# Nuclear relaxation and electronic correlations in quasi one-dimensional organic conductors

Denis Jerome, Pawel Wzietek, François Creuzet, Claude Bourbonnais, Klaus

Bechgaard, Patrick Batail

► To cite this version:

Denis Jerome, Pawel Wzietek, François Creuzet, Claude Bourbonnais, Klaus Bechgaard, et al. Nuclear relaxation and electronic correlations in quasi one-dimensional organic conductors. Journal de Physique I, 1993. hal-04963174

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Classification
*Physics Abstracts*
76.60E — 74.70K — 75.40E — 75.50E

# Nuclear relaxation and electronic correlations in quasi-one-dimensional organic conductors. II. Experiments

P. Wzietek (¹, ²), F. Creuzet (¹, *), C. Bourbonnais (¹, ²), D. Jérome (¹), K. Bechgaard (³) and P. Batail (¹)

(¹) Laboratoire de Physique des Solides, Université de Paris-Sud, bât. 510, 91405 Orsay, France

(²) Centre de Recherche en Physique du Solide, Université de Sherbrooke, Sherbrooke, Québec, Canada J1K-2R1

(³) H. C. Oersted Institute, DK-2100 Copenhagen, Denmark

*(Received 22 April 1992, accepted in final form 4 September 1992)*

**Abstract.** — In this paper we collect and detail recent results concerning ⁷⁷Se and ¹³C nuclear relaxation rate measurements obtained on several representatives of the (TMTSF)₂X and (TMTTF)₂X series of charge transfer salts as a function of temperature and hydrostatic pressure. From the temperature and pressure dependences of T₁⁻¹, for the compounds (TMTTF)₂PF₆, (TMTTF)₂Br, (TMTSF)₂PF₆ and (TMTSF)₂ClO₄, we are in a position to extract the nature, the amplitude, the statics, the dynamics and finally the dimensionality of spin correlations that characterize the unified phase diagram of both series of materials.

## 1. Introduction.

In this second paper of the series, we review and complete the analysis of the ⁷⁷Se and ¹³C nuclear relaxation data obtained for typical members of the series (TMTSF)₂X (X = PF₆ and ClO₄) and their sulphur analogs (TMTTF)₂X (X = PF₆ and Br) as a function of temperature and hydrostatic pressure. The pronounced quasi-one-dimensional anisotropy of these series of materials has been for long time considered as a key ingredient in the succession of phase transitions orchestrated by either the hydrostatic pressure, the anion or the sulphur-selenium substitution or even the application of a high magnetic field [1]. The spatial anisotropy of the electronic structure [2] promotes the building up of antiferromagnetic correlations which are omnipresent in these systems. An important and related energy scale of these correlations is found for sulphur compounds at low pressure and it corresponds to the temperature Tρ(100 ... 230 K) below which the resistivity loses its metallic character to become thermally activated [3] (see Fig. 1). In compounds like (TMTTF)₂PF₆ and (TMTTF)₂AsF₆, X-ray measurements [4] performed below Tρ have shown the existence of

<footnote>(*) Present address : Unité Mixte de Recherche CNRS-St-Gobain, 39 Quai L. Lefranc, B.P. 135, 93303 Aubervilliers Cedex, France.</footnote>
<figure><img src="image_2.png" /><figcaption>Fig. 1. — Resistivity vs. temperature for representatives of (TMTTF)₂X and (TMTSF)₂X series. After [3] and [11].</figcaption></figure>

another energy scale $T_{\text{SP}}^0(\sim 40..60 \text{ K})$ that marks the onset of a 1D lattice instability at the wavevector $2k_F$ and which evolves to a true 3D phase transition at $T_{\text{SP}}(10..20 \text{ K})$ with a static lattice distortion of the spin-Peierls (SP) character [3-7]. With the application of pressure, $T_\rho$ decreases and for $(TMTTF)_2PF_6$, 10 kbar of pressure is sufficient to yield the SP state unstable with respect to the formation of antiferromagnetic (AF) long range order below a Neel critical point $T_N \le 17 \text{ K}$ [5, 8]. In these pressure conditions, the AF phase transition presents the same features as those found for $(TMTTF)_2Br$ at ambient pressure where $T_\rho \approx 100 \text{ K}$ (Fig. 1) and $T_N \approx 15 \text{ K}$ [3, 5, 9, 10]. At higher pressure, the temperature range above $T_N$ with metallic properties increases and beyond some critical pressure which depends on the anion X, the transport properties remain metallic down to the vicinity of $T_N$ where AF critical fluctuations dominate ($T \approx T_\text{fl}$). Therefore, the characteristics of the AF transition smoothly evolve toward those found for the selenides series $(TMTSF)_2X$ with centrosymmetrical anions ($X = PF_6$, $AsF_6$, $TaF_6$...) and for which $T_N \sim 10 \text{ K}$ at ambient pressure (Fig. 1) [8]. As it is well known, the AF state becomes in turn unstable beyond a critical pressure $P_c \ge 7 \text{ (20 kbar for selenides (sulphurs) [8, 11, 12] leading for (TMTSF)₂X to the observation of superconductivity at the lower temperature scale } T_c \sim 1 \text{ K [11]. Despite the absence of firm evidence for superconductivity in sulphur compounds at very high pressure [8, 13], the unified phase diagram shown in figure 2 can be constructed in which antiferromagnetism acts as the central pivot for both series of materials. Here it is worthwhile to note that members of}$
<figure><img src="image_3.png" /><figcaption>Fig. 2. — Unified phase diagram and energy scales of (TMTTF)₂X and (TMTSF)₂X series as a function of hydrostatic pressure or anion X substitution. The phase diagram also includes the sulphur-selenide compound (TMDTDSF)₂PF₆.</figcaption></figure>

the recently synthesized mixed sulphur-selenium series (TMDTDSF)₂X (X = PF₆, ...) [14] are easily incorporated to this phase diagram. For example, (TMDTDSF)₂PF₆ compound with Tρ ≈ 100 K, T₀ₚ ≈ 20 K and Tₙ ≈ 7 K is located in the right hand side of the SP-AF boundary [14].

What catches the attention in this combined phase diagram is certainly the existence of multiple energy or temperature scales. One can also look at these as various length scales connected with electronic (spin or charge) or lattice correlations and which can be of different spatial dimensionalities. It is clearly of basic importance to bring out the microscopic origin of the rich structure of this phase diagram and especially to assess the fundamental role played by electronic correlations when extremely anisotropic conditions prevail [15, 16]. This can be only achieved by successive confrontations between theoretical predictions and experiments. It is along these lines that over the past ten years a great deal of efforts was devoted to the comparison of nuclear relaxation rate measurements in these materials with the T⁻¹ predictions obtained in the framework of the quasi-one-dimensional electron gas model [5, 14b, 17-23].

As extensively reviewed and discussed in the first paper, hereafter noted as I, the great interest in T⁻¹ measurements for the understanding of the phase diagram of figure 2 follows from the basic expression

$$T_{1}^{-1} = 2 \gamma_{N}^{2} T(g \mu_{B})^{-2} \int d^{D}q |A_{q}|^{2} \chi_{\perp}''(q, \omega_{N}) / \omega_{N}, \quad (1)$$
which is directly related to the statics, the dynamics and the dimensionality of spin correlations at all length scales. These are connected to the *temperature dependence* of spin correlations and thus to the temperature variation of $T_1^{-1}$ itself. Putting the emphasis on the temperature profile of $T_1^{-1}$ rather than in its *frequency* or *field* dependence marks an important difference with respect to previous NMR analysis of low dimensional materials. In the past, a lot of interest was indeed devoted to the study of spin dynamics in these systems as it can be obtained *via* the field dependence. From a series of works initiated by Boucher *et al*. [24], it was found that diffusive long wave length spin excitations for one-dimensional spin chains lead to a characteristic square root frequency dependence $T_1^{-1} \sim \omega_e^{-1/2}$ of the relaxation rate. The effect of diffusion was previously noted in connection with the EPR linewidth measurements [25]. The observation of this law in several insulating materials [26] demonstrated that from the $T_1^{-1}$ measurements it was possible to get clear information about the dimensionality of the long wavelength spin fluctuations. Later on, Soda *et al*. [27], presented in the same spirit a detailed analysis of the frequency dependence of $^1$H and $^1$D $T_1^{-1}$ data of the two-chain organic conductor TTF-TCNQ and showed that for both chains, uniform spin fluctuations are diffusive and one-dimensional in character. Following these lines of thought, similar studies were carried on several series of organic materials [28-30] including the Bechgaard salts [31-32].

In order to establish the existence of a diffusive component of spin fluctuations from the field variation of $T_1^{-1}$ however, one must be in a position to give a precise evaluation of the relative weight of the uniform ($T_1^{-1}[q \sim 0]$) and the staggered ($T_1^{-1}[q \sim Q_0]$) parts of the relaxation rate, which necessitates a full *temperature* study of each contribution. At a given temperature, diffusion of low-dimensional long wavelength spin fluctuations can be assessed only if $T_1^{-1}[q \sim 0] \gg T_1^{-1}[q \sim Q_0]$, which turns out to hold in the high temperature domain for organic conductors [5, 21-23, 27, 30]. At $T \approx 300$ K and for a field of 64 kOe or so, Stein *et al*. [32], reported the observation of a weak frequency dependence for the $^1$H relaxation of $(TMTSF)_2PF_6$ and $(TMTSF)_2ClO_4$ at ambient pressure which was attributed to a diffusive component. Within experimental error, all the $^{13}$C and the $^{77}$Se data presented in this work however, do not show any frequency dependence at ambient temperature and for fields up to 9 tesla. A possible explanation for this could reside in the amplitude of the external field which is not sufficiently large. In this case, the time scale $\omega_e^{-1}$ set by the electronic spin-flip process involved in a scalar hyperfine interaction like (1), is too long with respect to the characteristic time scale $\tau_c$ ($\omega_e \tau_c \ll 1$) of processes that do not conserve spin along the chains (e.g. interchain tunneling of uniform spin fluctuations) and which cut-off 1D diffusion [24]. If the field necessary to make $\omega_e \tau_c > 1$ is very large, one approaches the so-called collisionless or non-diffusive limit [33] where collisions have little influence on $q \sim 0$ spin fluctuations and can therefore be neglected. In the absence of field dependence for the observed $T_1^{-1}$, we will therefore assume that the collisionless limit is achieved so that the whole $T_1^{-1}$ analysis presented here for the sulphur and the selenides series focuses entirely on the temperature and the pressure dependences. This clearly contrasts with other interpretations [31-32] which associate a diffusive component to the relaxation rate of the Bechgaard salts in the very low temperature domain ($T \sim 4$ K).

