Quantum Electrodynamics and the Origins of the Exchange, Dipole-Dipole, and Dzyaloshinsky-Moriya Interactions in Itinerant Fermion Systems

TL;DR

This paper derives the fundamental magnetic interactions in itinerant fermion systems from a field-theoretic approach, providing insights into when dipole-dipole effects are significant, especially in weak ferromagnets and helimagnets.

Contribution

It introduces a field-theoretic framework that naturally derives exchange, dipole-dipole, and Dzyaloshinsky-Moriya interactions from electron-spin fluctuations.

Findings

Derived interaction expressions from a unified field theory

Estimated when dipole-dipole interactions are relevant

Discussed applications to weak ferromagnets and helimagnets

Abstract

It is shown how the exchange interaction, the dipole-dipole interaction, and the Dzyaloshinsky-Moriya interaction between electronic spin-density fluctuations emerge naturally from a field-theoretic framework that couples electrons to the fluctuating electromagnetic potential. Semi-quantitative estimates are given to determine when the dipole-dipole interaction, which is often neglected, needs to be considered, and various applications are discussed, with an emphasis on weak ferromagnets and on helimagnets.