Edge states in a ferromagnetic honeycomb lattice with armchair boundaries

We investigate the properties of magnon edge states in a ferromagnetic honeycomb lattice with armchair boundaries. In contrast with fermionic graphene, we find novel edge states due to the missing bonds along the boundary sites. After introducing an external on-site potential at the outermost sites we find that the energy spectra of the edge states are tunable. Additionally, when a non-trivial gap is induced, we find that some of the edge states are topologically protected and also tunable. Our results may explain the origin of the novel edge states recently observed in photonic lattices. We also discuss the behavior of these edge states for further experimental confirmations.