Ab initio cluster calculations of the magnetic properties of ZnO doped with transition metal ions

The magnetic properties of transition metal (TM) doped ZnO (TM = Mn2+, Co2+, and Ni2+) were determined by an embedded cluster approach using ab initio methods. We performed CASSCF (complete active space self-consistent field) calculations on clusters with one and two transition metal centers, respectively. In particular, we were interested in the magnetic exchange coupling between TM centers which are directly connected by an oxygen bridge. Two Mn as well as two Co centers are weakly antiferromagnetically coupled. For the investigation on the magnetic properties of Ni2+ doped ZnO it was necessary to include spin orbit coupling in the calculations. While without inclusion of spin orbit coupling the ground state of an isolated Ni2+ ion in ZnO is a 3E state, which should show a first order Zeeman interaction with the magnetic field, Ni2+ has a non-magnetic A1 ground state, when spin orbit coupling is included. The results of our calculations are in good agreement with experimental data for low temperatures and low concentrations of the transition metal centers.