  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.

Superconductivity