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Recently, there have been contrary claims of Kitaev spin-liquid behaviour andordered behavior in the honeycomb compound Ag$_3$LiIr$_2$O$_6$ based on variousexperimental signatures. Our investigations on this system reveal alow-temperature ordered state with persistent dynamics down to the lowesttemperatures. Magnetic order is confirmed by clear oscillations in the muonspin relaxation ($\mu$SR) time spectrum below 9 K till 52 mK. Coincidentally in$^7$Li nuclear magnetic resonance, a wipe-out of the signal is observed below$\sim$ 10 K which again strongly indicates magnetic order in the lowtemperature regime. This is supported by our density functional theorycalculations which show an appreciable Heisenberg exchange term in the spinHamiltonian that favors magnetic ordering. The $^7$Li shift and spin-latticerelaxation rate also show anomalies at $\sim$ 50 K. They are likely related tothe onset of dynamic magnetic correlations, but their origin is not completelyclear. Detailed analysis of our $\mu$SR data is consistent with a co-existenceof incommensurate N\'eel and striped environments. A significant andundiminished dynamical relaxation rate ($\sim 5$ MHz) as seen in $\mu$SR deepinto the ordered phase indicates enhanced quantum fluctuations in the orderedstate.

Unusual spin dynamics in the low-temperature magnetically ordered state of Ag$_{3}$LiIr$_{2}$O$_{6}$