Anisotropic ferromagnetism in carbon-doped zinc oxide from first-principles studies

A density functional theory study of substitutional carbon impurities in ZnO has been performed, using both the generalized gradient approximation (GGA) and a hybrid functional (HSE06) as exchange-correlation functional. It is found that the nonspinpolarized C-Zn impurity is under almost all conditions thermodynamically more stable than the C-O impurity which has a magnetic moment of 2 mu(B), with the exception of very O-poor and C-rich conditions. This explains the experimental difficulties in sample preparation in order to realize d(0) ferromagnetism in C-doped ZnO. From GGA calculations with large 96-atom supercells, we conclude that two C-O-C-O impurities in ZnO interact ferromagnetically, but the interaction is found to be short-ranged and anisotropic, much stronger within the hexagonal ab plane of wurtzite ZnO than along the c axis. This layered ferromagnetism is attributed to the anisotropy of the dispersion of carbon impurity bands near the Fermi level for C-O impurities in ZnO. From the calculated results, we derive that a C-O concentration between 2% and 6% should be optimal to achieve d(0)-ferromagnetism in C-doped ZnO.