In electronic systems, various interesting phenomena such as spin Hall effect and topological insulators originate from Berry curvature of Bloch wavefunctions. We theoretically study analogous phenomena for magnons (spin waves). We propose that the dipolar interaction gives rise to nonzero Berry curvature [1-3]. In a thin-film ferromagnet in a long-wavelength regime, we can calculate the Berry curvature for each magnonic band, and only when the magnetic field is out-of-plane, the Berry curvature is nonzero. When the exchange coupling is included, the magnonic bands are modified, and there appear a number of band anticrossing points. Around such an anticrossing point, the Berry curvature is enhanced. This Berry curvature gives rise to thermal Hall effect of magnons [1,2], and it also gives rise to a shift of wavepackets in reflection or refraction . Furthermore, in analogy to the quantum Hall effect for electrons, we can design topological magnon band structure. By introducing artificial spatial periodicity into the magnet, for example by fabricating nanostructures with two different magnets in a periodic structure or by making a periodic array of nanomagnets, we theoretically propose emergence of topological edge modes, analogous to those in electronic quantum Hall effect. The edge modes are chiral, and propagate along the edge of the magnet in one way. We call this a topological magnonic crystal [4,5].
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