Magnetic field distributions from longitudinally disordered pancake vortices

For the superconductor YBa₂Cu₃O_7-δ, the magnetic field probability distributions measured by μSR have been found to be reasonably represented by those produced by a more or less regular vortex lattice. For Bi₂Sr₂Ca₁Cu₂O_8-δ (BSCCO) the field probability distributions are not, except at quite low fields, such as 100 G. Further, it is known that the copper plane to copper plane coupling in BSCCO is quite weak. This has led Clem to posit pancake vortices, vortices referred to only one plane, as the building blocks of vortex lattices in this material. He has provided a solution for the magnetic field arising from one such vortex and shown that a regular lattice built from such pancakes produces the field distributions expected for the usual London solution vortices. The stacks of pancake vortices would be easily longitudinally disordered as a consequence of the very weak inter-layer coupling. In order to model μSR data on BSCCO a means to calculate fields from disordered stacks of pancake vortices has been developed. The vortices in a given plane were assumed to form a regular lattice of the appropriate inter-vortex spacing, then a three dimensional system of such layers was built up. Each subsequent layer of pancake vortices was allowed to be randomly displaced from the layer its predecessor. Thus in proceeding along a given stack, the pancakes lose registry with those below in a random walk. This cuts off the range of pancakes which are well ordered and leads to the high-field cutoff being reduced and the overall magnetic field distribution becoming more symmetric in agreement with the data. Results of this modeling are presented and compared to high-field data on BSCCO.