Time-Scale Renormalization of Correlation Decay Governs Li-Ion Transport in Garnet Solid Electrolytes

Ion transport in solids is a key determinant of next-generation energy technologies, especially solid-state batteries, fuel cells, and other electrochemical systems. However, designing a superionic conductor remains challenging because ionic conductivity arises from a coupled interplay among migration barriers, hopping frequencies, and the characteristic diffusion length scales of the mobile sublattice, with no universal mechanism across materials. Although compositional engineering improves diffusion, it is unclear how spatial and temporal correlations govern ion transport. Here, we introduce a relaxation-matched framework that combines intermediate scattering functions with decorrelation-time-resolved van Hove analysis to probe lithium-ion dynamics in pristine (Li₇La₃Zr₂O₁₂), Ga-substituted (Li_6.25Ga_0.25La₃Zr₂O₁₂), and high-entropy garnets (Li_5.75Ga_0.25La_2.5Nd_0.5Zr_0.75Ti_0.25Hf_0.25Ce_0.25Nb_0.25Ta_0.25O₁₂). Despite increasing compositional complexity and dynamical heterogeneity, the spatial signatures of Li-ion motion remain invariant at their characteristic decorrelation times, with both local Li-jump and long-range collective displacements collapsing onto a common length scale. However, compositional engineering leads to accelerated decay of ion correlations that compresses the associated time scales while preserving transport geometry. High-entropy substitution amplifies this effect by destabilizing intermediate-range order and promoting a dynamically percolating Li network. This framework provides a general route to disentangle spatial and temporal contributions to transport, identifying time-scale renormalization of correlation decay as a unifying design principle for superionic conductors.