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

We propose a strongly spin-orbit coupled metal to quantum magnet bilayer as a probe of quantum magnets lacking long range magnetic order, e.g., quantum spin liquids (QSLs), via examination of the voltage noise spectrum in the metal layer. The bilayer is held in equilibrium, and spin fluctuations arising across the interface are converted into voltage fluctuations in the metal via the inverse spin Hall effect. We show the theoretical workings of the system, and predict the frequency characteristics of the enhancement to the ac electrical resistance measured in the metal layer for three QSL models. We apply our model to the Heisenberg spin-1/2 kagome lattice model, a QSL consisting of fermionic spinons coupled to a U(1) gauge field, and the Kitaev model in the gapless QSL phase. In each case we extract characteristic features of a given QSL model, and therefore show that spectral analysis of the ac resistance across the metal layer in a single interface, equilibrium bilayer can test the relevance of a QSL model to a given candidate material.