Probing superconductivity with polarized neutrons and low-energy muons

A limited depth of magnetic field penetration is one of the most important properties of superconductors. It is usually assumed that in the Meissner state the field $B(z)$ decays exponentially with depth $z$. However, this cannot be the case, unless one deals with conventional type-II superconductors. For example, $B(z)$ is not exponential in nonlocal superconductors, but nonmonotonic and it even changes sign at a certain depth. Recently this nonlocal effect has been confirmed experimentally for a low-\textit{$\kappa $} superconductor. Nonlocality was also predicted for d-wave superconductors, where it can arise from the diverging coherence length near nodal points in momentum space. For such materials and especially for novel superconductors measurements of $B(z)$ may be crucial for interpretation. The $B(z)$ can be measured using Polarized Neutron Reflectivity (\textit{PNR}) and Low-Energy muon Spin Rotation (\textit{LE-$\mu $SR}) techniques. In this talk we will present a critical review of the capabilities of the \textit{PNR }and \textit{LE-$\mu $SR }techniques based on our studies of nonlocality in In.