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

Abstract

In positive muon spin rotation and relaxation ($μ^+$SR) spectroscopy, positive muons ($μ^+$) implanted into solid oxides are conventionally treated as immobile spin-probes at interstitial sites below room temperature. This is because each $μ^+$ 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 $μ^+$SR spectra observed in oxides have been attributed in most cases to the intrinsic properties of host materials. On the other hand, global $μ^+$ diffusion with an activation energy of $\sim$0.1~eV has been reported in some chemically-substituted perovskite oxides at cryogenic temperatures, although the reason for the small activation energy despite the formation of the strong O$μ$ bond has not yet been quantitatively understood. In this study, we investigated interstitial $μ^+$ diffusion in the perovskite oxide lattice using KTaO$_3$ cubic perovskite as a model system. We used the $μ^+$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 $μ^+$ diffusion obtained below room temperature were less than a quarter of the calculated classical potential barrier height for a bottleneck $μ^+$ 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 $μ^+$ at the positions in the O$μ$ bonding equilibrium state and a bond-breaking transition state was the primary cause of the reduction. This suggests that the assumption of immobile $μ^+$ in solid oxides is not always satisfied since such a significant decrease in diffusion barrier height can also occur in other oxides.