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 non-spinpolarized CZn​ impurity is under almost all
conditions thermodynamically more stable than the CO​ impurity which
has a magnetic moment of 2μB​, with the exception of very O-poor
and C-rich conditions. This explains the experimental difficulties in sample
preparation in order to realize d0-ferromagnetism in C-doped ZnO. From GGA
calculations with large 96-atom supercells, we conclude that two
CO​-CO​ 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 CO​ impurities in
ZnO. From the calculated results, we derive that a CO​
concentration between 2% and 6% should be optimal to achieve
d0-ferromagnetism in C-doped ZnO.Comment: 9 pages, 7 figure