# Unconventional magnetic field and pressure dependences of the ground state of the low-dimensional organic superconductor (BEDO-TTF)₂ReO₄ · H₂O

A. AUDOUARD¹, P. AUBAN-SENZIER², V. N. LAUKHIN¹,³(*), L. BROSSARD¹

D. JÉROME² and N. D. KUSHCH³

¹ Laboratoire de Physique des Solides (ERS CNRS 111), Service National des Champs Magnétiques Pulsés (UMS CNRS 819), INSA
Complexe Scientifique de Rangueil - 31077 Toulouse, France

² Laboratoire de Physique des Solides (URA CNRS 02), Université de Paris-Sud
91405 Orsay Cédex, France

³ Institute of Chemical Physics in Chernogolovka, Russian Academy of Sciences
Chernogolovka, MD 142432, Russia

(received 15 March 1996; accepted 22 April 1996)

PACS. 72.15Gd – Galvanomagnetic and other magnetotransport effects.

PACS. 74.70Kn – Organic superconductors.

PACS. 75.30Fv – Spin-density waves.

**Abstract.** – Magnetotransport experiments have been carried out in the two-dimensional organic metal (BEDO-TTF)₂ReO₄ · H₂O at temperatures down to 0.4 K and under hydrostatic pressure up to 11 kbar. When measured in magnetic field of a few teslas, the magnetoresistance is large and a steep resistance rise is observed below 4 K, which, as is the case for quasi-one-dimensional TMTSF-based compounds, is the signature of a spin density wave condensation. As already observed at ambient pressure, two series of Shubnikov-de Haas oscillations, linked to hole and electron orbits, are evidenced in the applied pressure range from 3.5 to 11 kbar. Both hole and electron orbit oscillation frequencies (respectively noted F<sub>h</sub> and F<sub>e</sub>) increase strongly as the pressure increases (d ln(F<sub>h,e</sub>)/dP = 0.07 kbar<sup>-1</sup>), while their ratio remains unchanged (F<sub>h</sub>/F<sub>e</sub> = 2). As the applied pressure increases, both cyclotron masses either slowly decrease or remain constant, keeping low values when compared to other 2D compounds.

*Introduction.* – Many organic superconductors are radical-cation salts of the organic donor bis(ethylenedithio)tetrathiafulvalene (BEDT-TTF) [1]. Bis(ethylenedioxy)tetrathiafulvalene (BEDO-TTF) is an isostructural analogue of BEDT-TTF which allows the synthesis of a number of conducting salts as well. However, for a given anion, the BEDO-TTF salt is not isostructural to the BEDT-TTF one [2]-[6] and only two compounds, (BEDO-TTF)₃Cu₂(NCS)₃ [2] and (BEDO-TTF)₂ReO₄ · H₂O [5], [6] have so far been found to be superconductors.

(BEDO-TTF)₂ReO₄ · H₂O is a quasi-two-dimensional (2D) compound which exhibits a metallic behaviour down to ~ 35 K although it undergoes several phase transitions as the temperature decreases. In the temperature range from 220 to 205 K, a first-order metal-metal transition occurs, which could be due either to some reorientation of the ReO₄ anions and (or) of the H₂O molecules [6], [7], or to a monoclinic (space group P2₁/n) to triclinic phase

<footnote>(*) Present address: Institut de Ciencia de Materials (CSIC), Campus de la UAB - 08193 Bellatera, Spain.</footnote>
<figure><img src="image_1.png" /><figcaption>Fig. 1.</figcaption></figure>

<figure><img src="image_2.png" /><figcaption>Fig. 2.</figcaption></figure>

Fig. 1. – Temperature dependence of the resistance of (BEDO-TTF)₂ReO₄·H₂O, normalised at 30 K, under a hydrostatic pressure of 11 kbar, for different values of the magnetic field.

