  Ternary Li halides, such as Li$_3$MeX$_6$ with, e.g., Me = In, Sc, Y and X =
Cl, Br, are in the center of attention for battery applications as these
materials might serve as ionic electrolytes. To fulfill their function, such
electrolytes must have an extraordinarily high ionic Li$^+$ conductivity.
Layer-structured Li$_3$InCl$_6$ represents such a candidate; understanding the
origin of the rapid Li$^+$ exchange processes needs, however, further
investigation. Spatially restricted, that is, low-dimensional particle
diffusion might offer an explanation for fast ion dynamics. It is, however,
challenging to provide evidence for 2D diffusion at the atomic scale when
dealing with polycrystalline powder samples. Here, we used purely
diffusion-induced $^7$Li nuclear magnetic spin relaxation to detect anomalies
that unambiguously show that 2D Li diffusion is chiefly responsible for the
dynamic processes in a Li$_3$InCl$_6$ powder sample. The change of the
spin-lattice relaxation rate $1/T_1$ as a function of inverse temperature $1/T$
passes through a rate peak that is strictly following asymmetric behavior. This
feature is in excellent agreement with the model of P. M. Richards suggesting a
logarithmic spectral density function $J$ to fully describe 2D diffusion.
Hence, Li$_3$InCl$_6$ belongs to the very rare examples for which 2D Li$^+$
diffusion has been immaculately verified. We believe that such information help
understand the dynamic features of ternary Li halides.
