Spin Orbit Torque in Graphene/Co Heterosystem

The spin-orbit torque (SOT) technique has opened new horizons for the development of innovative magnetic devices beyond memories and data storage. When graphene is attached to the surface of Co (001), the inversion symmetry is broken, which results in the onset of a built-in perpendicular electric field. As a result, in the presence of the large spin-orbit coupling of Co, Rashba effect emerges at the interface. Therefore, a spin density driven by a net current can be achieved at the interface, bringing SOT into such a heterostructure. With density functional theory, we show that Co atoms at the interface exhibit spin-momentum locking, which is in line with the exprtiments. Around the Fermi level, the graphene Dirac cones couple with the Co 3d states around the K and K' points, resulting in a spin texture odd in momentum k. This special spin texture promotes current-driven SOT. We then project the band structure obtained by first principles onto Wannier orbitals to get the tight-binding Hamiltonian. Non-equilibrium properties then are calculated using the Kubo formula. Our results show that the SOT can be used to electrically control the magnetization of the Co layer and to realize fast electronic device.