Fig. 2. – Temperature dependence of the resistance of (BEDO-TTF)₂ReO₄·H₂O normalised at 4.2 K, at ambient pressure (open symbols) and 11 kbar (full symbols), for different values of the magnetic field. Ambient pressure data is deduced from ref. [8].

transition [8]. Another phase transition, the nature of which still remains unknown too, has been evidenced at 90 K both by thermopower [5] and electron-spin resonance (ESR) [8] experiments. In the lower temperature range from 35 to 4 K, the dc resistance sharply increases while the 10 GHz microwave resistance rise either remains much smaller or is almost absent [6]. As was assumed in [6], the dc resistance increase has thus been attributed (see, e.g., ref. [9]) to the condensation of a spin density wave (SDW). This phase transition has also been evidenced by Hall effect and ESR measurements [8]. However, this SDW state is not very stable since it is suppressed by a rather low (1 kbar) hydrostatic pressure [10]. In addition, it competes or coexists with a superconducting state the onset temperature of which is 2.4 K [5], [6].

According to calculations, the room temperature Fermi surface (FS) consists in one hole and two electron tubes, their cross-section area amounting to 3.4 and 1.7 percent of the first Brillouin zone (FBZ) area, respectively [8]. As a matter of fact, two Shubnikov-de Haas (SdH) oscillations series have been observed at ambient pressure with frequency of $F_h = (76 \pm 2)$ T [8] (or 81 T [11]) and $F_e = (37 \pm 3)$ T [8], [11], respectively. These frequencies correspond to cylindrical carrier tubes, with their axes perpendicular to the conducting plane and with extremal cross-section areas equal to 1.5 (1.6) and 0.73 percent, respectively, of the FBZ area. The discrepancy by a factor of more than two between these values and the calculated ones can be ascribed to the phase transitions which, as above mentioned, occur on cooling.

In that respect, it is of a primary importance to get a more deeper insight into the (pressu- magnetic field, temperature) phase diagram of (BEDO-TTF)₂ReO₄·H₂O. We have thus investigated i) the temperature dependence of its resistance under pressure and magnetic field and ii) the pressure dependence of the cyclotron orbits by SdH oscillations analysis. Experiments have been performed in the pressure range 3.5 to 11 kbar, in magnetic fields up to 12 T and in the temperature range 300 K to 0.4 K.

*Experimental.* – Good-quality single crystals of (BEDO-TTF)₂ReO₄·H₂O were obtained by electrochemical oxidation of BEDO-TTF. The details of the synthesis are given in ref. [6]. Structural data were reported in [5]-[7]. The samples were mounted using the standard four-contact method with annealed platinum wires (20 µm in diameter) which were glued to the sample by graphite paste “DOTITE XC-12” JEDL/SVC. Alternating current (100 µA, 77 Hz) was applied along the best conduction direction *c* while the magnetic field was applied parallel to the *b*-axis (¹). The signal across the potential contacts was detected by a lock-in amplifier.

<footnote>(¹) The *a*, *b*, *c* crystallographic axes in ref. [6], [7] correspond to the −*c*, *c*−*a* and *b* axes, respectively,</footnote>
<figure><img src="image_3.png" /><figcaption>Fig. 3.</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>Fig. 4.</figcaption></figure>

Fig. 3. – Magnetoresistance data for (BEDO-TTF)₂ReO₄·H₂O at different pressure and temperature values. R is the field-dependent resistance and Rₙ is the extrapolated value of the zero-field resistance in the normal state at the given pressure.

F 1. – Oscillatory part of the magnetoresistance of (BEDO-TTF)₂ReO₄·H₂O at low temperature for different pressures indicated on the curves. Rₛₚ is the field-dependent semiclassical part of the magnetoresistance.

