Introduction

Superconductivity refers to the unusual electrical and magnetic behaviour exhibited by certain materials below their critical temperature T_c, usually near absolute zero. These phenomena include negligible resistance to electric current and the expulsion of external magnetic fields, and find application in Magnetic Resonance Imaging (MRI) and high capacity power transmission cables. Based on their response to the applied magnetic field H, superconductors fall into two major classes, type I and type II, as illustrated in Figure 1.1.

  

Figure 1.1: Phase diagram for (a) type I and (b) type II superconductors.

A type I superconductor exhibits the Meissner effect, the exclusion of the magnetic field from its interior, at an applied field H below its thermodynamic critical field H_c(T). Exceeding the thermodynamic critical field H_c(T) drives the type I material into the normal state. A type II superconductor also exists in the Meissner state for external fields Hweaker than its lower critical field H_c1(T), but for intermediate fields between this and its upper critical field H_c2(T), the type II material enters the vortex state. Here the external field penetrates the sample as a lattice of flux lines, each associated with one quantum of flux $\Phi_0$ [1] encircled by a vortex of supercurrent. The number of magnetic vortices grows linearly with the applied field H, until the superconductor becomes normal at H = H_c2(T). Type II materials generally superconduct at much higher temperatures T and fields H than those of type I, and fully realising their technological potential requires an improved understanding of the characteristics of the vortex state.

This thesis focusses on the behaviour of the vortex core radius $\rho$ as a function of temperature T in LuNi₂B₂C, as studied with muon spin rotation ($\mu$SR) spectroscopy. (For a discussion of the field dependence, see [2].) Whereas the core radius $\rho$ is often assumed to remain constant at low temperatures $T \ll T_c$, theoretical works [3][4][5] propose that the core radius $\rho$ should contract linearly with falling temperature $T \ll T_c$, and stop shrinking at a quantum limit temperature T₀, where the radius $\rho$ is on the order of a Fermi wavelength. Experimental confirmation of such a temperature dependence, known as the Kramer-Pesch effect, would necessitate a reconsideration of the common assumption that the radius $\rho$remains constant at low temperatures. To date, $\mu$SR observations [6][7] of the core radius $\rho$ have revealed only a fairly weak Kramer-Pesch effect. These experiments dealt with quasi two-dimensional materials, introducing the possibility of systematic overestimation of the core radius $\rho$ as a result of longitudinal disorder of vortices [7]. This complication has much less impact in the case of LuNi₂B₂C, a member of a new family of materials that exhibit unusual superconducting behaviour, because LuNi₂B₂C is nearly isotropic. This superconductor is thus a prime candidate with which to see the predicted Kramer-Pesch effect.

This thesis proceeds as follows. The next chapter outlines basic relevant superconductivity concepts, and goes into detail about the expected Kramer-Pesch effect and previous experimental results concerning it. A general overview of the properties of LuNi₂B₂C appears in Chapter 3, along with a quantitative estimate of the Kramer-Pesch effect anticipated for this superconductor. Chapter 4 describes the transverse field $\mu$SR technique and the experimental setup. Chapter 5 explains how the time dependent muon polarisation signal  P(t) is fitted to a nonlocal London model developed for borocarbides, and how the core radius $\rho$is calculated from the fitted internal magnetic field profile  B(r). It also examines the quality of the fits as a function of the penetration depth $\lambda$, the nonlocality parameter C and the core radius $\rho$. Chapter 6 presents the resulting temperature dependence of the fitted penetration depth $\lambda$ and nonlocality parameter C, and the extracted core radius $\rho$, for LuNi₂B₂C under a constant applied field of  $H = 1.2\,\mathrm{T}$. It compares the low temperature behaviour of the core radius $\rho$ measured in LuNi₂B₂C with the predicted Kramer-Pesch effect, as well as the core radius temperature dependences $\rho (T)$ observed previously in NbSe₂ and YBaCu₃O $_{7-\delta}$ under an applied field  $H=0.5\,\mathrm{T}$. This chapter also contrasts the internal magnetic field distributions n(B) of the nonlocal and local London models. Finally, Chapter 7 summarises these results and their implications.