# NMR Analysis of Spin Fluctuations in the Organic Conductor TTF[Ni(dmit)2)2]

Claude Bourbonnais, Pawel Wzietek, Denis Jerome, F. Creuzet, L. Valade, P. Cassoux

► To cite this version:

Claude Bourbonnais, Pawel Wzietek, Denis Jerome, F. Creuzet, L. Valade, et al., NMR Analysis of Spin Fluctuations in the Organic Conductor TTF[Ni(dmit)2)2]. EPL - Europhysics Letters, 1988, 6 (2), pp.177-182. 10.1209/0295-5075/6/2/014. [hal-04983385](https://hal.science/hal-04983385v1)

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Distributed under a Creative Commons Attribution 4.0 International License
*Europhys. Lett.*, **6** (2), pp. 177-182 (1988)

NMR Analysis of Spin Fluctuations in the Organic
Conductor TTF[Ni(dmit)₂]₂.

C. BOURBONNAIS(*) (§), P. WZIETEK(*), D. JEROME(*), F. CREUZET(*)

L. VALADE(**) and P. CASSOUX(**)

(*) Laboratoire de Physique des Solides

Université de Paris-Sud, 91405 Orsay Cedex, France

(**) Laboratoire de Chimie de Coordination du CNRS

Université P. Sabatier, 31077 Toulouse Cedex, France

(received 29 December 1987; accepted in final form 25 February 1988)

PACS. 71.45 – Collective effects.

PACS. 76.60E – Relaxation effects.

**Abstract.** – We present and analyse ¹H NMR relaxation ($T_1^{-1}$) data of the two-chain organic conductor TTF [Ni(dmit)₂]₂ as a function of temperature and magnetic field at ambient pressure. In the entire temperature domain studied between 1 and 300 K, we report important deviations to the normal metal Korringa law. We show that both $T_1$ temperature and field dependences can be well understood in terms of a typical balance between 1D uniform field-dependent and diffusive spin correlations, which dominate the relaxation enhancement above 60 K or so, and 1D antiferromagnetic fluctuations that strongly develop below this temperature with a power law temperature dependence. The successful comparison between theory and experiment strongly supports a model in which TTF-conducting chains are dominated by repulsive electron-electron interactions and 1D correlation effects down to the lowest temperature reached.

*Introduction.* – The NMR spin-lattice relaxation rate ($T_1^{-1}$) experiments are well known for their ability to probe the presence of electronic correlations in metallic systems [1]. Performed on the organic metal TTF-TCNQ, such experiments have demonstrated the important role played by repulsive electron-electron interactions for the electronic properties of this material [2, 3]. More recently, for the two extensively studied series of organic conductors (TMTTF)₂X and (TMTSF)₂X, $T_1^{-1}$ measurements performed on spin one-half nuclei ¹H, ⁷⁷Se and ¹³C turned out to be quite a useful tool for the characterization of the various phase transitions taking place in these compounds [3-5]. In general, these materials are dominated by $T_1^{-1}$ enhancements due to strong antiferromagnetic correlations over a quite large low-temperature domain. Scaling theory and direct renormalization group calculations [4, 6, 7] revealed that repulsive interactions and 1D many-body effects are at the origin of the antiferromagnetic correlations. It has been shown that they can enter as a basic ingredient for a novel type of pairing mechanism responsible for superconductivity in the Bechgaard salts [8].

<footnote>(§) Permanent address: Département de Physique, Université de Sherbrooke, Sherbrooke, Québec, Canada, J1K-2R1.</footnote>
In a similar spirit of investigation, this paper presents and analyses the first ambient pressure ¹H nuclear-relaxation data for the recently synthesized two-chain organic conductor TTF [Ni-(dmit)₂]₂ [9a]. This compound is metallic at ambient pressure, but according to the work of Brossard et al. [9b], it undergoes a superconducting transition at 1.6 K under 7 kbar. The $T_1^{-1}$ data, collected at $P=1$ bar as functions of temperature between (1 ÷ 300) K and magnetic field of (1.4 ÷ 90) kG have a purely electronic origin, since the protons belong solely to the TTF chains and are presumably free from rotational effects at all temperatures. Very little is known so far about the actual charge transfer occurring between the two component molecules of this salt. Unlike two-chain conductors such as TTF-TCNQ, the sign of cation and anion overlap integrals is the same [10]. Consequently, a parallel-band situation prevails and the Fermi surface exhibits at least two different sheets. However, the band filling is yet unknown on account of the different degrees of oxidation that Ni(dmit)₂ anions can take in the solid state.

