Hannay Angles in Magnetic Dynamics

TL;DR

This paper explores geometric phases, known as Hannay angles, in semi-classical magnetic dynamics, analyzing their effects on single-domain magnets, spin waves, and magnon transport, with implications for magnonic applications.

Contribution

It extends the classical Hannay angle framework to magnetic systems, deriving new insights into geometric phases in magnetization and magnon transport.

Findings

Hannay angles influence magnetization precession and ellipticity.

Derived a classical interpretation of magnon Berry phase.

Showed interference effects in magnon rings are tunable by Hannay angles.

Abstract

We consider, within the framework developed by Hannay for classical integrable systems [Journal of Physics A: Mathematical and General {\bf 18}, 221 (1985)], the geometric phases that occur in semi-classical magnetic dynamics. Such geometric phases are generically referred to as Hannay angles, and, in the context of magnetic dynamics, may arise as a result of both adiabatically-varying ellipticity and axis of magnetization precession. We elucidate both effects and their interplay for single-domain magnetic dynamics within a simple model with time-dependent anisotropies and external field. Subsequently, we consider spin waves and rederive, from our classical approach, some known results on what is commonly referred to as the magnon Berry phase. As an aside, these results are used to give an interpretation for geometric phases that occur in superfluids. Finally, we develop a Green's function formalism for elliptical magnons. Within this formalism, we consider magnon transport in a mesoscopic ring and show how it is influenced by interference effects that are tuned by the Hannay angle that results from a varying ellipticity. Our results may inform the field of magnonics that seeks to utilize spin waves in applications.