SUPERCONDUCTING AND MAGNETIC
INSTABILITIES IN(TMTSF)2X AND
(BEDT-TTF)2CONDUCTORS

Denis Jerome, François Creuzet, Claude Bourbonnais

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Denis Jerome, François Creuzet, Claude Bourbonnais. SUPERCONDUCTING AND MAGNETIC IN-STABILITIES IN(TMTSF)2X AND (BEDT-TTF)2CONDUCTORS. Physica B, 1986. hal-05011633

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Distributed under a Creative Commons Attribution 4.0 International License
SUPERCONDUCTING AND MAGNETIC INSTABILITIES IN (TMTSF)₂X AND (BEDT-TTF)₂CONDUCTORS

D. JEROME, F. CREUZET and C. BOURBONNAIS

Laboratoire de Physique des Solides, Université Paris-Sud, 91405 ORSAY (France)

The experimental investigation of the antiferromagnetic ground states in the (TMTSF)₂X series supports the models predicting magnetic long range order driven either by interchain exchange of 1D-2kF spin correlations or by 3D nesting of the Q-1-D Fermi surface. In the second situation ordering occurs at a temperature below the one-particle dimensionality cross-over Tₓ. We give experimental evidences supporting the pressure and magnetic field dependence of Tₓ.
We have also reviewed some necessary experimental requirements for the stabilisation of bulk superconductivity at 8.1 K in the Q-2-D strongly correlated conductor β-(BEDT-TTF)₂I₃.

### 1. ORGANIC SUPERCONDUCTIVITY ABOVE 8 K

Almost three years after superconductivity has been discovered in the (TMTSF)₂X series of organic conductors ¹ with a maximum critical temperature of 1.25 K for (TMTSF)₂ClO₄ under zero pressure ², the organic molecule, BEDT-TTF ³, has led to a new series of organic superconductors. Among the BEDT-TTF salts the first leading to superconductivity has been (BEDT-TTF)₂ReO₄, with a T_c of 1.4 above 5 kbar ⁴. Later, in 1985, Professor Schegolev's group published a T_c of 7.4 K in the β-phase of the triiodine salt of BEDT-TTF ⁵, namely (BEDT-TTF)₂I₃ called from now on β-(ET)₂I₃. A similar increase of T_c was also announced by a group in Japan ⁶. Furthermore, the last two groups have also reported in the same system a possible stabilization of superconductivity around 7 K at ambient pressure either after temperature cycling or after the release at ambient temperature of a previously applied pressure. However none of these works provided clear cut proofs for the stabilization of bulk superconductivity at 7 K under ambient pressure as either the drop of resistivity below T_c was not complete or no Meissner signal could be detected with a SQUID magnetometer ⁷.

At Orsay we have tried to clarify the establishment of superconductivity in (ET)₂I₃. We managed to stabilize a sharp superconducting transition under ambient pressure at 8.1 K following the hydrostatic pressure-temperature cycling procedure displayed in figure (1) ⁸. The existence of an AC-susceptibility signal related to the transition exactly similar in amplitude to the one obtained under a pressure of 1.3 kbar where Meissner effect has been established by magnetization measurements ⁷ shows that the superconducting state stabilized at 1 atm is indeed a bulk superconductor ⁹. This high-T_c (β-H) state of β-(ET)₂I₃ is however metastable since warming up to room temperature followed by a cooling down to helium temperature does not show superconductivity at 8.1 K, figure (2). Various experiments performed in temperature have established that the

<figure><img src="image_2.png" /><figcaption>FIGURE 1</figcaption></figure>

Superconducting transition at 8.1K in β-(BEDT-TTF)₂I₃ under 1 atm after sample preparation following the T-P path displayed in the insert.

