Ever since
Meissner and Ochsenfeld discovered the perfect diamagnetism
of superconductors in 1933,[169] the study of the behavior
of superconductors in an applied magnetic field has been a
principal activity of superconductivity experimentalists. One
reason is that perfect diamagnetism is a phenomenon peculiar
to superconductors, and thus is often used as a diagnostic
for the occurrence of superconductivity, as indeed was done
in the experiments described in this thesis. A second reason
is that critical field measurements provide a great deal of
information about the material being studied, as is
illustrated by the idealized results shown in Figure 
.
Figure a illustrates the
difference between type I and type II superconductors. The
group of type I superconductors is made up of almost all the
elemental superconductors. These materials exhibit a
first-order transition in an applied magnetic field. Due to
the supercooling effects associated with a first-order
transition, experiments on type I superconductors are often
complicated by hysteresis. Type II superconductors, on the
other hand, show a second-order, non-hysteretic transition in
a magnetic field. Type I superconductivity can be identified
experimentally by noting the presence or absence of
hysteresis and the differential paramagnetic effect (DPE) in
the field sweeps. The DPE is characterized by the occurrence
of a ``bump'' in the susceptibility just above Hc2
which is a property of the intermediate state of type I
superconductors.[106]
Available evidence suggests that most GIC superconductors are
of the type II variety, although some GIC's do have type I
transitions for a range of applied-field orientations.
Figure: a) dc magnetization versus field
for ideal type I and type II superconductors. Hc1
is the lower critical field, Hc is the
thermodynamic critical field, and Hc2 is the upper
critical field. kappa < 1/sqrt2
indicates type I superconductivity; kappa 0.8
indicates weak type II behavior; kappa 2 indicates
strongly type II behavior. b) ac susceptibility versus field
for ideal type II superconductor with kappa 0.8.
Adapted from Ref. [252].
As Figure a shows, there are two
characteristic fields of importance for a type II
superconductor. These are respectively termed the lower
critical field, Hc1, and the upper critical field,
Hc2. Hc1 is the field at which flux
first penetrates a long, thin cylindrical sample, the only
shape of sample for which ``demagnetization'' effects are not
important. Unfortunately the sensitive dependence of
Hc1 on sample shape makes its extraction from
actual experimental data difficult. The same comments apply
to trying to extract Hc, the thermodynamic
critical field, from magnetization curves of type I
superconductors. Sample shape does not impact upon the
measurement of the upper critical field, Hc2,
making it a much more accessible quantity experimentally.
Most of the rest of this discussion concerns the upper
critical field, which is defined theoretically as that
highest applied field at which superconductivity can nucleate
in a bulk superconductor.
The history of upper critical field experiments is a long and fruitful one, dating back to the recognition of the existence of the two types of superconductivity by Abrikosov in the late Fifties[3]. Hc2 measurements give direct information about the Ginzburg-Landau coherence length xi, a parameter defined for isotropic bulk superconductors by the equation:
where ø0 is the superconducting flux
quantum.[252] The
coherence length is one of several important length scales in
a superconductor. For example, there is also the field
penetration depth, Lambda, whose size relative to
xi determines whether the superconductivity is of type
I or type II (see Section ):
In addition, there is the transport mean free path l, whose size relative to xi determines whether the superconductivity is in the clean or dirty limit:
In layered superconductors, such as the superconducting graphite intercalation compounds, another natural length scale to consider is the lattice constant perpendicular to the carbon (graphene) planes. In the GIC's, this lattice constant is termed Ic. The most studied phenomena in the field of layered superconductors are due to the dependence of xi on temperature and crystallographic direction. The consequence of this variability is that in layered systems there is an additional, experimentally controllable, distinction between 3D-coupled and 2D-coupled superconductors:
where s is the layer spacing. The consequences of the
interplay of the various length scales for other layered
superconductors are discussed in Chapter .
Before turning to the results of critical field measurements
on C4KHg, it is appropriate to review how the
measurements were made.
