When quantum fluctuations destroy underlying long-range ordered states, novel quantum states emerge. Spin-liquid (SL) states of frustrated quantum antiferromagnets, in which highly correlated spins fluctuate down to very low temperatures, are prominent examples of such quantum states. SL states often exhibit exotic physical properties, but the precise nature of the elementary excitations behind such phenomena remains entirely elusive. Here, we use thermal Hall measurements that can capture the unexplored property of the elementary excitations in SL states, and report the observation of anomalous excitations that may unveil the unique features of the SL state. Our principal finding is a negative thermal Hall conductivity κ xy which the charge-neutral spin excitations in a gapless SL state of the 2D kagomé insulator volborthite Cu 3 V 2 O 7 (OH) 2 · 2H 2 O exhibit, in much the same way in which charged electrons show the conventional electric Hall effect. We find that κ xy is absent in the high-temperature paramagnetic state and develops upon entering the SL state in accordance with the growth of the short-range spin correlations, demonstrating that κ xy is a key signature of the elementary excitation formed in the SL state. These results suggest the emergence of nontrivial elementary excitations in the gapless SL state which feel the presence of fictitious magnetic flux, whose effective Lorentz force is found to be less than 1/100 of the force experienced by free electrons.spin liquid | frustrated magnetism | thermal transport S pin liquids (SLs) are novel states which can occur in a magnetic system when the underlying magnetic order gives way to quantum fluctuations (1). In such states the constituent spins are highly correlated but continue to fluctuate strongly down to temperatures much lower than the spin-interaction energy scale, J. Novel notions such as emergent gauge fields, topological order, and fractionalized excitations have been associated with collective phenomena in SLs. In particular, both experiments (2-5) and theories (6-11) suggest that SL states display many unusual properties. It has been reported, for instance, that low-energy spin excitations in organic insulators with a triangular lattice structure behave like mobile carriers in a paramagnetic metal with a Fermi surface (2, 3), in contrast with the charge degree of freedom which is gapped. A description in terms of an SL state with fractionalized spin excitations was incorporated to account for the excitation continuum signal detected in a kagomé antiferromagnet (4). A magnetization transport measurement has shown that a pyrochlore frustrated magnet exhibits the characteristics of a supercooled SL state (5). Exotic quasi-particles such as spinons (6-8), visons (9, 10), and photons (11) have been predicted theoretically. Despite these intensive activities, the precise characters of the elementary excitations in SL states remain, from an experimental point of view, to be pinned down.In conducting systems, it is the charge-transport properties...