The single crystal used for measurements had dimensions (2 × 0.4 × 0.05) mm³ and its room temperature conductivity was about 30 ohm⁻¹cm⁻¹. Magnetoresistance experiments under hydrostatic pressure were carried out using a non-magnetic “piston-cylinder” cell (6 mm inner diameter) with a silicon polymer liquid as the pressure medium. Pressures up to 14 kbar were applied at room temperature and the cell was placed in a ³He cryostat providing temperatures down to 0.4 K in a 12 T superconducting magnet. The temperature of the sample was varied between 0.4 K and 300 K and measured by calibrated ruthenium oxide, carbon glass and platinum sensors depending on different temperature ranges. The decrease of pressure on cooling was taken into account for estimating the pressure value at low temperature according to [12].

*Results and discussion.* – Let us consider first the temperature dependence of the resistance. Whereas the zero-field resistance decreases monotonously as the temperature decreases in the pressure range studied, the resistance exhibits a non-monotonous variation with a negative slope when measured in magnetic field of a few teslas, as evidenced for 11 kbar in fig. 1. In a large magnetoresistance which is reminiscent of the similar effect observed in conducting compounds belonging to the (TMTSF)₂X series when the magnetic field is parallel to the lowest conductivity direction [13], [14]. In addition, the steep rise of the resistance in magnetic field which is noticed below 4 K is similar to that observed in the temperature range close to the onset of the SDW ground state in (TMTSF)₂X compounds. It is worthwhile to notice that a resistance rise can also be deduced from magnetoresistance data recorded at ambient pressure [8] (see fig. 2). Hence, the data in fig. 1 and 2 suggest the stabilisation of a field-induced SDW state in (BEDO-TTF)₂ReO₄·H₂O at low temperature. It is known that SDW condensation in quasi-one-dimensional (Q1D) compounds is sensitive to both hydrostatic pressure and magnetic field which respectively deteriorates and improves the nesting of the Q1D sheets [15]. This accounts for the magnetic-field dependence of the resistivity of, e.g., the Q1D Bechgaard salt (TMTSF)₂PF₆ under pressure [16] but also of the (TMTSF)₂NO₃ salt, in its low-temperature 2D state, for which it has been shown that the magnetic field improves

<footnote>in ref. [5], [8]. In the present paper, the crystal axis system of ref. [5], [8], on which band structure calculations are based, is used.</footnote>
<figure><img src="image_5.png" /><figcaption>Fig. 5.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>Fig. 6.</figcaption></figure>

Fig. 5. – Fourier transform of the data in fig. 4. The inset shows the pressure dependence of the amplitude ratio $A_h/A_e$ where h and e indices, respectively, stand for hole and electron orbit (see text). Ambient pressure value is deduced from ref. [8].

Fig. 6. – Pressure dependence of the SdH oscillation frequency (a)) and cyclotron mass (c)) related to electron (e index) and hole (h index) orbits. The hole- to electron-related orbit frequency ratio is shown in b). Ambient pressure data are from ref. [8].

the nesting as well [13].

The FS nesting at the SDW condensation in $(BEDO-TTF)_2ReO_4 \cdot H_2O$ has been interpreted [8] on the basis of the hidden nesting concept [17] in which the 2D FS is regarded as composed of several sheets crossing each other, the 1D character of which being hidden by degeneracy removals. This model well accounts for DW condensation in 2D compounds such as the purple bronze $KMo_6O_{17}$ [17]. Contrary to the statement in ref. [8], we believe that a given pair of hidden 1D sheets in $(BEDO-TTF)_2ReO_4 \cdot H_2O$ can involve only one type of carriers (electrons or holes) [18]. Moreover, the anisotropy of the semiclassical part of the magnetoresistance at 15 teslas and ambient pressure [11] indicates the presence of 1D sheets so that the nesting may not be hidden. Whatever the nesting process, it certainly leads to a rather bad nesting, which accounts for the lack of stability of the SDW state. It is thus likely that the SDW condensation, which is suppressed by hydrostatic pressure of 1 kbar only, would be recovered under magnetic field.

