MAGNETISM OF TTF-TCNQ AND RELATED
COMPOUNDS: PRESSURE EFFECTS

Denis Jerome, Gen Soda, J.R. Cooper, Jean-Marc Fabre, Louis Giral

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Denis Jerome, Gen Soda, J.R. Cooper, Jean-Marc Fabre, Louis Giral. MAGNETISM OF TTF-TCNQ AND RELATED COMPOUNDS: PRESSURE EFFECTS. Solid State Communications, 1977, 10.1016/0038-1098(77)91440-5. [hal-04996345](https://hal.science/hal-04996345v1)

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# MAGNETISM OF TTF-TCNQ AND RELATED COMPOUNDS: PRESSURE EFFECTS*

D. Jérome, G. Soda,† J.R. Cooper‡

Laboratoire de Physique des Solides, Université Paris-Sud, 91405 Orsay, France

J.M. Fabre and L. Giral

Laboratoire de Chimie Organique Structurale, USTL, 34060 Montpellier, France

(Received 5 December 1976; in revised form 12 January 1977 by P.G. de Gennes)

Pressure coefficients of the spin susceptibility, nuclear relaxation rates and resistivity have been measured in TTF-TCNQ, TMTTF-TCNQ and HMTSF-TCNQ. We point out that the very large pressure coefficients are not in agreement with the significantly smaller coefficients measured in optical absorption experiments under pressure. We propose an explanation of the magnetic properties of TTF-TCNQ and related compounds in terms of itinerant one dimensional antiferromagnetism. Using the Shiba-Pincus Hubbard model calculation we derive a value $U/4t_{\parallel}$ close to unity which points towards the importance of correlations in the TTF-TCNQ family.

## 1. INTRODUCTION

AN IMPORTANT PROBLEM for conducting charge transfer salts belonging to the TTF-TCNQ family is understanding their magnetic properties, especially the temperature dependence of the spin susceptibility and the interpretation of nuclear spin-lattice relaxation rates $1/T_1$ [1].

We shall first see that a serious question arises when we try to discuss the behaviour of $\chi_S$ and $1/T_1$ of TTF-TCNQ in terms of current pictures [2, 3]. In Fig. 1 we have sketched the experimental temperature dependence of the quantity $\chi_S^2 T_1 T$ which corresponds to two different magnetic field situations for $T_1$, namely the low field limit $\omega_e \tau_\perp < 1$ where $T_1$ is field independent and the high field limit $\omega_e \tau_\perp > 1$ where $1/T_1 \propto 1/\sqrt{H_0}$ [4], ($\omega_e$ is the electron Larmor frequency and $\tau_\perp$ is the life-time of a carrier on a given chain, namely the hopping time between chains).

The dashed line (low field) corresponds to the theoretical temperature dependence expected from a RPA calculation of $1/T_1$ in one dimensional conductor in the case of negligible correlation effects, namely $n(E_F)U \approx 0$.

The dashed line (high field) corresponds

(schematically) to the expected temperature dependence of $\chi_S^2 T_1 T$ in a one dimensional electron gas in the presence of strong electron-electron repulsions, namely $n(E_F)U \lesssim 1$.

The non existence of electron-electron repulsions was decided on the basis of a relatively satisfactory agreement between RPA theory and low field $T_1$ data [3].

However, the temperature dependence of the high field $T_1$ would be in better agreement with a strong electron repulsion picture.

Obviously, the interpretation of the experimental data Fig. 1 is not at all satisfactory. There are two problems at hand:

(i) the field dependence of $T_1$, which has been interpreted by the frequency dependence of the spin autocorrelation function in one dimensional conductors [4, 5, 17].

(ii) the temperature dependence of $\chi_S$ which has not yet received a satisfactory explanation.

The temperature dependence of $\chi_S$ has been related to the development of a pseudo-gap in the density of states, at the Fermi level, as $T$ becomes smaller than the mean-field Peierls temperature [2, 6]. However besides the temperature dependence of $\chi_S$ itself there is no evidence for a "strong fluctuations" picture in the TTF-TCNQ family [7].

In KCP however, direct evidence of the fluctuations has been derived from a pressure study of the conductivity [8].

