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# Un réexamen du conducteur organique (TMTSF)2NO3

Denis Jerome

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Denis Jerome. Un réexamen du conducteur organique (TMTSF)2NO3. Comptes Rendus de l'Académie des Sciences - Series III - Sciences de la Vie, 1993. hal-05000207

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# The organic conductor (TMTSF)₂NO₃ revisited

Denis JÉROME

**Abstract** – This Note proposes an interpretation for the ambient pressure spin density wave transition of the organic conductor (TMFSF)₂NO₃ in terms of an excitonic instability of 2-D nested semimetallic pockets. This picture provides a very simple explanation for the absence in this compound of spin density wave phases induced under magnetic field.

## Un réexamen du conducteur organique (TMTSF)₂NO₃

*Résumé* – Cette Note suggère une interprétation de la phase à onde de densité de spin observée dans (TMTSF)₂NO₃ à pression atmosphérique en terme d'une instabilité excitonique entre poches semimétalliques bidimensionnelles emboîtées. Ce modèle présente l'avantage d'expliquer simplement l'absence de phases à ondes de densité de spin induites par le champ magnétique dans ce composé.

*Version française abrégée* – Parmi les divers composés qui constituent la série des sels de Bechgaard (TMTSF)₂X conducteurs quasi unidimensionnels (Bechgaard *et al.*, 1980) l'un deux (X=NO₃) se distingue par une mise en ordre originale de l'anion NO₃ à basse température.

Cet anion de géométrie triangulaire, donc non centrosymétrique, est situé sur un centre de symétrie de la structure cristalline. La minimisation de l'entropie impose au-dessous d'une température TAO une orientation des anions soit uniforme soit alternée suivant les trois axes cristallographiques principaux (Pouget, 1987). En ce qui concerne (TMTSF)₂NO₃ le vecteur d'onde Q caractérisant la mise en ordre des anions au-dessous de TAO = 45 K s'écrit Q=(1/2, 0, 0). La présence d'une telle modulation implique un repliement de la structure de bande autour des plans kx = ±π/2 a et une évolution de la surface de Fermi de quasi unidimensionnelle et métallique au-dessus de 45 K à quasi bidimensionnelle et semimétallique au-dessous de la température d'ordre des anions. Cette modification de surface de Fermi est illustrée sur la figure. La mise en ordre des anions n'est accompagnée que par une faible anomalie de la conductivité puisque malgré une forte diminution de la densité de porteurs, la vitesse au niveau de Fermi dont dépend la conductivité peut ne pas être fortement affectée par la transition. Le coefficient Seebeck est par contre très sensible à cette transition puiqu'à basse température il devient la somme pondérée de coefficients d'électrons et de trous. Les résultats expérimentaux (Bechgaard *et al.*, 1980) indiquent donc clairement que la stabilisation de l'état à onde de densité de spin au-dessous de 10 K (Tomić *et al.*, 1988) ne peut être interprétée par les propriétés d'emboîtement d'une surface Q-1-D comme c'est le cas pour X=PF₆ ou ClO₄ (état trempé; Tomić *et al.*, 1983).

Nous suggérons que l'état ODS de (TMTSF)₂NO₃ est la conséquence de l'emboîtement de poches d'électrons et de trous bidimensionnelles. Comme l'indique le modèle orthorhombique de la figure, un vecteur d'onde commensurable pour l'ODS Q=(1/2, 1/2) est possible dans ce cas en accord avec l'observation d'un champ électrique de décrochage de l'onde environ dix fois supérieur à celui d'une onde incommensurable comme pour PF₆ (Tomić *et al.*, 1989).

L'état fondamental ODS peut être lui aussi un semimétal bidimensionnel caractérisé par des poches d'épaisseur t_b²/t_a² suivant ka, où ta et tb représentent la dispersion suivant a

<footnote>Note présentée par Jacques FRIEDEL.</footnote>
et *b* respectivement, en accord avec l'observation d'oscillations de magnétorésistance à basse fréquence (≈65-75 T) (Kang *et al.*, 1990; Audouard *et al.*, 1993; Biškup *et al.*, 1993).

Dans ce modèle, l'absence d'état fondamental ODS sous haute pression est liée à une détérioration de l'emboîtement bidimensionnel due à l'accroissement des couplages transversaux. Une telle situation ne serait pas propice à la stabilisation de phases ODS sous forts champs magnétiques puisque sous haute pression les orbites sont déjà fermées en champ nul.

