Magnetic moment and coupling mechanism of iron-doped rutileTiO2from first principles

The magnetic ground state of Fe-doped rutile ${\mathrm{TiO}}_{2}$, an oxide-based dilute magnetic semiconductor, has been investigated within the hybrid-exchange approximation to density-functional theory. ${\mathrm{Fe}}_{x}{\mathrm{Ti}}_{1\ensuremath{-}x}{\mathrm{O}}_{2}$ with $x=0.125$ has been simulated by means of a 24-atom supercell with Fe doped substitutionally for Ti and this is established as the dilute limit through explicit comparison with calculations on a 192-atom supercell $(x=0.0156)$. A detailed study of the nature and stability of the predicted ground state with respect to variations in the oxidation state of the Fe ion, the delocalization or self-trapping of holes donated to the lattice, and the treatment of electronic exchange and correlation is presented. The ground state is found to be well described by a model based on an ${\mathrm{Fe}}^{3+}\text{\ensuremath{-}}{d}^{5}$ in a high spin state coupled to a partially delocalized hole accommodated in the $2p$ states of neighboring oxygen ions. No evidence is found for ferromagnetic coupling suggesting that the observed ferromagnetism in this system is dependent upon additional structural and/or electronic defects.