Relativistic ferromagnetic magnon at the zigzag edge of graphene

We study the spin-wave excitations near the zigzag edge of graphene. It is rather interesting that we obtain a single branch of relativistic ferromagnetic magnon due to the presence of the open boundary. Note that magnons in antiferomagnets appear in pairs, while the single brach magnon in ferromagnets does not have relativistic dispersion. Thus, the magnon near the zigzag edge of graphene is a hybrid of both, signaling its intrinsic property as a boundary excitation that must be embedded in a higher dimensional bulk system.