Ferromagnetic order induced on graphene by Ni/Co proximity effects

We build a tight-binding Hamiltonian describing Co/Ni over graphene, contemplating ATOP (a Co/Ni atom on top of each carbon atom of one graphene sublattice) and HCP (one Co/Ni atom per graphene plaquette) configurations. For the ATOP configuration the orbitals involved, for the Co/Ni, are the dz2-r2, which most strongly couples to one graphene sublattice and the dxz,dyz orbitals that couple directly to the second sublattice site. Such configuration is diagonal in pseudospin and spin space, yielding electron doping of the graphene and antiferromagnetic ordering in the primitive cell in agreement with DFT calculations. The second, HCP, configuration is symmetric in the graphene sublattices and only involves coupling to the dxz,dyz orbitals. The register of the lattices in this case allows for a new coupling between nearest-neighbor sites, generating nondiagonal terms in the pseudospin space and novel spin-kinetic couplings mimicking a spin-orbit coupling generated by a magnetic coupling. The resulting proximity effect in this case yields ferromagnetic order in the graphene substrate. We derive the band structure in the vicinity of the K points for both configurations, the Bloch wave functions and their spin polarization.