Ferromagnetism in defect-ridden oxides and related materials

The existence of high-temperature ferromagnetism in thin films and nanoparticles of oxides containing small quantities of magnetic dopants remains controversial. Some regard these materials as dilute magnetic semiconductors, while others think they are ferromagnetic only because the magnetic dopants form secondary ferromagnetic impurity phases such as cobalt metal or magnetite. There are also reports in d⁰ systems and other defective oxides that contain no magnetic ions. Here, we investigate TiO₂ (rutile) containing 1–5% of iron cations and find that the room temperature ferromagnetism of films prepared by pulsed-laser deposition is not due to magnetic ordering of the iron. The films are neither dilute magnetic semiconductors nor hosts to an iron-based ferromagnetic impurity phase. A new model is developed for defect-related ferromagnetism, which involves a spin-split defect band populated by charge transfer from a proximate charge reservoir—in the present case a mixture of Fe²⁺ and Fe³⁺ ions in the oxide lattice. The phase diagram for the model shows how inhomogeneous Stoner ferromagnetism depends on the total number of electrons N_tot, the Stoner exchange integral I and the defect bandwidth W; the band occupancy is governed by the d–d Coulomb interaction U. There are regions of ferromagnetic metal, half-metal and insulator as well as non-magnetic metal and insulator. A characteristic feature of the high-temperature Stoner magnetism is an anhysteretic magnetization curve, which is practically temperature independent below room temperature. This is related to a wandering ferromagnetic axis, which is determined by local dipole fields. The magnetization is limited by the defect concentration, not by the 3d doping. Only 1–2% of the volume of the films is magnetically ordered.