Although, in principle, relaxation time measurement techniques do not need to be detailed, in section 2 we comment on some particular aspects of our experimental approach which have enabled us to obtain high quality data necessary for a quantitative analysis.

Section 3 presents a collection of nuclear spin-lattice relaxation results on $(TMTTF)_2PF_6$, $(TMTTF)_2Br$, $(TMTSF)_2PF_6$ and $(TMTSF)_2ClO_4$ as a function of temperature and hydrostatic pressure and which cover the essential features of the unified phase diagram of figure 2. The analysis of the data is made in section 4. There, predictions of I for the quasi-one-dimensional electron gas model for 1D correlation effects, critical behavior and crossover phenomena are
systematically confronted to experimental data and it is shown how a rather coherent description of these complex systems can come out from such an analysis.

The last part of section 4 is devoted to a quantitative analysis of the temperature and pressure dependences of the magnetic susceptibility as it can be extracted from the relaxation rate measurements in the paramagnetic regime. Such an analysis is based on the well established empirical relationship $(T_1 T)^{-1} \propto \chi_s^2(T)$ at $P = 1$ bar between the measured relaxation rate and magnetic susceptibility over a large high temperature domain. Although this way of obtaining $\chi_s(T)$ does not lead to its absolute value, there are clear advantages in using the NMR approach under pressure compared to other kinds of magnetic measurements. Indeed, two standard methods have been used so far for the spin susceptibility investigation in organic salts : the Faraday and the EPR techniques and these become less accurate when one reaches high pressure. The Faraday method yields to the absolute value of the electronic spin susceptibility, but it requires corrections for the diamagnetic contribution from inner-shell electrons [34, 35]. Some Faraday susceptibility measurements under pressure have been carried out by Forro *et al.* [36] on (TMTSF)₂X but numerous corrections must be made for the pressure cell and the transmitting medium diamagnetism contributions. EPR is a more direct method for $\chi_s$ measurement but its sensitivity decreases rapidly when the resonance line width increases. Under pressure, EPR is a rather difficult technique since the sensitivity of the spectrometer may vary under pressure and actually only few results for organic conductors are available [37].

In contrast to other theoretical interpretations of $\chi_s(T)$ in organic conductors [38], our approach is uniquely based on the effect of electron-electron interaction in the framework of the 1D electron gas model as developed in I. When *constant pressure* data are compared to the results of a *constant volume* theory, it follows that for a non-singular quantity like $\chi_s(T)$, it is necessary to evaluate the effect of thermal expansion on the susceptibility. For this, the full *temperature and pressure* dependences of $\chi_s(T)$ need to be known and these can be extracted from its relation to $(T_1 T)^{-1/2}$.

## 2. Experimental.

All experiments have been performed on single crystal samples prepared by electrochemical methods [20]. For the sulphur compounds, selectively ¹³C 95% enriched (TMTTF)₂PF₆ and (TMTTF)₂Br samples have been used. Compared to powder samples, this has the advantage of eliminating the $T_1$ anisotropy and an exponential relaxation can be recorded. Furthermore, the powder spectrum is broadened by the Knight shift anisotropy. The experiments are performed on ⁷⁷Se in the 45 MHz range for the (TMTSF)₂PF₆ and (TMTSF)₂ClO₄ compounds. For the sulphur compound (TMTTF)₂PF₆ the central ¹³C sites have been observed at 45 MHz in the low temperature range and 33 MHz at high temperature. Finally, (TMTTF)₂Br data have been acquired at 60 MHz ($P = 1$ bar) and 30 MHz ($P = 13$ kbar). In contrast to previous experiments made on protons, for which methyl group rotation effects strongly contribute to the relaxation over a large temperature domain [9, 32, 40, 41, 42], these nuclei only probe the fluctuation field produced by the electrons since no other molecular motion at the Larmor frequency is expected to contribute to the relaxation. On the other hand, relaxation measurements on naturally abundant ⁷⁷Se present some technical difficulties due to a very poor signal-to-noise ratio, especially at high temperature and under pressure. We are usually led to use composite samples made of a few (2-4) aligned crystals.

The data at low temperatures except for (TMTTF)₂Br were obtained on a conventional broadband NMR spectrometer where the amplitude of the z-magnetization was measured by integrating the free induction decay signal. In other experiments a commercial Fourier
transform spectrometer has been used. The spectra of ⁷⁷Se in (TMTSF)₂PF₆ and (TMTSF)₂ClO₄ are made up of 4 well resolved lines corresponding to 4 non-equivalent Se sites [43], with a residual linewidth of ~ 2 kHz due mainly to the dipolar broadening by the methyl group protons. For Se, the knight shift is known to be much larger than the chemical shift and it governs the position of the lines [31]. The *T*₁ is found to be site independent within the experimental error (± 10%) which is consistent with a rather weak spatial anisotropy of knight shifts and with spin density calculations [44]. The relaxation is exponential over nearly two decades for the magnitude of magnetization.

We should comment here on some particular points concerning the experiments on ⁷⁷Se at high temperature (100-300 K). Its relaxation rate is larger than that of ¹³C and special care must be taken when *T*₁ is of the order of the free induction decay length *T*₂*. Owing to the time consuming adjustment of the π-pulse at every temperature, we have used the inversion-recovery sequence with special care on the phase cycling necessary to extract the *z* component of the magnetization. In addition, during the signal averaging, the coherent noise, e.g. the acoustic ringing, has been suppressed by alternatively changing the length of the detection pulse (from approximately *π*/2 to 3 *π*/2).

In both sulfur compounds studied it is the central carbons that were observed. These can take two non-equivalent positions in the unit cell, giving two resonance frequencies separated by the difference of knight/chemical shifts. In highly enriched samples, however, each line will split in general into a doublet due to C-C dipolar coupling. For central carbon, the strength of this coupling (few kHz) is comparable to the separation of Larmor frequencies. In such a case, as it is well known for strongly coupled spin systems [45a], several difficulties appear in the relaxation measurements.

First, partially relaxed spectra depend in a complicated way on the initial non-equilibrium state of the system, and thus, the preparation procedure (pulse calibration, etc.) is subject to severe conditions, to avoid the mixing of population differences resulting in non-exponential decays. Moreover, for a coupled pair of spins the observed *T*₁'s are always weighted averages of transition probabilities of the two spins, where the weight factors depend on the ratio : coupling constant (*J*)/shift difference (Δ) (these factors are : cos² *φ* and sin² *φ* with tan *φ* = *J*/2 *Δ* which can be easily shown by calculating the transition probabilities between the exact eigenstates of the system). This point is of particular importance, because it can, in principle, introduce systematic errors into the temperature dependence of *T*₁.

In all experiments on (TMTTF)₂Br, the crystal was oriented in a way to cancel the dipolar interaction, i.e. the *b*' axis approximatively parallel to the applied field [45b]. We then observed two lines of ~ 2 kHz width separated by about 100 ppm at 300 K. This is close to the value found by Bernier *et al.* [45c], for (TMTSF)₂ClO₄. The relaxation rates of the two lines are different by a factor of 3 or so, which is also consistent with the knight shifts ratio of ~ 1.5 in (TMTSF)₂ClO₄. This ratio does not exhibit any variation with temperature and pressure.

A more detailed discussion is needed for the case of (TMTTF)₂PF₆ where we used the same crystal orientation. (*H*₀//c*) as the one of a previous work at low temperature [5] in order to get a consistent set of data. The typical spectrum is shown in figure 3b. Here, the dipolar splitting is close to the shift difference so that the two central lines overlap. We found that, within the experimental error, the relaxation is characterised by a single *T*₁ for all the spectrum, and this, at all temperatures. Since the averaging of transition probabilities cannot account itself for such a difference between these two compounds (the weight factors ratio is estimated to be of the order of 10), we performed an additional experiment at higher field, where all lines become resolved (Fig. 3a). Here the relaxation shows the same characteristics as for (TMTTF)₂Br. This clearly shows that the averaging is due to spin diffusion between the spin pairs of adjacent TMTTF molecules. The spin diffusion rate, related to the coupling strength between neighbouring spin pairs is of several hundreds Hertz. Therefore, it is faster than the
<figure><img src="image_4.png" /><figcaption>Fig. 3. — ¹³C spectra of a single crystal of (TMTTF)₂PF₆ (H₀ // c*) at room temperature for a) H₀ = 9.4 T, and b) H₀ = 3.1 T. At high field, the relaxation times of the two doublets are: ~5 ms (left) and ~13 ms (right). At low fields, all the lines have the same T₁ at about 8 ms.</figcaption></figure>

relaxation at all temperatures (the T₁ inhomogeneity over the spectrum is about 10% at 300 K and disappears at lower temperature). The relaxation rate has been calculated by integrating the whole spectrum. As long as the T₁'s of both nuclei are governed by the same phenomena, as it is (TMTTF)₂Br, this procedure is reliable for the study of the temperature dependence of the relaxation rate.

