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#

Conclusions

This thesis reports SR measurements of the internal magnetic
field distribution *n*(*B*) in LuNi_{2}B_{2}C at temperatures *T* between
and
,
under a
magnetic field
applied parallel to the crystal *c* axis.
The 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 and core radius
with temperature *T* in LuNi_{2}B_{2}C.

Nonlocality plays an important role in the vortex state of LuNi_{2}B_{2}C.
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
in LuNi_{2}B_{2}C increases slightly from
at temperature
to
at
.
The form of the measured penetration depth temperature variation
agrees with that expected for a BCS *s*-wave superconductor, although the
error bars suffice in size for the observed temperature dependence
to be consistent with weak linear growth. Such a linear rise in the
penetration depth
at low temperatures would imply the
presence of low energy delocalised quasiparticles. However the
considerably reduced steepness of the possible linear growth in LuNi_{2}B_{2}C
relative to that observed for YBa_{2}Cu_{3}O_{6.95} means that the energy
gap
anisotropy in LuNi_{2}B_{2}C is much less than would be generated
by line nodes.

The core radius
in LuNi_{2}B_{2}C 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
,
as
determined by comparison with NbSe_{2} data, greatly exceeds the proposed
.
However, the extrapolated quantum
limit temperature
for LuNi_{2}B_{2}C agrees well
with the expected value
.
Surprisingly, the behaviour
of the core radius
with reduced temperature *T*/*T*_{c} is
almost identical in nearly three-dimensional LuNi_{2}B_{2}C and
quasi two-dimensional NbSe_{2}. This similarity indicates that longitudinal
disorder of vortices exerts negligible influence on SR measurements of
the vortex core radius ,
and that quasiparticles in these two
superconductors act in much the same manner. As is the case for NbSe_{2},
the weakness of the observed Kramer-Pesch effect in LuNi_{2}B_{2}C 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.

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** Up:** Astria Price's M.Sc. Thesis, Oct. 2001
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*Jess H. Brewer *

2001-10-31