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We propose an experimental method utilizing a strongly spin-orbit coupledmetal to quantum magnet bilayer that will probe quantum magnets lacking longrange magnetic order, e.g., quantum spin liquids, via examination of thevoltage noise spectrum in the metal layer. The bilayer is held in thermal andchemical equilibrium, and spin fluctuations arising across the single interfaceare converted into voltage fluctuations in the metal as a result of the inversespin Hall effect. We elucidate the theoretical workings of the proposed bilayersystem, and provide precise predictions for the frequency characteristics ofthe enhancement to the ac electrical resistance measured in the metal layer forthree candidate quantum spin liquid models. Application to the Heisenbergspin-$1/2$ kagom{\'e} lattice model should allow for the extraction of anyspinon gap present. A quantum spin liquid consisting of fermionic spinonscoupled to a $U(1)$ gauge field should cause subdominant $\W^{4/3}$ scaling ofthe resistance of the coupled metal. Finally, if the magnet is well-captured bythe Kitaev model in the gapless spin liquid phase, then the proposed bilayercan extract the two-flux gap which arises in spite of the gapless spectrum ofthe fermions. We therefore show that spectral analysis of the ac resistance inthe metal in a single interface, equilibrium bilayer can test the relevance ofa quantum spin liquid model to a given candidate material.

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