Electrically controllable spin pumping in graphene via rotating magnetization

We investigate pure spin pumping in graphene by imposing a ferromagnet (F) with rotating magnetization on top of it. Using the generalized scattering approach for adiabatic spin pumping, we obtain the spin current pumped through magnetic graphene to the normal (N) region. This spin current which can be easily controlled by gate voltages, reaches sufficiently large values measurable in current experimental setups. The spin current reaches its maximum when one of the spins is completely filtered because of its vanishing density of states in the ferromagnetic part. In order to study the effect of the ferromagnetic part length on the pumped spin current, the N—F—N structure is considered. It is found that in contrast to the metallic ferromagnetic materials the transverse spin coherence length can be comparable to the length of F. Subsequently, due to the quantum interferences inside the middle F region, the spin current becomes an oscillatory function of $JL/\hslash v_{\text{F}}$ in which J is the spin splitting and L is the length of F. Finally controllability of the pumped spin into two different normal sides in the N—F—N hybrid device gives rise to the spin battery effect. (paper)