Probing quantum spin liquids in equilibrium using the inverse spin Hall effect

We propose an experimental method utilizing a spin orbit coupled metal to quantum magnet bilayer that will probe quantum magnets lacking long range magnetic order, e.g., quantum spin liquids, via a dc resistance measurement across the metal. The bilayer is held in thermal and chemical equilibrium, and spin fluctuations arising across the single interface are converted into voltage fluctuations in the metal as a result of the inverse spin Hall effect. In thermal equilibrium, changes to the voltage noise in the metal are measurable as changes to the resistance via the fluctuation dissipation theorem. We examine the theoretical workings of the proposed bilayer system, and offer predictions for the temperature scaling of the enhancement to the dc resistance measured across the metal for three quantum spin liquid models. We consider the Heisenberg spin-$1/2$ kagom{\'e} lattice model and extract the spinon gap. We find characteristic $T^3$ scaling of the dc resistance enhancement for the Kitaev model in the gapless phase. Finally, for fermionic spinons coupled to a $U(1)$ gauge field we find subdominant $T^{4/3}$ scaling of the dc resistance enhancement. We therefore show that our proposed bilayer can test the relevance of a quantum spin liquid model to a given candidate material.