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  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 gif .

Figure gifa 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 gifa 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 gif):

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 gif . Before turning to the results of critical field measurements on C4KHg, it is appropriate to review how the measurements were made.

next up previous contents
Next: Experimental Methods: Hc2 Up: Upper Critical Field Previous: Upper Critical Field (Alison Chaiken)
Wed Oct 11 22:59:57 PDT 1995