Pressure (via increased interchain coupling) is efficient in suppressing the charge fluctuations existing between $T_p^0$ and the actual temperature $T_p$ of the phase

<footnote>* This work is part of a general study of the electronic properties of one-dimensional organic conductors supported by a CNRS ATP A 206 and a DGRST contract 75-7-0820.</footnote>

<footnote>† Present address: Institute of Physics of the University, Zagreb, Yugoslavia.</footnote>

<footnote>‡ Present address: Faculty of Sciences, Osaka University, Toyonaka, Osaka-560, Japan.</footnote>
<table><caption>Table 1. Summary of the pressure coefficients in the TTF-TCNQ family. The pressure band broadening of the HMTSF-TCNQ has not yet been measured. We assume, arbitrarily, a value equal to that of TSeF-TCNQ. The experimental value of the spin susceptibility is given at T = 300 K</caption><thead><tr><th></th><th>χ<sub>S</sub> experimental<br>10<sup>-4</sup> emu/mole</th><th>∂ ln χ<sub>S</sub>/∂P<br>% kbar<sup>-1</sup></th><th>B<br>10<sup>-2</sup> × μΩ cm K<sup>-2</sup></th><th>∂ ln B/∂P<br>% kbar<sup>-1</sup></th><th>∂ ln 1/T<sub>1</sub>/∂P<br>% kbar<sup>-1</sup></th><th>∂ ln t<sub>||</sub>/∂P<br>% kbar<sup>-1</sup></th></tr></thead><tbody><tr><td>TTF</td><td>6 [2]</td><td>-9 ± 2</td><td>2.2 [14]</td><td>-17 ± 1 [14]</td><td>-23 ± 2</td><td>+ 2 [13, 28]</td></tr><tr><td>TMTTF</td><td>5 [2]</td><td>-9 ± 1</td><td></td><td></td><td>-19.5 ± 2</td><td></td></tr><tr><td>TSeF</td><td>3.3 [10]</td><td></td><td>1.6 [12]</td><td></td><td></td><td>+ 2.2<br>[13, 28]</td></tr><tr><td>HMTSF</td><td>1.4 [11]</td><td></td><td>~ 0.3</td><td>-12 ± 2 [5]</td><td>-8 [17]</td><td>(+ 2.2)</td></tr></tbody></table>

<figure><img src="image_2.png" /><figcaption>Fig. 1. The $χ_S^2 T_1 T$ quantity as function of the temperature at low and high fields (full lines), according to reference [4]. Schematic behaviour of $χ_S^2 T_1 T$ for $n(E_F)U = 0$ and $n(E_F)U$ near unity in one dimensional RPA theory (dashed lines).</figcaption></figure>

<figure><img src="image_3.png" /><figcaption>Fig. 2. Pressure dependence of $1/T_1$ at 300 K in the low field limit. ▲ HMTSF-TCNQ, (at 45 MHz); ■ TMTTF-TCNQ, (at 18 MHz); ● TTF-TCNQ (at 18 MHz).</figcaption></figure>

transition, where 3 dimensional ordering occurs. Accordingly, we could expect qualitative changes in the temperature dependence of $χ_S$ between 53 and 300 K under pressure in TTF-TCNQ and in related compounds such as TMTTF-TCNQ.

## 2. EXPERIMENTAL

The proton spin lattice relaxation times have been measured in TTF-TCNQ, TMTTF-TCNQ and HMTSF-TCNQ, at room temperature, up to 10 kbar, in a helium gas high pressure equipment. The experimental data are presented in Fig. 2, (low field limit) and the pressure coefficients are reported in Table 1.

The spin susceptibility was measured directly by low field EPR experiments, at 40 MHz, using a crossed coil NMR spectrometer at ambient pressure, and using a single coil gated beam tube amplifier for the pressure experiments.

We have proved in a previous publication that all the static spin susceptibility for TMTTF-TCNQ and for TTF-TCNQ is included in the lorentzian NMR line [9].

<figure><img src="image_4.png" /><figcaption>Fig. 3. Pressure dependence of $χ_S$ in TTF-TCNQ normalized to the ambient pressure value; △ 340 K, ♦ 295 K, ▲ 220 K, ◦ 170 K.</figcaption></figure>
<figure><img src="image_5.png" /><figcaption>Fig. 4. Temperature dependence of χ_S in TMTTF-TCNQ at various pressures.</figcaption></figure>

The pressure and temperature domains of measurements are determined by the EPR line broadening occurring under pressure and (or) at low temperature.

The χ_S results are presented in Figs. 3 and 4, and the pressure coefficients listed in Table 1.

The resistivity of several metallic charge transfer salts follows a nearly quadratic temperature dependence in the conducting state [12]. The coefficient *B* of the *T*² law has been studied in TTF-TCNQ up to 6 kbar [14] and its pressure dependence has proved particularly large (see Table 1).

