Conclusions

This thesis reports $\mu$SR measurements of the internal magnetic field distribution n(B) in LuNi₂B₂C at temperatures T between $T = 2.6\,\mathrm{K}$ and $T = 10\,\mathrm{K}$, under a magnetic field $H = 1.2\,\mathrm{T}$ applied parallel to the crystal c axis. The $\mu$SR data are analysed with a nonlocal London model [11] developed specifically for borocarbide superconductors, assuming the square vortex lattice appropriate for these temperature T and external field H conditions. The results of this analysis enable a number of conclusions to be drawn regarding nonlocality and the behaviour of the penetration depth $\lambda$and core radius $\rho$ with temperature T in LuNi₂B₂C.

Nonlocality plays an important role in the vortex state of LuNi₂B₂C. The incorporation of first order nonlocal corrections into the traditional London model improves the fit quality dramatically by qualitatively modifying the fitted internal magnetic field distribution n(B). In comparison to the field distribution n(B) produced for a square vortex lattice by the basic London model, the inclusion of these nonlocal terms considerably diminishes the spectral weight of the low field shoulder and generates a small peak at the lowest field B in the distribution n(B).

The penetration depth $\lambda$ in LuNi₂B₂C increases slightly from $\lambda \approx 950\,\textrm{\AA}$ at temperature $T = 2.6\,\mathrm{K}$ to $\lambda \approx 1100\,\textrm{\AA}$ at $T = 10\,\mathrm{K}$. The form of the measured penetration depth temperature variation  $\lambda (T)$ agrees with that expected for a BCS s-wave superconductor, although the error bars suffice in size for the observed temperature dependence  $\lambda (T)$to be consistent with weak linear growth. Such a linear rise in the penetration depth $\lambda$ at low temperatures would imply the presence of low energy delocalised quasiparticles. However the considerably reduced steepness of the possible linear growth in LuNi₂B₂C relative to that observed for YBa₂Cu₃O_6.95 means that the energy gap $\Delta$ anisotropy in LuNi₂B₂C is much less than would be generated by line nodes.

The core radius $\rho$ in LuNi₂B₂C contracts linearly upon cooling through the investigated temperature interval. The rate of core shrinkage is remarkably slower than anticipated from the predicted Kramer-Pesch effect. The zero temperature core radius  $\rho(0) = 64(1)\,\textrm{\AA}$, as determined by comparison with NbSe₂ data, greatly exceeds the proposed $\rho(0) \sim 1/k_F = 4\,\textrm{\AA}$. However, the extrapolated quantum limit temperature $T_0 = 1.0(4)\,\mathrm{K}$ for LuNi₂B₂C agrees well with the expected value  $T_0 = 0.7(1)\,\mathrm{K}$. Surprisingly, the behaviour of the core radius  $\rho / \rho(0)$ with reduced temperature T/T_c is almost identical in nearly three-dimensional LuNi₂B₂C and quasi two-dimensional NbSe₂. This similarity indicates that longitudinal disorder of vortices exerts negligible influence on $\mu$SR measurements of the vortex core radius $\rho$, and that quasiparticles in these two superconductors act in much the same manner. As is the case for NbSe₂, the weakness of the observed Kramer-Pesch effect in LuNi₂B₂C points to the need for theoretical work on the temperature dependence of vortex structure to take into account zero point motion of vortices and vortex-vortex interactions.