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The Magnetic Penetration Depth
and the Vortex Core Radius
in Type-II Superconductors

Jeff E. Sonier

B.Sc. - University of Wester Ontario - 1991
M.Sc. - University of British Columbia - 1994
Doctor of Philosophy (herewith) - Department of Physics and Astronomy
University of British Columbia - 6 April 1998


In this thesis, muon spin rotation (µSR) measurements of the internal magnetic field distribution in the vortex state of the high-Tc superconductor YBa2Cu3O$_{7-\delta}$ and the conventional type-II superconductor NbSe2 are presented. From the measured field distributions, the ``characteristic length scales of superconductivity'' are extracted. It is found that both the $\hat{a}$-$\hat{b}$ plane magnetic penetration depth $\lambda_{ab}$and the vortex-core radius r0 (which is closely related to the coherence length $\xi_{ab}$) vary as functions of temperature and magnetic field in both materials.

The behaviour of $\lambda_{ab}(H,T)$ and r0(H,T) at low temperatures is found to be substantially different in YBa2Cu3O$_{7-\delta}$ from what is observed in NbSe2. This reflects the unconventional nature of the pairing mechanism in this compound. The temperature dependence of $\lambda_{ab}$ in the vortex state of YBa2Cu3O$_{7-\delta}$agrees well with microwave cavity measurements in the Meissner state. The magnetic field dependence of $\lambda_{ab}$ in YBa2Cu3O$_{7-\delta}$ is found to be considerably stronger than in NbSe2. This is likely due to both the nonlinear and the nonlocal effects associated with nodes in the superconducting energy gap. However, in NbSe2 (where nonlocal effects are negligible), it is not clear whether the field dependence of $\lambda_{ab}$ can be explained solely in terms of the nonlinear effects associated with an isotropic s-wave energy gap.

The vortex-core radius r0 is found to decrease with increasing magnetic field in both superconductors. The reduction in the vortex-core size appears to be due to the increased strength of the vortex-vortex interactions. An important consequence of this variation with field is that $\xi_{ab}$ in the vortex state, which is generally regarded to be extremely small in the high-Tc compounds, is comparatively large at low magnetic fields.

The vortex-core radius is also found to increase with increasing temperature. The strength of this variation is considerably weaker in YBa2Cu3O$_{7-\delta}$ than in NbSe2. One possible interpretation is that the quantum limit is realized at much higher temperatures in the high-Tc compound. The measured temperature dependence of r0 in both superconductors is weaker than current theoretical predictions for an isolated vortex.

Finally, the effects of vortex pinning and thermal fluctuations of the vortex lines are considered. It is found that the vortex lattice is strongly pinned in YBa2Cu3O$_{7-\delta}$.The vortex lattice in the underdoped compound YBa2Cu3O6.60 is found to exhibit quasi-2D behaviour. In particular, a field-induced transition of the 3D-vortex lattice to a 2D-vortex lattice is observed--which appears to be due to the small $\hat{c}$-axis coherence length and vortex pinning in the CuO2 layers of this material. Also, the 3D-solid vortex lattice in YBa2Cu3O6.60 at low temperatures is found to melt and/or undergo a transition to a 2D-vortex lattice as the temperature is increased.

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