Slow convergence of spin-wave expansion and magnon dispersion in the 1/3 plateau of the triangular XXZ antiferromagnet

TL;DR

This paper investigates the magnon excitation spectrum in a triangular XXZ antiferromagnet's 1/3-plateau phase, revealing slow convergence of spin-wave expansion for S=1/2 and improved experimental agreement with second-order corrections.

Contribution

It introduces a novel expansion in lpha = J_{xy}/J_{zz} and demonstrates its effectiveness in accurately calculating magnon dispersion for various spins.

Findings

Spin-wave expansion converges slowly for S=1/2.

Second-order lpha expansion improves agreement with experiments.

Linear spin-wave theory is quantitatively inaccurate for the studied system.

Abstract

Motivated by recent experiments on the quantum magnet K$_{2}$Co(SeO$_{3}$)$_{2}$, we study theoretically the excitation spectrum of the nearest-neighbour triangular XXZ model in the limit of strong easy-axis anisotropy, within the up-up-down (1/3-plateau) phase. We make an expansion in $\alpha =J_{xy}/J_{zz}$ instead of $1/S$ and calculate the magnon dispersion for any value of the spin $S$ at second order in $\alpha$, with two important conclusions: (i) the 1/S expansion converges very slowly for S=1/2, making spin-wave theory quantitatively inaccurate up to very large orders; (ii) compared to the linear spin-wave predictions, our magnon dispersion presents a much better agreement with experimental results on K$_{2}$Co(SeO$_{3}$)$_{2}$, for which $\alpha \simeq 0.08$.