Proximity Induced Exchange Splitting in Graphene*

We perform an ab-initio study of the proximity effect in a two-dimensional (2D) heterostructure composed of graphene and a thin film ferromagnetic insulator (europium oxide, EuO). Two different structures are considered i) graphene on a EuO layer and ii) graphene sandwiched between two EuO layers. Both structures show two-fold degenerate low-energy bands at the $\Gamma $ point in the Brillouin zone, however, the former heterostructure shows a clear energy gap in the spectrum whereas the latter exhibits degenerate band crossings. The two different spectra result from a competition of proximity induced exchange splitting on the graphene sheet and sub-lattice mass induced due to the crystal field effect. Addition of spin-orbit coupling in the sandwiched structure indicates lifting of this two-fold degeneracy leading to band anti-crossings if the inversion symmetry perpendicular to the graphene plane is broken.