Spectroscopic evidence for a first-order transition to a possible orbital Fulde-Ferrell-Larkin-Ovchinnikov state

. The transition manifests itself as a sudden enhancement of the superconducting gap with prominent hysteresis by sweeping the in-plane magnetic field well below the upper critical field. Such a first-order transition quickly disappears once the magnetic field tilts away from the in-plane direction by about one degree, and it depends sensitively on disorder. Furthermore, we obtain a comprehensive phase diagram of the phase transition as a function of magnetic field, temperature, and the sample thickness. These observed behaviors can be reproduced by the theory that considers the energetics between a uniform Ising superconductor and the orb-FFLO state.