# Cooperative Phenomena in (TMTSF)2ClO4 NMR Relaxation

F Creuzet, C Bourbonnais, Denis Jerome, K Bechgaard, A Moradpour

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F Creuzet, C Bourbonnais, Denis Jerome, K Bechgaard, A Moradpour. Cooperative Phenomena in (TMTSF)2ClO4 NMR Relaxation. Molecular Crystals and Liquid Crystals, 1985, 119 (1), pp.45 - 51. 10.1080/00268948508075132. hal-05010464

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## Molecular Crystals and Liquid Crystals

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## Cooperative Phenomena in (TMTSF)₂ClO₄ NMR Relaxation

F. Creuzetª, C. Bourbonnaisª, D. Jéromeª, K.

Bechgaardª & A. Moradpourª

ª Laboratoire de Physique des Solides (associé au CNRS) Bât. , 510, Université Paris-Sud, 91405, Orsay, France

Published online: 17 Oct 2011.

**To cite this article:** F. Creuzet, C. Bourbonnais, D. Jérome, K. Bechgaard & A. Moradpour (1985) Cooperative Phenomena in (TMTSF)₂ClO₄ NMR Relaxation, Molecular Crystals and Liquid Crystals, 119:1, 45-51

**To link to this article:** http://dx.doi.org/10.1080/00268948508075132

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COOPERATIVE PHENOMENA IN (TMTSF)₂ClO₄ NMR RELAXATION

F. Creuzet, C. Bourbonnais, D. Jérôme, K. Bechgaard and A. Moradpour

Laboratoire de Physique des Solides (associé au CNRS)
Bât. 510, Université Paris-Sud, 91405 Orsay (France)

Abstract - ¹H and ⁷⁷Se NMR relaxation data on relaxed (TMTSF)₂ClO₄ are presented and an interpretation is proposed for the non-Korringa behaviour which is based on the existence of one-dimensional 2kF spin correlations.

INTRODUCTION

The organic conductor tetramethyltetraselenafulvalenium-perchlorate (TMTSF)₂ClO₄ is well known for its conducting properties at ambient pressure for all temperatures and in a wide range of magnetic fields, provided great care is taken to cool the sample slowly (10 K/hour for the so-called R-state) ¹. We have performed NMR relaxation rate measurements on both ¹H and ⁷⁷Se (I = 1/2) nuclei in this metallic domain, in order to investigate the low-temperature response of the electron gas. As it was suggested in a previous work ² we have found that the usual Korringa law is not verified in this system. In the present work, the T⁻¹ behaviour at low temperature will be correlated with the predictions of standard quasi-1D models. The large T₁ anomaly between 1.2 and 40 K in fields extending from 1 kOe up to 64 kOe is interpreted as the existence of well developed one dimensional spin-density wave (SDW) cooperative phenomena, emphasizing that the temperature dependence of 1/T₁ is not compatible with a single-particle description of the conduction state.

EXPERIMENTAL RESULTS

Details concerning the preparation and the structure of the (TMTSF)₂X compounds can be found elsewhere ³. For both ¹H and ⁷⁷Se nuclei, T₁ was determined recording the free induction signal after a π-π/2 sequence, changing the delay between the two pulses. An exponential decay was observed over more than one decade.
Data of <sup>77</sup>Se relaxation rates at various fields in relaxed (<i>TMTSF</i>)<sub>2</sub>ClO<sub>4</sub> are collected in Fig. 1. the Korringa law is fairly

<figure><img src="image_3.png" /><figcaption>FIGURE 1</figcaption></figure>

<sup>77</sup>Se lattice relaxation rate in relaxed (<i>TMTSF</i>)<sub>2</sub>ClO<sub>4</sub>.

o H<sub>o</sub> = 64.2 kG // b'

● H<sub>o</sub> = 31.9 kG // b'

× H<sub>o</sub> = 21.0 kG // b'

Δ H<sub>o</sub> = 6.0 kG powder

□ H<sub>o</sub> = 31.9 kG // c

well obeyed, without field dependence in the higher temperature regime 25-40 K. At lower temperature, the spin-lattice relaxation rate is strongly enhanced, compared to the expected Korringa behaviour, and a field dependence can be clearly detected (between 6 and 20 K). Below 6 K or so, another Korringa regime seems to be approached. The linewidth was found rather large compared to 1/γT<sub>2</sub> (22 G at 30 kG, 44 G at 64 kG) but almost linear in field and may be attributed to a distribution of Knight-shifts corresponding to different <sup>77</sup>Se sites.

For <sup>1</sup>H, the results are quite similar though as already studied before <sup>4-5-2</sup>, it is necessary to estimate the contribution to the relaxation rate due to the quantum tunnelling of methyl groups at low temperature. This contribution was extrapolated with the assumption of an activated behaviour <sup>6</sup>. Figure 2 displays the only points for which the relaxation is due to interaction with the
<figure><img src="image_4.png" /><figcaption>FIGURE 2</figcaption></figure>

¹H spin lattice relaxation in relaxed (TMTSF)₂ClO₄.