On the one hand, a strong 3D character of the electronic structure has been suggested on the basis of short S···S intermolecular contacts existing between like molecules as well as unlike molecules [9d]. On the other hand, a tight-binding band structure calculation has revealed the existence of a pronounced one-dimensionality of the energy spectrum [10].

The present NMR study was undertaken in order to clarify the question of electronic dimensionality of this material. For the analysis of the data, we present a detailed calculation of the long-wavelength ($q \sim 0$) part of $T_1^{-1}$ for which diffusive, electron-electron and magnetic-field effects on spin fluctuations enter in an essential way. Together with the previous results [4, 6, 7] for the staggered $q \sim 2k_F$ contribution to $T_1^{-1}$, we conclude that the strong $T_1^{-1}$ enhancement observed in TTF [Ni-(dmit)₂]₂ over the whole temperature range studied is highly consistent with the pronounced 1D character of correlations in TTF chains.

*Experimental results.* – About 30 mg powder samples have been used in all experiments. The relaxation time was measured with a conventional pulsed NMR spectrometer in the (6 ÷ 45) MHz frequency range and with a commercial resolution spectrometer above and up to 390 MHz. A standard relaxation recovery technique was used. The magnetization recovery was found to be exponential over a decade in the amplitude of the magnetization.

The temperature dependence of the proton relaxation time is shown in fig. 1. Deviations to the Korringa law ($T_1^{-1} \propto T$) are clearly visible from the upward (downward) curvature of $T_1^{-1}$ vs. $T$ at high (low) temperature. When one looks at the plot of $(T_1 T)^{-1}$ vs. $T$, these deviations correspond to enhancements of the relaxation which reveal a stronger temperature dependence below 50 K than above 150 K. Figure 2 shows the frequency dependence of the quantity $(T_1 T)^{-1}$ in the range of (6 ÷ 390) MHz (magnetic field of (1.4 ÷ 90) kG). At ambient temperature, $(T_1 T)^{-1}$ is frequency independent below 150 MHz (30 kG) or so and begins to decrease above this value. At 90 kG, about 40% reduction is obtained which in amplitude is reminiscent of the $T_1^{-1}$ field-induced depression typically found in 1D conductors [2a, 3]. At lower temperature ($T = (200 \div 77)$ K), no appreciable decrease of the relaxation could be detected up to 90 kG.

*Theory.* – For itinerant electronic systems like the organic conductors, we start from the Moriya $T_1^{-1}$ formula in one dimension [1]:

$$T_1^{-1} = 2\gamma_N^2 |A|^2 T \int \frac{dq}{2\pi} \chi_{\perp}''(q, \omega_N)/\omega_N, \quad (1)$$

where we have used $\hbar = k_B = 1$. A is the hyperfine local matrix element between the conduction electrons and the nuclear spin, $\omega_N = \gamma_N H_0$ is the nuclear Larmor frequency and $\gamma_N$ is the gyromagnetic ratio of the nucleus. $\chi_{\perp}''(q, \omega_N)$ is the imaginary part of the transverse magnetic susceptibility at the wave vector $q$ and frequency $\omega_N$. The local nature of the
<figure><img src="image_2.png" /><figcaption>Fig. 1. – Temperature dependence of $T_1^{-1}(\times)$ and $(T_1T)^{-1}(\circ)$ at $P = 1$ bar and $H = 10.5$ kG for TTF[$Ni(dmit)_2]_2$. The continuous lines are the fits obtained from the theoretical $T_1^{-1}[q]$ expressions for $q \sim 0$ (eq. (5)) and $q \sim 2k_F$ (eq. (2)). See the theory and the discussion sections.</figcaption></figure>

