We report magnetic-field and angular-dependent high-resolution specific-heat measurements of the organic superconductor ${\beta }^{\prime \prime }\mathrm{\text{−}}(\mathrm{BEDT}\mathrm{\text{−}}\mathrm{TTF}{)}_2{\mathrm{SF}}_5{\mathrm{CH}}_2{\mathrm{CF}}_2{\mathrm{SO}}_3$. When the magnetic field is aligned precisely within the conducting BEDT-TTF layer, at low temperatures a clear upturn of the upper critical field beyond the Pauli limit of 9.73 T is observed, hinting at the emergence of a Fulde-Ferrell-Larkin-Ovchinnikov state. This upturn disappears when the field is oriented out of plane by more than $\sim 0.5\mathrm{deg}$. For smaller out-of-plane angles, the specific-heat anomaly at $T_c$ sharpens and a second peaky phase transition appears within the superconducting state.

• Received 17 February 2012

DOI:https://doi.org/10.1103/PhysRevLett.109.027003