Antiferromagnetic dispersion relations and nature of magnon pressure

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-12 square-lattice and the spin-12 simple cubic lattice antiferromagnet, our results are valid for arbitrary bipartite geometry. •Systematic effective field theory analysis of antiferromagnetic films and crystals.•Dispersion relations of antiferromagnetic magnons in magnetic and staggered fields.•Systematic analysis of the impact of the spin-wave interaction in the pressure.