Spin-dependent Goos–Hänchen shift and spin beam splitter in gate-controllable ferromagnetic graphene

The transmission and Goos–Hänchen (GH) shift for charge carriers in gate-controllable ferromagnetic graphene induced by ferromagnetic insulator are investigated theoretically. Numerical results demonstrate that spin-up and spin-down electrons exhibit remarkably different transmission and GH shifts. The spin-dependent GH shifts directly demonstrate the spin beam splitting effect, which can be controlled by the voltage of gate. We attribute the spin beam splitting effect to the combination of tunneling through potential barrier and Zeeman interaction from the magnetic field and the exchange proximity interaction between the ferromagnetic insulator and graphene. In view of the spin beam splitting effect and the spin-dependent GH shifts, the gate-controllable ferromagnetic graphene might be utilized to design spin beam splitter.