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

Abstract

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${}_{\mathrm{Zn}}$ impurity is under almost all conditions thermodynamically more stable than the C${}_{\mathrm{O}}$ impurity which has a magnetic moment of $2{\ensuremath{\mu}}_{\mathrm{B}}$, 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${}_{\mathrm{O}}$-C${}_{\mathrm{O}}$ 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${}_{\mathrm{O}}$ impurities in ZnO. From the calculated results, we derive that a C${}_{\mathrm{O}}$ concentration between 2$%$ and 6$%$ should be optimal to achieve ${d}^{0}$-ferromagnetism in C-doped ZnO.