Measurements under pressure at high temperatures (T > 100 K) have been performed with a CuBe 8 mm inner diameter cell cooled by a thermal exchanger with liquid nitrogen. The liquid flow was automatically controlled in order to minimize the temperature gradients in the cell. The RF circuity was mounted as close as possible to the sample (10 cm) but was thermally isolated and temperature controlled to ensure the long time stability required for averaging.

When performing high pressure experiments at low temperatures, it is important to circumvent any pressure loss on cooling, especially near the freezing point of the pressurized medium. To minimize this effect, we have used an externally controlled pressure system. Isopentane is pressurized in a primary chamber where the pressure is controlled by a manganine gauge. A capillary tubing drives the pressure to the cooled cell where an intensifying piston creates the high pressure in the experimental chamber. Two different liquids were used to create high pressure: freon in the measuring chamber and isopentane in the low pressure stage of the intensifier. Since the freezing point of freon (300 K at 14 kbar) always occurs well above the one of isopentane, losses could be compensated until complete freon solidification and therefore are kept within 500 bar at 10 kbar.

All experiments under pressure and at high temperature have been performed at lower field (about 3 Tesla) but we have checked that the relaxation rate does not exhibit any field dependence up to the highest field we used at room temperature (9 Tesla).
### 3. Results.

The $^{13}$C $T_1^{-1}$ temperature dependence for $(TMTTF)_2PF_6$ compound at $P = 1$ bar and 13 kbar is shown in figure 4. The low temperature profiles clearly emphasizes the different nature of the ground state at each pressure. At ambient pressure, the system develops a spin-Peierls instability at $T_{SP} \approx 19$ K below which $T_1^{-1}$ drops rapidly to zero. Above $T_{SP}$ and below $T_{SP}^0 \approx 40$ K or so, there is also a sizeable depression of the relaxation rate. These results are clearly consistent with X-ray measurements [4] which show a 1D lattice softening below 60 K and a true lattice distortion of the spin-Peierls type well below 19 K. Similar depressions take place for the EPR spin susceptibility at the same temperature as shown in figure 4. It is of interest to point out here that essentially the same features in the X-ray [4] resistivity [3, 6], and $\chi_s(T)$ (Faraday) [6-7] results were obtained in another spin-Peierls compound, $(TMTTF)_2AsF_6$. In figure 6, we report $T_1^{-1}$ and $\chi_s(T)$ data below $T_{SP}$ on a semi-log scale showing an activated behavior with a gap $\Delta_{SP} \approx 3.5 T_{SP}$, that apparently satisfies a BCS like relation for both quantities. Above 40 K, $T_1^{-1}$ is found to be temperature independent up to 65 K or so, where it starts to increase with an upward curvature. The $T_1^{-1}$ and $\chi_s(T)$ temperature profiles do not show any anomaly near $T_\rho \approx 220$ K where the resistivity minimum occurs (Fig. 1). This indicates the very interesting property of separation between charge and spin degrees of freedom. Furthermore, the enhancement of $T_1^{-1}$ above 65 K is directly related to the one of $\chi_s(T)$ [5]. Indeed, figure 7 clearly shows the existence of the following scaling relation

$$T_1^{-1} = C_1 + C_0 T \chi_s^2(T) \quad (2)$$

above $T_{SP}^0$. This emphasizes that an important contribution to the relaxation comes from long wavelength uniform spin fluctuations. As for the constant term $C_1$, it will be shown to come from 1D AF correlations (see next Sect.).

<figure><img src="image_5.png" /><figcaption>Fig. 4. — Temperature dependence of the $^{13}$C relaxation rate for $(TMTTF)_2PF_6$ at 1 bar (circles) and 13 kbar (triangles). The low temperature data are from [5]. In the inset: power law analysis of $T_1^{-1}$ in the critical domain of the AF transition at 13 kbar.</figcaption></figure>
<figure><img src="image_6.png" /><figcaption>Fig. 5. — EPR susceptibility of (TMTTF)₂PF₆ as a function of temperature. The low temperature region is detailed in the inset.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>Fig. 6. — Thermally activated behavior of $T_i^{-1}$ (right scale) and $\chi_s$ (left scale) as a function of $1/T$ for (TMTTF)₂PF₆ below $T_{SP}$ at 1 bar.</figcaption></figure>

At $P = 13$ kbar, the spin-PEierls state of (TMTTF)₂PF₆ is no longer stable [5, 8]. Instead, figure 4 shows that $T_i^{-1}$ develops a singular behavior which corresponds to the onset of magnetic ordering at $T_N \approx 17$ K. From the log-log plot in the insert, the power law

$$T_i^{-1} \sim \dot{r}_{AF}^{-9} \qquad (3)$$
<figure><img src="image_8.png" /><figcaption>Fig. 7. — Linear dependence of the measured $T_1^{-1}$ (Fig. 3) on $T\chi_s^2(T)$ (Fig. 5) for $(TMTTF)_2PF_6$ at 1 bar.</figcaption></figure>

takes place near $T_N$ where in the notation of I, $r_{AF} = [(T - T_N)/T_N]^{-\delta}$ and $\dot{\theta} \approx 1/2 \pm 0.05$. It is attributed to an AF type of critical ordering (see next Sect.). The reduced width $\Delta t_{\text{fl}} \equiv (T_{\text{fl}} - T_N)/T_N \approx 0.6$ for the emergence of these critical fluctuations above $T_N$ is rather large. At higher temperature, the relaxation rate becomes temperature independent and the plateau of relaxation is seen up to 80 K, where an increase of $T_1^{-1}$ emerges with a much less pronounced upward curvature than the one found at 1 bar. If we assume that the empirical relation (2) is still valid, these data show that the amplitude of uniform fluctuations is sizeably reduced under pressure.

Looking now at the effect of anion substitution in the sulphur series, figure 8 shows the temperature profiles of the ¹³C relaxation rate for each NMR line of the non-equivalent center carbons of $(TMTTF)_2\text{Br}$ at 1 bar [23]. At this pressure, the compound presents a resistivity minimum at $T_\rho \approx 100$ K (Fig. 2) and it is known to become antiferromagnetic below $T_N \approx 15$ K. For both NMR lines, the relaxation rate shows a clear singularity near $T_N$ which is quite similar to the one found for the $PF_6$ compound at 13 kbar (Fig. 4). The critical behavior can be best fitted to the same expression (3) with the critical exponents $\dot{\theta} \approx 0.45$ and $0.5$ respectively to each line. As for the critical width, its amplitude $\Delta t_{\text{fl}} \approx 0.6$ is consistent with the one found for $(TMTTF)_2\text{PF}_6$ at 13 kbar. The slight departure
from the value $\dot{\theta} = 1/2$ reflects the experimental error which is again less than 10 %. It is worth noting that the above ¹³C data confirms the previous ¹H $T_1^{-1}$ temperature variation of reference [9] obtained up to 30 K and above which the methyl-group rotation contribution to $T_1^{-1}$ becomes important. The close similarity to the PF₆ salt under pressure is again obviously clear in the paramagnetic regime. Indeed, the resistivity (Fig. 1) and relaxation rate (Fig. 8) data are consistent with a complete separation between charge and spin degrees of freedom. The plateau of relaxation is well defined up to 75 K where the increase of $T_1^{-1}$ becomes apparent. Furthermore, using the EPR susceptibility data shown in figure 9a, we have checked in figure 9b that for both NMR lines, relation (2) is well satisfied.

We now turn our attention to the Bechgaard salt compound (TMTSF)₂PF₆, figure 10a shows the ⁷⁷Se $T_1^{-1}$ vs. T profiles at P = 1 bar, 5.5 and 10 kbar up to 300 K. From the data, we see that the upward curvature of $T_1^{-1}$ with T is still present in the high temperature regime but its amplitude decreases with pressure. There is no resistivity minimum reported for the Bechgaard salts ($T_ρ < T_η$, see Fig. 1) and the paramagnetic regime is well characterized by metallic properties [11]. At low temperature and for $P < P_c \approx 6.9$ kbar [11, 46], the ground state is antiferromagnetic. This is illustrated by the figure 10a, where at 1 bar and 5.5 kbar, $T_1^{-1}$ is clearly singular at $T_N \approx 12$ K and $T_N \approx 8.7$ K. Figure 10b shows that the critical variation near the transition still obey equation (2) where again $\dot{\theta} = 1/2 \pm 10\%$ over a decade in temperature. The critical width $\Delta t_\eta \approx 0.8$ (1 bar), 1 (5.5 kbar) is also large and is similar to those found in sulphur compounds. At 10 kbar $> P_c$, AF ordering is unstable and (TMTSF)₂PF₆ undergoes a superconducting phase transition near 1 K. Nevertheless, figure 10a, shows that a rather large enhancement of the relaxation rate below 30 K still remains. This enhancement is independent of the symmetry of the anion since very similar results are found for the ⁷⁷Se $T_1^{-1}$ data of (TMTSF)₂ClO₄ in the so-called relaxed state at ambient pressure ($> P_c$) (Fig. 11). This large enhancement above $P_c$ has also been confirmed by other groups [40, 47]. It has also been reported for (TMTSF)₂FSO₃ at 10 kbar ($> P_c \approx 7$ kbar) [17]. From the data of figures 4, 8, 10 and 11, it is interesting to observe that this temperature scale for selenides is clearly lower than the one found for the emergence of the $T_1^{-1}$ plateaus in the sulphur compounds thereby suggesting that the AF component of relaxation is less developed in the Bechgaard salts. As for the high pressure region, the upward curvature of the relaxation profiles is rather well pronounced for both (TMTSF)₂PF₆ and

<figure><img src="image_9.png" /><figcaption>Fig. 8. — $T_1^{-1}$ vs. T data for the two central carbon sites in (TMTTF)₂Br at 56 kG. The insert shows the power law divergence near $T_N$.</figcaption></figure>
<figure><img src="image_10.png" /><figcaption>Fig. 9. — a) Temperature dependence of the EPR susceptibility for (TMTTF)₂Br at 1 bar; b) Relaxation rate data vs. Tχs² for the two NMR lines of (TMTTF)₂Br.</figcaption></figure>

