Quantitative measurements of the magnetic field profile in superconductors

Measurement of the magnetic field profile $B(z)$, $z$ being the distance from the sample surface, in the Meissner state of superconductors is one of the longest standing problems of experimental superconductivity. Importance of $B(z)$ follows, in particular, from the fact, that it provides a direct way to determine the key intrinsic parameters, such as the London penetration depth at zero temperature $\lambda_L(0)$ and the Pippard coherence length $\xi_0$. None of these parameters is known with justified uncertainty for $any$ superconductor. $B(z)$ can be measured using Low-Energy Muon Spin Rotation spectroscopy (LE-$\mu$SR) and Polarized Neutron Reflectometry (PNR). To verify abilities of these techniques for quantitative measurements of $B(z)$ in unconventional superconductors and to examine the nonlocal electrodynamics effect predicted by Pippard in 1953, we performed an extensive series of cross LE-$\mu$SR and PNR measurements of $B(z)$ with two extreme type-I superconductors, In and Sn. Results obtained at the initial stage of this project were reported last year. Now the project is completed. Results unambiguously validate the nonlocal effect. Conditions which have to be met to use LE-$\mu$SR and/or PNR for measurements of $\lambda_L(0)$ and $\xi_0$ will be discussed.