<figure><img src="image_3.png" /><figcaption>FIGURE 2</figcaption></figure>

AC susceptibility signal in β-(ET)₂I₃, under 1.6 kbar (a), after pressure release at low temperature (b), after annealing above 131 K (c), after annealing at 125 K (d).
domain of stability of the β-H state at 1 atm extends up to 125 K. Without preliminary pressure-temperature cycling the phase of β-(ET)$_2$I$_3$ which is in thermal equilibrium at low temperature is the phase displaying superconductivity at 1.4 K or so(the β-L phase)$^{10}$.

The stabilisation of superconductivity at 8.1K in β-(ET)$_2$I$_3$ has been understood by suggesting 8 that the β-H and β-L phases correspond respectively to the structure stable at room temperature and to the modulated phase observed below 200 K 11.

We conclude by saying that β-(ET)$_2$I$_3$ is indeed a high T$_c$ organic superconductor when compared to the C(TMTSF)$_2$X series in the absence of structural phase transition establishment below 200-185 K.

Since β-(ET)$_2$I$_3$ is a material showing superconductivity at a temperature about 5 or 6 times the T$_c$ observed in the (TMTSF)$_2$X series it is particularly interesting to perform a comparative study of the normal state properties of the two families. First, both series are half-filled band conductors. Secondly, optical reflectance data suggest that the 1-D character is somewhat more pronounced for (TMTSF)$_2$X than for β-(ET)$_2$I$_3$. The Fermi surface of (TMTSF)$_2$X is open($t/t_b \sim 10$) whereas the band anisotropy, $t_a/t_b \sim 2-3$, 12,13 of β-(ET)$_2$I$_3$ indicates that the FS is likely to be very near the border between open and close. In spite of a marked 2-D character, the nuclear spin relaxation behaviour of β-(ET)$_2$I$_3$ reveals a spectacular enhancement bound to the superconducting transition which has been related to low dimensionality effects 14 and is in agreement with band anisotropy $t_a/t_b = 2$ and $t_b/t_c > 50$. The depression of the FIR oscillatory strength 13 and the Faraday susceptibility 15 show that Coulomb correlations play a dominant role in β-(ET)$_2$I$_3$. The enhancement of the uniform susceptibility above the bare band value amounts to 3-4 and 2 for β-(ET)$_2$I$_3$ and (TMTSF)$_2$ClO$_4$ respectively.

In spite of large Coulomb correlations, no magnetic ordering has yet been observed in β-(ET)$_2$I$_3$. Instead, it is precisely with such a material that a significant increase of the superconducting transition has been achieved. This fact shows that Coulomb interactions and 3D kinetic couplings are two important factors governing the onset of instabilities at low temperature in Q-1D organic conductors.

## 2. COULOMB AND 3-D KINETIC COUPLINGS IN (TMTSF)$_2$X: PRECURSOR REGIME

In the last few years NMR relaxation studies performed on ¹H and ⁷⁷Se nuclei in (TMTSF)$_2$ClO$_4$ have clearly revealed a deviation to Korringa-like relaxation arising below 25-30 K $^{16}$. This feature has been attributed to the onset of one dimensional magnetic cooperative phenomena above a cross-over region between 1-D and 3-D behaviour located at $\sim 8$ K in (TMTSF)$_2$ClO$_4$ in a magnetic

field of 31.9 kOe. As 25 K is also the temperature where ClO$_4^-$ anions order in (TMTSF)$_2$ClO$_4^-$ it was important to perform a similar NMR study in a system where no such lattice modification could be detected at low temperature, namely (TMTSF)$_2$PF$_6$.

The results obtained in (TMTSF)$_2$PF$_6$ are summarized in figure 3.

<figure><img src="image_4.png" /><figcaption>FIGURE 3</figcaption></figure>

$^{77}$Se spin-lattice relaxation rate in (TMTSF)$_2$ClO$_4$, dotted lines and in (TMTSF)$_2$PF$_6$, continuous lines, H = 3 T//b'.

