Muon-Spin Motion at the Crossover Regime between Gaussian and Lorentzian Distribution of Magnetic Fields

TL;DR

This paper develops a comprehensive mathematical framework to describe muon-spin relaxation in materials with magnetic field distributions that are intermediate between Gaussian and Lorentzian shapes, enhancing the analysis of local magnetic states.

Contribution

It derives exact muon-spin relaxation functions for the crossover regime between Gaussian and Lorentzian distributions, applicable to all intermediate magnetic field distributions.

Findings

Derived exact relaxation functions for crossover regimes

Unified description of Gaussian and Lorentzian distributions

Applicable to various magnetic field distribution scenarios

Abstract

The muon spin relaxation method ({\mu}SR) is a powerful microscopic tool to probe electronic states of materials observing local magnetic field distributions on the muon. It often happens that a distribution of local magnetic fields shows intermediate state between Gaussian and Lorentzian shapes. In order to generally describe intermediate field distributions, we dealt the convolution of two isotropic distributions in the three dimension and derived exact muon-spin relaxation functions which can be applied to all crossover regimes between the Gaussian and Lorentzian.