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We scrutinize the magnetic properties of $\kappa$-(BEDT-TTF)$_2$Hg(SCN)$_2$Clthrough its first-order metal-insulator transition at $T_{\rm CO}=30$ K bymeans of $^1$H nuclear magnetic resonance (NMR). While in the metal we findFermi-liquid behavior with temperature-independent $(T_1T)^{-1}$, therelaxation rate exhibits a pronounced enhancement when charge order sets in.The NMR spectra remain unchanged through the transition and no magnetic orderstabilizes down to 25 mK. Similar to the isostructural spin-liquid candidates$\kappa$-(BEDT-TTF)$_2$Cu$_2$(CN)$_3$ and$\kappa$-(BEDT-TTF)$_2$Ag$_2$(CN)$_3$, $T_1^{-1}$ acquires a dominant maximum(here around 5 K). Field-dependent experiments identify the low-temperaturefeature as a dynamic inhomogeneity contribution that is typically dominant overthe intrinsic relaxation but gets suppressed with magnetic field.

Impurity Moments Conceal Low-Energy Relaxation of Quantum Spin Liquids