(TMTTF)₂ClO₄. The ⁷⁷Se results of figure 12 at ambient pressure show that the T⁻¹ vs. T curves at high temperature are indeed quite similar. From the 1 bar static susceptibility data of Miljak et al. [35] and Cooper et al. [34] for the ClO₄ and the PF₆ compounds respectively, we have verified (Fig. 13) that the relation (2) is still satisfied. From the high temperature dependence however, C₁ ≈ 0, which is indicative of a weak AF contribution. In figure 14, deviations to the (T₁T⁻¹) ∝ χs²(T) law for the two salts are shown on a different scale. For the PF₆ salt for example, deviations become apparent near 180 K (χs²(T) ≈ 3.5) where C₁ tends to grow significantly as the temperature is lowered. This corresponds to the temperature range where the relaxation rate of (TMTTF)₂PF₆ becomes larger than the one of (TMTTF)₂ClO₄ (Fig. 12). For the latter compound, the deviations seen in figure 13 only appear near 30 K where the enhancement of (T₁T⁻¹) becomes huge and AF correlations become dominant.
<figure><img src="image_11.png" /><figcaption>Fig. 10. — a) Temperature dependence of $^{77}$Se $T_1^{-1}$ in $(TMTTF)_2PF_6$ at $P = 1$ bar (circles), 5.5 kbar (squares) and 10 kbar (triangles). In the inset, the low temperature data of reference [19]. b) log-log plot of $T_1^{-1}$ vs. $T - T_N$ in the critical domain of $(TMTSF)_2PF_6$ at 1 bar (circles right scale) and 5.5 kbar (squares, left scale).</figcaption></figure>

In figure 13, we have plotted for comparison the proportionality relation between $T_1^{-1}$ and $T\chi_s^2(T)$ for both sulphur and selenides series. It is clear that the amplitude of $C_1$, extrapolated from the high temperature region is only sizeable for the sulphur series. It is worthwhile to note that the value of $C_1$ for the bromine salt turns out to be intermediate between the one of $(TMTTF)_2PF_6$ and $(TMTSF)_2PF_6$ salts.
<figure><img src="image_12.png" /><figcaption>Fig. 11. — Low temperature $^{77}\text{Se } T_1^{-1}$ vs. T data of $(\text{TMTSF})_2\text{ClO}_4$ in the relaxed state : full circles, 31.9 kG // b'; full triangles, 6.0 kG (powder) ; open squares, 31.9 kG // c* ; open diamond-shaped, 21 kG // b'.</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>Fig. 12. — $^{77}\text{Se } T_1^{-1}$ vs. T data for $(\text{TMTSF})_2\text{PF}_6$ (circles) and $(\text{TMTSF})_2\text{ClO}_4$ (triangles) at P = 1 bar. The field circles and triangles correspond to the low temperature data of figures 10a and 11, respectively.</figcaption></figure>
<figure><img src="image_14.png" /><figcaption>Fig. 13. Plots of $T_1^{-1}$ (Fig. 12) vs. the measured $T_5^2(T)$ of references [34, 35] for $(TMTSF)_2PF_6$ and $(TMTSF)_2ClO_4$ above 50 K. The results of figures 7 and 9b for $(TMTTF)_2PF_6$ (squares) and $(TMTTF)_2Br$ (dashed line) are reported for comparison.</figcaption></figure>

<figure><img src="image_15.png" /><figcaption>Fig. 14. $^{77}$Se $(T_1 T)^{-1}$ enhancement of figure 12 as a function of $\chi_s^2$ data of [34, 35] for $(TMTSF)_2PF_6$ (circles) and $(TMTSF)_2ClO_4$ (triangles).</figcaption></figure>
**4. Analysis.**

**4.1 THE MODEL.** — It was soon inferred that for each compound of the sulphur series at low pressure, the existence of a resistivity minimum at $T_ρ \gg T_N$ is a direct consequence of the relevance of 1D electronic umklapp processes. Barisic and Brazovskii [48] and Emery *et al.* [16], indeed suggested that the combined influence of the 4 $k_F$ anion potential and the apparent slight dimerization of the organic stacks must open a gap $\Delta_D$ in the electronic spectrum of the chains at $\pm 2 k_F$. This leads to an effective half-filled band at low temperature and electronic umklapp effects will strongly influence the nature as well as the amplitude of correlations. If one assumes that far from the critical point the compounds can be described by 1D physics, repulsive interactions between electrons will invariably lead to the creation of a correlation gap $\Delta_ρ$ and of an insulating behavior below $T_ρ \approx \Delta_ρ/\pi$. These properties are well known to follow from the 1D repulsive Hubbard model and its continuum generalization, namely the so-called 1D electron gas model. As described in I and largely discussed in the literature [49], the direct electron-electron interaction in the latter model is parametrized in terms of four couplings constants $g_i = 1, 4$ for left and right moving electrons. They all reduce to the one-site repulsion $U$ in the Hubbard limit. This model is particularly interesting for the present compounds since the amplitude of $g_3$ is directly related to the amplitude of electronic umklapp processes and in turn to the dimerization responsible for the insulating gap $\Delta_ρ$ [48]. From its amplitude, an effective bare value of $g_3$ can be found as a function of pressure [14, 50]. A very peculiar characteristic of the 1D physics of this model is the complete separation between long wavelength charge and spin excitations. As a consequence of this spin-charge separation, the absolute value of $\chi_s(T)$ allows the determination of $g_1$ and $g_4$ (see Sect. 5) and this independently of $g_3$ and the combination $2g_2-g_1$ which are connected to the charge excitations. The latter strongly influence the strength of AF correlations and the value of $T_N$ [15, 50]. This property is invariably observed in all sulphur compounds that present a resistivity minimum. For $(TMTTF)_2PF_6$ and $(TMTTF)_2Br$ compounds at ambient pressure for example, figures 5 and 9a show that the long wavelength spin degrees of freedom which contribute to $\chi_s(T)$ remain clearly unaffected in the temperature range where the resistivity minimum occurs [7]. The effect of hydrostatic pressure is of interest since it reduces the dimerization and this will diminish the amplitude of $g_3$. Therefore, it will shift the resistivity minimum at lower temperature. This has been found to be consistent with the resistivity data of Creuzet *et al.* [8] for $(TMTTF)_2PF_6$ and $(TMTTF)_2Br$ under pressure and also with the absence of resistivity minimum for all the Bechgaard salts at ambient pressure. These are indeed less dimerized than the sulphur compounds [16]. It is from these experimental facts and the central role played by the antiferromagnetism in the combined phase diagram of both series that the 1D electron gas model has attracted considerable attention for the theoretical interpretation of these materials [51].

As shown in I, the quasi-1D generalization of this model with the inclusion of the small transverse hopping integrals is necessary to assure the existence of long range ordering. For both sulphur and selenides series the band structure calculations as well as several experiments lead to the anisotropic sequence of $t_a \approx 15 \ t_{\perp b} \approx 450 \ t_{\perp c}$ between the **a**, **b** and **c** direction hopping integrals. Despite similar anisotropy ratio $t_{\perp b}/t_a$ between the two families, the amplitude of $t_a$ differs sizeably however. According to Ducasse *et al.* [2b] at 1 bar, $E_F \approx 1\ 300$ K for $(TMTTF)_2PF_6$ compound while $E_F \approx 2\ 500$ K for the $(TMTSF)_2PF_6$. In presence of a 1D correlation gap $\Delta_ρ$, transverse single electron band motion is essentially frozen below $T_ρ$ and it is through an effective interchain exchange mechanism (IEX) which has a kinetic origin that interchain propagation of AF correlations can lead to long range order at a finite $T_N$ [15]. As we will discuss next, temperature dependence of NMR relaxation rate
experiments can provide a more direct and quantitative test for the predictions of this model especially concerning the nature, the amplitude, the statics, the dynamics and the dimensionality of spin correlations.

## 4.2 SCALING FEATURES.

*Sulphur compounds.* — Let's first look at the temperature variation of the $^{13}$C $T_1^{-1}$ in (TMTTF)$_2$PF$_6$ at 13 kbar ($T_N$ ≈ 17 K; $T_ρ$ ≈ 75 K) [5] and (TMTTF)$_2$Br at $P$ = 1 bar ($T_N$ ≈ 15 K; $T_ρ$ ≈ 100 K) [23] which are typical antiferromagnets of the sulphur series at low pressure. As already mentioned in section 3, the log-log plots of the figures 4 and 8 for the critical behavior lead to the value $\dot{\theta} = 1/2 \pm 10\%$ in both cases. According to the results of the section of 2, the AF contribution to the nuclear relaxation rate, for a quasi-1D electron gas model with a 1D correlation gap $\Delta_ρ$ near $T_N$, is given by

$$T_1^{-1}[q \sim Q_0] \approx \dot{C}(Q_0) \dot{r}_{AF}^{-1/2} \quad (4)$$

Here $\dot{C}(Q_0)$ is a temperature independent quantity (cf. Eqs. (I-6) and (I-57)). This $T_1^{-1}$ expression results from a RPA treatment of the interchain AF exchange (IEX) coupling while the 1D part of the problem is treated rigorously. As for the critical index $\dot{\theta} = 1/2$, it is a 3D result that combines Gaussian exponents for the AF susceptibility, the correlation length and the relaxation time for fluctuations. The Gaussian critical width $\Delta t_{fl} = (T_{fl} - T_N)/T_N$ for the emergence of critical fluctuations above $T_N$ is obtained from the temperature $T_{fl}$ at which the critical contribution to $T_1^{-1}$ exceeds the paramagnetic one. This quantity reflects the non-universal features of the model used. Whenever $T_ρ \gg T_N$, the transition is driven by the IEX coupling and from (I-62), it is given by

$$\Delta t_{fl} = \pi^4 [32 \gamma \delta (\pi T_N / v_F) \dot{\xi}_{0a} \dot{\xi}_{0b} \dot{\xi}_{0c}] T_N^{-1} \quad (5)$$

where according to I, $\delta \le 1$ and $\gamma = 1$. For the IEX mechanism, the transverse coherence lengths $\dot{\xi}_{0b}$ and $\dot{\xi}_{0c}$ are small quantities ($< 1$) while $(\pi T_N / v_F) \dot{\xi}_{0a} \sim 1$ so that $\Delta t_{fl} \sim 1$ which is large in agreement with the results of figures 4 and 8 for which one has $\Delta t_{fl} \sim 0.6$ for sulphur compounds. It should be stressed however, that the anisotropy with respect to the third direction should be quite large in these compounds ($\dot{\xi}_{0b} \gg \dot{\xi}_{0c}$) so that it may appear somewhat surprising that no 2D critical effects are seen above $T_N$. The reason for this is not clear so far.

