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We report the phase diagram of $\lambda$-(BETS)$_2$GaCl$_4$ from rfpenetration depth measurements with a tunnel diode oscillator in a pulsedmagnetic field. We examined four samples with 1100 field sweeps in a range ofangles with the magnetic field parallel and perpendicular to the conductingplanes. In the parallel direction, $H_{c2}$ appears to include a tricriticalpoint at 1.6 K and 10 T with a phase line that increases to 11 T as thetemperature is decreased to} 500 mK. The second phase line forms a clearlydefined high field low temperature region satisfying several of the conditionsof the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state. We show remarkably goodfits of $H_{c2}$ to WHH in the reentrant $\alpha>1$, $\lambda_{so}=0$ regime.We also note a sharp angle dependence of the phase diagram about the fieldparallel orientation that characterizes Pauli paramagnetic limiting and furthersupports the possibility of FFLO behavior. Unrelated to the FFLO study, atfields and temperatures below $H_{c2}$ and $T_c$, we find rich structure in thepenetration depth data that we attribute to impurities at the surface alteringthe superconducting properties while maintaining the same crystallographic axesas $H_{c2}$.

Superconducting phase diagram and FFLO signature in $\lambda$-(BETS)$_2$GaCl$_4$ from rf penetration depth measurements