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 $B(z)$ (0<z2000.3em0exnm measured from the surface). All the investigated samples [Nb:κ0.7(2), Pb:κ0.6(1), Ta:κ0.5(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 λL is extracted. In the case of Pb the clean limit coherence length ξ₀ is obtained. Furthermore we find that the temperature dependence of the magnetic penetration depth follows closely the two-fluid expectation 1∕λ²∝1-(T∕Tc)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 ξ₀. This effect, which is not taken self-consistently into account in the mentioned models, should be more pronounced in the lowest κ regime consistently with our findings.