Phase diagrams and excitations of anisotropic $S=1$ quantum magnets on the triangular lattice

TL;DR

This paper explores the phase diagrams and magnetic excitations of anisotropic $S=1$ quantum magnets on a triangular lattice, revealing new degenerate regions and flat-band spectra through analytical and numerical methods.

Contribution

It introduces an extended model with XXZ anisotropy, maps phase diagrams, and analyzes excitation spectra, providing new insights into anisotropic quantum magnetism on the triangular lattice.

Findings

Identification of an additional degenerate phase region.

Discovery of flat lowest-energy bands in certain states.

Systematic calculation of ordered moments and spectra.

Abstract

The $S=1$ bilinear-biquadratic Heisenberg exchange model on the triangular lattice with a single-ion anisotropy has previously been shown to host a number of exotic magnetic and nematic orders [Moreno-Cardoner $\textit{et al.}$, Phys. Rev. B $\textbf{90}$, 144409 (2014)], including an extensive region of "supersolid" order. In this work, we amend the model by an XXZ anisotropy in the exchange interactions. Tuning to the limit of an exactly solvable $S=1$ generalized Ising-/Blume-Capel-type model provides a controlled limit to access phases at finite transverse exchange. Notably, we find an additional macroscopically degenerate region in the phase diagram and study its fate under perturbation theory. We further map out phase diagrams as a function of the XXZ anisotropy parameter, ratio of bilinear and biquadratic interactions and single-ion anisotropy, and compute corrections to the total ordered moment in various phases using systematically constructed linear flavor-wave theory. We also present linear flavor-wave spectra of various states, finding that the lowest-energy band in three-sublattice generalized (i.e. with $S^z=\pm1,0$) Ising/Blume-Capel states, stabilized by strong exchange anisotropies, is remarkably flat, opening up the way to flat-band engineering of magnetic excitation via stabilizing non-trivial Ising-ordered ground states.