Spin-wave Scattering in the Effective Lagrangian Perspective

TL;DR

This paper uses effective Lagrangian methods to analyze spin-wave scattering in magnetic systems, highlighting the role of spontaneous symmetry breaking and low energy theorems, with applications to ferro- and antiferromagnets.

Contribution

It introduces a unified effective Lagrangian framework for studying spin-wave scattering, including effects of external fields and approximate symmetries, bridging condensed matter and Lorentz-invariant theories.

Findings

Derivation of low energy theorems for spin-wave scattering

Analysis of external magnetic and anisotropy field effects

Demonstration of the universality of the effective Lagrangian approach

Abstract

Nonrelativistic systems exhibiting collective magnetic behavior are analyzed in the framework of effective Lagrangians. The method, formulating the dynamics in terms of Goldstone bosons, allows to investigate the consequences of spontaneous symmetry breaking from a unified point of view. Low energy theorems concerning spin-wave scattering in ferro- and antiferromagnets are established, emphasizing the simplicity of actual calculations. The present work includes approximate symmetries and discusses the modification of the low energy structure imposed by an external magnetic and an anisotropy field, respectively. Throughout the paper, analogies between condensed matter physics and Lorentz-invariant theories are pointed out, demonstrating the universal feature of the effective Lagrangian technique.