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Using thermodynamic measurements, neutron diffraction, nuclear magneticresonance, and muon spin relaxation, we establish putative quantum spin-liquidbehavior in Ba$_3$InIr$_2$O$_9$, where unpaired electrons are localized onmixed-valence Ir$_2$O$_9$ dimers with Ir$^{4.5+}$ ions. Despite theantiferromagnetic Curie-Weiss temperature on the order of 10 K, neitherlong-range magnetic order nor spin freezing are observed down to at least 20mK, such that spins are short-range correlated and dynamic over nearly threedecades in temperature. Quadratic power-law behavior of both the spin-latticerelaxation rate and specific heat indicates the gapless nature of the groundstate. We envisage that this exotic behavior may be related to an unprecedentedcombination of the triangular and buckled honeycomb geometries ofnearest-neighbor exchange couplings in the mixed-valence setting.

Persistent low-temperature spin dynamics in the mixed-valence iridate Ba$_{3}$InIr$_{2}$O$_{9}$