Abstract
We present the first $^{13}\mathrm{C}$ NMR measurements carried out in the superconducting state of a two-dimensional organic superconducting single crystal. Spin lattice relaxation rate and Knight shift are reported for magnetic fields parallel and perpendicular to the conducting layers. For perpendicular fields, the relaxation is dominated by the electronic excitations in the vortex cores. From the field dependence of ${({T}_{1})}^{\ensuremath{-}1}$ we obtain the upper critical field [${H}_{c2}(0)=10$ T]. In parallel orientation, the absence of field dependence reveals the existence of a lock-in state, where only relaxation by superconducting excitations is expected. The ${({T}_{1})}^{\ensuremath{-}1}$ then exhibits a ${T}^{3}$ law suggesting an unconventional pairing with a very anisotropic gap.
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