Many new superconductors under development are anisotropic, and many of them have heavy electron masses. The anisotropy and heavy electrons are two important qualities that favor Pauli limiting in superconductors. We call a superconductor Pauli limited when the interaction of the applied magnetic field with the electron spin limits the superconducting state, in contrast to orbital limiting, the more common behavior where vortices eventually destroy the superconducting state. An exotic state called the FFLO state, is expected in clean superconductors that are Pauli limited. To understand the next generation of superconductors in high magnetic fields, we need to understand the Pauli limit and the FFLO state.

Because of the special measurement techniques that we have developed and the materials we study we have chosen to study the effects Pauli limiting. In the past year we have published or submitted papers that show different aspects of Pauli limited behavior in anisotropic superconductors. We showed that &alpha-(ET)₂NH₄Hg(SCN)₄ is Pauli limited, but is not clean enough to show a first order H_c2 at low temperatures (or it is too anisotropic, causing fluctuations of the order parameter) In &kappa-(ET)₂Cu(NCS)₂, which is cleaner as measured by the parameter r = l/&xi, where l is the mean free path and &xi is the superconducting coherence length, we have evidence of a first-order phase transition at H_c2, when t = T/T_c < 0.54. We have repeatedly looked for the appearance of the FFLO state in this material and have not found it. In CeCoIn₅ however, we have observed clear evidence of the FFLO state using our TDO, and our data agrees with specific heat measurements. CeCoIn₅ is unique at present, because of its heavy effective electron masses and because r > 30.

The H-T Phase diagram of &alpha-(ET)2NH4Hg(SCN)4 shows strong Pauli limiting.	The H-T Phase diagram of &kappa-(ET)2Cu(NCS)2 never saturates. The crtitical field continues to rise as the temperature is lowered.
In CeCoIn5 there is a separate FFLO state at high fields and low temperatures. As the magnetic field is raised at low temperatures, two phase transitions are seen. (See more details about this experiment.)

On the next page we look more carefully at the conditions necessary for Pauli limiting.