First-principles calculations of electronic and magnetic properties of carbon doped TiO2 clusters

We present spin-polarized density functional calculations of ferromagnetic properties of (TiO2)n and the substitutionally carbon doping TinO2n−mCm clusters with n = 1–10 and m = 1–2. We analyze the eigenvalue spectra, charge transfer, molecular orbitals, spin densities and induced magnetic moments of (TiO2)n clusters with single and double carbon substitution. The results show that the carbon doping clusters have similar geometries to parent (TiO2)n clusters with slightly larger Ti–O bond length and the clusters with n ⩾ 3 become stable due to the structural transformation to extended three dimensional structures. We find that the HOMO–LUMO gap, although dependent on carbon concentration, reduces substancially and is lower for the spin-down electrons as compared to spin-up electrons. A surprising finding is that an odd-even oscillation observe in the exchange energy and the clusters with even ‘n’ are ferromagnetically more stable than odd ‘n’. The results show that the doping induces magnetic moment of ∼2μB per carbon atom in all the cases with small but significant induced magnetic moments at oxygen and titanium site due to delocalization of carbon ‘p’ orbitals. All clusters with two carbon impurities show ferromagnetic interaction, except when carbon atoms share the same titanium atom as the nearest neighbor and is predominantly mediated through π- and σ-bonds in the three-dimensional clusters. These results demonstrate that the ferromagnetic interaction is significantly enhanced in the extended 3D clusters and oxygen connectivity appears to play a key role in stabilizing these interactions in Ti–O network connecting two carbon atoms.