Spin filtering in a ferromagnetic graphene superlattice

We have studied spin transport in monolayer and bilayer ferromagnetic graphene superlattice, based on transfer matrix method. The ferromagnetic insulator layers with exchange energy Eex, are in contact with the gate electrode. The magnetization in ferromagnetic insulator layers aligned in the z or negative z-direction. We find that the conductivity of the systems has an oscillatory behavior with respect to the gate voltage and it depends on the spin state of electron. It has been shown that the spin current can be controlled by gate voltage and in proper width of the wells and barriers it is possible to filter electron with a specific spin