Ces remarques permettent de rendre compte de l'absence de phases ODS induites par un champ magnétique dans $NO_3$ sans faire appel à un modèle reliant l'absence d'état supraconducteur à celle de phases ODS induites sous champ magnétique.

The so called “Bechgaard salts” comprise the family of quasi 1-D (Q-1-D) conductors with formula $(TMTSF)_2X$ where $TMTSF$ is the organic molecule tetramethyltetraselenafulvalene and $X$ is a monoanion which can be either centrosymmetric ($PF_6$, $AsF_6$) or non-centrosymmetric ($ClO_4$, $ReO_4$, $NO_3$, etc.) (Bechgaard *et al.*, 1980).

The role played by these anions on the physical properties depends critically on their particular symmetry. Centrosymmetric anions set the lattice periodicity and make the Q-1-D band half-filled. However, non-centrosymmetric anions can have a more dramatic effect since they occupy inversion centers in the structure (Pouget, 1987). Consequently, they are statistically disordered at high temperature with two equally occupied inversely related orientations, whereas at low temperature the minimization of the entropy imposes an ordering at $T_{AO}$ below which the anions adopt either a uniform or an alternate orientation along the three crystallographic axes. The new Bragg reflections below $T_{AO}$ are governed by the wave vector **Q**.

In $(TMTSF)_2ClO_4$ (from now on we shall not write the organic molecule), the ordering $Q=(0, 1/2, 0)$ at 24 K (Pouget, 1983) gives rise to an electron dispersion suppressing the spin density wave (SDW) phase which otherwise is stable in the absence of anion order (quenched sample) (Tomić *et al.*, 1983). The superconducting phase of such an anion ordered state ($T_c=1.2$ K) (Bechgaard *et al.*, 1981) is destroyed by orbital effects under a small magnetic field of 1 KOe //c*. In addition, SDW phases are stabilized at low temperatures in moderate magnetic fields (Ribault *et al.*, 1983).

$ReO_4$ behaves differently since the $Q=(1/2, 1/2, 1/2)$ ordering at 180 K wipes out the whole Fermi surface and the ambient pressure ground state is a non-magnetic insulator with a well defined energy gap of about 2,000 K (Pouget *et al.*, 1982). The anion ordering $Q=(1/2, 1/2, 1/2)$ of $ReO_4$ shifts to $(0, 1/2, 1/2)$ under pressure (Moret *et al.*, 1986) making the ground state superconducting at 1.7 K under 10 kbar (Parkin *et al.*, 1981).

Field induced spin density wave phases (FISDW) are also observed at high fields (Kang *et al.*, 1991 *a*) very much like the phenomenon which is observed in the compound $ClO_4$ (Pouget *et al.*, 1982). FISDW phases have been understood within the framework of a mean-field theory of repulsively interacting electrons (Héritier *et al.*, 1984; Yamaji, 1985).

However, Yakovenko (1989) has suggested a model going beyond the mean field theory in which the sequence of FISDW phases takes place only if the sign of the interaction between electrons at zero field corresponds to superconductivity, i. e. negative. This suggestion has received some support with the unusual behaviour of $NO_3$ in which the conducting state stabilized at low temperature under pressure reveals neither superconductivity (Mazaud, 1981) nor FISDW phases (Kang *et al.*, 1990).
We suggest in this letter an alternate approach which explains the absence of FISDW phases in NO₃. This model is based on the idea of a nested 2-D excitonic phase for the stabilization of the SDW phase below 10 K at ambient pressure (Bechgaard *et al.*, 1980; Tomić, 1988).

<figure><img src="image_3.png" /><figcaption>Schematic Fermi surface for a Q-1-D conductor (left) and a semimetallic Fermi surface below T AO (right) with Q = (1/2, 0).

Vue schématique d'une surface de Fermi d'un conducteur quasi unidimensionnel (gauche) et de la surface au-dessous de T AO (droite) avec Q = (1/2, 0).</figcaption></figure>

The electronic structure of the Q-1-D conductor is strongly affected by the anion ordering at Q=(1/2, 0, 0) occuring at T AO=45 K (Moret et al., 1983). The electron dispersion changes from that of a 1-D conductor (1 hole/unit cell) to that of a compensated two dimensional semimetal below T AO, neglecting the very weak coupling along the c-direction. The figure displays an illustration of this transition for an orthorombic (2-D) structure.

