  Spin excitation in a nano-graphite ribbon with zigzag edges is investigated
theoretically. Due to the strongly localized nature of the states near Fermi
energy, the effective Hamiltonian for the low energy physics is given by
Heisenberg Hamiltonian with the nearest neighbor exchange coupling. The action
corresponding to the effective Hamiltonian is mapped to that of the O(3)
nonlinear sigma model. It is shown that the spin excitation has a gap when the
number of the zigzag lines is even, whereas the excitation becomes gapless in
case of the odd number of the zigzag lines.
