  Quasielastic neutron scattering (QENS) measurements combined with first
principles based moleculardynamics calculations were conducted to study the
dynamics of Li$^+$ ions in a solid-state electrolyte
La$_{2/3-x}$Li$_{3x}$TiO$_{3}$ (LLTO) with $x=0.13$. By using a large
$^7$Li-enriched single crystal sample, a QENS signal was clearly observed along
the three principal axes [110], [111], and [001] at a temperature ($T$) of 600
K. Wave vector dependence of the linewidth of the QENS signal along each
direction was explained well using the Chudley-Elliot model for jumps between
the A sites of the perovskite lattice through the bottleneck square, which was
also supported by molecular dynamics calculations. At $T=600$ K, the estimated
self-diffusion coefficient of Li$^+$ ($D_{Li}$) in the $ab$ plane
[$D^{ab}_{Li}=(6.8\pm0.5)\times 10^{-6}$ cm$^2$/s] was slightly larger than
that along the $c$ axis [$D^{c}_{Li}=(4.4\pm0.3)\times 10^{-6}$ cm$^2$/s],
suggesting quasi-isotropic diffusion, that is, the three-dimensional diffusion
of Li$^+$ ions. The decrease in $D_{Li}$ with decreasing $T$ was reasonably
explained by a thermal activation process with the activation energy determined
from ionic-conductivity measurements. Furthermore, the estimated values of the
self-diffusion coefficient of Li$^+$ ions are comparable to those in the
sulfide-based Li$^+$ ion conductor, Li$_{7}$P$_{3}$S$_{11}$, although its ionic
conductivity is 10 times larger than that for LLTO. The obtained microscopic
information on Li$^+$ diffusion in LLTO clarifies how to understand the Li
conduction mechanism in LLTO and Li$_{7}$P$_{3}$S$_{11}$ in a unified manner
and can provide a way to increase the Li$^+$ ionic conductivity in oxide-based
solid electrolytes.
