Plaquette order in classical spin liquid stabilized by strong off-diagonal exchange

TL;DR

This paper discovers a new classical spin liquid phase in honeycomb lattice magnets with strong off-diagonal exchange, characterized by plaquette flux order and a thermal phase transition breaking cubic symmetry.

Contribution

It reveals a novel classical spin liquid with flux order driven by off-diagonal exchange and details the nature of its thermal phase transition.

Findings

Identifies a new classical spin liquid phase with flux order.

Demonstrates a thermal phase transition at T_c ≈ 0.04|Γ|.

Shows symmetry breaking via plaquette flux ordering.

Abstract

We report a new classical spin liquid in which the collective flux degrees of freedom break the translation symmetry of the honeycomb lattice. This exotic phase exists in frustrated spin-orbit magnets where a dominant off-diagonal exchange, the so-called $\Gamma$ term, results in a macroscopic ground-state degeneracy at the classical level. We demonstrate that the system undergoes a phase transition driven by thermal order-by-disorder at a critical temperature $T_c \approx 0.04 |\Gamma|$. At first sight, this transition reduces an emergent spherical spin-symmetry to a cubic one: spins point predominantly toward the cubic axes at $T < T_c$. However, this seems to simply restore the cubic symmetry of the $\Gamma$ model, and the non-coplanar spins remain disordered below $T_c$. We show that the phase transition actually corresponds to plaquette ordering of hexagonal fluxes and the cubic symmetry is indeed broken, a scenario that is further confirmed by our extensive Monte Carlo simulations.