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

We report on the theoretical prediction of asymmetric edge spin waves, propagating in opposite directions at the boundaries of antiferromagnetic honeycomb nanoribbons with zigzag and bearded edges. The simultaneous propagation of edge spin waves along the same direction on both edges of the nanoribbons is forbidden. These asymmetric exchange spin waves at the edge boundaries are analogous to the nonreciprocal surface spin waves reported in magnetic thin films. Their existence is related to the nontrivial symmetry underlying these nanoribbons types. The discretized bulk and the edge exchange spin waves are calculated for the long wavelength part of the nanoribbon Brillouin zone (BZ), using the classical field spin wave theory and notably appropriate boundary conditions. In the absence of an external magnetic field in our study, the asymmetric edge spin waves propagate with equal frequencies and along opposite directions. The edge spin waves are characterized by linear dispersion relations for magnetically isotropic nanoribbons. For magnetically anisotropic nanoribbons, our calculations show that the energy gap between the edge and bulk spin waves is enhanced for both types of zigzag and bearded nanoribbons. The large energy gap separates the edge modes from overlapping the bulk ones. Also, we explain why our results for anisotropic zigzag nanoribbons go beyond previous studies based on a quantum approach in the linear spin wave approximation.