Valley filtering in graphene under a magnetic proximity

We investigate valley-dependent electronic transport properties of graphene in close proximity to a thick ferromagnetic insulator (FI). It is found that spin-resolved valley filtering can be achieved under the interplay between the stray field emanated from the FI and the exchange-proximity interaction. In the intraband-tunneling regime, there exists a window of Fermi energy where both the spin and valley polarization of the output current are almost complete $(\ensuremath{\approx}\ensuremath{-}100%)$. In the interband-tunneling regime, the valley polarization can approach $100%$ or $\ensuremath{-}70%$ near some conductance peaks, while the spin polarization is near $100%$ in a wide window of Fermi energy. The role of valley-Zeeman coupling is examined for both cases. The spin-valley filtering is found to be tunable by electric gating. Our findings are helpful for designing a spin-valley filter based on graphene with imprinted ferromagnetism.