As can be seen from Table 1, large differences in the magnitude of χ_S and *B* are noticed among the various conducting compounds. Roughly speaking, χ_S and *B* are large in TTF-TCNQ but become smaller in the seleniurn salts, especially in HMTSF-TCNQ.

### 3. DISCUSSION

Admittedly, it is tempting to explain the temperature dependence of χ_S with the “large fluctuations” picture which is probably valid for KCP. Taking this point of view let us compare the temperature dependence of χ_S in both one dimensional conductors under pressure.

The susceptibility of KCP has been measured indirectly view the Knight shift of ¹⁹⁵Pt [15] under pressure.

A 20 kbar pressure weakens strongly the charge fluctuations and consequently shrinks the temperature domain (*T*<sub>P</sub>,*T*<sub>P</sub><sup>0</sup>) in which the latter may influence χ_S. In TMTTF-TCNQ however, besides a large pressure effect on χ_S no qualitative changes in the temperature dependence of χ_S are observed. (Fig. 5). Therefore the existence of a common explanation for the temperature dependence of χ_S in both 1D conductors KCP and TMTTF-TCNQ seems unlikely.

We shall now investigate some other possible explanations for the spin susceptibility

(i) Bernstein et al. [16] have proposed the possibility that the overlap between wave functions belonging to chains of different nature, namely TTF and TCNQ, may have a significant effect on the band structure. The effect of the hybridization is to dig a hole of approximate width equal to the interchain coupling [5] in the density of states at the Fermi level. Therefore the thermal excitation of carriers, through the so-called hybridization gap, gives rise with temperature to an initial increase of the Pauli spin susceptibility.

Since pressure enhances the interchain coupling [17], one can expect, at constant temperature, a decrease of the spin susceptibility as observed experimentally. However, similarly pressure should lead to a significant decrease of the longitudinal conductivity, in contradiction with the large increase which is actually observed [14].

(ii) Some variation in *n*(*E*<sub>F</sub>) and consequently in χ_S and T<sub>1</sub><sup>-1</sup> is expected to come from different bandwidths in various compounds, or from a band broadening occurring under pressure.

Since the tight binding band model seems to describe adequately the energy bands of π overlapping wave functions of these salts [18], some estimation of the pressure broadening can be performed.

The sound velocity is given by the energy dispersion spectrum of the longitudinal acoustic phonon [19]. We find $c = 3.8 \times 10^5$ cm sec⁻¹, in TTF-TCNQ. We therefore derive an elasticity coefficient $c_{11} = 3 \times 10^{11}$ dyne/cm² and a longitudinal compressibility $\partial \ln b/\partial P = -0.43\%$ kbar⁻¹. The reasonable assumption of a Slater parameter $bQ = 5$ for the π wave functions of TTF-TCNQ leads to the bandwidth pressure dependence $\partial \ln t_{\parallel}/\partial P = +2\%$ kbar⁻¹.

The pressure coefficient of the non-interacting electron bandwidth derived here is also in good agreement with the pressure dependence of the plasma frequency edge in TTF-TCNQ and TSeF-TCNQ [13].

The small pressure coefficients of the non interacting electron band cannot possibly account for the nearly 4 times larger coefficient measured for the spin susceptibility of TTF-TCNQ or TMTTF-TCNQ.

(iii) Comparing the spin susceptibility of TTF-TCNQ and HMTSF-TCNQ, Table 1, we can try to calculate χ_S for the two compounds from the knowledge of the intra-chain overlap integral *t*<sub>||</sub> and of the filling of the band. An estimate of *t*<sub>||</sub> can be made in the tight binding band model from the knowledge of plasma frequencies in TTF-TCNQ and HMTSF-TCNQ [11]. With a charge transfer of 0.55 and 0.74 e/molecule in TTF-TCNQ and HMTSF-TCNQ respectively [20, 21], *t*<sub>||</sub> and the effective mass along the *b*-direction become 0.23 eV, 2.8*m*<sub>0</sub> in TTF-TCNQ and 0.32 eV 2*m*<sub>0</sub> in HMTSF-TCNQ.
<figure><img src="image_6.png" /><figcaption>Fig. 5. Temperature dependence of χ<sub>S</sub> in KCP (left-hand scale) at 0 and 20 kbar and of χ<sub>S</sub>(T) - χ<sub>S</sub>(80 K) in TMTTF-TCNQ (right-hand scale) at 0 and 8 kbar.</figcaption></figure>

With these values we compute the spin susceptibility per formula unit, [$\chi_S^P = 4\mu_B^2 n(E_F)$], 0.7 × 10<sup>-4</sup> emu/mole in TTF-TCNQ and 0.30 × 10<sup>-4</sup> emu/mole in HMTSF-TCNQ.

