Physica B 374–375 (2006) 243–246 Nonlocal Meissner screening A. Suter a,Ã , E. Morenzoni a , N. Garifianov a,b , R. Khasanov a,c , E. Kirk d , H. Luetkens a,e , T. Prokscha a , M. Horisberger f a Laboratory for Muon Spin Spectroscopy, Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland b Kazan Physical-Technical Institute, 420029 Kazan, Russian Federation c Physics Institute, University of Zurich, CH-8057 Zurich, Switzerland d Laboratory for Astrophysics, Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland e Institut fu ¨r Metallphysik und Nukleare Festko¨rperphysik, TU Braunschweig, 38106 Braunschweig, Germany f Laboratory for Neutron Scattering, Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland Abstract Implanting 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 BðzÞð0ozt200 nm, z the distance from the surface). All the investigated samples [Nb: k ’ 0:7ð2Þ, Pb: k ’ 0:6ð1Þ, Ta: k ’ 0:5ð2Þ] show clear deviations from the simple exponential BðzÞ expected in the London limit, and reveal the nonlocal response of these superconductors. From a quantitative analysis within the Pippard and BCS models the London penetration depth l L is extracted. Both, the Pippard and BCS description of BðzÞ, are less accurate the smaller k is. We attribute this discrepancy to the fact that the decrease of the superfluid density on approaching the surface on the length scale x is not taken self- consistently into account in the mentioned models. Such an effect should be more pronounced in the lowest k regime, consistent with our findings. r 2005 Published by Elsevier B.V. PACS: 76.75.+i; 74.25.q; 74.78.Db Keywords: Muon-spin rotation; Superconductivity; Nonlocal effects; Magnetic field imaging 1. Introduction and theoretical background One of the fundamental properties of a superconductor is the Meissner–Ochsenfeld effect [1]. It states that at low magnetic fields and frequencies a superconductor expels or excludes any magnetic flux from its core. However, at the surface the field penetrates on a typical length scale l called the magnetic penetration depth. Pippard showed [2] that the general functional form of BðzÞ is rather complex, only simplifying to the well-known BðzÞ/ expðz=lÞ in the limit x5l, where x is the coherence length of the super- conductor. The magnetic field profile in the Meissner state has the following form 1 [3]: BðzÞ¼ B ext 2 p Z q q 2 þ m 0 K ðqx; T ;‘Þ sin ðqzÞ dq. (1) m 0 K ðqx; T ;‘Þ is the so-called integral kernel. x is the BCS coherence length, roughly speaking the extension of a Cooper pair. In the London limit (x5l L ) the kernel has the form m 0 K ðqx; T ;‘ ! 1Þ ¼ 1=l 2 L and therefore BðzÞ/ expðz=l L Þ. For the analysis to follow we used the more general Pippard kernel [2] m 0 K P ðqx P ; T ;‘Þ¼ 1 l 2 ðT Þ x P ðT ;‘Þ x P ð0;‘Þ gðqx P ðT ;‘ÞÞ, ARTICLE IN PRESS www.elsevier.com/locate/physb 0921-4526/$ - see front matter r 2005 Published by Elsevier B.V. doi:10.1016/j.physb.2005.11.065 Ã Corresponding author. Tel.: +41 56 3104238; fax: +41 56 3103294. E-mail address: andreas.suter@psi.ch (A. Suter). 1 This form is only valid for specular reflection of the charge carriers from the surface. However, it can be shown [3] that the boundary conditions are only weakly influencing the form of BðzÞ.