Comparisons between the behaviours of (TMTSF)$_2$PF$_6$ under pressure (P>8 kbar) and (TMTSF)$_2$ClO$_4$ reveals a quite similar temperature dependence of $T_c^{-1}$ in the low temperature domain which allow us to rule out the effect of anion ordering on the behaviour of the relaxation rate and strongly supports the model of Bourbonnais 18 in which the 1-D to 3-D cross-over T can be depressed from the bare-band value at $\sim 80$ K down to the 8 K temperature region by strong intra-chain particle-particle correlations.

Theoreticians have proposed two possibilities for the onset of antiferromagnetic long-range order (AFLRO) observed at low temperature in (TMTSF)$_2$X.

(i) A strongly correlated antiferromagnetic phase stabilized by inter-chain exchange interaction (IEX) between 1D-2k$_F$ spin correlations$^{19}$ of adjacent chains leading to a modulation wave-vector not related to the actual shape of the Fermi surface.

(ii) An AF phase induced by nesting properties of the open (but warped) Fermi surface (NAF) exhibiting a transverse wave vector such as $\vec{Q}_T = (2k_F, b''/4, xc'')$.
One can summarize very crudely the theoretical picture, saying that IEX-AFLRO sets in at $T_{N-IEX}$ when the renormalized transverse overlap integral $\frac{1}{T}$ is not pertinent in the temperature region of the transition, (i.e. $T_{N-IEX} > T_N$) while in the opposite situation the 3D-NAP-AFLRO takes over $T > T_N$. We shall now review some experimental evidences (NMR and transport properties) supporting the above-mentioned theoretical models.

AFLRO corresponding to two different experimental conditions can be achieved at low temperature in $(TMTSF)_2PF_6$ and $(TMTSF)_2ClO_4^-$ (i) At atmospheric pressure($T_N$ = 12K) or under pressure as long as $P<8$ Kbar.

(ii) Under pressure ($P>8$ Kbar for $(TMTSF)_2PF_6$) and large magnetic fields // c''.

Figures (4) et (5) show the behaviour of the resistivity above $T_N$ for the two situations where AFLRO can be stabilized at low temperature $^{21}$. Under 7 kbar fig.(4), AFLRO resistive transition at 5 K is very sharp (the same sharpness as at 1 bar) with practically no resistive precursor regime observed above $T_N$(in zero magnetic field). The AFLRO state existing at high field ($H=8.8$ T, $P$ = 9 kbar) below 1.8 K is announced by a broad resistive precursor regime starting at 20 K and possibly above, fig.5.

Comparatively, the relaxation rate reveals a different behaviour. An extended precursor regime is observed below 30 K (see data at 5.5 kbar in fig.(3) with $T_N$ = 8.7 K $^{17}$). This is in striking contrast with the behaviour of the resistivity at zero field on fig.4. Notice that the NMR data have been obtained in a field of 3 T and not in zero field. However, we feel that their comparison with the zero field resistive T-dependence in fig.(4) is meaningful since the transverse magnetoresistance is known to be very small when the magnetic field is aligned along the b'-direction $^{22}$.

NMR data related to the establishment of the AFLRO stabilized under high magnetic field are shown on the composite figure 6''. The relaxation rate is nearly independent of the field orientation down to 8-10 K. At lower temperatures for fields parallel to b' a Korringa-like behaviour is recovered below the dimensionality cross-over $T_N \sim 5$ K whereas the divergence of $1/T_1$ for fields //c'' is the signature of the onset of AFLRO at 1.8 K($H$ = 7.4 T//c'').

Summarizing the previous data, we notice that the onset of AFLRO stabilized under high magnetic field occurs at $T_N$ smaller than the cross-over

''This figure is based on $(TMTSF)_2ClO_4$ NMR as the $(TMTSF)_2PF_6$ NMR investigation under pressure has not yet been completed at high fields //c''. However, it is known from figure (3) that qualitatively the same T-dependence of $T^{-1}$ exists for $ClO_4^-$ salts at low pressure and $PF_6$ salts under pressure.

