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 $B\left(z\right)$ ($0<z\lesssim 200\mathrm{nm}$ measured from the surface). All the investigated samples [$\mathrm{Nb}:\kappa \simeq 0.7\left(2\right)$, $\mathrm{Pb}:\kappa \simeq 0.6\left(1\right)$, $\mathrm{Ta}:\kappa \simeq 0.5\left(2\right)$] show clear deviations from the simple exponential $B\left(z\right)$ 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 ${\lambda }_L$ is extracted. In the case of Pb the clean limit coherence length ${\xi }_0$ is obtained. Furthermore we find that the temperature dependence of the magnetic penetration depth follows closely the two-fluid expectation $1∕{\lambda }^2\propto 1-{(T∕T_c)}^4$. While $B\left(z\right)$ 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 ${\xi }_0$. This effect, which is not taken self-consistently into account in the mentioned models, should be more pronounced in the lowest $\kappa$ regime consistently with our findings.

• Received 6 January 2005

DOI:https://doi.org/10.1103/PhysRevB.72.024506