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

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 [1]. We demonstrate that the system undergoes a phase transition driven by thermal order-by-disorder at a critical temperature T_c ≈ 0.04 |Γ|. Interestingly, while the cubic symmetry is broken at T < T_c, spins in the low temperature phase remain disordered. We show that this phase transition actually corresponds to plaquette ordering of hexagonal fluxes. By introducing a proper order parameter to describe this translational symmetry breaking, we performed extensive Monte Carlo simulations and finite-size analysis to investigate the nature of the plaquette-ordering transition. We also study the dynamical behavior of fluxes and the influence of other types of interactions on the phase transition.[1] I. Rousochatzakis and N. B. Perkins Phys. Rev. Lett. 118, 147204 (2017).