  We report measurements of the dynamics of isolated $^{8}$Li$^{+}$ in single
crystal rutile TiO$_{2}$ using $\beta$-detected NMR. From spin-lattice
relaxation and motional narrowing, we find two sets of thermally activated
dynamics: one below 100 K; and one at higher temperatures. At low temperature,
the activation barrier is $26.8(6)$ meV with prefactor $1.23(5) \times 10^{10}$
s$^{-1}$. We suggest this is unrelated to Li$^{+}$ motion, and rather is a
consequence of electron polarons in the vicinity of the implanted
$^{8}$Li$^{+}$ that are known to become mobile in this temperature range. Above
100 K, Li$^{+}$ undergoes long-range diffusion as an isolated uncomplexed
cation, characterized by an activation energy and prefactor of $0.32(2)$ eV and
$1.0(5) \times 10^{16}$ s$^{-1}$, in agreement with macroscopic diffusion
measurements. These results in the dilute limit from a microscopic probe
indicate that Li$^{+}$ concentration does not limit the diffusivity even up to
high concentrations, but that some key ingredient is missing in the
calculations of the migration barrier. The anomalous prefactors provide further
insight into both Li$^{+}$ and polaron motion.
