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)(0<z<=200nm measured from the surface). All the investigated samples [Nb: kappa simeq 0.7(2), Pb: kappa simeq 0.6(1), Ta: kappa simeq 0.5(2)] show clear deviations from the simple exponential B(z) expected in the London limit, thus revealing the non-local 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 also the clean limit coherence length xi0 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(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 xi0. 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.
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