The observation of a linear temperature dependence below 50K for
is in agreement with the microwave cavity
measurements of Hardy et al.
on similar
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
SR studies,
which found a much weaker
low-temperature
behaviour for
[9].
The likelihood of impurity scattering
playing a role in suppressing
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
SR experiments.
The difficulties in analyzing 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
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
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
is somehow linked
to the
-
anisotropy in the penetration depth, not
considered here.
It is important to stress that none of the previous
SR studies included
-
anisotropy in
determining the temperature dependence of
,
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
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
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
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 SR
measurements. This study gives
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
values obtained,
there is exciting new qualitative information to be obtained from this
SR study.
Namely, evidence for unconventional pairing of carriers in the superconducting
state of
and the possible existence of a low-temperature
field dependence for
.