Observation of nonexponential magnetic penetration profiles in the Meissner state: A manifestation of nonlocal effects in superconductors

Implanting fully polarized low energy muons on the nanometer scale beneath the surface of a superconductor in the Meissner state enabled us to probe the evanescent magnetic field profile $B(z)$ ($0lz\ensuremath{\lesssim}200\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ measured from the surface). All the investigated samples [$\mathrm{Nb}:\ensuremath{\kappa}\ensuremath{\simeq}0.7(2)$, $\mathrm{Pb}:\ensuremath{\kappa}\ensuremath{\simeq}0.6(1)$, $\mathrm{Ta}:\ensuremath{\kappa}\ensuremath{\simeq}0.5(2)$] show clear deviations from the simple exponential $B(z)$ expected in the London limit, thus revealing the nonlocal response of these superconductors. From a quantitative analysis within the Pippard and BCS models the London penetration depth ${\ensuremath{\lambda}}_{L}$ is extracted. In the case of Pb the clean limit coherence length ${\ensuremath{\xi}}_{0}$ is obtained. Furthermore we find that the temperature dependence of the magnetic penetration depth follows closely the two-fluid expectation $1∕{\ensuremath{\lambda}}^{2}\ensuremath{\propto}1\ensuremath{-}{(T∕{T}_{c})}^{4}$. While $B(z)$ for Nb and Pb are rather well described within the Pippard and BCS models, for Ta this is only true to a lesser degree. We attribute this discrepancy to the fact that the superfluid density is decreased by approaching the surface on a length scale ${\ensuremath{\xi}}_{0}$. This effect, which is not taken self-consistently into account in the mentioned models, should be more pronounced in the lowest $\ensuremath{\kappa}$ regime consistently with our findings.