The time dependence of muon spin relaxation spectra and spin correlation functions

TL;DR

This paper develops a microscopic theory for muon spin relaxation spectra, analyzing how different spin correlation functions influence the relaxation behavior in zero-field conditions.

Contribution

It introduces a theoretical framework connecting spin correlation functions to muon depolarization spectra, including exponential, power-law, and diffusion models.

Findings

Exponential correlation functions reproduce stochastic spin theory limits.

Power-law correlations lead to stretched exponential relaxation.

Simple spin diffusion results in root-exponential muon spectra.

Abstract

The existing theory of the microscopic interpretation of the dynamical contribution to zero-field muon depolarization spectra in a longitudinal geometry is developed. The predicted relaxation of the muon depolarization is calculated from two forms of the spin correlation function. First, when the spin correlation function has an exponential form with a single wave vector dependent relaxation rate is considered, it is shown that this form of the spin correlation function reproduces the slow and fast fluctuation limits of stochastic spin theory regardless of the choice of microscopic spin model. Second, if the spin correlation function is a homogeneous scaling function (such as a power-law decay with time), as suggested by the mode-coupling theory of spin dynamics, this results in a stretched exponential relaxation of the muon spectra. For simple spin diffusion, the muon spectra are shown to be relax with a root-exponential form.