Low internal magnetic fields in anisotropic superconductors

Abstract

This thesis is a theoretical, numerical study of the magnetic fields which exist in the anisotropic, high temperature superconductors like YBa\sb2Cu\sb3O\sb{7-\delta}, or YBCO for short, using both the anisotropic London theory and simulations based on existing muon spin rotation techniques. The thesis first describes the muon spin rotation ($\mu$SR) techniques, and then gives a brief discussion of superconductivity with regard to the London theory of anisotropic, type II superconductors. Next, numerical results of the application of this theory to YBCO are presented. Three dimensional surface plots of the magnetic field components within the flux line lattice (FLL) are shown, as well as the corresponding contour plots of the fields. Field distributions are calculated from these surfaces, and the graphs are presented. These distributions correspond to the real part of the Fourier transform of the muon histogram, and a comparison between data taken on a polycrystalline sample and the theoretical prediction is made. In addition, variation of the field distributions with parameters such as penetration depth, angle of the average field, and the magnitude of the average field is discussed. The last part of the thesis is a theoretical study of the behavior of muons which have stopped within a superconductor. The muons are assumed to stop uniformly throughout the FLL area, and the precession of each about its local field is recorded as the projection of its polarization along each of three mutually perpendicular detectors. The depolarization of these signals as a function of time is an indication of the existence of transverse field components which exist within the FLL due solely to the anisotropy of the material. In order to further investigate these off axis fields, we have developed an extension of the usual $\mu$SR techniques, coupled with Fourier analysis, which yields new information. For example, with the proper analysis procedure, one may determine to good precision the direction of the average internal field B with respect to the applied field H\sb{a}. Other quantities, which we call moments of the field distribution, may also be determined