Structure and magnetism of the $(2 \times 2)$-FeO(111) surface
Based on ab initio calculations we determine the features and relative stability of different models proposed to describe the $(2 \times 2)$-FeO(111) reconstruction. Our results suggest that both wurtzite and spinel-like environments are possible, and their coexistence explains phenomena of biphase ordering. The surface phase diagram reflects a competition of charge and magnetic compensation effects, and reveals the important influence of the substrate on the final surface structure. Though antiferromagnetic couplings are dominant, frustration and the delicate balance of surface and bulk exchange interactions lead to a net surface magnetization that accounts for the large measured values.