Graphene magnetoresistance in a parallel magnetic field: Spin polarization effect

We develop a theory for graphene magnetotransport in the presence of carrier spin polarization as induced, for example, by the application of an in-plane magnetic field (B) parallel to the two-dimensional graphene layer. We predict a negative magnetoresistance alpha proportional to B-2 for intrinsic graphene, but for extrinsic graphene we find a nonmonotonic magnetoresistance which is positive at lower magnetic fields (below the full spin polarization) and negative at very high fields (above the full spin polarization). The conductivity of the minority spin band (-) electrons does not vanish as the minority carrier density (n(-)) goes to zero. The residual conductivity of (-) electrons at n(-)=0 is unique to graphene. We discuss experimental implications of our theory.