Antiferromagnetic spin fluctuations in the metallic phase of quasi-two-dimensional organic superconductors

We give a quantitative analysis of the previously published nuclear magnetic resonance (NMR) experiments in the kappa-(ET)(2)X family of organic charge-transfer salts. The temperature dependence of the nuclear-spin relaxation rate 1/T-1, the Knight shift K-s, and the Korringa ratio K is compared to the predictions of the phenomenological spin-fluctuation model of Moriya and Millis, Monien, and Pines (M-MMP), that has been used extensively to quantify antiferromagnetic spin fluctuations in the cuprates. For temperatures above T-NMR similar or equal to 50 K, the model gives a good quantitative description of the data in the metallic phases of several kappa-(ET)(2)X 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 dimerized organic charge-transfer salts materials by the resonating valence bond (RVB) theory. We propose specific 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.