Ion Jump Motion as the Background for Muon Diffusion in Battery Materials Research Using $\mu$SR

Numerical simulations of muon spin relaxation ($\mu$SR) in ion diffusion were performed using the {\sl extended} Kubo-Toyabe (KT) relaxation function $G_z^{\rm EA}(t)$ that incorporates an Edwards-Anderson type autocorrelation function for the jump motion of ions. The analysis of the generated $\mu$SR spectra using the conventional KT function $G_z^{\rm KT}(t;\Delta_{\rm KT},\nu_{\rm KT})$ (mimicking the previous analysis procedure) suggest that the anomalous peak in the fluctuation rate $\nu_{\rm KT}$ around a specific temperature $T^*$ and associated decrease of the linewidth $\Delta_{\rm KT}$ above $T^*$, often observed in the previous $\mu$SR studies on ion diffusion, originate from the sharp increase in the ion jump rate $\nu_{\rm i}$ against that of the muon $\nu_\mu$ with increasing temperature. This indicates that a more detailed reanalysis of the vintage data using $G_z^{\rm EA}(t)$ is useful for the proper evaluation of $\nu_{\rm i}$ and $\nu_\mu$. Meanwhile, it also suggests that the $\mu$SR results showing no such anomaly convey little information on ion diffusion.