Berry's phase and Quantum Dynamics of Ferromagnetic Solitons

TL;DR

This paper investigates the quantum dynamics of ferromagnetic solitons, highlighting the role of Berry phase effects, spin parity, and external fields in their propagation and dispersion characteristics.

Contribution

It introduces a quantum field theory incorporating Berry phase effects for ferromagnetic solitons and reveals how spin parity influences their quantum behavior and dispersion relations.

Findings

Berry phase causes a halving of the Brillouin zone for half-integer spins.

Destructive interference suppresses soliton hopping for half-integer spins.

External fields can tune the soliton dispersion between different spin states.

Abstract

We study spin parity effects and the quantum propagation of solitons (Bloch walls) in quasi-one dimensional ferromagnets. Within a coherent state path integral approach we derive a quantum field theory for nonuniform spin configurations. The effective action for the soliton position is shown to contain a gauge potential due to the Berry phase and a damping term caused by the interaction between soliton and spin waves. For temperatures below the anisotropy gap this dissipation reduces to a pure soliton mass renormalization. The gauge potential strongly affects the quantum dynamics of the soliton in a periodic lattice or pinning potential. For half-integer spin, destructive interference between soliton states of opposite chirality suppresses nearest neighbor hopping. Thus the Brillouin zone is halved, and for small mixing of the chiralities the dispersion reveals a surprising dynamical correlation: Two subsequent band minima belong to different chirality states of the soliton. For integer spin, the Berry phase is inoperative and a simple tight-binding dispersion is obtained. Finally it is shown that external fields can be used to interpolate continuously between the Bloch wall dispersions for half-integer and integer spin.