Magnetic properties

The existence of the Meissner-Ochsenfeld effect, the exclusion of a magnetic field from the interior of a superconductor, is direct evidence that the superconducting state is not simply one of infinite electrical conductivity. Instead, it is a true thermodynamic equilibrium state, a new phase which has lower free energy than the normal state at temperatures below the transition temperature and which somehow requires the absence of magnetic flux.

The exclusion of magnetic flux by a superconductor costs some magnetic energy. So long as this cost is less than the condensation energy gained by going from the normal to the superconducting phase, the superconductor will remain completely superconducting in an applied magnetic field. If the applied field becomes too large, the cost in magnetic energy will outweigh the gain in condensation energy, and the superconductor will become partially or totally normal. The manner in which this occurs depends on the geometry and the material of the superconductor. The geometry which produces the simplest behavior is that of a very long cylinder with field applied parallel to its axis. Two distinct types of behavior may then occur, depending on the type of superconductor—type I or type II.

Below a critical field Hc which increases as the temperature decreases below Tc, the magnetic flux is excluded from a type I superconductor, which is said to be perfectly diamagnetic. For a type II superconductor, there are two critical fields, the lower critical field Hc1 and the upper critical field Hc2. In applied fields less than Hc1, the superconductor completely excludes the field, just as a type I superconductor does below Hc. At fields just above Hc1, however, flux begins to penetrate the superconductor, not in a uniform way, but as individual, isolated microscopic filaments called fluxoids or vortices. Each fluxoid consists of a normal core in which the magnetic field is large, surrounded by a superconducting region in which flows a vortex of persistent supercurrent which maintains the field in the core.

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