This paper presents the frequency dependance of the proton spin-lattice relaxation time T1 at several temperatures and pressures in TTF-TCNQ(D4) and TTF(D4)-TCNQ. It is shown that only backward (q = 2 kF) and forward (q = 0) scatterings contribute to the nuclear relaxation induced by the modulation of the hyperfine field in these one-dimensional conductors. At medium fields, H 0 ~ 30 kOe, the frequency dependence of T1 originates from the diffuse character of the spin density wave excitations around q = 0, leading to T1-1 αH0- 1/2 . The enhancement of T1 -1, is at low fields, limited by the existence of a finite interchain coupling (tunnelling type). We find, within a RPA analysis, close correlations between the pressure and temperature dependences of the spin excitations diffusion constant and the collision time derived from the longitudinal conductivity. The interpretation of the NMR data in terms of a Hubbard model excludes both big U and small U pictures. However, we point out the importance of the electron-electron interactions on the relaxation rate of TTF-TCNQ. We derive a ratio U/4 t II ~ 0.9 for the TCNQ chain. We also assume that besides charge density waves fluctuations existing between 300 K and the phase transition at 53 K, electron-electron interactions make an important contribution to the temperature dependence of the spin susceptibility. Finally, we give a unified description of quasi one dimensional conductors in which the various systems are classified according to the transverse tunnelling coupling and the electron lifetime. It follows from this description that for TTF-TCNQ and its derivatives, transverse couplings (tunnelling and Coulomb) are large enough to justify the use of a mean-field theory
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