The physical conditions required for the existence of collective ferromagnetism in non-magnetic oxides, due to intrinsic point defects such as vacancies, were considered. Hafnia was used as an example because it had previously been noted theoretically that charge-neutral Hf vacancies in HfO2 had partially-occupied electronic levels within the band gap. The vacancies thus carried a non-vanishing local magnetic moment. Density functional super-cell calculations had also shown that 2 such vacancies could interact ferromagnetically if they were separated by up to third-nearest neighbor distances. This suggested that Hf vacancies could explain the observed collective ferromagnetism in thin HfO2 films. A previously developed methodology was used here in order to question whether such vacancies could lead to collective ferromagnetism. By applying this methodology to HfO2, it was found that Hf vacancies appeared in a few possible charge states, but that not all of these had a local magnetic moment. The energy required to form such vacancies was calculated as a function of the chemical potential and Fermi energy and the equilibrium concentration of those vacancies which had a non-vanishing local magnetic moment were estimated from this as a function of growth temperature and O pressure. It was found that, under the most favorable equilibrium growth conditions, the concentration of Hf vacancies, with a magnetic moment, at room temperature did not exceed 6.4 x 1015/cm3 (2.2 x 10−7%). An independent calculation was made of the minimum Hf vacancy concentration required to achieve wall-to-wall percolation in the HfO2 lattice, given the range of the magnetic VHf-VHf interaction (5 neighbors) obtained from the present super-cell calculations. It was found that the minimum percolation concentration (13.5%) required for collective ferromagnetism was 8 orders of magnitude higher than the equilibrium vacancy concentration in HfO2 under the most favorable growth conditions. It was concluded that equilibrium growth could not lead to ferromagnetism.

Nonstoichiometry as a Source of Magnetism in Otherwise Nonmagnetic Oxides - Magnetically Interacting Cation Vacancies and their Percolation. J.Osorio-Guillén, S.Lany, S.V.Barabash, A.Zunger: Physical Review B, 2007, 75[18], 184421 (9pp)