Antiferromagnetic Dispersion Relations and Nature of Magnon Pressure

TL;DR

This paper derives higher-order corrections to magnon dispersion relations in antiferromagnets under aligned magnetic and staggered fields, revealing attractive magnon-magnon interactions affecting pressure.

Contribution

It introduces a method to separate noninteracting and interacting magnon contributions in the pressure, with results applicable to various bipartite lattices.

Findings

Magnon-magnon interaction in pressure is attractive.

Higher-order dispersion corrections are derived.

Results are valid for arbitrary bipartite geometries.

Abstract

We derive higher-order corrections in the magnon dispersion relations for two- and three-dimensional antiferromagnets exposed to magnetic and staggered fields that are mutually aligned. "Dressing" the magnons is the prerequisite to separate the low-temperature representation of the pressure into a piece due to noninteracting magnons and a piece that corresponds to the magnon-magnon interaction. Both in two and three spatial dimensions, the interaction in the pressure turns out to be attractive. While concrete figures refer to the spin-$\frac{1}{2}$ square-lattice and the spin-$\frac{1}{2}$ simple cubic lattice antiferromagnet, our results are valid for arbitrary bipartite geometry.