Magnetism from 2p States in Alkaline Earth Monoxides: Trends with Varying N Impurity Concentration

$2p$-based magnetic moments and magnetic coupling are studied with density functional based methods for substitutional N in the alkaline earth monoxide series MgO, CaO, SrO, BaO. The hole is rather strongly localized near the N$^{2-}$ ion, being somewhat more so when strong on-site interactions are included in the calculations. Strong magnetic coupling is obtained in the itinerant electron limit but decreases strongly in the localized limit in which the Coulomb repulsion within the N $2p$ shell (U) is much greater than the N $2p$ impurity bandwidth (W). We find that this limit is appropriate for realistic N concentrations. Ordering on a simple cubic sublattice may maximize the magnetic coupling due to its high directionality.