Berry curvature of magnons coupled with elastic and electromagnetic waves in ferromagnets

The Berry curvature is a differential-geometric quantity defined in terms of the Bloch wavefunctions, and it manifests itself in Hall effects, in the shift of wavepackets, and even in various topological phases. Recently we calculated the Berry curvature of magnons in ferromagnetic films with dipole-exchange interactions. The Berry curvature of magnons is enhanced at the crossings of the eigenmodes due to the hybridizations between them.
In this presentation, we calculate the Berry curvature in the systems of magnons coupled with elastic waves and with electromagnetic waves. First, we reformulate the eigenmode problem in order to calculate the Berry curvature, and present the result of the Berry curvature of coupled waves. The Berry curvature also has a peak at the crossing point of the dispersions of the constituent waves, and it depends on the direction of the magnetization and the wavevector, similarly to the previous work. In particular, for the magnons coupled with the elastic waves, the behavior of the Berry curvature around k=0 is largely modified by the coupling.
We also discuss behaviors of the Berry curvature around k=0 for the waves for the magnons coupled with electromagnetic waves, and discuss its difference from the magnetoelastic waves.