As discussed in I, the choice of a different mechanism for the phase transition can lead to a quite different value for $\Delta t_{fl}$. In this respect, a 3D logarithmic nesting (NAF) mechanism of antiferromagnetism, would lead to different precursors (see Sect. I-6) and to a smaller amplitude for $\Delta t_{fl}$ [41]. In that sense, the amplitude of the precursors to the transition can give valuable indication on the type of microscopic mechanism involved in the propagation of AF correlations for the transition.

In the framework of the quasi-1D electron gas model, the presence of a correlation gap $\Delta_ρ \sim \pi T_ρ \sim 300$ K for both compounds in their respective pressure conditions would correspond to the temperature scale for strong electronic umklapp scattering. This yields a power law exponent $\gamma$ of the 1D 2 $k_F$ AF response function $(\chi(2 k_F, T) \sim T^{-\gamma})$ that is exactly equal to unity. This exponent together with the exact relation $\nu = z = 1$ for the coherence length and
the dynamical exponents in 1D leads to a temperature independent 2 $k_F$ contribution to the
relaxation rate. From (I-59) and (I-30), this contribution reads

$$
\begin{align}
T_1^{-1}[q \sim 2 k_F] &= \pi^3 \gamma_N^2 N (E_F)^2 |A_{Q_0}|^2 \bar{\chi}_{1D}(\Delta_\rho/E_F) \Delta_\rho \cdot \tag{6} \\
&\equiv C_1. \nonumber
\end{align}
$$

Therefore the observation of a temperature independent $T_1^{-1}$ for all strongly correlated sulphur compounds (see Figs. 4, 8 and also Ref. [42]) over a large temperature domain of their paramagnetic regimes can be considered as a direct evidence for strong 1D AF correlations together with a quantitative test for the relevance of 1D umklapp processes.

In the temperature range covered by the present set of experiments, the weak umklapp
coupling sector where $T \gg \Delta_\rho$ and according to (I-59) and (I-31) one would get

$$
T_1^{-1}[q \sim 2 k_F] \sim T(T/E_F)^{-\gamma_0}, \quad (7)
$$

with $\gamma_0 < 1$, is not reached at ambient temperature. As we will see below however, this is no
longer true for the selenides series or other series of compounds [30] for which there is no
resistivity minimum. In this respect, it is worth noting that the recent $T_1^{-1}$ measurements of the
mixed compound (TMDTDSF)₂PF₆ revealed the existence of the weak coupling regime (7)
above $T_ρ \sim 100$ K [14b]. In this compound however, the resistivity minimum is less sharp
suggesting that the scaling to the regime of strong umklapp processes (5) is much more gradual
than it is for sulphur compounds studied here for which transients are apparently weaker.

At sufficiently high temperatures for all sulphur compounds, another important contribution
adds to the relaxation giving rise to an increase of $T_1^{-1}$ with an upward curvature. For
(TMTTF)₂PF₆ at ambient pressure, figure 4 shows that it emerges around 65 K while under
13 kbar the emergence occurs near 100 K. The latter range corresponds to the one of
(TMTTF)₂Br at ambient pressure and this temperature dependent contribution to $T_1^{-1}$
apparently scales with a good accuracy as the square of the temperature dependence of the
static and uniform EPR susceptibility $\chi_s$ (cf. Eq. (2) and Figs. 7 and 9). From the analysis
given in appendix A of I, uniform spin fluctuations of the 1D electron gas model correspond to
paramagnons. In contrast to the situation that prevails in higher dimensions, these excitations
are not damped in 1D and furthermore, they are decoupled from the uniform charge excitations
[49]. The dynamics of paramagnons is then purely harmonic and according to (I-98), this
yields the following relation :

$$
T_1^{-1}[q \sim 0] = C_0 T[\chi_s(T)]^{(5-D)/2} \quad (8)
$$

From the observed $T\chi_s^2$ dependence of the relaxation, it follows then that not only 1D AF
correlations are detectable by NMR but also 1D uniform spin fluctuations. These can impose a
quite distinctive temperature dependence of the relaxation. Furthermore, the existence of such
a scaling relation tells us that both $\chi_s$ and $T_1^{-1}$ are influenced by paramagnons. In the
bosonization formulation, it is also well known that it is the same kind of harmonic excitations
that lead to phase fluctuations involved in the power law behavior of $\chi(2 k_F, T) \sim
T^{-\gamma}$ with $\gamma = 1$ [52].

It is worthwhile to note that in the more isotropic $D=3$ intermetallic systems like
TiBe$_2$ and YCo$_2$ [53], the commonly observed linear dependence $T_1^{-1} \propto T\chi_s(T)$ for the nuclear
relaxation has been precisely ascribed to collisionless paramagnons.

From the above results in $D=1$, it must be noted that a $T\chi_s^2(T)$ law for $T_1^{-1}$ should not be
confused with the Korringa law $T_1^{-1} \propto T[N(E_F)]^2$, which stands for an non-interacting metal
in any dimension. Actually, the identification $\chi_s^0 \sim N(E_F)$ within the Korringa law only holds
for a purely non-interacting system at $T \to 0$ K. In correlated systems like the sulphur compounds where the Fermi surface is destroyed by a Mott-Hubbard localization, this identification is clearly meaningless. Moreover, this turns out to be also true within a Fermi liquid picture where the dynamics of uniform spin correlations coincides with the one of paramagnons [23] and which therefore leads to the scaling form (8).

From the direct calculations of I, the full expression of $T_1^{-1}$ for the quasi-1D electron gas model in the 1D paramagnetic regime $\Delta_p > T \gg T_N$ is given by

$$T_1^{-1} = C_0 T \chi_s^2(T) + C_1$$

which coincides with the empirical form (2). From the temperature independent expression (6) for $C_1$ and (7), its amplitude via the 1D AF power law response factor $\bar{\chi}_{1D}(\Delta_p/E_0) \Delta_p$ will decrease with $T_p$. This is quite interesting when one compares the $C_1$ amplitudes for $(TMTTF)_2Br$ and $(TMTTF)_2PF_6$ obtained by the low temperature extrapolation of $T_1^{-1}$ vs. $T\chi_s^2(T)$ of figure 13. One then finds that $C_1$ indeed decreases with $T_p$ and for the two NMR lines of the Bromine salt, $C_1 \approx 7.5 \text{ s}^{-1}$ and $\approx 2.5 \text{ s}^{-1}$, and falls in between the value for $(TMTTF)_2PF_6$ ($T_p \approx 220 \text{ K}$ $C_1 \approx 9 \text{ s}^{-1}$) and the value $C_1 \approx 0$ found for the members of the $(TMTSF)_2X$ series from an extrapolation made in the high temperature region.

*Spin-Peierls instability.* — X-ray experiments first performed by Pouget *et al.* [4], on $(TMTTF)_2PF_6$ at ambient pressure have revealed the presence of 1D diffuse scattering below 60 K connected to the onset of 1D lattice fluctuations at the wavevector at $2 k_F$. The driving force of these fluctuations has an electronic character and comes from the bond correlations at $2 k_F$ which couple to the lattice through the electron-phonon (acoustic) interaction [50]. Below the Mott-Hubbard charge localization $T_p$, it turns out that the 1D $2 k_F$ bond charge and AF response functions become equally singular [50]. Therefore, the coupling of the bond correlations to phonons below $T_p$ will favor a lattice instability at the same wavevector. This corresponds to the so-called spin-Peierls instability. The doubling of the lattice periodicity in the chain direction will lead to the formation of spin singlets which will affect the temperature dependences of the spin susceptibility and the nuclear relaxation rate as well as the tendency to AF long range ordering. From the figures 4 and 5, a pseudo-gap in the spin degrees of freedom is clearly visible below $T_{sp}^0 = 40 \text{ K}$ for both $T_1^{-1}$ and $\chi_s$. This 1D temperature scale shows the existence of large lattice fluctuations in agreement with X-ray measurements and it marks a clear change of regime for 1D AF correlations. These features can be understood within the scaling picture of I, where from the extended scaling relation (I-16), one can write in the 1D domain:

$$T_1^{-1}[q \sim 2 k_F] = \dot{A}'_{\infty} T \left(\frac{T_{\rho}}{E_F}\right)^{-\gamma_0} \left(\frac{T_{sp}^0}{T_{\rho}}\right)^{-1} \left(\frac{T}{T_{sp}^0}\right)^{-\gamma(T)}, \quad (9)$$

for $T_1^{-1}$ at $T_{sp} < T \le T_{sp}^0$. In this expression, transient effects between the various regimes of relaxation have been neglected. $\gamma(T)$ is the critical index of the 1D AF response function in the $T < T_{sp}^0$ domain. In the presence of a pseudo-gap, it can be considered as a temperature dependent quantity that is directly related to the depression of the spin susceptibility in the same range of temperature. Actually, this follows from a formal relationship between the exponent $\gamma$ and the spin compressibility at $T \to 0$ K [52]. Assuming that at 40 K for $(TMTTF)_2PF_6$, the susceptibility has already reached its zero temperature saturation value in the absence of phonons, the semi-phenomenological arguments of references [14b, 15a] leads to the following expression

$$\gamma(T) = 2 - \chi_s(T_{sp}^0)/\chi_s(T), \quad (10)$$
for $T_{sp} < T \le T_{sp}^0$. From the data of the figure 5, one can see that a reduction of 35% of $\chi_s$ at 20 K leads to $\gamma(T_{sp}) \approx 0.46$. Therefore, according to (9), this leads to about 30% of decrease in $T_{-1}^{-1}[q \sim 2 k_F]$ from its temperature independent value just above $T_{sp}^0$ and this is consistent with the 25% reduction observed in figure 4.

