  The simple Hubbard Hamiltonian with the mean field approximation is used to
know about the energy bands and spin susceptibilities of zigzag graphene
nanoribbons. Depending on the electron doping, antiferromagnetic or
ferromagnetic configurations are possible; in the former, an energy gap exits
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 susceptibility square 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.
