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Effect of non-magnetic impurities on the magnetic states of anatase TiO$_2$

The electronic and magnetic properties of TiO$_2$, TiO$_{1.75}$, TiO$_{1.75}$N$_{0.25}$, and TiO$_{1.75}$F$_{0.25}$ compounds have been studied by using \emph{ab initio} electronic structure calculations. TiO$_2$ is found to evolve from a wide-band-gap semiconductor to a narrow-band-gap semiconductor to a half-metallic state and finally to a metallic state with oxygen vacancy, N-doping and F-doping, respectively. Present work clearly shows the robust magnetic ground state for N- and F-doped TiO$_2$. The N-doping gives rise to magnetic moment of $\sim$0.4 $μ_B$ at N-site and $\sim$0.1 $μ_B$ each at two neighboring O-sites, whereas F-doping creates a magnetic moment of $\sim$0.3 $μ_B$ at the nearest Ti atom. Here we also discuss the possible cause of the observed magnetic states in terms of the spatial electronic charge distribution of Ti, N and F atoms responsible for bond formation.