<figure><img src="image_3.png" /><figcaption>Fig. 2. – Field (frequency) dependence of $(T_1T)^{-1}$ at 300 K (×), 200 K (○) and 77 K (+) for TTF[$Ni(dmit)_2]_2$. The broken lines are the theoretical curves drawn using (2) and (7) with $\tau_\perp = 3 \cdot 10^{-12}$ s and $\tau_\perp/\tau_i = 50$ and the parameters of the fit of fig. 1. The three points close together on the left ($H_0^{-1/2} \approx 0.1$) correspond to the same frequency 390 MHz.</figcaption></figure>
hyperfine matrix element makes $T_1^{-1}$ sensible to electronic correlations of all values of $q$. For the single-chain problem, it is the uniform ($q \sim 0$) and staggered ($q \sim 2k_F$) type of correlations that dominate the relaxation. In ref. [4, 6, 7], it was shown that $2k_F$ antiferromagnetic correlations impose the following power law enhancement to $T^{-1}$:

$$ (T_1 T)^{-1}[q \sim 2k_F] = K_0 \zeta(T) [T/E_F^*]^{-\gamma_{1D}}, \quad (2) $$

where $\zeta(T) = [2(\gamma_{1D} + 1)(1 - g_1/2\pi v_F)^2]^{-1}(1 - g_1/\pi v_F^* \ln T/E_F^*)^{1/2}$ and for $E_F^* > T > \omega_e$, $\omega_e$ being the electronic Larmor frequency. For a conductor such as TTF [Ni(dmit)$_2$]$_2$, the TTF band filling is presumably different from one-half, otherwise electronic localization effects due to correlations should be probably observable. Therefore, the power law exponent $\gamma_{1D}$ of the $2k_F$ spin susceptibility becomes $\gamma_{1D} \approx (2g_2 - g_1)/2\pi v_F^*$, in first-order renormalization group approach [11]. Here, $g_1$ and $g_2$ are the backward and the forward parts of the repulsive electron-electron interaction. $v_F^* = v_F(1 - g_1/2\pi v_F)$ [$E_F^* = E_F(1 - g_1/2\pi v_F)$] is the renormalized Fermi velocity energy which coincides with the one of uniform spin excitations [12]. $K_0 = \pi\gamma_N^2|A|^2 N(0)^2$ and $N(0) = 1/\pi v_F$ is the bare density of states at the Fermi level. Owing to the strongly metallic character of TTF [Ni(dmit)$_2$]$_2$ [9], impurity scattering will affect only the small-$q$ electron-hole correlations [2a, 3]. These correlations are nonsingular and acquire a diffusive character at $q < l_i^{-1}$, where $l_i$ is the elastic mean free path for spin fluctuations. These effects enter in $T_1^{-1}$ through the magnetic susceptibility $\chi(q, \omega)$ at small $q$ and $\omega$.

Our approximation scheme for $\chi$ starts from the Fermi liquid approach of Lee et al. [12], in which only the $g_1$-dependence of the small-$q$ electron-hole channel matters. The related correlations are nonsingular and for $g_1(T)/2\pi v_F^* < 1$ they can be summed up in the random phase approximation. Finally we assume that each small-$q$ electron-hole excitation satisfies the diffusion equation. This leads to the impurity-averaged susceptibility expression

$$ \tilde{\chi}_{\perp}(q, \omega) = \tilde{\chi}_{\perp}^{0}(q, \omega) / [1 - (1/2)g_{1}(T)\tilde{\chi}_{\perp}^{0}(q, \omega)]. \quad (3) $$

The upper bar on every quantity stands for the impurity averaging. $\tilde{\chi}_{\perp}^0$ is the bare diffusive susceptibility namely, the so-called «diffusion» [13]

$$ \tilde{\chi}_{\perp}^{0}(q, \omega) = \chi^{0*} \left( \frac{Dq^2 + \tau^{-1}}{Dq^2 + \tau^{-1} - i\omega} \right). \quad (4) $$

