Comparison of different methods for analyzing μSR line shapes in the vortex state of type-II superconductors

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 for extracting 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 lambda and xi obtained for any value of the Ginzburg-Landau parameter k = lambda/xi. The smaller the applied magnetic field, the smaller the possibility of finding the correct value of xi. A simultaneous determination of lambda and xi without any restrictions is very problematic, regardless 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 over the whole range of applied fields H-c1 << H less than or similar to 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 experiments on the vortex state in type-II superconductors.