Finite-temperature behavior of a classical spin-orbit-coupled model for $\textrm{YbMgGaO}_4$ with and without bond disorder

TL;DR

This study uses Monte Carlo simulations to analyze the finite-temperature behavior of a spin-orbit-coupled model for YbMgGaO4, revealing a continuous transition in the pure system and disorder-induced fragmentation, which may explain experimental observations.

Contribution

It provides the first large-scale classical Monte Carlo analysis of the model, demonstrating the impact of bond disorder on the system's ordering and extending the Imry-Ma argument.

Findings

A single continuous stripe-ordering transition is observed in the pure model.

Weak bond disorder destroys the transition by creating large domains.

Disorder effects may explain the lack of observed order in experiments.

Abstract

We present the results of finite-temperature classical Monte Carlo simulations of a strongly spin-orbit-coupled nearest-neighbor triangular-lattice model for the candidate $\mathrm{U}(1)$ quantum spin liquid $\mathrm{YbMgGaO}_4$ at large system sizes. We find a single continuous finite-temperature stripe-ordering transition with slowly diverging heat capacity that completely breaks the sixfold ground-state degeneracy, despite the absence of a known conformal field theory describing such a transition. We also simulate the effect of random-bond disorder in the model, and find that even weak bond disorder destroys the transition by fragmenting the system into very large domains -- possibly explaining the lack of observed ordering in the real material. The Imry-Ma argument only partially explains this fragility to disorder, and we extend the argument with a physical explanation for the preservation of our system's time-reversal symmetry even under a disorder model that preserves the same symmetry.