Instabilities of spin-liquid states in a quantum kagome antiferromagnet

The emergent behavior of spin liquids that are born out of geometrical frustrationmakes them an intriguing state of matter. We show that in the quantum kagome antiferromagnet ZnCu3(OH)(6)SO4 several different correlated yet fluctuating states exist. By combining complementary local-probe techniqueswith neutron scattering, we discover a crossover from a critical regime into a gapless spin-liquid phase with decreasing temperature. An additional unconventional instability of the latter phase leads to a second, distinct spin-liquid state that is stabilized at the lowest temperatures. We advance such complex behavior as a feature common to different frustrated quantum magnets.