  We give a quantitative analysis of the previously published nuclear magnetic
resonance (NMR) experiments in the k-(ET)2X family of organic charge transfer
salts by using the phenomenological spin fluctuation model of Moriya, and
Millis, Monien and Pines (M-MMP). For temperatures above T_nmr ~ 50 K, the
model gives a good quantitative description of the data in the metallic phases
of several k-(ET)2X materials. These materials display antiferromagnetic
correlation lengths which increase with decreasing temperature and grow to
several lattice constants by T_nmr. It is shown that the fact that the
dimensionless Korringa ratio is much larger than unity is inconsistent with a
broad class of theoretical models (such as dynamical mean-field theory) which
neglects spatial correlations and/or vertex corrections. For materials close to
the Mott insulating phase the nuclear spin relaxation rate, the Knight shift
and the Korringa ratio all decrease significantly with decreasing temperature
below T_nmr. This cannot be described by the M-MMP model and the most natural
explanation is that a pseudogap, similar to that observed in the underdoped
cuprate superconductors, opens up in the density of states below T_nmr. Such a
pseudogap has recently been predicted to occur in the dimerised organic charge
transfer salts materials by the resonating valence bond (RVB) theory. We
propose specific new experiments on organic superconductors to elucidate these
issues. For example, measurements to see if high magnetic fields or high
pressures can be used to close the pseudogap would be extremely valuable.
