Theoretical study of the magnetic interaction of Cr-doped ZnO with and without vacancies

First-principles density-functional theory (DFT) calculations have been performed to study the magnetic properties of ZnO:Cr with and without vacancies. The results indicate that the doping of Cr in ZnO induces obvious spin polarization around the Fermi level and a total magnetic moment of 3.77μ_B. The ferromagnetism (FM) exchange interaction between Cr atoms is short-ranged and decreases with increasing Cr separation distance. It is suggested that the FM state is not stable with low concentration of Cr. The presence of O vacancies can make the half-metallic FM state of the system more stable, so that higher Curie temperature ferromagnetism may be expected. Nevertheless, Zn vacancies can result in the FM stability decreasing slightly. The calculated formation energy shows that V_Zn+Cr_Zn complex forms spontaneously under O-rich conditions. However, under Zn-rich conditions, the complex of V_O+Cr_Zn forms more easily. Thus, ZnO doped with Cr may exhibit a concentration of vacancies that influence the magnetic properties.