  We show that there are strong similarities in the spin lattice relaxation of
non-magnetic organic charge transfer salts, and that these similarities can be
understood in terms of spin fluctuations. Further, we show that, in all of the
kappa-phase organic superconductors for which there is nuclear magnetic
resonance data, the energy scale for the spin fluctuations coincides with the
energy scale for the pseudogap. This suggests that the pseudogap is caused by
short-range spin correlations. In the weakly frustrated metals
k-(BEDT-TTF)_2Cu[N(CN)_2]Br, k-(BEDT-TTF)_2Cu(NCS)_2, and
k-(BEDT-TTF)_2Cu[N(CN)_2]Cl (under pressure) the pseudogap opens at the same
temperature as coherence emerges in the (intralayer) transport. We argue that
this is because the spin correlations are cut off by the loss of intralayer
coherence at high temperatures. We discuss what might happen to these two
energy scales at high pressures, where the electronic correlations are weaker.
In these weakly frustrated materials the data is well described by the chemical
pressure hypothesis (that anion substitution is equivalent to hydrostatic
pressure). However, we find important differences in the metallic state of
k-(BEDT-TTF)_2Cu_2(CN)_3, which is highly frustrated and displays a spin liquid
insulating phase. We also show that the characteristic temperature scale of the
spin fluctuations in (TMTSF)_2ClO_4 is the same as superconducting critical
temperature, which may be evidence that spin fluctuations mediate the
superconductivity in the Bechgaard salts.