<figure><img src="image_5.png" /><figcaption>FIGURE 4</figcaption></figure>

T-dependence of the resistivity of $(TMTSF)_2PF_6$ under 7 kbar in zero and 7 T//c'' applied field.

temperature $T_X$ which can be detected either on resistive or on relaxation experiments (in $PF_6$ at 9 kbar under 8.8 T//c'' $T_N$=1.8 K and $T \sim 2.5$ K, fig.(5), in $ClO_4^-$ at 1 bar under 7.4 T//c'' $T_N$ = 1.8 K and $T \sim 4$ K, fig.6). On the other hand, whenever the AFLRO state is stable in zero applied magnetic field, $PF_6$ at 5.5 kbar, fig.(3) or $PF_6$ at 7 kbar, fig.(4) no cross-over temperature is seen in the experimental data. We have argued in reference$^{17}$ that the broad minimum of $T^{-1}$ around 25 K followed by a strong enhancement at lower temperature is not the signature of a dimensionality cross-over but rather marks the onset of a power law temperature dependence of strongly developed 1-D spin correlations.

<figure><img src="image_6.png" /><figcaption>FIGURE 5</figcaption></figure>

T-dependence of the resistivity of $(TMTSF)_2PF_6$ under 9 kbar in various magnetic fields.
### 3. TWO AFLRO STATES IN (TMTSF)₂X: EXPERIMENTAL EVIDENCES

Transport properties and NMR investigations do support the theoretical model leading to IEX or NAF antiferromagnetic long range orders in (TMTSF)₂X compounds. Well-defined Shubnikov-de Haas oscillations have been reported in (TMTSF)₂PF₆ below 9 K at ambient pressure²³. The frequency of these oscillations 229 T for H//c: corresponds to rather large F.S. cross sections (≈3% of the Brillouin zone area). Such cross sections require a choice of wave-vector in the spin modulated state which does not optimize nesting properties of the Fermi surface. Furthermore, below ≈5 K the transverse magnetoresistance saturates at high fields and the oscillations vanish²³. We take this fact as an evidence for a possible change in the topology of the semimetallic F.S. of the AFLRO state arising around 5 K. Below 5 K the size of the remaining electrons or holes pockets should be much smaller than at T>5 K, implying the existence of a wave-vector in the AFLRO with non zero transverse components. Indeed, two recent analysis of ¹H NMR rotation NMR pattern of (TMTSF)₂PF₆²⁴,²⁵ lead to a wave-vector $\vec{Q} = (2\vec{k}_F, 0.24 \hat{b}^\dagger, 0c^\dagger)$ at 4.2 K and 1.2 K. Consequently a IEX-NAF transition is likely to occur in (TMTSF)₂PF₆ in the vicinity of T, ≈5 K at ambient pressure with a concomitant variation of the magnetic modulation wave-vector.

Furthermore, T should be increasing under pressure since it is related to the bare band interchain coupling $t_{⊥}^{18}$. Actually, NMR data in fig. (3) indicate values of T in the neighbourhood of 8 and 12 K at 8 and $t_{⊥}$ 11 kbar respectively. Figure (7) provides a rough sketch of the pressure dependence of $T_X$ and $T_N$ in materials such as (TMTSF)₂PF₆.

The rapid suppression of the AFLRO state under pressure occurs at a critical pressure above which the 3D-character of the band structure is dominant. The nesting of the Fermi surface is thus not good enough to support the stabilization of an AFLRO even with a transverse wave-vector in the modulated state.

However, in sufficiently large transverse magnetic field Gor'kov and Lebed²⁶ have shown that the electrons in this Q-1-D conductor are one dimensionalized by the effect of the field. Hence, the conductor becomes unstable above a certain threshold field against the formation of a sequence of phase transitions between different AFLRO states characterized by a transverse wave vector²⁷. Transport properties²⁸ and magneto-calc Lorimétrie data²⁹,³⁰ are consistent with the existence of transverse modulation wave-vectors (i.e. AFLRO of the NAF kind) for (TMTSF)₂ClO₄ and (TMTSF)₂PF₆ (under pressure) in the T-H domain, T<3 K and H<10 T. Outside the latter T-H region the detection of large pockets of carriers in (TMTSF)₂ClO₄ and (TMTSF)₂PF₆ by magneto-transport measurements³¹ is in good agreement with a longitudinal modulation wave-vector which is no

