Fulde-Ferrell-Larkin-Ovchinnikov superconductivity in the layered organic superconductor β "-(BEDT-TTF ) 4[(H3O ) Ga (C2O4)3] C6H5NO2

Resistance and magnetic torque measurements are reported in a layered organic superconductor, β "-(BEDT_{-TTF ) 4}[(H₃O ) Ga (C_2O4)3] C₆H₅NO₂ with T_c=4.8 K, where BEDT-TTF stands for bis(ethylenedithio)tetrathiafulvalene. Because of the large anion between the BEDT-TTF conducting layers, the superconductivity of this salt is highly anisotropic. In magnetic fields parallel to the conducting layers for T =0.4 K, the magnetic torque shows a large diamagnetic signal associated with hysteresis up to ∼21 T, suggesting the upper critical field H_{c 2}≳21 T at 0.4 K. The large reduction of the diamagnetic signal is observed above 16 T, which shows a Fulde and Ferrell and Larkin and Ovchinnikov (FFLO) phase transition. For T =0.5 K, the interlayer resistance has nonzero value in a wide field region up to H_{c 2}, arising from the Josephson vortex dynamics. Successive dips in the second derivative curves of the resistance are observed between 16 T and H_{c 2}, which are ascribed to the commensurability effect between the Josephson vortex lattice and the order parameter oscillation of the FFLO phase. The commensurability effect is observed only in nearly parallel fields, showing that the FFLO phase is stable in a very limited field angle region. The temperature-field phase diagram is determined.