Spin Excitation in Nano-Graphite Ribbons with Zigzag Edges

Spin excitation in a nano-graphite ribbon with zigzag edges is investigated theoretically. Due to the strongly localized nature of the states near the Fermi energy, the effective Hamiltonian for the low-energy physics is given by the 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 the case of an odd number of zigzag lines.