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"One of the fundamental quantities of a superconductor is the magnetic penetration depth, \u03BB, which is the characteristic length scale that a magnetic field penetrates into the surface of a superconductor while in the Meissner state. In the clean limit the absolute value of \u03BB is directly related\nto the superfluid density ns via 1/\u03BB\u00B2 = \u03BC\u03BFe\u00B2ns/m\u2217 , where m\u2217 is the effective mass. Consequently, its variation as a function of temperature, doping and orientation are of central importance in testing microscopic theories of exotic superconductors. A low energy beam of spin polarized muons has recently been developed, at the Paul Scherrrer Institute, to directly measure \u03BB in a superconductor. When a muon (\u03BC+) decays, it emits a fast decay positron preferentially along the direction of its spin due to the parity violating decay.\nThe time evolution of statistical average direction of the spin polarization of the muon ensemble depends sensitively on the local magnetic field which can be monitored as a function of the mean depth of implantation. In this way it is possible to measure the field profile near the surface of a superconductor and extract the magnetic penetration depth in a direct manner which is not otherwise possible with conventional bulk methods.\nIn this thesis, accurate measurements of \u03BB and its anisotropy (\u2261 \u03BBa /\u03BBb) have been made for three different oxygen (x = 6.52, 6.92 and 6.998) contents of YBa\u2082Cu\u2083O\u2086\u208Ax as well as in\nBa(Co\u2080.\u2080\u2087\u2084Fe\u2080.\u2089\u2082\u2086\u208E\u2082As\u2082. The measured values of \u03BB and the in-plane anisotropies are considerably different from that reported in the literature, using less direct methods. The a \u2013 b anisotropy is surprisingly insensitive to x in YBa\u2082Cu\u2083O\u2086\u208Ax . We observe an exponential decay of the magnetic field and corresponding supercurrent density deep inside the crystals. Small deviations from the London model are observed which indicate there is a suppression of the supercurrent density close to the surface. The measured (\u03BB) values are also found to depart substantially from the Uemura relation Tc\u03B1 1/\u03BB\u00B2 ."@en
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