Hidden Plaquette Order in a 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 the 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 T_{c}≈0.04|Γ|. This transition reduces the emergent spherical spin symmetry to a cubic one: spins point predominantly toward the cubic axes, yet seem to remain disordered at T