Perfect Spin-filtering in graphene monolayer-bilayer superlattice with zigzag boundaries.

We show that the spontaneous magnetization is formed at the zigzag boundary between monolayer and bilayer graphene by the self-consistent calculation based on Hubbard model. In a monolayer- bilayer graphene superlattice with zigzag boundaries, it is surprising that nearly 100% spin polarization is achieved in the energy window around the Dirac point, no matter the magnetization configuration at two boundaries is parallel or antiparallel. The reason is that the low-energy transport is only influenced by the magnetization at one edge, but not by that at the other. The underlying physics is unveiled by the spin-split band structure and the distribution of the wave-function pertaining to the lowest (highest) subband of electron (hole).