Analysis of spin current in ferromagnetic graphene junctions

Magnetization transport in a ferromagnetic/normal/ferromagnetic graphene junction has been investigated. Inspired by a seminal paper [Phys. Rev. B 66, 014,407, 2002], the longitudinal and transverse components of spin current i.e. components parallel and perpendicular to the magnetization direction in the ferromagnetic layer have been studied. It has been shown that only when the reflected and transmitted waves from the interface between two normal/ferromagnetic layers have the same angle as that of the incident wave, there will be no torque associated with the transport of longitudinal spin current. In general, for an arbitrary direction of magnetization, all spin current components are coexisted and therefore the parallel and the perpendicular components of spin transfer torque are existed. Therefore it is not possible to draw a general conclusion that the torque associated with the transport of longitudinal spin current is always zero.