Upper Critical Field and Phase Diagram Studies for $\lambda$-(BETS)$_2$GaCl$_4$

The upper critical fields for the highly anisotropic organic superconductor $\lambda\textnormal{-}(\textnormal{BETS})_2\textnormal{Ga}\textnormal{Cl}_4$ have been studied by measuring the in-plane RF penetration depth with a tunnel diode oscillator technique in pulsed fields. At zero field we found a $T_c$ of 5 K. With the field perpendicular to the conducting layers we extrapolate $H_{c2,T=0}$ to 2.8 T and with the field parallel $H_{c2,T=0}$ is 11 T. With the field applied parallel to the conducting layers, for $T > 0.5T_c$ the $H_{c2}$ follows the superconducting gap function $\sqrt{1-\frac{T}{T_c}}$, then saturates below $0.5 T_c$. Below 0.35$T_c$ we see a clear enhancement of 1.5 T in $H_{c2}$ and in addition there is a second phase line at a lower field than $H_{c2}$. These features are both characteristic of the FFLO state. We will discuss this second phase line in relation to the Pauli Limit as calculated in a semi-empirical method and compare our phase diagram to previous results.