The reduction in $\gamma(T)$ due to 1D spin-Peierls lattice fluctuations will also affect the critical AF transition. From (I-44), one indeed gets for $T_N$.

$$T_N \approx T_{\rho} [\tilde{J}_{\perp b}]^{1/\gamma(T)}, \quad (11)$$

at $\tilde{J}_{\perp b} \ll 1$, which is reduced by a factor $\sim (\tilde{J}_{\perp b})^{\frac{1-\gamma(T)}{\gamma(T)}} < 1$, from its value in absence of lattice fluctuations. This reduction plays an important role in making long range spin-Peierls ordering more stable. The effect of pressure on (10) and (11) is also of interest. Indeed, as discussed in reference [50], the amplitude of the $2 k_F$ bond charge correlations and in turn of the value of $T_{sp}^0$ are proportional to $T_\rho$ which decreases under pressure. This will favor a SP to AF crossover in the type of ordering under pressure [7, 8, 50].

**Selenides series.** — The analysis of the relaxation rate for the Bechgaard salts series is slightly different from the sulphur compounds at low pressure. The main reason for that is the absence of a correlation gap in the paramagnetic regime for all members of the series (Fig. 1). For all these systems the AF critical point whenever it exists, will be characterized by the inequality $T_\rho < T_N$. It should be emphasized however, that the Bechgaard salts are only a « few kilobars apart » from the sulphur compounds. (TMTTF)₂Br for example, has the lowest $T_\rho$ at ambient pressure and under 5 kbar or so, Creuzet *et al.* [8] have shown that $T_\rho$ is no longer well separated from the 3D AF critical domain so that the characteristics of the phase diagram for the AF transition become quite similar to those of the (TMTSF)₂X series with centrosymmetric anions like PF₆, AsF₆... Similar properties have been found for (TMTTF)₂PF₆ but for pressures higher than 20 kbar [8]. Whenever the resistivity minimum $T_\rho$ is relevant to the paramagnetic regime, $T_N$ is found to *increase* under pressure whereas it *decreases* for pressures where $T_\rho$ is no longer seen. This property has been shown to be the signature of the evolution of the IEX coupling from the strong coupling (cf. (I-44)) to the weak 1D umklapp coupling (cf. (I-67)) regions [50, 54].

In the following, the analysis of critical relaxation for (TMTSF)₂PF₆ will be made in this framework. Of course retaining only the IEX coupling will become less and less accurate as the pressure increases and $T_N$ decreases. This occurs because of the emergence of a coherent 2D band motion due to the single particle dimensionality crossover at the temperature $T_X^1$ (cf. Sect. 5 of I). As $T_X^1$ is approached from above, the 1D electron-electron and $2 k_F$ electron-hole channels tend to decouple from each other and as the temperature is further lowered, the curvature of the Fermi surface becomes sufficiently coherent for the nesting properties at the wavevector ($2 k_F, \pi$), if any, drive the AF transition at sufficiently low temperature. The crossover takes place gradually however, so that a quantitative treatment of the region of the phase diagram where $T_N$ becomes small would require the complete evaluation of the so-called crossover scaling function of $T_{-1}^{-1}$ which takes into account all the transients relative to the decoupling of the two channels and the interplay between the two IEX and NAF mechanisms of the transition. The calculation of transients is beyond the scope of the present analysis and will not be discussed here [55].

As shown in I, the full 3D expression for the nuclear relaxation near $T_N$ in the absence of a correlation gap keeps the same form (4). Similarly to what has been found for the sulphur compounds, the critical behavior of (TMTSF)₂PF₆ at $P = 1$ bar and 5 kbar (Fig. 10) leads to
an exponent $\dot{\theta} \approx 1/2 \pm 10\%$ which is consistent with 3D ordering effects. These results also confirmed previous $^1$H relaxation data of Stein et al. [41] at ambient pressure. In contrast to the data of the figure 10, the latter were obtained within a temperature decade closer to $T_N$. Therefore 3D Gaussian ordering effects are apparently present over a large temperature domain above $T_N$ and again, as for sulphur compounds, no evidence for 2D critical effects are found. Furthermore, despite a decrease in $T_N$ under pressure, the temperature width for critical fluctuations $\Delta t_{\Omega} \approx 0.8 \dots 1$ remains as large as those found for sulphur compounds.

As for the paramagnetic regime of $(TMSF)_2PF_6$ which is metallic, the data of figures 12 and 13 show that the upward curvature of the relaxation which again scales according to the 1D law $T\chi_s^2(T)$, appears relatively early in temperature. From figure 14, deviations to this law seen below 200 K at ambient pressure indicate the emergence of the AF part of the relaxation. It is therefore weaker in amplitude than the one found for sulphur compounds. Without strong umklapp effects and the absence of a resistivity minimum, 1D AF fluctuations are characterized by a smaller value for the 1D exponent $\gamma_0$ in $T_1^{-1}[2 k_F, T]$ (cf. (I-31) and (I-59)) namely,

$$ 
\begin{aligned}
T_1^{-1}[2 k_F, T] &= \text{Cst.} T \left( \frac{T}{E_F} \right)^{-\gamma_0} \\
&= C_1(T),
\end{aligned} 
\quad (12) $$

where $\gamma_0 < 1$. The subtraction of the uniform $C_0 \chi_s^2(T)$ contribution from the $(T_1 T)^{-1}$ data allows us to extract the temperature dependence of the AF component of $(T_1 T)^{-1}$ which well above the critical domain should scale according to the 1D power law (I-31): $\bar{\chi}(2 k_F, T) \sim T^{-\gamma_0}$. From figure 15, one finds an exponent $\gamma_0 \approx 0.9$. At very high temperatures, the AF contribution is negligible in comparison to the uniform one and this explains why the linear relationship between $T_1^{-1}$ and $T\chi_s^2(T)$ essentially extrapolates to zero from the high temperature region (Fig. 13). In turn, the results of figure 13 show how the sulphur compounds can be antiferromagnetically more correlated than the Bechgaard salts. This difference is therefore consistent with the one known for electronic umklapp effects. As we will see however, the amplitudes of uniform correlations for both series are not so different at ambient pressure.

Not too far above the critical pressure $P_c$ for superconductivity, there is no AF ordering and the $(TMSF)_2X$ compounds with $X = PF_6, ClO_4$. remain metallic down to a superconducting critical point $T_c \sim 1$ K (Figs. 1, 2) [11]. As one can see, the relaxation data of figures 10 and 11 for $(TMSF)_2PF_6$ at 10 kbar and for $(TMSF)_2ClO_4$ in the relaxed state at $P \approx 1$ bar respectively, show that a strong enhancement of the relaxation persists from 30 K or so down to $T_c$. A similar enhancement was confirmed by other groups for the perchlorate salt [40, 47]. Moreover, it was also observed for both $^1$H and $^{77}$Se $T_1^{-1}$ of $(TMSF)_2FSO_3$ at 10 kbar and in the same range of temperatures. This shows that this huge non-critical enhancement is independent of the anion symmetry. It then appears to be a common characteristic of the normal state for the Bechgaard salts above their superconducting critical point. It was proposed in reference [17], that since the uniform susceptibility shows no anomaly in this range of temperatures and considering the fact that these systems are not very far from an AF ground state in the phase diagram, the enhancement can be naturally attributed to the existence of large antiferromagnetic spin fluctuations. These fluctuations cannot be considered as critical however, since there is no broadening of the NMR $^{77}$Se line associated to them [17, 19a]. This is also consistent with pronounced metallic conditions [11] and the monotonic decrease for $(TMSF)_2ClO_4$ of the EPR line [56] in this temperature range. From the full expression for the nuclear relaxation (Eq. (I-100)), namely

$$ T_1^{-1} = C_0 T\chi^2(T) + \dot{C}(Q_0, T) \dot{r}_{AF}^{-1/2} \quad (13) $$
<figure><img src="image_16.png" /><figcaption>Fig. 15. — 1D AF auxiliary response function $\bar{\chi}(2 k_F \cdot T)$ vs. $T$ for $(TMTSF)_2PF_6$ as it can be extracted from the data of figure 14 well above $T_N$. The continuous line corresponds to a power law with $\gamma_0 \approx 0.9$.</figcaption></figure>

It was first suggested that the 1D power law enhancement $(T_1 T)^{-1}$ [$2 k_F, T$] ~$\bar{\chi}_{1D}(2 k_F, T)$ ~$T^{-\gamma_0}$ alone ($\dot{r}_{AF} \approx 1$) can explain the plateaus of relaxation of the figures 10a and 11 by taking $\gamma_0 \sim 1$. The rapid drop of $T_1^{-1}$ below 10 K was in turn interpreted as the freezing of the growth of AF fluctuations at ($2 k_F, 0$) due to the dimensionality crossover in the single particle properties at $T_X^1$. This interpretation first presupposes that the uniform contribution to the relaxation becomes suddenly negligible when the AF component of the relaxation rate emerges. As we have seen, a similar, though more gradual situation, really occurs for the sulphur compounds where the plateaus of relaxation seen above the Neel temperature do correspond to the value $\gamma = 1$ and as well as a small uniform contribution (Figs. 3, 7). $\gamma = 1$ however, is known to be the maximum value $\gamma$ can reach in the strong umklapp coupling domain with no magnetic anisotropy [49]. Moreover, for the Bechgaard salts, there is no resistivity minimum at high temperature and thus no strong coupling conditions prevail for the electronic umklapp scattering so that $\gamma$ should be smaller than unity. This means that the source of $T_1^{-1}$ enhancement though not critical, is probably not purely one-dimensional in character. Sizeable corrections though non critical due to the proximity of an antiferromagnetic ground state should be included in order to completely overcome the uniform contribution to the relaxation in a relatively small temperature interval [20]. If one assumes that the scale of $T_X^1$ does correspond to 10 K, this means that the anomalous enhancement occurs in a temperature domain where transients between the nesting at the wavevectors ($2 k_F, 0$) and ($2 k_F, \pi$) are present and play an important role [20]. It should be stressed here that deviations to perfect 2D nesting at ($2 k_F, \pi$) are much more effective to frustrate the occurrence of AF long range ordering below $T_X^1$ than well above where the IEX mechanism should dominate. In the latter case, only small corrections to $T_N$ are found.
## 5. Uniform susceptibility measured by NMR.