□ H₀ = 1.1 kG powder

● H₀ = 4.0 kG // b'

○ H₀ = 12.2 kG // b'

electron spins. At this stage, the 77Se and ¹H results scale together with a ratio of hyperfine constants [a(Se)/a(H)]² ~ 2.10³. Although the field dependence between 4 and 12kOe is reliable, the large enhancement of the relaxation rate at 1 kOe cannot be easily attributed to an intrinsic electronic effect, since parasitic

relaxation due to magnetic impurities cannot be completely ruled out at low fields. However, no important effect of paramagnetic impurities has been reported so far via susceptibility measurements in these materials prepared by electrochemical method, and this effect may be attributed to the proximity of the superconducting transition.

## THEORY

Clearly, these data are not consistent with the single-particle description of the conducting state and here, we will try to correlate the results with the predictions of a low-dimensional theory. The general expression of $T_l^{-1}$ is ⁸:

$$T_l^{-1} = \gamma_N^2 |A|^2 \frac{\chi''(\vec{q}, \omega_N)}{\tanh(\omega_N/2T)}, \quad (1)$$

where A is the contact hyperfine matrix element taken as q independent, γN gives the gyromagnetic ratio of the nucleus and χ''⊥ stands for the imaginary part of the retarded SDW correlation function. We have calculated, in the g-ology picture, the contribution of the 1D-2kF component of χ''⊥ (the q ~ 0 component being
negligible to the $T_1^{-1}$ enhancement since the uniform magnetic susceptibility is constant below 50 K $^7$). In order to predict SDW enhancement, we assume that the interactions can be described within the "g-ology" picture and we will focus our attention on the repulsive and gapless ($g_1, g_2, g_3$) domain where both SDW and triplet pairing can occur $^{9-10=11=12}$.

We keep in mind that the three-dimensional (3D) electronic motion will take place at low temperature, due to interchain single electron hopping. The cross-over temperature $T_x$ was shown to be reduced in comparison with the non-interacting electron gas value $T_x^° = t_⊥/π^{14-15}$, because of strong intrachain correlations : $T_x = T_x^° (t_⊥/E_F)^{α/1-α}$ where $1>α>0$ depends on the interactions $^{16}$.

In the 1D regime, the formula (1) can be modified, using the Kramers-Krönig relation :

$$ \frac{\chi''_{\perp} (q+2k_F, \omega_N)}{\omega_N} \approx \frac{2}{(\eta+1)} \bar{\chi}'_{\perp}(T) \quad \text{for } \omega_N \ll T; |v_F q| < T \quad (2) $$

where $\bar{\chi}'(T) = \frac{\partial \chi'_1}{\partial \ln(E_o/T)}$ and $\chi'_1$ is the real part of the total retarded susceptibility. The sum around $2 k_F (|v_F q| < T)$ leads to :

$$ T_1^{-1} = \frac{4\gamma_N^2 |A|^2}{\pi^2 v_F (\eta+1)} \cdot T \cdot \chi'_\perp(T) \quad (3) $$

This is obtained from the asymptotic properties of $\chi'_\perp(T,q,\omega) \sim (\text{Max}(T,v_F q,\omega)/E_o)^{-\eta} 9-16$. $E_o$ is a cut-off energy (temperature) for strong intrachain SDW enhancement characterized by a positive power law exponent $\eta$. Scaling arguments for $\bar{\chi}'$ with $E_o$ tell us that $0<E_o<E_F$. $E_o$ is very difficult to predict for organic compounds and it will be taken as an adjustable parameter of the problem. For $T_x < T < E_o$ the expression for $T_1^{-1}$ becomes : $T_1^{-1} = CT(T/E_o)^{-\eta}$. Here C is a constant which gives the slope of $T_1^{-1}$ vs T at $T > E_o$.
<figure><img src="image_5.png" /><figcaption>FIGURE 3</figcaption></figure>

When $T \to T_x$, the enhancement saturates at $(T_x/E_o)^{-\eta}$ because of 3D couplings, and if we neglect the possibility of a true phase transition below $T_x$, the spin lattice relaxation rate approaches a 3D renormalized Korringa behaviour down to $T = 0$. This typical behaviour of $T_l^{-1}$ is shown on Fig. 3a for the value of $\eta$ ($\eta = 0.9$; $\eta = 1.2$).

