Antiferromagnet with two coupled antiferromagnetic sublattices in a magnetic field

TL;DR

This paper analyzes the magnon spectrum of a two-sublattice antiferromagnet in a magnetic field, revealing how inter-sublattice interactions influence spectral gaps and mode splitting, with implications for materials like DTN.

Contribution

It provides a comparative analysis of the 1/S expansion and magnon Bose-Einstein condensation methods for calculating spectral gaps in antiferromagnets with two sublattices.

Findings

1. The 1/S expansion qualitatively captures the gap behavior near the saturation field.

2. The 1/S method overestimates the gap magnitude at high fields.

3. Inter-sublattice interactions cause spectral gaps and mode splitting.

Abstract

We discuss the magnon spectrum of an antiferromagnet (AF) in a magnetic field $h$ consisting of two interpenetrating AF sublattices coupled by the exchange interaction at T=0. One-ion easy-plane anisotropy is also taken into account. We calculate using the 1/S expansion the gap in the spectrum which is a manifestation of the order-by-disorder effect in this system and the optical magnon mode splitting. Both of these phenomena originate from the inter-sublattice interaction. We calculate also the gap value at $h\approx h_c$ in the leading order of the small parameter $(h_c-h)/h_c$ using the magnon Bose-Einstein condensation treatment, where $h_c$ is the saturation field. By comparing results obtained within these two approaches we conclude that the 1/S expansion gives a qualitatively correct result at $h\sim h_c$ even at large one-ion anisotropy but it overestimates the gap value. The application is discussed of these results to the actively studied AF of the considered type $\rm NiCl_2$-$\rm 4SC(NH_2)_2$ (DTN).