  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.
