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

Achille Mauri; Frédéric Mila

doi:10.1103/physrevb.111.l180402

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arXiv · 2501.03887

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

Achille Mauri·Frédéric Mila

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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 $\alpha \simeq 0.08$.

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Achille Mauri, Frédéric Mila. 2025-01-07. Slow convergence of spin-wave expansion and magnon dispersion in the 1/3 plateau of the triangular XXZ antiferromagnet. https://doi.org/10.1103/physrevb.111.l180402

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