Here, $\chi^{0*} = 1/\pi v_F^*$ and $D = v_F^{*2}\tau_i$ is the spin fluctuation diffusion constant with $\tau_i$ the diffusion time ($l_i = v_F^*\tau_i$). $\tau^{-1}$ acts as a diffusion cut-off which includes the interchain escape frequency [2a] $\tau_{\perp}^{-1}$ and $\omega_e$ [13] that is, $\tau^{-1} = \tau_{\perp}^{-1} + \omega_e$. One must note that here $\tau_{\perp}$ is a transverse escape time of uniform spin fluctuations and for which the condition $\tau_{\perp} > \tau_i$ is satisfied in (4). The tunnelling energy of $q=0$ electron-hole excitation in a clean system is estimated to be $\tau_{\perp}^{-1} \sim t_{\perp}^2/E_F^*$, where $t_{\perp}$ is the interchain single-electron hopping amplitude. Therefore, $\tau_{\perp}^{-1}$ is expected to be temperature independent. The temperature dependence here comes from the two singular channels of 1D correlations, Cooper and Peierls, which «screen» $g_1$ [11] that is, $g_1(T) = g_1/[1 + (\pi v_F^*)^{-1}g_1 \ln(E_F^*/T)]$.

Using (3), and integrating in (1) over $q$ for $|q| \le l_i^{-1}$, we finally get for the temperature- and field-dependent diffusive part of the relaxation

$$ (T_1 T)^{-1}[q \sim 0, H] = \frac{2}{\pi} K_0 \left[ \left(1 - g_1/2\pi v_F\right) \left(1 - g_1(T)/2\pi v_F^*\right) \right]^{-2} C(\omega_e), \quad (5) $$

where

$$ C(\omega_e) = \sqrt{\tau_{\perp}/\tau_i}(\omega_e \tau_{\perp} + 1)^{-1/2} \operatorname{arctg} \left[ \sqrt{\tau_{\perp}/\tau_i} / \sqrt{\omega_e \tau_{\perp} + 1} \right]. $$
The limiting cases of this expression are of interest. i) At high field where $\omega_e \tau_\perp \gg 1$, $\omega_e \tau_i < 1$, we get the characteristic square-root field dependence: $(T_1 T)^{-1}[q \sim 0, H] \propto \chi(T)^2/\sqrt{\omega_e \tau_i}$. In the extremely high-field limit, where $\omega_e \tau_i \gg 1$, the spin diffusion is cut off by the field and $(T_1 T)^{-1}[q \sim 0, H] \propto \chi(T)^2/\omega_e \tau_i$ [2a, 3]. Therefore, the diffusive part of the relaxation vanishes in the high-field limit [2a]. ii) In the opposite limit, where $\omega_e \tau_\perp \to 0$, $(T_1 T)^{-1} \cdot [q \sim 0, H] \propto \chi^2$ becomes field independent. The «crossover» between the cases i) and ii) occurs for $\omega_e \tau_\perp \simeq 1$, in agreement with the result of Soda *et al.* [2a]. In contrast to this work, however, the uniform part of the relaxation enhancement is proportional to the square of the temperature-dependent uniform magnetic susceptibility. This is consistent with what has been already found on experimental grounds at high temperature in the context of (TMTTF)₂PF₆ [4b]. It follows then that in 1D, both $T_1^{-1}$ [$q \sim 0$] and $T_1^{-1}$ [$q \sim 2k_F$] provide deviations to the Korringa type of relaxation. In general, for 1D conductors the $q \sim 0$ enhancement is large and should dominate in the high-temperature domain, while it decreases monotonically following $\chi^2$ as T decreases. On the other hand, the staggered enhancement is weak at high temperature, while its power law singularity, that builds up for $\gamma_{1D} > 0$ and $T \to 0$, takes over at sufficiently low temperature. The situation is quite different for a quasi-1D conductor below its single-particle dimensionality crossover $T_{x1}$, where a Korringa-like profile (no enhancement) is recovered for both uniform and staggered $T_1^{-1}$ parts at $T < T_{x1}$ [4a, c, 14].

Furthermore, $T_{x1}$ is the energy scale that controls the field-induced depression of $T_1^{-1}[q \sim 0, H]$. At $T < T_{x1}$ ($d=2$), it is rather easy to show that $(T_1 T)^{-1}[q \sim 0, H] \propto \chi^2(T_{x1}) \ln[\tau_\perp/\tau_i/(\omega_e \tau_\perp + 1) + 1]$ which is logarithmically dependent on the field when $\omega_e \tau_\perp \gg 1$. In three dimensions $(T_1 T)^{-1}[q \sim 0, H]$ is field independent for $\omega_e \tau_i < 1$.

