Graphene-based electronic spin lenses

We theoretically demonstrate the capability of a ferromagnetic-normal interface in graphene to focus an electron wave with a certain spin direction. The essential feature is the negative refraction Klein tunneling, which is spin resolved when the exchange energy of ferromagnetic graphene exceeds its Fermi energy. Exploiting this property, we propose a graphene normal-ferromagnetic-normal electronic spin lens through which an unpolarized electronic beam can be collimated with a finite spin polarization. Our study reveals that magnetic graphene has the potential to be the electronic counterpart of the recently discovered photonic chiral metamaterials that exhibit a negative refractive index for only one direction of the circular polarization of the photon wave.