Revisiting $\mu$SR Studies of Ion Dynamics in the Light of Extended Kubo-Toyabe Model

TL;DR

This paper extends the dynamical Kubo-Toyabe model to better analyze muon spin relaxation data, leading to a reinterpretation of ion dynamics in Na_xCoO_2 and resolving previous inconsistencies in the field.

Contribution

It introduces an extended dKT model that improves the analysis of muSR data, challenging prior sodium-ion diffusion interpretations and supporting muon self-diffusion.

Findings

Supports muon self-diffusion over sodium-ion diffusion

Resolves inconsistencies in previous ion diffusion studies

Provides a more accurate model for spin relaxation analysis

Abstract

The dynamical Kubo-Toyabe (dKT) function is extended to describe the spin relaxation under the coexisting dynamical and static internal magnetic fields. A detailed re-evaluation of the previous $\mu^\pm$SR data in Na$_x$CoO$_2$ using this function disfavors the conventional interpretation based on sodium-ion diffusion and instead supports the $\mu^+$ self-diffusion scenario. This also resolves the long-standing inconsistencies in the dKT-function-based $\mu$SR studies on ion diffusion from the viewpoint of classical over-barrier-jump mechanism.