Comparison of different methods for analyzing $\mu$SR line shapes in the vortex state of type-II superconductors

TL;DR

This paper compares various theoretical models for analyzing $bc$SR spectra in the vortex state of type-II superconductors, assessing their accuracy and limitations in extracting key parameters like penetration depth and coherence length.

Contribution

It provides a comprehensive comparison of analytical and exact Ginzburg-Landau models for $bc$SR analysis, highlighting their validity ranges and reliability in parameter extraction.

Findings

High magnetic fields cause strong correlation between $bc$ and $be$.

Low magnetic fields make it difficult to accurately determine $be$.

The second-moment method reliably estimates $bc$ across a wide field range.

Abstract

A detailed analysis of muon-spin rotation ($\mu$SR) spectra in the vortex state of type-II superconductors using different theoretical models is presented. Analytical approximations of the London and Ginzburg-Landau (GL) models, as well as an exact solution of the GL model were used. The limits of the validity of these models and the reliability to extract parameters such as the magnetic penetration depth $\lambda$ and the coherence length $\xi$ from the experimental $\mu$SR spectra were investigated. The analysis of the simulated $\mu$SR spectra showed that at high magnetic fields there is a strong correlation between obtained $\lambda$ and $\xi$ for any value of the Ginzburg-Landau parameter $\kappa = \lambda/\xi$. The smaller the applied magnetic field is, the smaller is the possibility to find the correct value of $\xi$. A simultaneous determination of $\lambda$ and $\xi$ without any restrictions is very problematic, independent of the model used to describe the vortex state. It was found that for extreme type-II superconductors and low magnetic fields, the fitted value of $\lambda$ is practically independent of $\xi$. The second-moment method frequently used to analyze $\mu$SR spectra by means of a multi-component Gaussian fit, generally yields reliable values of $\lambda$ in the whole range of applied fields $ H_{c1} \ll H \lesssim H_{c2}$ ($H_{c1}$ and $H_{c2}$ are the first and second critical fields, respectively). These results are also relevant for the interpretation of small-angle neutron scattering (SANS) experiments of the vortex state in type-II superconductors.