Distinguishing Ion Dynamics from Muon diffusion in Muon Spin Relaxation

We propose a model to describe the fluctuations in the internal magnetic field due to ion dynamics observed in the muon spin relaxation ($\mu$SR) by an Edwards-Anderson type autocorrelation function that separates the quasi-static and dynamic components of the correlation by a parameter $Q$ (where $0\le Q\le1$). Our Monte Carlo simulations for this model showed that the time evolution of muon spin polarization deviates significantly from the Kubo-Toyabe (KT) function. To further validate the model, the results of simulations were compared with the $\mu$SR spectra observed in a hybrid organic-inorganic perovskite FAPbI$_3$ [with FA referring to HC(NH$_2)_2$], where local field fluctuations associated with the rotational motion of FA molecules and quasi-static fields from the PbI$_3$ lattice are presumed to coexist. The least-squares curve fitting showed reasonable agreement with the model with $Q=0.947(3)$, and the fluctuation frequency of the dynamical component was obtained. This result opens the door to the possibility of experimentally distinguishing fluctuations due to dynamics of ions around muons from those due to self-diffusion of muons. Meanwhile, it suggests the need to carefully consider the spin relaxation function when applying $\mu$SR to the issue of ion dynamics.