In the previous section, we found that the high temperature $T_1^{-1}$ variation invariably scales with the product $T\chi_s^2(T)$ which results from 1D features of spin fluctuations. This suggests an original approach for the obtention of the temperature variation of the spin susceptibility $\chi_s(T)$ as a function of hydrostatic pressure. This will allow direct comparisons with the 1D electron gas model prediction for $\chi_s(T)$ as given in the appendix A of I and an estimation of the value of the coupling constant $g_1/\pi v_F$, under pressure, can therefore be made for the compounds studied [30].

As we have already shown, the scaling relation (2) is very well followed by quite a large temperature domain. Deviations to the $T_1^{-1} \sim T\chi_s^2(T)$ law due to critical or 1D AF fluctuations makes it impossible to extract the uniform part as $T \to 0$ K, but on the other hand, we already know that for the compounds under study at ambient pressure, the uniform susceptibility varies very little in temperature up to about 50 K. Therefore, in the following analysis, only the data obtained above this range will be considered.

*Selenides series.* — The confrontation of the theoretical prediction for a non-singular quantity like $\chi_s(T)$ with the experimental data is not straightforward however. This is so because all the data presented in section 3 are obtained at *constant pressure* while the theoretical expression (I-A-21) is deduced from a *constant volume* theory. It was already suggested by Forro *et al.* [36, 57] that the reduction of the bandwidth due to thermal expansion of the unit cell would contribute for the $\chi_s(T)$ enhancement at high temperature. As we will show below, this gives rise to a sizeable effect and cannot be neglected.

Without making reference to any particular model, there is a simple method to evaluate this contribution using thermodynamic identities. For a 1D chain, let us suppose that the spin susceptibility $\chi_s(T, a)$ is a function of the temperature and the unit cell parameter $a$ which is itself directly related to the transfer integral and the bandwidth. The measured susceptibility is then a « constant pressure » susceptibility :

$$ (\chi_s)_p = \chi_s(T, a(T, P)). \qquad (14) $$

A quantity called « constant volume susceptibility » is defined as :

$$ (\chi_s)_v = \chi_s(T, a(T = 0, P)), \qquad (15) $$

and for a given pressure one has the following relation :

$$ \Delta\chi_s = (\chi_s)_p - (\chi_s)_v = \int_0^T dT \left( \frac{\partial\chi_s}{\partial P} \right)_T \left( \frac{a}{\partial a} \right)_T \left( \frac{\partial a}{\partial T} \right)_P \qquad (16) $$

Here $(\partial\chi_s/\partial P)_T$ is known from our measurements while the other derivatives can be obtained from the structural studies. As all the data necessary for the calculation are available only for $(TMTSF)_2PF_6$, the following analysis will be restricted to this compound.

In order to apply (16) to our « NMR susceptibility » given by

$$ (T_1 T)^{-1/2} [q \sim 0] \propto \chi_s(T), $$

we need to calculate $(\partial\chi_s/\partial P)_T$ at each $T$ and $P$. This can be derived from $dT_1/dP$ with quite a good accuracy using the fact that the relaxation time is linear with pressure, as shown in figure 16. At this stage, we have no general arguments to explain such a linearity, but direct calculations will confirm it. The thermal expansion and compressibility coefficients as a function of temperature and pressure have been taken from the X-ray studies of Gallois *et al*.
<figure><img src="image_17.png" /><figcaption>Fig. 16. — $(T_1 T)^{-1/2}$ and $T_1$ vs. pressure for $(TMTSF)_2PF_6$ at 292 K (full circles), 200 K (full triangles), and 100 K (open squares). The continuous lines are the fits calculated using the parameters from table I.</figcaption></figure>

[43]. In figure 17, we show the temperature dependence of $(T_1 T)^{-1/2}$ for $(TMTSF)_2PF_6$ and the corresponding constant volume corrected data obtained by a numerical integration of (16). It clearly appears that the corrected $\chi_s(T)$ does not lead to a nearly temperature independent Pauli susceptibility as should be expected for a non-correlated metal. Below 100 K, one finds that the correction $\Delta\chi_s$ is negligible because of the weak pressure dependence of $\chi_s$. $\Delta\chi_s$ decreases with pressure but the $(\chi_s)_p/(\chi_s)_v$ ratio remains essentially constant indicating that the Coulomb enhancement depends strongly on the bandwidth, as expected.

<figure><img src="image_18.png" /><figcaption>Fig. 17. — $^{77}$Se $(T_1 T)^{-1/2}$ vs. T at for $(TMTSF)_2PF_6$ different pressures, the dashed (continuous) lines correspond to the calculations at constant volume (pressure) using the parameters of table I. The open symbols are the corrected data at constant volume.</figcaption></figure>
We note here that (16) reduces to the simplified formula of reference [57] only if none of the quantities under the integral depends on temperature. For $(TMSF)_2PF_6$, $(\partial\chi/\partial P)_T$ is roughly linear in $T$. Neglecting this dependence would easily overestimate the correction $\Delta\chi_s$ by a factor of order 2.

The remaining temperature dependence of $(\chi_s)_v$ will be analyzed in terms of the electron-electron interaction enhanced susceptibility

$$ \chi_s(T) = \chi_s^0(T) \left[ 1 - \frac{1}{2} g_1(T) \chi^0(T) \right]^{-1}, \quad (17) $$

where for the elementary spin susceptibility

$$ \begin{aligned} \chi_s^0(T) &= \frac{1}{2} g^2 \mu_B^2 \chi^0(T) \\ &= \frac{1}{4} g^2 \mu_B^2 (\chi_{++}^0(T) + \chi_{--}^0(T)), \end{aligned} $$

we keep track of the temperature dependence of the Fermi distribution factors (cf. (I-A-19)). The temperature dependent electron-electron backward scattering amplitude is given by

$$ g_1(T) = g_1 / [1 + (\pi v_F^*)^{-1} g_1 \ln(E_F^*/T)], \quad (18) $$

in first order of the renormalization group (cf. (I-21a)). The renormalized velocity for spin excitations is

$$ v_F^* = v_F(1 - g_4 / 2 \pi v_F). \quad (19) $$

Note that here we are making use of the renormalized high energy cut-off $E_F^* = E_F(1 - g_4 / 2 \pi v_F)$ [30, 58]. In the following, long wavelength spin fluctuations will be treated in the Hubbard limit where the bare values of the coupling constants reduce to a single local repulsion parameter $U = g_1 = g_4$ [59]. It should be stressed here that an independent determination of $g_4$ would require the knowledge of the absolute value of the zero temperature limit of $\chi_s$ at different pressures which is not possible from our NMR determination.

The expression (17) contains two adjustable parameters: the Fermi energy and the coupling $g_1$. The pressure effect on $\chi_s$ comes through the $E_F(P)$ (and $v_F(P)$) dependence. Knowing the value of $E_F$, one can calculate the coupling $g_1$ at different pressures directly from the constant volume corrected susceptibility $(\chi_s)_v$. But we can get more information putting the $E_F(T, P)$ function into (17) and using the whole set of data of figure 17. According to the band structure calculations [2] and X-ray data [45] showing that longitudinal (intrachain) transfer integral is almost linear in temperature and pressure in the range 100-300 K, we get two more unknown quantities which are the thermal $(dE_F/dT)$ and pressure $(dE_F/dP)$ coefficients of the bandwidth (supposed to be constant in the whole T-P domain studied). We thus have to fit our experimental curves using four free parameters. This task is not as difficult as it appears because there is no strong interaction between them. Indeed, $g_1$ will be mainly sensitive to the high temperature curvature of $(\chi_s)_v$; $dE_F/dP$ can be well determined with $\chi_s$ values at three different pressures while $dE_F/dT$ is related to $\Delta\chi_s$, leaving the Fermi energy as the free parameter. Therefore, on fitting all the six curves of figure 17 at the same time by setting arbitrary value of $E_F(0 \text{ K}, 1 \text{ bar})$ and adjusting the other constants, we always found a unique solution within a 5-10% error on each of them. The results are rather close to the band structure calculations for which $E_F \approx 3 \text{ 100 K}$ [2] since reasonable fits can be obtained only for $2 \text{ 500 K} < E_F(0 \text{ K}, 1 \text{ bar}) < 3 \text{ 500 K}$.

