Nuclear relaxation and electronic correlations in quasi-one-dimensional organic conductors. I. Scaling theory

In this paper the results of the scaling theory for the quasi-one-dimensional electron gas model are used to make a detailed analysis of the temperature variation of the nuclear relaxation rate for quasi-one-dimensional conductors which present an antiferromagnetic critical point. From the extended dynamic scaling hypothesis, we show how the statics, the dynamics and the dimensionality of antiferromagnetic and uniform spin fluctuations are involved in the power law behaviours of $T^{-\,1}_1$ for both the normal and the critical temperature domains. The full expressions of the antiferromagnetic contribution to $T^{-\,1}_1$, the related critical indices as well as the dimensionality crossover scaling functions are derived in the cases where either the interchain exchange or the quasi-1D nesting of the Fermi surface drives the transition. As for the influence of uniform spin fluctuations, a derivation for the temperature dependent enhancement of the magnetic susceptibility $\chi_{\rm s}(T)$ in one dimension is given. It is found that the harmonic character of collisionless paramagnons yields to the following scaling law $T^{-\,1}_1 \sim T[\chi_{\rm s}(T)]^{(5-D)/2}$ which dominates at high temperature with an indice that depends on the dimensionality $D$ of the system. All the direct calculations are shown to be consistent with the scaling hypothesis