  We report on the theoretical prediction of asymmetric edge spin waves,
propagating in opposite directions on the edges of honeycomb nanoribbons with
zigzag and bearded edges boundaries. The simultaneous propagation of edge spin
waves in the same direction on both edges of these nanoribbons is hence
predicted to be forbidden. These asymmetric edge exchange spin waves are
analogous to the nonreciprocal surface spin waves reported in magnetic thin
films. Their existence is related to the nontrivial symmetry underlying the
nanoribbons under study. The edge and discretized bulk exchange spin waves are
calculated in the long wavelength part of the Brillouin zone using the
classical spin wave theory approach and appropriate boundary conditions. In the
absence of an external magnetic field in our study, the asymmetric edge spin
waves propagate with equal frequencies and opposite directions, since the
energy dispersion relation is independent of the sign of the wavevector
components in the long wavelength part of the Brillouin zone. The edge spin
waves are characterized by linear dispersion relations for magnetically
isotropic nanoribbons. Introducing magnetic anisotropy in the calculation
significantly enhances the energy gap between the edge and bulk spin waves in
both types of nanoribbons. Based on our calculation, the large energy gap
allows separate excitation of bulk and edge modes as their energies are no more
overlapping.
