The in-plane lattice constants of close-packed planes of fcc and hcp Ni and Co match that of graphite almost perfectly so that they share a common two dimensional reciprocal space. Their electronic structures are such that they overlap in this reciprocal space for one spin direction only allowing us to predict perfect spin filtering for interfaces between graphite and (111) fcc or (0001) hcp Ni or Co. First-principles calculations of the scattering matrix show that the spin filtering is quite insensitive to amounts of interface roughness and disorder which drastically influence the spin-filtering properties of conventional magnetic tunnel junctions or interfaces between transition metals and semiconductors. When a single graphene sheet is adsorbed on these open $d$-shell transition metal surfaces, its characteristic electronic structure, with topological singularities at the K points in the two dimensional Brillouin zone, is destroyed by the chemical bonding. Because graphene bonds only weakly to Cu which has no states at the Fermi energy at the K point for either spin, the electronic structure of graphene can be restored by dusting Ni or Co with one or a few monolayers of Cu while still preserving the ideal spin injection property.
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