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We have recently reported the first direct calorimetric observation of amagnetic-field-induced first-order phase transition into a high-field FFLOsuperconducting state at the Clogston-Chandrasekar `Pauli' paramagnetic limit$H_p$ in a 2D superconductor$\kappa-{\textrm{(BEDT-TTF)}}_2{\textrm{Cu}}{\textrm{(NCS)}}_2$. The high-fieldstate is both higher entropy and strongly paramagnetic, as thermodynamicallyrequired for the FFLO state. Here we compare our results with theoreticalpredictions for the field dependence of the high-field FFLO state in the 2Dlimit, revealing tentative evidence for transitions between FFLO states ofdiffering order parameter. We also present calorimetric evidence for a 1storder phase transition into the FFLO state for a second 2D organicsuperconductor:${\beta}^{\prime\prime}-{\textrm{(BEDT-TTF)}}_2{\textrm{SF}}_5{\textrm{(CH)}}_2{\textrm{(CF)}}_2{\textrm{(SO)}}_3$.

Magnetic-field-induced 1st order transition to FFLO state at paramagnetic limit in 2D superconductors