NMR in the 2D Organic Superconductors

We review recent NMR studies of the layered organic superconductors of the (BEDT)$_2$X family. First the normal state properties discussed. The central issue is the importance of the interplay between antiferromagnetism and superconductivity in these materials demonstrated by the observation of a pseudogap developing prior to the superconducting transition. An extended analysis of the Knight shift and the nuclear relaxation rate gives an evidence for strong antiferromagnetic fluctuations enhanced by Coulomb repulsion and the nesting of the Fermi surface. The NMR data show some analogy with High $T_{\rm c}$ superconductors however the comparison is not straightforward as there is no clear evidence for spin-charge decoupling. The use of high pressure to tune the amplitude of AF fluctuations enables us to draw a general phase diagram of the family. In the second part the NMR experiments in the superconducting state are presented. One of the fundamental questions addressed by these experiments is the symmetry of the order parameter related to the pairing mechanism. The most spectacular NMR measurements are those performed in the lock-in state, which give access to the density of superconducting excitations at low energy. These experiments suggest that the pairing state may be unconventional featuring an anisostropic superconducting gap, possibly with nodes. Finally, the NMR contribution to the understanding of the nature of the vortex state is discussed in the context of recent results on $\kappa$-(ET)$_2$Cu[ N(CN)$_2$] Br where the $^1$H relaxation was used as a probe of the vortex density fluctuations.