# Graphite and Graphene as Perfect Spin Filters

The structure of graphene - a single layer of graphite - is such that the carbon p_{z} states form two half occupied, constant velocity bands which intersect at the Fermi energy at the K point in reciprocal space, so that graphene is a zero gap semiconductor. This gives rise to a host of interesting properties which have only recently been observed experimentally. However, for device applications the constant velocity is problematic because it means that the electrons have an infinite effective mass which makes it impossible to control the transport properties by means of external fields. We have pointed out that graphene is almost perfectly lattice matched to hexagonal boron nitride (*h*-BN) and that placing a sheet of graphene on top of *h*-BN leads to the opening of a small gap at the Fermi energy and give the electrons a finite effective mass [1].

We have also observed that the in-plane lattice constants of graphene and graphite match the surface lattice constants of (111) Co, Ni and Cu almost perfectly and that these metals have no majority spin states near to the high symmetry K point at or close to the Fermi energy while ferromagnetic Co and Ni do have states with minority spin character there (Fig.1) irrespective of whether they are fcc or hcp. It follows that in the absence of symmetry-lowering, perfect "spin filtering" should occur for graphite on top of a flat Ni or Co (111) surface [2]. The effectiveness of the spin filtering is demonstrated for a current-perpendicular-to-the-plane (CPP) structure with *n *graphene layers sandwiched between semi-infinite Ni electrodes. Five layers of graphene are sufficient to attenuate the majority spin electrons essentially completely leading to an ideal magnetoresistance (Fig.2). The spin filtering is quite insensitive to roughness and disorder (inset).

[1] G. Giovannetti, P.A. Khomyakov, G. Brocks, P.J. Kelly and J. van den Brink, *Substrate-induced band gap in graphene on hexagonal boron nitride: Ab initio density functional calculations,* Phys. Rev. B **76**, 073103 (2007).

[2] V.M. Karpan, G. Giovannetti, P.A. Khomyakov, M. Talanana, A.A. Starikov, M. Zwierzycki, J. van den Brink, G. Brocks and P.J. Kelly, *Graphite and Graphene as Perfect Spin Filters,* Phys. Rev. Lett. **99**, 176602 (2007).

**Figure 1. **fcc Fermi surface (FS) projections onto a plane perpendicular to the [111] direction for Co majority (a) and minority (b) spins, for Ni majority (c) and minority (d) spins and for Cu (e). The number of FS sheets is shown by the color bar. For graphene and graphite, surfaces of constant energy are centered on the K point (f ).

**Figure 2. **Conductances of a Ni│Gr* _{n}*│Ni junction as a function of the number of graphene layers

*n*for ideal junctions. Inset: magnetoresistance as a function of

*n*for: (circles) ideal junctions; (diamonds) Ni│Gr

*│Cu*

_{n}_{50}Ni

_{50}│Ni junctions where the surface layer is a disordered alloy; (squares) Ni│Gr

*│Ni junctions where the top layer of one of the electrodes is rough with only half of the top layer sites occupied (sketch).*

_{n}