  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.