The enhancements of the experimental values over the calculated values are 8 and 4 for TTF-TCNQ and HMTSF-TCNQ respectively.

We have seen above that neither the “strong fluctuations” model of 1D conductors nor the non-interacting electron band model give a satisfactory explanation for the spin susceptibility.

In the following we shall propose another approach, based on the existence of large electron-electron repulsions. We shall see that the picture of a strongly correlated 1D electron gas allows a consistent interpretation of all data available on the TTF-TCNQ family, including HMTSF-TCNQ.

An attempt to calculate the thermal properties of a 1D itinerant antiferromagnet has been performed with the Hubbard model for the half filled band situation [22]. The effect of non-half filling has been further taken into account but only at zero temperature by Shiba [23].

In the half-filled band treatment, the susceptibility of the itinerant antiferromagnet behaves like that of a paramagnet at high temperature, reaching a maximum when $kT_{max} \approx E_F/3$, and decreasing towards a zero temperature finite value as a result of short range ordering (calculated exactly for an infinite length chain).

The half-filled band zero temperature value of the susceptibility is attained within 10% at a temperature $\approx 1/5T_{max}$ [22].

Approximating the zero temperature value by the value of the susceptibility at 80 K, ($\chi_S(80\text{K}) = 2.7 \times 10^{-4}$ emu/mole in TTF-TCNQ and $\chi_S(80\text{K}) = 2.2 \times 10^{-4}$ emu/mole in TMTTF-TCNQ [2]) a comparison of the experimental results with the non-half filled band computation can be performed. We therefore derive the

existence of a finite $U/4t_\parallel$ ratio resulting in the enhancement of the low temperature susceptibility with respect to the non-interacting electron susceptibility. For TTF-TCNQ and TMTTF-TCNQ we obtain from the above comparison a value $U/4t_\parallel \sim 1.1$, (or $U \sim 1.1$ eV with the choice $t_\parallel \sim 0.25$ eV).

No high temperature calculation exists yet for the non-half-filled band case. However upon-half filling increases the susceptibility per electron at low temperature, and it is predictable that it will do likewise at high temperature [23].

Therefore, at the moment, we cannot account for the temperature dependence of the susceptibility of TTF-TCNQ between 100 and 300 K by the Shiba-Pincus model.

From the interpretation of $\chi_S(T)$ in TTF-TCNQ and from that of the nuclear relaxation rate we can say that correlations play an important role, and that $1 < U/4t_\parallel < 2$.

A value of $U/4t_\parallel$ close to unity in TTF-TCNQ seems reasonable. Had $U/4t_\parallel$ been found much larger, the ground state would have had to be that of a magnetic insulator, as in NMP-TCNQ where $U/4t_\parallel \ge 2$ [24].

In HMTSF-TCNQ however, $U/4t_\parallel$ seems to be smaller than unity. Correlations play therefore a weaker role in the magnetism and transport properties, as indicated by the pressure coefficient of $T^{-1}$ in HMTSF-TCNQ (Table 1) which is a factor 2 only larger than that provided by the pressure band broadening. Performing a similar comparison between the low temperature Hubbard model [23] and the susceptibility of TMTTF-TCNQ under pressure, we derive a value $U/4t_\parallel = 0.35$ at 8 kbar [13] we can therefore tentatively conclude that electron-electron repulsions depend rather strongly on pressure (decreasing from $\approx 1$ eV to $\approx 0.4$ eV under 8 kbar).

Following a similar interpretation for the other compounds in the TTF-TCNQ family we obtain $U \approx 0.8$ and 0.45 eV in TSeF-TCNQ and HMTSF-TCNQ respectively.

An interesting result of this pressure study is the large pressure dependence suggested for $U$. We can account for it as follows.

Several screening mechanisms have been proposed for $U$:

(i) intrachain screening. (ii) interchain screening among which we can distinguish: (a) that originating in the free carriers and, (b) that originating in the excitonic mechanism of high polarizability molecules [25].

