Abstract

This thesis describes $\mu$SR observations of the internal magnetic field distribution n(B) as a function of temperature in LuNi₂B₂C ( $T_c = 16.0\,\mathrm{K}$, $H_{c2}(0) = 7\,\mathrm{T}$), under a magnetic field of $H = 1.2\,\mathrm{T}$ applied parallel to the crystal $\hat{c}$ axis. The $\mu$SR polarisation signal is fitted to a nonlocal London model, assuming a square vortex lattice. By incorporating first order nonlocal corrections, this model achieves significantly better fits than the local London model. The fitted penetration depth temperature dependence  $\lambda (T)$ follows the form expected for a BCS s-wave superconductor, although the dependence is also consistent with a slight linear increase in the penetration depth $\lambda$ with rising temperature. The rate of any such linear growth, however, is smaller than would be expected for an energy gap $\Delta$ with line nodes. The fitted core radius temperature dependence $\rho (T)$ reveals a Kramer-Pesch effect, or linear contraction of the vortex core radius $\rho$ upon cooling at low temperatures $T \ll T_c$, that is weaker than predicted. The Kramer-Pesch effect found for this nearly three-dimensional superconductor is almost identical to that seen in quasi two-dimensional NbSe₂, implying that quasiparticles behave similarly in LuNi₂B₂C and NbSe₂ despite their different dimensionalities, and that longitudinal disorder of vortices has negligible impact on $\mu$SR determinations of the vortex core radius $\rho$. The surprisingly small magnitude of the Kramer-Pesch effect suggests that future theoretical work on the temperature dependence of vortex structure should consider zero point motion of vortices and intervortex interactions.