Abstract

We consider, within the framework developed by Hannay for classical integrable systems (Hannay, 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.

Highlights

  • Within the framework developed by Hannay for classical integrable systems [Journal of Physics A: Mathematical and General 18, 221 (1985)], the geometric phases that occur in semi-classical magnetic dynamics

  • 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

  • We focus on the geometric phases that arise in the semi-classical spin dynamics of ordered magnetic systems

Read more

Summary

SINGLE-DOMAIN MAGNETIZATION DYNAMICS

We consider a single-domain ferromagnet well below the Curie temperature. Its direction of magnetization m ≡ M/Ms, with Ms the saturation magnetization, obeys the Landau-Lifshitz equation [13]. The equibrium magnetization direction m0 is determined by solving m0 × δE[m0]/δm0 = 0 for m0, with the restriction that |m0| = 1 Both the shape of the ellipse and the orientation of the plane in which it lies are time-independent if the micromagnetic energy is time-independent. Let us consider linearized dynamics on and let φ be the angle between the magnetization projected on the plane perpendicular to m0, with some fixed axis in the same plane (see Fig. 1). In the present case of linearized dynamics, the action variable is the area of the ellipse, which is proportional to the energy that the small deviation of the magnetization from its equilibrium direction m0 costs. We will consider the situation that the direction of both field and anistropy can be time-dependent, but not their magnitude, so that the energy is constant. We first discuss them separately, finishing with a discussion of their interplay

Toy model
Time-dependent anisotropy
Circular precession in a time-dependent magnetic field
Elliptical precession in a time-dependent magnetic field
SPIN WAVES
INTERMEZZO
MAGNON TRANSPORT
Boundary conditions
Full Text
Published version (Free)

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call