$rm{Sr_2CuTe_{0.5}W_{0.5}O_6}$ is a square-lattice magnet with super-exchange between S=1/2 $rm{Cu^{2+}}$ spins mediated by randomly distributed Te and W ions. Here, using sub-K temperature and 20 $rm{mu}$eV energy resolution neutron scattering experiments we show that this system transits from a gapless disorder-induced quantum spin liquid to a new quantum state below $rm{T_f}$ = 1.7(1) K, exhibiting a weak frozen moment of <S>/S ~ 0.1 and low energy dynamic susceptibility,${chi}({hbaromega})$ linear in energy which is surprising for such a weak freezing in this highly fluctuating quantum regime.
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