Ag₃LiIr₂O₆ is a Kitaev spin liquid candidate material synthesised from α−Li₂IrO₃ via topotactic reaction. We use ⁷Li nuclear magnetic resonance (NMR) to investigate the physical properties of two samples of Ag₃LiIr₂O₆ based on Knight shift and spin-lattice relaxation rate 1/T_1. The first sample is shown via X-ray diffraction to contain stacking faults between the honeycomb layers and displays a second NMR peak. The small values of its distinct Knight shift and 1/T₁ suggest that they become non-magnetic at low temperatures. The second sample contains only one sharp ⁷Li peak.
In the second sample, 1/T₁ (acquired by fitting the recovery curve with a stretched exponential function) increases with decreasing temperature and reaches a broad maximum around 40 K. 1/T₁ then exhibits a second, sharp peak at 10 K and becomes vanishingly small below it. We use numerical Inverse Laplace Transform T₁ (ILTT1) analysis based on Tikhonov regularization to determine the distribution of 1/T₁. We demonstrate in the 1/T₁ distribution that some components of 1/T₁ peak at 9 K, while an increasing fraction of Li sites with 1/T₁ two orders of magnitude lower emerges below 9 K. These details are not revealed by the conventional stretch fit, hence the use of ILTT1 analysis.