Design of graphene spin beam splitter based on Brewster's law

Spin beam splitter is one of the building blocks of graphene spintronics. Here, we adopt the concept of electron optics and design a new type of spin beam splitter by analogy with Brewster's law. The device is a pristine/ferromagnetic/pristine (P/M/P) graphene junction, where the M region is formed by a proximity effect of ferromagnetic insulators, such as EuO, and acts as an "optically thinner medium" relative to the P region. It is found that, when standing waves are formed in the M region with a length of integral multiple of the half longitudinal wavelength of electrons, electrons with the corresponding spin can pass completely through the junction and only electrons with the other spin are reflected by the P/M interface. This manifests Brewster's law and a spin beam splitter. It is also demonstrated that, due to the strong electric field effect of graphene, the Brewster angles for both spins can be monotonically modulated by a gate voltage in the M region in the whole range of -pi/2 to pi/2. Thus, our proposed spin beam splitter is not only an easily implemented and widely tunable build block for spintronics but also an interesting demonstration of electron optics.