Effective Field Theory Approach to Ferromagnets and Antiferromagnets in Crystaline Solids

TL;DR

This paper develops a systematic effective field theory framework for describing low-energy spin waves in ferromagnetic and antiferromagnetic crystalline solids, incorporating symmetry breaking, spin-orbit effects, and electromagnetic interactions.

Contribution

It provides a comprehensive construction of effective lagrangians for spin waves in crystals, explicitly including symmetry considerations and next-to-leading order effects.

Findings

Effective lagrangians for spin waves in crystals are derived.

Explicit inclusion of spin-orbit and magnetic dipole interactions.

Coupling to electromagnetic fields is systematically incorporated.

Abstract

We present a systematic construction of effective lagrangians for the low energy and momentum region of ferromagnetic and antiferromagnetic spin waves in crystalline solids. We fully exploit the spontaneous symmetry breaking pattern $SU(2)\to U(1)$, the fact that spin waves are its associated Goldstone modes, the crystallographic space group and time reversal symmetries. We show how to include explicit SU(2) breaking terms due to spin-orbit and magnetic dipole interactions. The coupling to electromagnetic fields is also discussed in detail. For definiteness we work with the space group $R\bar 3 c$ and present our results to next to leading order.