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Abstract: Topological matters have attracted lots of attention in recent years because of their interesting and exotic properties. One such property is the existence of unidirectional and topologically protected surface/edge states that are robust against internal and external perturbations. The study was initially exclusive for electron systems and was believed to be a quantum phenomenon. It is now known that the topological states can exist in classical mechanics and photonics. Topological states can also exist in magnetic materials govern both by quantum mechanics at the zero temperature and by classical magnetization dynamics at finite temperatures. Magnetic materials are highly correlated spin systems that do not respect the time-reversal symmetry. The low-energy excitations of magnetic materials are spin waves whose quanta are magnons. In the ambient temperature, the magnetization dynamics of real magnetic material shall be govern by the Landau- Landau-Lifshitz-Gilbert (LLG) equation. Like electronic materials that can be topologically nontrivial, magnetic materials govern by the LLG equation can also be topologically nontrivial with topologically protected edge spin waves. Unlike the normal spin waves that are very sensitive to the system changes and geometry, these edge spin waves are robust against internal and external perturbations such as geometry changes and spin wave frequency change. Therefore, the magnetic topological matter is of fundamental interest and technologically useful in magnonics. We will see several examples of magnonic topological materials, including pyrochlore [1] and stacked honeycomb [2] ferromagnets as Weyl magnons, as well as perpendicularly magnetized two-dimensional films with Dzyaloshinskii-Moriya and/or pseudodipolar interactions as generic magnonic insulators [3,4]. The edge spin waves in these magnonic materials are robust against perturbations. An interesting functional magnonic device called beamsplitter and interferometer can be made out of a domain wall in a strip. It is shown that an in-coming 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. |