Ferromagnetism in Carbon doped Zinc Oxide Systems

We report spin polarized density functional calculations of ferromagnetic properties of a series of ZnO clusters and solid containing one or two substitutional carbon impurities. We analyze the eigen value spectra, spin densities and molecular orbitals, and induced magnetic moments for ZnC, Zn$_{2}$C, Zn$_{2}$OC, carbon substituted clusters Zn$_{n}$O$_{n}$ (n=3--10, 12) and ZnO solid. The results show that the doping induces magnetic moment of the $\sim$2 $\mu_{B}$ in all the cases. All the systems with two carbon impurities show ferromagnetic interaction except when the carbon atoms share the same Zn atom as the nearest neighbor. This ferromagnetic interaction is predominantly mediated via $\pi$ bonds in ring structures and through $\pi$ and $\sigma$ bonds in three dimensional structure. The calculations also show that the interaction is significantly enhanced in solid, bringing out the role of dimensionality of Zn-O network connecting two carbon atoms.