the addition of empirical nonlocal external potentials to the standard density functional Hamiltonian. After this correction, both Co and Cr form occupied localized states in the gap and empty resonances low inside the CB. In otherwise undoped ZnO, Co and Cr remain paramagnetic, but electron-doping instigates strong ferromagnetic coupling when the resonant states become partially occupied.