Probing Low Energy Excitation by ¹³C NMR in the Field-Driven Inhomogeneous Superconducting State of β” Compound

Non-zero momentum Cooper pairs, such as has been proposed in underdoped cuprates (pair density wave state) or the field-induced version (FFLO) pertaining to specific organic superconductors, has attracted extensive research interest recently. Towards quantifying the low-lying magnetic excitations of field-induced inhomogeneous superconductivity (FFLO), ¹³C (T₁T)^-1 is studied in the layered superconductor β”-(BEDT-TTF)₂SF₅CH₂CF₂SO₃ over a wide range of fields and temperatures. Enhancement of (T₁T)^-1 over the normal state case is most pronounced in the vicinity of the phase boundaries, uniform-SC/FFLO and FFLO/normal. Modeling the NMR relaxation rate based on both the isolated and dense domain wall picture results in relaxation rates too small to account for the observations. The discrepancy calls for considering other contributions, for example the possibility for significant relaxation associated with extended state quasiparticles near to the phase boundary. Specific heat results lend support to this interpretation. A large enhancement of (T₁T)^-1 at tilted fields is suggested to be associated with interlayer decoupling.