Asymmetric dynamics of edge exchange spin waves in honeycomb nanoribbons with zigzag and bearded edges boundaries

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.