Electron scattering in a graphene nanoribbon in the presence of ferromagnetic layer and Rashba interaction

We study the possibility to control the spin polarization and spin-dependent transport in a graphene sheet by considering a ferromagnetic layer in the presence of the Rashba spin-orbit interaction. Studying the scattering problem with the help of the Green function (which was found explicitly), we obtained simple analytical expressions for the spin dependent transmission probability. Using the small exchange parameter and Rashba coupling constant, we can obtain any degree of spin polarization, but in the case of a small interaction region, only for slow electrons.