Effective interactions in a graphene layer induced by the proximity to a ferromagnet

Abstract The nature of the induced couplings in graphene due its proximity to a ferromagnetic insulator is analysed. We combine general symmetry principles and simple tight-binding descriptions to study different orientations of the magnetization. We find that, in addition to a simple exchange field, a number of other terms arise. Some of these terms act as magnetic orbital couplings, and others are proximity-induced spin–orbit interactions. We find different sets of couplings depending on the orientation of the magnetization. Typically, the magnitudes of all the studied couplings are similar, and the individual strengths are very sensitive to the details of the structure. Depending on these values, we show that a variety of phases, including anomalous Hall effect regimes, are possible.