Microscopic study of the Fulde-Ferrell-Larkin-Ovchinnikov state in an all-organic superconductor

Quasi-two dimensional superconductors with sufficiently weak interlayer coupling allow magnetic flux to penetrate in the form of Josephson vortices for in-plane applied magnetic fields. A consequence is the dominance of the Zeeman interaction over orbital effects. In the clean limit, the normal state is favored over superconductivity for fields greater than the paramagnetic limiting field, unless an intermediate, inhomogeneous state is stabilized. Presented here are nuclear magnetic resonance (NMR) studies of the inhomogeneous (FFLO) state for $\beta^{\prime \prime}$-(ET)$_2$SF$_5$CH$_2$CF$_2$SO$_3$. The uniform superconductivity-FFLO transition is identified at an applied field value of 9.3(0.1) T at low temperature ($T=130$ mK), and evidence for a possible second transition between inhomogeneous states at $\sim11$ T is presented. The spin polarization distribution inferred from the NMR absorption spectrum compares favorably to a single-Q modulation of the superconducting order parameter.