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We report on the theoretical prediction of asymmetric edge spin waves,propagating in opposite directions on the edges of honeycomb nanoribbons withzigzag and bearded edges boundaries. The simultaneous propagation of edge spinwaves in the same direction on both edges of these nanoribbons is hencepredicted to be forbidden. These asymmetric edge exchange spin waves areanalogous to the nonreciprocal surface spin waves reported in magnetic thinfilms. Their existence is related to the nontrivial symmetry underlying thenanoribbons under study. The edge and discretized bulk exchange spin waves arecalculated in the long wavelength part of the Brillouin zone using theclassical spin wave theory approach and appropriate boundary conditions. In theabsence of an external magnetic field in our study, the asymmetric edge spinwaves propagate with equal frequencies and opposite directions, since theenergy dispersion relation is independent of the sign of the wavevectorcomponents in the long wavelength part of the Brillouin zone. The edge spinwaves are characterized by linear dispersion relations for magneticallyisotropic nanoribbons. Introducing magnetic anisotropy in the calculationsignificantly enhances the energy gap between the edge and bulk spin waves inboth types of nanoribbons. Based on our calculation, the large energy gapallows separate excitation of bulk and edge modes as their energies are no moreoverlapping.

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