Substituting the fitted parameters into
expression (5.2) reveals the spatial profile of the
internal field
B(r) within the sample.
Figure 5.3 displays the profile around a flux line generated by
an external field
at temperature
.
The inset contains the internal field distribution n(B) belonging to
this spatial profile and, for comparison, the real amplitude of the FFT
of the recorded precession signal
.
The two distributions
are similar; however, as alluded to in Section 5.1, the finite time
span of the SR data broadens the FFT and creates rapid oscillations
in it. This ringing is especially visible in the high field B tail of
the FFT, despite the FFT having undergone apodisation to smooth it. Apodisation
effectively convolutes the FFT with a Gaussian function, and so broadens the
distribution still further. Nuclear dipolar fields and slight vortex lattice
disorder also broaden this distribution.
The small peak in the FFT at field
arises from muons that miss the sample. The maximum peak in the FFT,
and in the fitted field distribution n(B), occurs for the field B
located at the midpoint between nearest neighbour vortices. The shoulder
corresponding to fields B weaker than this, expected for a square vortex
lattice according to the local London model, is absent here in both the fitted
field distribution n(B) and the FFT of the recorded
polarisation
.
This lack of a sizeable low field shoulder is a
consequence of nonlocality. The effect of nonlocality on the field
distribution n(B) appears in more detail in the next chapter. The very
high fields B in the field distribution n(B) of a flux line lattice derive
from the vortex core region.
A useful definition of the radius
of a vortex core is the
distance r from the core centre to the point where the supercurrent
density J(r) is greatest. Applying one of Maxwell's equations,