Gate-tunable spin torque and edge current in magnetized graphene nanoribbons caused by spin-orbit coupling

Motivated by recent experiments that demonstrate gate-tunable spin-orbit coupling (SOC) in graphene heterostructures, we investigate the effect of SOC on the magnetic response of graphene. In particular, we demonstrate that in the magnetized zigzag nanoribbons, the geometric confinement combined with the Rashba SOC cause peculiar magnetic
responses. The first is a transverse susceptibility roughly proportional to the SOC, which implies a gate-controllable spin torque on the magnetization. Secondly, the equilibrium spin current produced by the Rashba SOC is largely affected by the presence of the magnetization. Moreover, an in-plane magnetization pointing in the transverse direction produces a laminar flow of edge currents, whose spatial profile is symmetric at the two edges.