Spin-density-wave instability in graphene doped near the van Hove singularity

We study the instability of the metallic state toward the formation of a different ground state in graphene doped near the van Hove singularity. The system is described by the Hubbard model and a field theoretical approach is used to calculate the charge and spin susceptibility. We find that for repulsive interactions, within the random phase approximation, there is a competition between ferromagnetism and the spin-density wave (SDW). It turns out that a SDW with a triangular geometry is more favorable when the Hubbard parameter is above the critical value U-c (T), which depends on the temperature T, even if there are small variations in the doping. Our results can be verified by angle-resolved photoemission spectroscopy or neutron scattering experiments in highly doped graphene.