Li Jump Diffusion and Long-Range Transport in Garnet Single Crystals: Spanning the kHz-GHz Range

Understanding and controlling Li-ion transport in garnet-type oxides is central to advancing solid electrolytes for all-solid-state energy storage systems. Garnet electrolytes have long been recognized for their high ionic conductivity, and the availability of large single crystals now enables a direct, frequency-resolved view of Li-ion dynamics over a broad time window. In such structurally and chemically homogeneous systems, responses from electrical and nuclear magnetic resonance measurements are expected to align, yielding a consistent picture of frequency-dependent Li-ion hopping processes. Here, we investigate single-crystalline Li_6.5La₃Zr_1.5Ta_0.5O₁₂ and probe ion dynamics from the kHz to GHz range using a combination of ⁷Li nuclear spin relaxation (NSR) and electrical conductivity spectroscopy. Long-range transport (5 × 10^-4 S cm^-1 at 293 K) is consistently described by activation energies in the range of 0.41 to 0.47 eV, whereas localized ion dynamics, observed, e.g., by laboratory-frame NSR, are associated with much lower barriers of approximately 0.22 eV. In comparison with single-crystalline Li₆La₃ZrTaO₁₂, which exhibits reduced ionic mobility, we propose that changes in ionic mobility are compensated by a higher effective charge-carrier concentration N _c in systems with lower Li contents. For Li_6.5La₃Zr_1.5Ta_0.5O₁₂, the Li⁺ mobility is higher by approximately 1 order of magnitude; however, the resulting conductivity only slightly exceeds that of Li₆La₃ZrTaO₁₂, presumably due to a lower density of mobile charge carriers. This finding highlights that N _c is a key parameter to consider in these systems that indeed sensitively governs the practical ionic conductivity.