Charge and magnetic states of rutile TiO₂ doped with Cr ions

We observe that the electronic and magnetic properties of Cr-doped rutile TiO₂ single crystals are highly dependent on growth conditions. The ferromagnetic component of magnetic susceptibility is observed to be enhanced for samples grown under oxygen-rich conditions. To understand the charge state of Cr dopants and their role in response to an external magnetic field, we carry out density functional theory calculations for Cr-doped rutile TiO₂. Using the results of formation energy calculations in the presence of oxygen vacancies and Cr atom substitution at the Ti sites, we demonstrate that the + Cr3 state is a source of Curie-Weiss-type magnetic response, whereas the + Cr4 defect states contribute to the ferromagnetic component. We also provide the electronic structures of various defect configurations and attempt to explain the optical and electronic properties of the Cr-doped system.