Spin-valley splitting of electron beam in graphene

We study spatial separation of the four degenerate spin-valley components of an electron beam in a EuO-induced and top-gated ferromagnetic/pristine/strained graphene structure. We show that, in a full resonant tunneling regime for all beam components, the formation of standing waves can lead sudden phase jumps ∼−π and giant lateral Goos-Hänchen shifts as large as the transverse beam width, while the interplay of the spin and valley imaginary wave vectors in the modulated regions can lead differences of resonant angles for the four spin-valley flavors, manifesting a spin-valley beam splitting effect. The splitting effect is found to be controllable by the gating and strain.