uSR Studies of High-Tc Superconductors: Effect of Vortex Lattice Disorder on TF-uSR Measurements of the Magnetic Penetration Depth and Nuclear Contribution to the ZF-uSR Relaxation Spectrum

Muon Spin Rotation/Relaxation ($\mu$SR) is an experimental technique widely used to probe magnetism in high-temperature (high $T_c$) superconductors. This thesis consists of two distinct $\mu$SR studies of high-$T_c$ materials: namely, transverse-field (TF) $\mu$SR measurements of the iron-arsenic superconductor BaFe$_{2-x}$Co$_x$As$_2$ and a zero-field (ZF) $\mu$SR investigation of the cuprate superconductor La$_{2-x}$Sr$_x$CuO$_4$ (LSCO). A model for severe random frozen disorder of the vortex lattice in BaFe$_{2-x}$Co$_x$As$_2$ is developed and used to explain limitations imposed on TF-$\mu$SR measurements of the superconducting magnetic penetration depth in doped iron-arsenic superconductors. In the latter part of the thesis, ZF-$\mu$SR measurements on LSCO show no evidence for spontaneous magnetic order in the pseudogap regime. Instead, experiments suggest that the random nuclear dipole moments are the dominant contribution to the ZF-$\mu$SR relaxation. To determine the exact form of the nuclear contribution to the ZF-$\mu$SR signal, the nuclear contribution is modeled quantum mechanically and compared to the experimental results.