Magnetic topological states are investigated theoretically and numerically. It is shown that ferromagnetically interacting spins on a two-dimensional honeycomb lattice with nearest-neighbor interactions, which is governed by the Landau-Lifshitz-Gilbert equation, can be topologically nontrivial with gapped bulk spin waves and topologically protected gapless edge spin waves. These edge spin waves are robust against defects and perturbations, and should be superb channels of processing and manipulating spin waves, in contrast to the normal spin waves that are very sensitive to defects as well as sample geometry. Because of the unidirectional nature of these topologically protected edge spin waves, a spin-wave beam splitter can be made out of a domain wall in a strip. It is shown that an incoming spin-wave beam along one edge splits into two spin-wave beams propagating along two opposite directions on the other edge after passing through a domain wall.

• Received 4 October 2016
• Revised 14 January 2017

DOI:https://doi.org/10.1103/PhysRevB.95.014435