Berry phase of magnons in textured ferromagnets

TL;DR

This paper investigates how topologically nontrivial magnetization profiles in ferromagnets induce a Berry phase in magnons, affecting their energy spectrum and interference patterns, with potential experimental observations.

Contribution

It demonstrates the influence of magnetic anisotropy on the magnon Berry phase and proposes experimental setups to observe these effects in mesoscopic ferromagnetic rings.

Findings

Magnetic anisotropy suppresses the Berry phase magnitude.

Magnons acquire a Berry phase analogous to the Aharonov-Bohm effect.

Magnon spectrum becomes quantized under a topological field.

Abstract

We study the energy spectrum of magnons in a ferromagnet with topologically nontrivial magnetization profile. In the case of inhomogeneous magnetization corresponding to a metastable state of ferromagnet, the spin-wave equation of motion acquires a gauge potential leading to a Berry phase for the magnons propagating along a closed contour. The effect of magnetic anisotropy is crucial for the Berry phase: we show that the anisotropy suppresses its magnitude, which makes the Berry phase observable in some cases, similar to the Aharonov-Bohm effect for electrons. For example, it can be observed in the interference of spin waves propagating in mesoscopic rings. We discuss the effect of domain walls on the interference in ferromagnetic rings, and propose some experiments with a certain geometry of magnetization. We also show that the nonvanishing average topological field acts on the magnons like a uniform magnetic field on electrons. It leads to the quantization of the magnon spectrum in the topological field.