---
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.'
author:
- 'D. Belitz'
- 'T.R. Kirkpatrick'
title: 'Quantum Electrodynamics and the Origins of the Exchange, Dipole-Dipole, and Dzyaloshinsky-Moriya Interactions in Itinerant Fermion Systems'
---

Introduction {#sec:I}
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Understanding the origin of ferromagnetism was one of the success stories of applying quantum mechanics to solid-state systems. Classically, magnetic moments interact via the dipole-dipole interaction, which is much too weak to explain magnetic order at as high a temperature as is observed in, e.g., iron or nickel.[@Ashcroft_Mermin_1976] The explanation of this conundrum was found to be the exchange interaction mechanism, which leads to a spin-spin interaction that is governed by the Coulomb interaction via the Pauli principle. This was first understood in the context of atomic and molecular physics in the 1920s, and applied to solid-state physics in the 1950s.[@Ashcroft_Mermin_1976] Somewhat ironically, a straightforward application 