Phase diagrams and excitations of anisotropic <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>S</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math> quantum magnets on the triangular lattice

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 et al., Phys. Rev. B 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, the ratio of bilinear and biquadratic interactions, and single-ion anisotropy, and we 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 ${S}^{z}=\ifmmode\pm\else\textpm\fi{}1,0)$ 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 nontrivial Ising-ordered ground states.

Topics & Concepts