Survey of Pauli Limiting and FFLO behavior in organic superconductors

Superconducting effects near the Pauli paramagnetic limit have drawn increased attention recently, with several suggestions of inhomogeneous superconductivity (Fulde-Ferrell-Larkin-Ovchinikov) at high magnetic fields and low temperatures. Many of these studies have been done on layered superconductors when the magnetic field is oriented exactly parallel to the conducting layers to suppress orbital limiting. We compare the normalized phase diagrams found by RF penetration depth measurements on $\kappa$-(ET)$_2$Cu(NCS)$_2$, CeCoIn$_5$, $\alpha$-(ET)$_2$NH$_4$Hg(SCN)$_4$, $\beta^{\prime\prime}$-(ET)$_2$SF$_5$CH$_2$CF$_2$SO$_3$, and $\lambda$-(BETS)$_2$GaCl$_4$. In most of these materials, we have found possible inhomogeneous phases below reduced temperatures $(T/T_c)$ in the range 0.1 to 0.3. We also inspect some measurable sample characteristics for clues to the formation or absence of the inhomogeneous state. We will recommend $\kappa$-(ET)$_2$Cu[N(CN)$_2$]Br, which seems not to have an inhomogeneous state, for further phase diagram study.