V, Nb and Ta doping of anatase TiO$_{2}$: from a dilute magnetic semiconductor to a transparent conducting oxide*

We have investigated by means of first-principle supercell calculations the effects of doping anatase TiO$_{2}$ by V, Nb and Ta. We find: ({\em i}) V doping makes TiO$_{2}$:V ferromagnetic. A single V impurity has a magnetic moment of 1.0 $\mu_{B}$/V atom with an electronic configuration $a_1^2\, t_{1+}^3\, t_{1-}^3\, t_{2+}^1\, t_{2-}^0\, e_+^{0}\, e_-^0$. The ferromagnetic interaction between two V impurities is found to extend to more than fifth neighbors, with calculated ferromagnetic stabilization energy raging from 124 meV at the first neighbor to 27 meV at the fifth neighbor. ({\em ii}) Nb and Ta doping of TiO$_{2}$ makes the system conductive, but not magnetic. The calculated equilibrium free-electron concentration ($n_{e}$) at $T = 1000$K for Ti-rich--O-poor growth conditions is $2.7 \times10^{21}$ and $5.9 \times10^{21}$ cm$^{-3}$ for Nb and Ta doping respectively, whereas pure TiO$_{2}$ is calculated to have a electron density of only $1.8 \times10^{18}$ cm$^{-3}$ due to intrinsic defects. Thus, Nb and Ta doping of TiO$_{2}$ enhance dramatically the electron concentration and hence are good transparent conductor oxides.