Hidden Plaquette Order in a Classical Spin Liquid Stabilized by Strong Off-Diagonal Exchange

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 Γ 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 Tc ≈ 0.04|Γ|. At first sight, this transition reduces an emergent spherical spin-symmetry to a cubic one: spins point predominantly toward the cubic axes at T < Tc. However, this seems to simply restore the cubic symmetry of the Γ model, and the non-coplanar spins remain disordered below Tc. 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.

Gapless quantum spin liquid in a honeycomb Γ magnet

“…So far, we have confirmed that there is no magnetic ordering in the honeycomb Γ model, yet little is known about the lattice symmetry breaking. Very recently, there is a proposal of plaquette ordering stemming from a broken translational symmetry in the classical Γ model 38 . It is thus of interest to examine whether there is a plaquette ordering in the quantum situation.…”

“…In contrast to the Kitaev model 13 , analytical solution of the honeycomb Γ model has not been found yet 36 . Previous classical studies have demonstrated that its ground state is a classical spin liquid 37 followed by a flux-ordered spin liquid, which is stabilized in a finite temperature window 38 . Given the infinite classical ground-state degeneracy 37 , determining the precise quantum nature of Γ model is nontrivial, and existing numerical works have already led to conflicting results.…”

Honeycomb-lattice Gamma model in a magnetic field: hidden Néel order and spin-flop transition

“…In particular, the anisotropic exchange, also called the Γ interaction [33] is shown to play an important role in compounds such as RuCl 3 . The Γ model on the honeycomb lattice is defined as [34][35][36]…”

“…The extensive degeneracy associated with the classical ground state is characterized by an emergent global O(3) rotational symmetry and a local Z 2 gauge-like symmetry [34]. While the local Ising-gauge symmetry cannot be spontaneously broken [37], the continuous O(3) degeneracy is lifted by quantum or thermal fluctuations [34,35]. Interestingly, the spontaneous breaking of the O(3) symmetry actually corresponds to a breaking of lattice translation symmetry.…”

“…Interestingly, the spontaneous breaking of the O(3) symmetry actually corresponds to a breaking of lattice translation symmetry. Through the order-by-disorder mechanism, fluctuations thus induce a sharp phase transition below which an exotic spin liquid with a hidden √ 3× √ 3 plaquette order emerges as the semiclassical ground state [35].…”