DISCUSSION

From the low field experimental data (Fig. 3b), a departure from the Korringa behaviour is clearly seen at $E_o \approx 25$ K. Using the $T_l^{-1}$ expression, the fit of the power law enhancement for $T < E_o$ gives $\eta \approx 1.1$, indicating the presence of strong SDW effects. The crossover temperature appears to be at $T_x \approx 8$ K. From the accepted values of $T_x^\circ$ found in the literature¹⁵ for (TMTSF)₂ClO₄ ($T_x^\circ = t_\perp/\pi \approx 30..80$ K), this means strong 1D collective effects. With the accepted range of anisotropy $t_\perp/E_F \approx 1/10..1/30$¹⁷⁻¹⁸ $T_x \approx 8$K implies $\alpha = 1/4..1/2$ which is compatible with $\eta$ and quite reasonable for organic conductors. Furthermore, the enhancement factor $(T_x/E_o)^{-\eta} \approx 3.5$ agrees pretty well with the observed one which is equal to 3 or so. Beside the apparent residual component of $T_l^{-1}$ as $T \to 0$, the relevant linear shape is essentially parallel to the one predicted.

The effect of large magnetic field (64 kOe) may be understood as orbital effects which reduce $t_\perp$ and consequently the cross-
over temperature. One must also note that the magnetic anisotropy of couplings is increased at low temperature and high field, and this can modify the SDW enhancement. The field dependence reported by Azevedo et al. on $(\text{TMTSF})_2\text{PF}_6$ has to be reinterpreted taking into account these new phenomena. Moreover, recent data at room temperature$^{21}$ rule out the possibility of spin diffusive processes for the $T_i^{-1}$ field dependence at low temperature.

## CONCLUSION

We have presented new NMR results which cannot be explained by usual single particle theory. However, the good agreement between experiment and a quasi-1D theoretical approach of $T_i^{-1}$ strongly suggests that 1D cooperative phenomena are effective down to 8 K or so in $(\text{TMTSF})_2\text{ClO}_4$. We want to emphasize that, from the 1D theoretical point of view, electron-hole SDW fluctuations can coexist with triplet pairing ones. Therefore, the strong $T_i^{-1}$ enhancement for fields smaller than the superconducting critical field ($H_0 \sim 1$ kOe) observed at low temperature may reflect some magnetic character for the precursor effects occuring in the vicinity of the superconducting instability which have been also revealed by other studies$^{23}$. Furthermore, this work suggests that 1D physics should be taken into account down to low temperatures.

## REFERENCES

1. Takahashi T., Jérôme D., Bechgaard K. J. Phys. Lett. **43** (1982) L565.
Tomic S., Jérôme D., Monod P., Bechgaard K., J. Phys. Lett. **43** (1982) L839.

2. Takahashi T., Jérôme D., Bechgaard K., J. Physique **45** (1984) 945.

3. Bechgaard K., Carneiro K., Rasmussen F.B., Olsen M., Rindorf G., Jacobsen C.S., Pedersen H., Scott J.C., J. Am. Chem. Soc. **103** (1981) 2440.

4. Scott J.C., Pedersen H.J., Bechgaard K., Phys. Rev. B24 (1981) 475.

5. Creuzet F., Takahashi T., Jérôme D., Fabre J.M., J. Phys. Lett. **43** (1982) L755.

6. We have used the classical formula :
$$T_1^{-1} = c\left[\frac{\tau_c}{1+\omega^2\tau_c^2} + \frac{4\tau_c}{1+4\omega^2\tau_c^2}\right] \text{ with } \tau_c = \tau_o \exp\left(-\frac{E}{kT}\right)$$

7. Miljak M., Cooper J.R., Bechgaard K., J. Physique C3 44 (1983) 893.

8. Moriya T., J. Phys. Soc. Japan 18 (1963) 516.

9. Solyom J., Adv. Phys. 28 (1979) 201.

10. Barisic S., Brazovskii S., Recent Development in Condensed Matter Physics, Ed. J. Devreese (Plenum, N.Y.) vol. 1 (1981) 317.

11. Emery V.J., Bruinsma R., Barisic S., Phys. Rev. Lett. 48 (1982) 1039.

12. Gorkov L.P., JETP Lett. 34 (1981) 578.

13. Bourbonnais C., this conference and to be published.

14. Barisic S., J. Physique C3 44 (1983) 991.

15. Emery V.J., J. Physique C3 44 (1983) 977.

16. Luther A., Peschel I., Phys. Rev. B9 (1974) 2911.

17. Jérôme D., Schulz H.J., Adv. Phys. 31 (1982) 299.

18. Jacobsen C.S., Tanner D.S., Bechgaard K., Phys. Rev. Lett. 46 (1981) 1142.

19. Azevedo L.J., Schirber J.E., Engler E.M., Phys. Rev. B (to be published).

20. Azevedo L.J., Schirber J.E., Engler E.M., Phys. Rev. B27 (1983) 5842.

21. Stein P.C., Thesis Université Paris-Sud Orsay, to be submitted.

22. A more detailed version of this work will appear in J. Physique Lett. 45 (1984) L755-765.

23. D. Jérôme, this conference.