Spin Wave Mode of Edge-Localized Magnetic States in Nanographite Zigzag Ribbons

We consider the low-energy magnetic excitations of nanographite ribbons with zigzag edges. The zigzag ribbons possess almost flat bands at the Fermi level which cause a ferrimagnetic spin polarization localized at the edge sites. The spin wave mode of this magnetic state is investigated by a random phase approximation of the corresponding Hubbard model. This result is used to derive an effective Heisenberg model with ladder structure. Although this system has a spin gap (Haldane type), our analysis shows that the gap is small and the tendency towards ferrimagnetic correlation at the edges is strong.