Understanding muon diffusion in perovskite oxides below room temperature based on harmonic transition state theory

In positive muon spin rotation and relaxation ($\mu^+$SR) spectroscopy, positive muons ($\mu^+$) implanted into solid oxides are conventionally treated as immobile spin-probes at interstitial sites below room temperature. This is because each $\mu^+$ is thought to be tightly bound to an oxygen atom in the host lattice to form a muonic analogue of the hydroxy group. On the basis of this concept, anomalies in $\mu^+$SR spectra observed in oxides have been attributed in most cases to the intrinsic properties of host materials. On the other hand, global $\mu^+$ diffusion with an activation energy of $\sim$0.1~eV has been reported in some chemically-substituted perovskite oxides at cryogenic temperatures, although the reason for the small activation energy despite the formation of the strong O$\mu$ bond has not yet been quantitatively understood. In this study, we investigated interstitial $\mu^+$ diffusion in the perovskite oxide lattice using KTaO$_3$ cubic perovskite as a model system. We used the $\mu^+$SR method and density functional theory calculations along with the harmonic transition state theory to study this phenomenon both experimentally and theoretically. Experimental activation energies for global $\mu^+$ diffusion obtained below room temperature were less than a quarter of the calculated classical potential barrier height for a bottleneck $\mu^+$ transfer path. The reduction in the effective barrier height could be explained by the harmonic transition state theory with a zero-point energy correction; a significant difference in zero-point energies for $\mu^+$ at the positions in the O$\mu$ bonding equilibrium state and a bond-breaking transition state was the primary cause of the reduction. This suggests that the assumption of immobile $\mu^+$ in solid oxides is not always satisfied since such a significant decrease in diffusion barrier height can also occur in other oxides.