Relationship between local hydride ion dynamics and ionic conductivity in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>LaH</mml:mi> <mml:mrow> <mml:mn>3</mml:mn> <mml:mo>−</mml:mo> <mml:mn>2</mml:mn> <mml:mi

We performed muon spin rotation and relaxation ($μ$SR) experiments to investigate the microscopic mechanism behind the high ionic conductivity ($σ$) exhibited by hydride (H$^-$) ions in lanthanum hydroxide LaH$_{3-2x}$O$_x$. The $μ$SR spectra observed at 5--300 K in a sample with $x\approx0.25$ consist primarily of two components which are attributed to muons occupying tetrahedral (Tet) and octahedral (Oct) sites common to H$^-$. The spectra also indicate that muons at the Oct sites (Mu$_{\rm O}$) appear nearly stationary in the time scale of $μ$SR ($\sim$10$^{-5}$ s), whereas those at the Tet sites (Mu$_{\rm T}$) are subject to the fluctuating local fields. The cusp-like peak in the fluctuation rate around 160 K and the decrease in linewidth at higher temperatures probed by Mu$_{\rm T}$ suggest that the jump motion of both Mu$_{\rm T}$ (via the vacant Oct sites) and surrounding Oct-site H$^-$ contributes to spin relaxation and that the fluctuation frequency is widely distributed. These results indicate that the implanted Mu behave as Mu$^-$ and that the jump motion of Mu$^-$/H$^-$ is restricted by the availability of nearby vacant sites. On the other hand, the activation energy for the jump is estimated to be 0.11(3) eV, which is significantly different from $\sim$1.3 eV evaluated from the temperature dependence of $σ$ at high temperatures ($\gtrsim400$ K). In our attempt to resolve this discrepancy, we discuss problems inherent in interpreting $σ$ using the Arrhenius equation, and demonstrate that the behavior of H$^-$ ions can be better explained as a viscous fluid exhibiting a glass transition.