<figure><img src="image_7.png" /><figcaption>FIGURE 6
T-dependence of $^{77}\text{Se T}$-1 in (TMTSF)₂ClO₄ at H = 6.4 T // b' and H = 7.4 T//c: below 4.5 K.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>FIGURE 7
Typical T-P phase diagram for (TMTSF)₂PF₆-like compounds. The shaded area near P refers to a narrow region where coexistence between AFLRO and superconductivity is possible.</figcaption></figure>

longer the one giving the best nesting of the Fermi surface ³². These features can be understood by a model which is sketched in figure 8 for (TMTSF)₂ClO₄, but the same picture should apply to (TMTSF)₂PF₆ under pressure as well. As the net effect of the magnetic field is to diminish the effective interchain kinetic coupling ($t_{⊥} \approx t_{||}/H$ following Gor'kov ³³) we can expect $T_X$ to decrease at large fields and possibly cross the $T_{N-NAF}$ critical temperature. At higher fields the situation which is recovered is similar to the IEX-AFLRO of (TMTSF)₂PF₆ between 12 and 5 K at ambient pressure. This seems to be a natural interpretation of the very high field data.

### 4. CONCLUSION

The comparison between theory and experiments has emphasized several features which can be summarized as follows:
<figure><img src="image_9.png" /><figcaption>FIGURE 8</figcaption></figure>

Typical T-H phase diagram for (TMTSF)₂ClO₄-like compounds (or (TMTSF)₂PF₆ under pressure). Tₓ is depressed under magnetic field. The IEX state becomes stable at very large fields.

There exists in the (TMTSF)₂X series, a number of experimental indications suggesting two possibilities for antiferromagnetic ordering.

-a) a semimetallic AFLRO state stabilized by interchain exchange interaction with large pockets of carriers (>$\lambda$ 3% BZ).

-b) a quasi-semiconducting AF state with very few carriers (< 1% BZ) driven by the nesting properties of the 3D Fermi surface.

The IEX and NAF states are respectively stable above and below the renormalized temperature regime $T_x$ establishing the separation between 1D ($T>T_c$) and 3D physics ($T<T_c$). Since $T_c$ can be varied either by pressure or by the application of a large magnetic field IEX-NAF transitions are expected in a generalized T-P-H phase diagram of (TMTSF)₂X.

The normal conducting state above a IEX transition is dominated by strongly developed 1-D correlations exhibiting at the same time an isotropic magnetic character (observed by the enhancement of $1/T_1$ below 30 K) and an anisotropic superconducting character (giving rise to the large conductivity at low temperature, the anomalously large and anisotropic magnetoresistance and the strong DC collective mode in the far-infrared regime ¹³). When $T_c$ is large, typically larger than 5 K, a superconducting state may become stable at low temperature, for instance in (TMTSF)₂ClO₄, and the divergence of the 1D-2kₓ correlations stops at 8-6 K. Under high magnetic field however, the superconducting state is destroyed by the pair-breaking phenomenon and an antiferromagnetic state of the NAF nature can be stabilized.

Coming back for the conclusion to (ET)₂I₃ we may wonder why no AF ordering has yet been observed in this conductor in spite of the large coulombic effects?. The answer lies probably in the

amplitude of transverse kinetic coupling larger in (ET)₂I₃ than in (TMTSF)₂X preventing the onset of one-dimensional IEX and even 3D-NAF states. Examination of β-(ET)₂I₃ NMR data allows the location of $T_c$ around 15 K where as superconductivity occurs at $8 \times K^{14}$. We wish to conclude by saying that x 2 commensurability, strong coulombic repulsions and moderate one dimensionality may all be factors influencing favourably the quest for high $T_c$ superconductivity in organic conductors.

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