Spin susceptibilities in zigzag graphene nanoribbons

The simple Hubbard Hamiltonian with the mean field approximation is used to find out the energy bands and spin susceptibilities of a zigzag graphene nanoribbon. Depending on the electron doping, either antiferromagnetic or ferromagnetic configurations are possible; in the former, an energy gap exists which is proportional to the Hubbard parameter, while in the latter the up and down spin bands intersect the Fermi level. Due to the two dimensional nature of the system a square susceptibility matrix is necessary to explain the self-correlations and correlations between spins in the ribbon unit cell. The transverse spin susceptibilities are computed and the static case for ferromagnetic solutions is examined, as a function of the electron doping.