Berry curvature for magnetoelastic waves

The Berry curvature for magnons in ferromagnetic films gives rise to new phenomena such as thermal Hall effect and a shift of a magnon wave packet at the reflection at the edge of the magnetic film. In this paper, we calculate the Berry curvature of magnetoelastic waves in ferromagnets. In order to calculate the Berry curvature, we first formulate the eigenvalue equation into a Hermitian form from the dynamical equation of motion. We find that the Berry curvature of the magnetoelastic waves shows a peak at the crossing point of the dispersions of magnons and elastic waves, and its peak value is dependent on the hybridization gap at the crossing point. In addition, the behavior of the Berry curvature in the long-wavelength limit changes drastically by the magnetoelastic interaction. We calculate the effect of dipolar interactions in a magnetic film on the Berry curvature, and we find a sign change by increasing the film thickness. The effect of the Berry curvature may be detected by measuring the shift of a wave packet for magnetoelastic waves at a reflection at the edge of a magnet and we find that a shift shows an abrupt change when the wave vector changes across the crossing point.