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A detailed analysis of muon-spin rotation ($\mu$SR) spectra in the vortexstate of type-II superconductors using different theoretical models ispresented. Analytical approximations of the London and Ginzburg-Landau (GL)models, as well as an exact solution of the GL model were used. The limits ofthe validity of these models and the reliability to extract parameters such asthe magnetic penetration depth $\lambda$ and the coherence length $\xi$ fromthe experimental $\mu$SR spectra were investigated. The analysis of thesimulated $\mu$SR spectra showed that at high magnetic fields there is a strongcorrelation between obtained $\lambda$ and $\xi$ for any value of theGinzburg-Landau parameter $\kappa = \lambda/\xi$. The smaller the appliedmagnetic field is, the smaller is the possibility to find the correct value of$\xi$. A simultaneous determination of $\lambda$ and $\xi$ without anyrestrictions is very problematic, independent of the model used to describe thevortex state. It was found that for extreme type-II superconductors and lowmagnetic fields, the fitted value of $\lambda$ is practically independent of$\xi$. The second-moment method frequently used to analyze $\mu$SR spectra bymeans 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 neutronscattering (SANS) experiments of the vortex state in type-II superconductors.

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