Predicting d$^0$ magnetism

Predicting magnetism originating from 2$p$ orbitals is a delicate problem, which depends on the subtle interplay between covalency and Hund's coupling. Calculations based on density functional theory and the local spin density approximation fail in two remarkably different ways. On the one hand the excessive delocalization of spin-polarized holes leads to half-metallic ground states and the expectation of room temperature ferromagnetism. On the other hand, in some cases a magnetic ground state may not be predicted at all. We demonstrate that a simple self-interaction correction scheme modifies both these situations via an enhanced localization of the holes responsible for the magnetism and possibly Jahn-Teller distortion. In both cases the ground state becomes insulating and the magnetic coupling between the impurities weak.