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.