We show that a bilayer graphene flake deposited above a ferromagnetic insulator can behave as a spin-filtering device. The ferromagnetic material induces exchange splitting in the graphene flake, and due to the Fano antiresonances occurring in the transmission of the graphene flake as a function of flake length and energy, it is possible to obtain a net spin current. This happens when an antiresonance for one spin channel coincides with a maximum transmission for the opposite spin. We propose these structures as a means to obtain spin-polarized currents and spin filters in graphene-based systems.
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