**Discussion.** – From the $T_1^{-1}$ data of fig. 1, it is clear that neither the high- nor the low-temperature relaxation properties are consistent with a Korringa-like behaviour. In the light of the results presented in the previous section, our data rather suggest that the quite large enhancement that takes place at low temperature compared to its much lower amplitude at high temperature is compatible with the characteristic temperature balance between the $q \sim 0$ and the $q \sim 2k_F$ type of spin fluctuations in one dimension. In order to support more quantitatively this interpretation, the low-field data of fig. 1 have been fitted to the sum $T_1^{-1} = T_1^{-1}[q \sim 0] + T_1^{-1}[q \sim 2k_F]$ obtained from (2) and (5). The important parameters needed to control the temperature dependence for the total relaxation are the exponent $\gamma_{1D}$, the coupling $g_1/2\pi v_F$ and the Fermi energy $E_F$. $K_0$ and $C(\omega_e)$ serve as temperature-independent adjustable constants.

Taking the range of values $E_F \simeq (1200 \div 1800)$ K for the TTF chains Fermi energy which are comparable with values obtained from band calculations of Kobayashi *et al.* [10], and with what is currently accepted for TTF-TCNQ [2, 3], equally good fits of the data were thus obtained for the intermediate coupling parameters $\gamma_{1D} \simeq 0.7$, $g_1/2\pi v_F \simeq 0.53 \div 0.63$ and for $C(\omega_e) = 10 \div 14$, $K_0/N(0)^2 \simeq 1.1 \cdot 10^5$. This leads to $g_2/2\pi v_F \simeq 0.6 \div 0.56$ and to $E_F^* \simeq (565 \div 650)$ K. The quality of the fit is particularly sensitive to $\gamma_{1D}$ and at fixed $\gamma_{1D}$, the value of C increases with $E_F^*$. This proves to be internally consistent with the previous estimate of $\tau_\perp$ which implies that $C \propto \sqrt{\tau_\perp/\tau_i} \propto E_F^*/t_\perp \sqrt{l_i}$ at low field thereby indicating a large anisotropy of the electronic spectrum. From fig. 1, it is clear that the present model with the above set of parameters give a very good account of the data. If we now turn our attention to the $T_1^{-1}$ field relaxation data at 300 K presented in fig. 2, the 40% or so $T_1^{-1}$ depression for $30 \le H \le 90$ kG can be reasonably accounted for by the square-root frequency dependence of $(T_1 T)^{-1}[q \sim 0, H] \propto (\omega_e \tau_\perp)^{-1/2}$ in (5), taking $\tau_\perp \simeq 3 \cdot 10^{-12}$ s $\simeq \omega_e^{-1}$ at $H_0 \simeq 19$ kG, for the escape time. From the above range of values for C obtained at $\omega_e \tau_\perp \ll 1$ one gets for the spin fluctuation scattering time $\tau_i = (3 \div 6) \cdot 10^{-14}$ s which is larger than the
transport scattering (inelastic) time commonly found in such systems at 300 K ($\tau_{tr} \sim 10^{-15}$ s) [3]. Using these values and the expressions (2) and (7), the field dependence of $(T_1 T)^{-1}$ at $T=300$ K, 200 K and 77 K are plotted in fig. 2. The predicted field-induced depression of $T_1^{-1}$ at 200 K and 77 K is, therefore, small.

Metallic properties at ambient pressure, a weak magnetoresistance, the absence of EPR signal and the existence of superconductivity under pressure were taken as indices of pronounced 3D properties of TTF $[Ni(dmit)_2]_2$. The $^1$H relaxation data presented in this work at ambient pressure indicate that as far as the TTF chains are concerned their electronic properties are 1D in agreement with the band calculation of Kobayashi et al. [10]. The absence of 3D SDW formation at low temperature in spite of strongly repulsive interactions can possibly be attributed to interstacks frustration effects due to the mismatch between the several Fermi wave vectors. Further experimental work is needed, however, to make a complete characterization of the dimensionality of correlations including resonance studies on the $Ni(dmit)_2$ chains which are now in progress.

One of us (CB) would like to thank the Centre National de la Recherche Scientifique (CNRS) for the program «Chercheur Associé».

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