The excitonic screening can be pressure dependent since the polaron binding energy $E_B$ is very sensitive to the distance $R(N-S(Se))$, varying roughly like $R^{-4}$ or possibly $R^{-6}$. The effective interaction given by this screening mechanism is $U_0 - 2E_B$ [26]. With the starting
values $U_0 = 2$ eV and $2E_B = 1$ eV the pressure dependence of $U$ which was observed in TTF-TCNQ is accounted by a transverse compressibility smaller than $1\% kbar^{-1}$.

Actually the transverse compressibility of TTF-TCNQ measured by neutron diffraction techniques [27] is significantly weaker; $0.32\% kbar^{-1}$.

As the molecules are likely to rotate under pressure, a macroscopic determination of the compressibility can not give enough information for the calculation of the pressure dependence of the excitonic screening.

We shall now attempt, on the basis of large correlations, to propose a possible explanation for the resistivity.

At low temperature, short range order exists in the 1D itinerant antiferromagnet. As temperature is raised there occurs through creation of spin fluctuations a disorder in the spin alignment. Above a characteristic temperature of the spin system such as $kT_{ex} \sim J$, (intra-chain spin coupling) short range order is totally destroyed. Spin fluctuations may scatter the carriers through an inelastic scattering with exchange of momentum $2k_F$ and energy transfer $\sim kT_{ex}$ [28]. The electron relaxation time is then given in terms of the interaction between carriers and spin waves by

$$ \frac{1}{\tau} \sim \frac{G^2}{t_{\parallel}} \left( \frac{T}{T_{ex}} \right)^2 . $$

This process contributes to the resistivity up to a temperature which is of the order of $T_{ex}$ ($\sim 350-400$ K in TTF-TCNQ). The mechanism involved here bears some resemblance with the scattering of carriers against spin fluctuations in nearly magnetic metals [29]. The pressure dependence of $1/\tau$ going like $\chi_S^2/t_{\parallel}$ since $\chi_S \sim T_{ex}^{-1}$ is in very good agreement with the data of Table 1 for TTF-TCNQ.

This model introduces the necessary connection between $\chi_S$ and resistivity, and provides a possible explanation for the temperature dependence of the resistivity in strongly correlated organic conductors such as TTF-TCNQ.

This mechanism for resistivity, though appealing, has an inherent difficulty, since the free carriers and the spin fluctuations degrees of freedom to the same system of electrons. Therefore, although momentum is trans-

ferred from one degree of freedom to the other it is not clear how it is dissipated [30]. One way out of this difficulty is to ascribe spin waves and free carriers to different bands or chains. Strictly speaking the treatment of the resistivity presented above applies to a 3-dimensional magnetic electron gas. However it seems that for quasi 1D systems, as long as RPA applies (namely for the large 3D coupling situation) a law $\rho \sim \chi_S^2 T^2$ for the resistivity is derived in close agreement with the crude picture presented in this article [31].

In conclusion we have reported in this paper the values of pressure coefficients of susceptibility, nuclear relaxation time and resistivity of TTF-TCNQ and some related compounds.

We have shown that the particularly large pressure coefficient does not allow an interpretation based solely on a non-interacting electron picture. We emphasize that the usual experimental test for the presence of electron-electron interactions (the Korringa law) may be ambiguous because of the special frequency dependence of $T_1$ in 1D systems [4]. Using the simplest Hubbard model for one dimensional itinerant magnetism, we derived a value $U/4t$ which is close to unity in TTF-TCNQ and which becomes smaller under pressure.

Basing their argument on optical absorption data, other authors have argued for the existence of correlation effects in a large variety of charge transfer compounds [32] (including Li-TCNQ [33], NMP-TCNQ, TTF-TCNQ, TSeF-TCNQ and HMTSF-TCNQ). A common value $U \sim 1$ eV was attributed to all these compounds, suggesting therefore that the TCNQ chains may be strongly correlated.

We have shown, however, in the present report, that although large $U$ values are plausible for TTF-TCNQ, significantly smaller $U$ values are needed for HMTSF-TCNQ and even for TSeF-TCNQ. In this work we have not investigated the implications of the correlated model on the nuclear relaxation rate. The behaviour of the relaxation rate will be the matter of an extended study in a forthcoming publication [34].

*Acknowledgements* – We thank M. Weger and S. Barišić for useful discussions and C. Berthier, L. Zuppiroli and C. Weyl for their help at an early stage of the work. We are grateful to K. Bechgaard with whom we had fruitful cooperation. We thank G. Delplanque and G. Malfait for their help in the experimental techniques.

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