Phonon Hall viscosity from spinon interactions

Quantum spin liquids, exotic states of frustrated quantum magnets that are characterized by fractionalized spinon excitations, host a multitude of remarkable phenomena. While there have been many proposals to realize these states in actual materials, spin liquids are not directly sensitive to conventional experimental local probes and their unambiguous experimental observation has remained elusive. Here, we study the coupling of spinon excitations to phonons in a model that captures the magnetic-field-driven transition from the square-lattice Néel state to a state where Néel order coexists with a chiral spin liquid. We show how the broken time-reversal symmetry in the spin degrees of freedom can induce a non-dissipative phonon Hall viscosity. Our results suggest that the Hall viscosity can capture signatures of an underlying spin-liquid phase. As the Hall viscosity leads to a phonon thermal Hall effect, this study also offers some insight into recent experiments detecting anomalous thermal transport in the pseudogap phase of the cuprate superconductors.