From the expression (16), it is clear that the enhancement contribution is gradually suppressed at high pressures when $\tilde{g}_1 = g_1 / \pi v_F$ becomes small. This high pressure limit can be
attained above 40 kbar or so, where this constant has dropped by a factor of 10. Actually, this could occur for even lower pressures since the compressibility coefficient increases with pressure [45]. At low pressures then, $\tilde{g}_1$ slightly exceeds unity and is therefore located in the medium-strong coupling sector. Although we are not in a position to evaluate the constant volume susceptibility for $(TMTTF)_2ClO_4$, a similar analysis can be carried out for this compound and from the data of the figure 11, it is clear that the value of the coupling constant $\tilde{g}_1$ or $\tilde{U}$ would be quite close to the one found for the PF$_6$ salt at ambient pressure.

*Sulphur compounds.* — For $(TMTTF)_2X$ compounds in the paramagnetic regime, the uniform part of the expression (2) can be easily obtained if the 1D AF constant $C_1$ is subtracted from the total $T_1^{-1}$. Even if from the $T \to 0$ K extrapolation of $T_1^{-1}$ (Figs. 7 and 9b), this constant can not be determined with a high degree of accuracy, it is easy to see that due to large values of $T_1^{-1}$, the resulting error on $\chi_s$ will be negligible in this temperature domain. In the case of $(TMTTF)_2Br$, the data of figure 9b lead to $C_1 \approx 2 \text{ s}^{-1}$ at 1 bar while at 12 kbar the resistivity minimum is no longer observed [8a] and we can put $C_1 \approx 0$ as for $(TMTTF)_2PF_6$. For $(TMTTF)_2PF_6$ at 1 bar and 13 kbar, the data of the figures 4 and 7 give $C_1 \approx 9 \text{ s}^{-1}$ and $6 \text{ s}^{-1}$ respectively.

Since for the sulphur compounds, no X-ray data under pressure are available so that the $(\chi_s)_v$ calculation using (15) cannot be carried out. The thermal expansion $dE_F/dT$ coefficient thus remains as an independent parameter and the solution is not unique for a given $E_F$. Band calculations of reference [2] gives only the Fermi energy at 300 K. In table I, we give several possible solutions. The difference between the corresponding values of $\chi_s(T, P)$ however, is found to be always smaller than the experimental error. The theoretical fits are shown in the figures 18 and 19 (and correspond to the first set of parameters in both cases). For $(TMTTF)_2Br$, the fit has been done on the relaxation rate of one of the carbon sites (the lower $T_1^{-1}$). For both compounds, $\tilde{g}_1$ remains large although the values found for $(TMTTF)_2Br$ are smaller. For $(TMTTF)_2Br$ at 12 kbar, the results of figure 19 show a growing discrepancy between theory and experiment below 200 K. This is mainly attributed to the AF contribution to the relaxation rate which has not been subtracted from the total $T_1^{-1}$. Such a contribution

<figure><img src="image_19.png" /><figcaption>Fig. 18. — Calculated uniform component of $^{13}$C $(T_1 T)^{-1/2}$ vs. T for $(TMTTF)_2PF_6$ (continuous lines) at different pressures from the parameters of table I.</figcaption></figure>
<figure><img src="image_20.png" /><figcaption>Fig. 19. — Calculated uniform component of ¹³C (T₁T⁻¹/²) vs. T for (TMTTF)₂Br (continuous lines) at different pressures from the parameters of table I.</figcaption></figure>

<table><caption>Table I. — Set of parameters used in the fit of the spin susceptibility for representatives of (TMTSF)₂X and (TMTTF)₂X series.</caption><thead><tr><th></th><th>E<sub>F</sub> (0 K, 1 bar)<br>[K]</th><th>1 (dE<sub>F</sub>/dT)<br>[%/300 K]</th><th>1 (dE<sub>F</sub>/dp)<br>[%/kbar]</th><th>g&#771;<sub>1</sub> (0 K, 1 bar)</th></tr></thead><tbody><tr><td>(TMTSF)<sub>2</sub>PF<sub>6</sub> :<br>NMR results</td><td>3 100</td><td>7</td><td>2.21</td><td>1.16</td></tr><tr><td>Band calculations [2b]</td><td>3 100</td><td>13.7-7.5 <sup>(1)</sup></td><td>0.75-1.9 <sup>(2)</sup></td><td></td></tr><tr><td>(TMTTF)<sub>2</sub>PF<sub>6</sub> :<br>NMR results (Fig. 18)</td><td>1 600<br>1 600</td><td>15<br>10</td><td>2.76<br>2.23</td><td>0.99<br>1.11</td></tr><tr><td>Band calculations [2b]</td><td>1 600</td><td>15</td><td>—</td><td></td></tr><tr><td>(TMTTF)<sub>2</sub>Br :<br>NMR results (Fig. 19)</td><td>1 800<br>2 000<br>2 000</td><td>15<br>15<br>10</td><td>2.77<br>2.70<br>2.19</td><td>0.87<br>0.88<br>1.01</td></tr><tr><td>Band calculations [2b]</td><td>1 460 <sup>(3)</sup></td><td></td><td>—</td><td></td></tr></tbody></table>

<footnote>(1) At 1 bar and 6.5 kbar.</footnote>

<footnote>(2) At 4 K and 300 K.</footnote>

<footnote>(3) At 300 K.</footnote>
should be important even in the absence of a correlation gap, as it occurs for example in $(TMTSF)_2PF_6$ which has a comparable $T_N$ and a growing AF $T_1^{-1}$ component in the same temperature range (cf. Fig. 15). Another, though extrinsic, source can be due to spin diffusion assisted relaxation resulting from a partial overlapping of the two NMR lines at lower fields (here 31 kG) and in this region of temperature. This latter possibility is further supported by the $T_1$ ratio for both lines which is not temperature independent in this temperature region.

If we now compare the amplitude of $\tilde{g}_1$ for both series, we see from table I that the values obtained for $(TMTSF)_2PF_6$ and $(TMTTF)_2PF_6$ at ambient pressure are nearly the same. Actually, this is consistent with similar amplitudes for the temperature variation of $\chi_s$ up to 300 K in both cases (see Refs. [34-35] and Figs. 5 and 9a). This leads to the interesting consequence that under sufficiently high pressures, the characteristics of the AF phase transition of $(TMTTF)_2PF_6$ will become similar to those of $(TMTSF)_2PF_6$. In contrast however, $(TMTSF)_2PF_6$ will be much less correlated as regard to uniform correlations. From the results of table I, it is clear that the same is true for $(TMTTF)_2Br$. This absence of « scaling » for $\tilde{g}_1$ from sulphur to selenides series under hydrostatic pressure can actually be seen as a consequence of spin-charge separation. Indeed, from the 1D electron gas model the amplitude of the AF correlations is strongly dependent upon the strength of the umklapp coupling term $g_3$ and the combinaison $2g_2 - g_1$ [60]. These are coupled by 1D many-body effects (see for example, Eq. (I-21)) and they are known to be both connected to uniform charge degrees of freedom [49]. In contrast, $g_1$ is connected to uniform spin excitations (cf. (17)), and it varies independently of $g_3$ as a consequence of the spin charge-separation. Therefore, since $g_3$ is related to the half-filling character of the band and thus to the amplitude of the $4k_F$ dimerization along the organic stacks, it will be strongly affected by pressure [16]. Under sufficiently high pressure then, $T_\rho$ goes to zero and the amplitude of AF fluctuations joins smoothly the one found in the selenides series at low pressure which are well known to be less dimerized. The $T_1^{-1}$ results of both families in figure 12 clearly supports this. As for the reduced $\tilde{g}_1$ coupling however, if it is nearly the same at ambient pressure for both series which is suggested by the similar amplitude for the temperature variation of $\chi_s(T)$, it is clear that as far as uniform spin degrees are concerned there will no possibility of « scaling » between them under pressure.

**6. Summary and concluding remarks.**

In summary, the temperature dependencies of $(T_1 T)^{-1}$ for all compounds studied, were found to invariably follow the square of the measured (RPE or Faraday) uniform and static susceptibility $\chi_s^2(T)$ over a wide temperature domain in the paramagnetic regime. The enhancement that emerges at sufficiently low temperature has been shown to come from the growth of antiferromagnetic correlations and whenever a Neel critical point exists, it evolves to a singularity of the form $(T - T_N)^{-1/2}$ within a large 3D critical domain. The experimental results are found to fit remarkably well the predictions of the scaling theory of the quasi-one-dimensional electron gas model. In the large temperature domain that characterizes all the non-ordered phases, the temperature variation of both the uniform and antiferromagnetic parts of the relaxation can be fully understood in terms of power laws with the critical indexes predicted for a one-dimensional system with electronic umklapp effects. For members of the sulphur series, these lead to strong antiferromagnetic spin fluctuations at low temperature with universal critical exponents whereas they are much less developed in the selenides giving rise to non-universal features. As for the uniform spin fluctuations, their amplitude at ambient pressure is essentially the same for both series and their dynamic is harmonic and coincides with the one of 1D free spin bosons (paramagnons). From the theoretical expression for the 1D
magnetic susceptibility and the relaxation data corrected at constant volume, we have been able to estimate the bare repulsive value for the backward scattering amplitude $g_1$ of the 1D electron gas model as a function of pressure. At ambient pressure, the ratio $g_1/\pi v_F$ is found to be essentially the same for the two series. It follows that contrary to what is apparently observed for antiferromagnetic fluctuations, the amplitude of uniform spin correlations for the sulphur series does not scale under pressure onto the one of the selenides at ambient pressure.

**Acknowledgments.**

One of us (P. W.) would like to thank the *Canadian Institute of Advanced Research* (CIAR) and the *Centre de Recherche en Physique du Solide* (C.R.P.S.) of Université de Sherbrooke for financial support. C. B. was partly supported by a « Chercheur Associé » contract of the *Centre National de la Recherche Scientifique* (C.N.R.S.), the *Natural Sciences and Engineering Research Council of Canada* (NSERC) and by a « Jeunes Chercheurs » grant of *Le Fonds pour la Formation de Chercheurs et l'Aide à la Recherche* (FCAR) of the province of Québec.

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