Non-linear spin wave theory in the strong easy-axis limit of the triangular XXZ model

TL;DR

This paper develops a non-linear spin wave theory for the triangular XXZ model with strong easy-axis anisotropy, revealing quantum order-by-disorder effects and comparing theoretical spectra with experiments.

Contribution

It introduces a novel effective boson model on the honeycomb lattice for the triangular XXZ model in the strong anisotropy limit, incorporating quantum corrections and analyzing spectrum evolution.

Findings

Effective boson model interpolates between spin-wave and strong-coupling regimes.

Quantum corrections modify the spectrum significantly as a function of V.

Theoretical spectrum shows qualitative agreement with experimental data on K2Co(SeO3)2.

Abstract

Motivated by recent experimental studies, we investigate the spectrum of the nearest-neighbour triangular XXZ model within the $1/S$ expansion, in the limit in which the exchange couplings present a strong easy-axis anisotropy $J_{xy}/J_{zz} \ll 1$. We show that in the limit in which $1/S \to 0$ and $J_{xy} \to 0$ at fixed $V = J_{zz}/(S J_{xy})$, the triangular spin model can be reduced to an effective boson model with quartic interactions on the honeycomb lattice. This effective model interpolates between a spin-wave ($V \to 0$) and a strong-coupling limit ($V \to \infty$), and encodes in a simple framework the regimes discussed by Kleine et al. [Z. Phys. B Condens. Matter 86, 405 (1992); 87, 103 (1992)]. For zero field, the classical ground state of the model presents an accidental degeneracy, which has a particularly simple form and which can be expressed in terms of a simple symmetry of the classical energy. The model thus offers a particularly transparent realization of a theory with quantum order-by-disorder and a pseudo-Goldstone mode. We analyze the spectrum at zero magnetic field by calculating the self-energy at one-loop order, using a self-consistent renormalization of the gap and the energy scale. Within the self-consistent approximation considered here, the corrections present a complex evolution as a function of $V$. We discuss the one-loop corrections in comparison with the spectrum observed experimentally in K$_{2}$Co(SeO$_{3}$)$_{2}$.