Observation of the Fulde-Ferrell-Larkin-Ovchinnikov state in the quasi-two-dimensional organic superconductor $kappa$-(BEDT-TTF)$_2$Cu(NCS)$_2$

Single crystals of the layered organic type II superconductor, $kappa$-(BEDT-TTF)$_{2}$Cu(NCS)$_{2}$, have been studied in magnetic fields of up to 33 T and at temperatures between 0.5 K and 11 K using a compact differential susceptometer. When the magnetic field lies precisely in the quasi-two-dimensional planes of the material, there is strong evidence for a phase transition from the superconducting mixed state into a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, manisfested as a change in the rigidity of the vortex system. The behaviour of the transition as a function of temperature is in good agreement with theoretical predictions.