Origin of magnetic moments in defective TiO 2 single crystals

In this Brief Report we show that ferromagnetism can be induced in pure ${\text{TiO}}_{2}$ single crystals by oxygen ion irradiation. By combining x-ray diffraction, Raman scattering, and electron-spin resonance spectroscopy, a defect complex, i.e., ${\text{Ti}}^{3+}$ ions on the substitutional sites accompanied by oxygen vacancies, has been identified in irradiated ${\text{TiO}}_{2}$. This kind of defect complex results in a local $({\text{TiO}}_{6\ensuremath{-}x})$ stretching Raman mode. We elucidate that ${\text{Ti}}^{3+}$ ions with one unpaired $3d$ electron provide the local magnetic moments.