Conclusion

The observation of a linear temperature dependence below 50K for $1/ \lambda _{ab}^{2}$ is in agreement with the microwave cavity measurements of Hardy et al. on similar $\mbox{YBa$_{2}$ Cu$_{3}$ O$_{6.95}$ }$ crystals in zero applied field [6]. Both experiments provide further evidence for unconventional pairing of carriers in the superconducting state. These results of course contradict previous $\mu ^{+}$SR studies, which found a much weaker low-temperature behaviour for $\lambda_{ab}$ [9]. The likelihood of impurity scattering playing a role in suppressing $\lambda_{ab}$ in such a way as to simulate conventional s-wave behaviour has been made more plausible by recent measurements on Zn-doped crystals [84,88]. These measurements show a distinct weakening of the linear term at low temperatures due to the added Zn impurity. Thus it is possible that the presence of impurities, as well as a lack of good low-temperature data may have lead to a misinterpretation in some of the previous $\mu ^{+}$SR experiments.

The difficulties in analyzing $\mu ^{+}$SR data of this nature have been addressed as much as possible in this study. The large number of variable parameters requires one to make some plausible assumptions in the fitting procedure. Fortunately, all variations of the analysis considered in this report arrive at the same conclusion regarding the behaviour of $\lambda _{ab} (T)$ at low temperatures; namely, a strong linear term exists. Furthermore, the strength of the linear term is comparable for all forms of analysis considered. This implies that the observed low-temperature linear dependence of $1/ \lambda _{ab}^{2}$ is not an artificial manifestation of the fitting procedure itself. This notion is further supported by the obseravtion of a linear term in the single gaussian fits, which provide a crude estimate of the second moment.

The weakening of the linear term at 1.5T (or conversely, the strengthening of the linear term at 0.5T) was surprising indeed. The magnetic penetration depth is not expected to be field dependent in this low-field regime. Theoretically there is no low-field limit associated with the field distribution used to model the vortex lattice. Eq. (3.9) is simply an extension of the London model which has no low-field limit.

One possible explanation for the observed field dependence is quasiparticle scattering off of the vortex cores, which we know to be static, as evidenced by the field-shifted results of Fig. 4.5. One can imagine this effect to be enhanced at higher magnetic fields, where the flux-line density is greater in the sample. A scattering process of this nature may be similar to the impurity scattering which appears to weaken the linear term in the Zn-doped samples.

It is possible that the observed low-temperature field dependence for $\lambda_{ab}$ is somehow linked to the $\vec{a}$-$\vec{b}$ anisotropy in the penetration depth, not considered here. It is important to stress that none of the previous $\mu ^{+}$SR studies included $\vec{a}$-$\vec{b}$ anisotropy in determining the temperature dependence of $\lambda_{ab}$, either. Consequently, it cannot be held accountable for the observation of a linear term in the present study.

Another puzzling observation comes from the comparison of the temperature dependence of $\lambda_{ab}$ with that obtained from the microwave cavity measurements. The 1.5T data agrees well with the microwave results for all forms of the analysis. On the other hand, the 0.5T data shows poor agreement with the microwave measurements. The better agreement with the higher-field $\mu ^{+}$SR data is surprising since the microwave measurements were performed in zero static magnetic field. However, there are some questions as to whether the two types of measurements can be compared at this level due to the very different nature of the two methods. In the microwave studies the measured penetration depth pertains to the length scale over which very weak shielding currents flow around the perimeter of the sample. In the $\mu ^{+}$SR studies one is measuring the penetration depth associated with supercurrents circulating around the vortex cores in the bulk of the sample.

Finally, something must be said about the uncertainty in the $\mu ^{+}$SR measurements. This study gives $\lambda_{ab} (0)$ in the range 1347 - 1451Å and 1437 - 1496Å depending on the analysis, for the 0.5T and 1.5T fields, respectively. However, the errors in these results are difficult to determine. The systematic errors are much larger than the statistical errors quoted in Table 4.1 and those which appear on the graphs throughout this report. Thermal and magnetic field fluctuations during the experiment are difficult to assess, but these uncertainties are likely negligible compared to those introduced in the fitting procedure. Although there is some question regarding the accuracy of the $\lambda_{ab} (0)$ values obtained, there is exciting new qualitative information to be obtained from this $\mu ^{+}$SR study. Namely, evidence for unconventional pairing of carriers in the superconducting state of $\mbox{YBa$_{2}$ Cu$_{3}$ O$_{6.95}$ }$ and the possible existence of a low-temperature field dependence for $\lambda_{ab}$.