The Q-1-D metal to 2-D semimetal transition may not induce any significant modification of the conductivity since this quantity is given by the integral of the electron velocity over the Fermi surface (Mott and Jones, 1936) which is not strongly modified by the ordering as long as the anion induced gap remains small compared to the transverse coupling t<sub>b</sub> (Grant, 1983). However, this transition should be visible through thermopower measurements. At high temperature the Seebeck coefficient is determined by the sign of the carriers (holes) and shows a linear temperature dependence (Bechgaard *et al.*, 1980). Below 45 K, the Seebeck coefficient becomes an average of the individual thermopower from each electron and hole pockets weighted by their conductivities, namely S = (σ<sub>1</sub> S<sub>1</sub> + σ<sub>2</sub> S<sub>2</sub>)/(σ<sub>1</sub> + σ<sub>2</sub>), where S<sub>1</sub> and S<sub>2</sub> have opposite signs. The sharp drop of S(T) which has been observed in NO<sub>3</sub> below 45 K (Bechgaard *et al.*, 1980) supports the model of metal to semimetal transition. Consequently, the stabilization of the SDW phase at 10 K cannot be explained by the regular model based on the nesting of Q-1-D Fermi surfaces. However, good nesting can be inferred in the semimetallic regime between electron and hole tubes separated by the wave vector Q=(1/2, 1/2) and could in turn lead to an excitonic transition (Jérome *et al.*, 1967).
The excitonic transition which is proposed here takes advantage of the nesting of the 2-D pockets whereas in the original excitonic instability proposed for a 3-D semimetal (Jérome *et al.*, 1967) without nesting the transition temperature was restricted only to a very low temperature regime ($T_c$ less than the exciton binding energy).

Several consequences can be inferred from this model.

(i) Unlike PF₆, the wave vector of the SDW phase at ambient pressure could be commensurate, $Q=(1/2, 1/2)$. This is supported by the observation of a threshold field for non linear conduction which is about ten times larger in NO₃ than in PF₆ (Kang *et al.*, 1991 *b*; Tomić *et al.*, 1989).

(ii) The ambient pressure SDW phase should have the structure of a semimetal corresponding to the non-tested portions of the original 2-D tubes with very small 2-D pockets as evidenced by the magnetoresistance oscillations with frequency 75 T (Kang *et al.*, 1990; Audouard *et al.*, 1993; Biškup *et al.*, 1993) related to $t_b=t_b^2/t_a$ similar to the frequency of the FISDW phases in PF₆ (Kang *et al.*, 1991 *a*).

(iii) Increasing pressure deteriorates the 2-D nesting and suppresses the SDW phase in agreement with the experiments (Mazaud, 1981).

(iv) No FISDW phases can thus be stabilized at large magnetic fields at variance with open Fermi surface conductors since the electronics structure is already at zero field that of a semimetal with closed orbits.

*In conclusion*, we have suggested that the absence of FISDW phases in NO₃ can easily be understood if the ambient pressure SDW phase is a 2-D nested excitonic phase. This approach decouples the superconducting instability from the possibility to stabilize SDW phases at high fields.

It is important to know whether the absence of superconductivity in NO₃ is an intrinsic effect [possible lowering of N(E<sub>F</sub>) in the semimetallic regime or suppression of the interchain pairing mediated by the exchange of antiferromagnetic spin fluctuations (Bourbonnais, 1987) or the consequence of a large amount of impurities in this particular compound]. It would also be very interesting to search for magnetoresistance oscillations in the semimetallic regime stabilized at zero temperature under pressure with a frequency related to $t_b$ in the range of 200-300 T [so far not observed (Kang *et al.*, 1990)]. At high frequency oscillation of this kind has recently been observed at high fields in the zero pressure SDW phase (Audouard *et al.*, 1993). Further evidences for the commensurability of the ambient pressure SDW phase should also be looked for by non-linear transport and NMR measurements.

I acknowledge fruitful discussions with G. Montambaux, W. Kang, and J. P. Pouget.

Note remise le 28 juin 1993, acceptée le 20 juillet 1993.

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<footnote>Laboratoire de Physique des Solides associé au CNRS, Université Paris-Sud, 91405 Orsay, France.</footnote>