An EFT for anisotropic anti-ferromagnets: gapped Goldstones, pseudo-Goldstones, and phase transitions

TL;DR

This paper develops a low-energy effective field theory for anisotropic antiferromagnets under magnetic fields, revealing phenomena like gapped Goldstones, pseudo-Goldstones, and phase transitions, with applications to materials like nickel oxide and dark matter research.

Contribution

It introduces a novel EFT framework capturing complex phenomena in anisotropic antiferromagnets, including quantization and symmetry considerations, and matches it to microscopic models.

Findings

Identification of gapped Goldstones and pseudo-Goldstones in the EFT.

Explicit quantization procedure in magnetic fields with single-time derivatives.

Matching of EFT to nickel oxide's microscopic theory.

Abstract

We build and discuss a low energy effective field theory for anisotropic anti-ferromagnets in presence of an external magnetic field. Such an effective theory is simple yet rich, and features a number of phenomena such as the appearance of gapped Goldstones, pseudo-Goldstones and a "spin flop" phase transition, all within the regime of validity of the theory. We also discuss in detail, the quantization procedure of the free theory in the presence of a magnetic field, which is made non-trivial by the presence of a single-time derivative term. This class of materials make a precious test field for exotic phenomena in quantum field theory. Moreover, we explicitly perform the matching of the effective theory to the short distance theory of a specific anti-ferromagnet, namely, nickel oxide. The latter is particularly relevant in light of recent proposals of employing this material towards the hunt for light dark matter. As a byproduct of our study, we also re-evaluate the role played by discrete symmetries in magnetic materials, presenting it in a way that is completely consistent with the proper low energy EFT ideology.