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In the muon spin relaxation (µSR) measurements, the distribution (described by linewidth D) of internal magnetic field H(t) and its temporal fluctuations (with mean fluctuation rate n) can be observed by implanting spin-polarized muons into a material. However, distinguishing whether the fluctuations are caused by the diffusive motion of the muon itself or the motion of the ions around it, is difficult. In this study, by reviewing the strong collision model, which is an assumption used to describe spin relaxation, we observed that the difference in the cause of the fluctuation appeared as a difference in the spin relaxation function. The new model reproduces well the spin relaxation owing to the local rotational motion of cation molecules observed in hybrid perovskites; this opens the way to distinguish the cause of fluctuations solely from the µSR data.

When a muon exhibits jump-diffusion in a nonmagnetic material, the configuration of the nuclear magnetic moments around the muon changes simultaneously before and after the site change. The fluctuation of H(t) owing to these jumps is well approximated by the strong collision model [where the autocorrelation of H(t) is given by equation H(t)H(0)~D²exp(-nt)], and the time evolution of the muon spin polarization, G_z(t), is described by the dynamical Kubo–Toyabe (KT) relaxation function. However, if the H(t) fluctuations are due to the jump diffusion of ions, only a part of the ion configuration around the muon changes in one jump, and the strong collision model is not necessarily expected to be applicable.

Therefore, we performed Monte Carlo simulations for G_z(t) using a model in which the fluctuations of H(t) owing to ion motion were described by an Edwards–Anderson type autocorrelation function with the quasi-static and dynamic components of the autocorrelation separated by parameter Q [where H(t)H(0)~QD²exp(-nt) + (1-Q)D²], and G_z(t) was noted to deviate significantly from the KT function. To further verify this model, we compared the µSR spectra observed in the hybrid organic–inorganic perovskite FAPbI₃ [FA refers to HC(NH₂)₂] with the simulation results. The least-squares curve fitting results showed excellent agreement with the model with Q = 0.947(3), yielding reasonable fluctuation frequencies for the dynamical component. This result opens the possibility of experimentally distinguishing between fluctuations owing to the dynamics of ions around muons and fluctuations owing to the self-diffusion of muons.

Written by T. U. Ito and R. Kadono