Turn now on the magnetoresistance data. An overview of the magnetic-field dependence of the normalised resistance is displayed in fig. 3, where $R$ and $R_N$ stand for the field-dependent resistance and the extrapolated value of the zero-field resistance in the normal-state, respectively, at the considered temperature and pressure values. It can be seen that the almost linear semiclassical part of the magnetoresistance $((R_{SC} - R(B=0))/R_N)$ increases with increasing pressure and decreasing temperature, while the magnetoresistance oscillation amplitude increases with decreasing pressure or temperature. The oscillatory part of the magnetoresistance at low temperature, calculated as $(R - R_{SC})/R_{SC}$, is displayed in fig. 4 for some values of the hydrostatic pressure at the lowest temperatures. At a given pressure and in the considered field range, the oscillations are roughly of the same amplitude as those recorded for the strongly 2D compound $\alpha$-(BEDT-TTF)$_2$TlHg(SeCN)$_4$ [19]. Fourier analysis of the data in fig. 4 reveals two series of SdH oscillations as displayed in fig. 5. Low ($F_e$) and high ($F_h$) frequency oscillations can be associated with electron and hole orbits, respectively, as has been asserted at ambient pressure [8]. As the applied pressure increases, the oscillation frequency of both series increases linearly (see fig. 6(a)), $F_h$ remaining higher than $F_e$ by a factor of
2 from ambient pressure up to 11 kbar (see fig. 6b)). It can be noticed that the pressure sensitivity of the oscillation frequency ($d\ln(F)/dP = 0.07 \text{ kbar}^{-1}$) is high when compared to $\alpha$- or $\kappa$-phase compounds such as $\alpha$-(ET)$_2$TlHg(SeCN)$_4$ [19] or $\alpha$-(ET)$_2$KHg(SCN)$_4$ [20], for which $d\ln(F)/dP = 0.02 \text{ kbar}^{-1}$, or $\alpha$-(ET)$_2$NH$_4$Hg(SCN)$_4$ [21] or $\kappa$-(ET)$_2$Cu(SCN)$_2$ ($d\ln(F)/dP = 0.03 \text{ kbar}^{-1}$) [22]. This can be understood, keeping in mind that the orbits involved in the SdH oscillations result from the imperfect nesting of 2D carrier tubes which make them certainly very sensitive to the details of the FS. The SdH oscillations amplitude ratio $A_h/A_e$, measured at low temperature, strongly decreases as the pressure increases (see inset of fig. 5), which may reflect a different pressure-induced warping of hole and electron tubes. Dingle temperature is $(1.6 \pm 0.2)$ K and $(0.9 \pm 0.2)$ K for e- and h-orbits, respectively, in the pressure range covered by the experiments. The pressure-dependence of the cyclotron mass related to both electron ($m_{ce}$) and hole ($m_{ch}$) orbits is displayed in fig. 6c). In the range from 3.5 kbar up to 11 kbar, the cyclotron mass related to both orbits either slightly decreases or remains constant while $m_{ce}$ remains higher than $m_{ch}$ roughly by a factor of two.

It can be noticed that the cyclotron masses are rather low ($1.5m_0$ and $0.8m_0$ for $m_{ce}$ and $m_{ch}$, respectively, at 3.5 kbar) when compared to the cyclotron mass related to unnested 2D orbits in other ET salts such as $\kappa$-(ET)$_2$Cu(SCN)$_2$ [22], $\beta$-(ET)$_2$IBr$_2$ [23], etc. In these compounds, the large cyclotron mass is usually thought to be the signature of strong electron-electron interactions [22]. Since (BEDO-TTF)$_2$ReO$_4 \cdot H_2O$ undergoes a SDW transition, it is likely that electron correlations are important, which would yield a large cyclotron mass. However, as stressed above, the measured cyclotron masses are related to nested small orbits so that the energy dispersion, and thus the bare band masses, are likely strongly modified. As a matter of fact, in charge density wave (CDW) compounds for which electron correlations are weak, the cyclotron mass is usually even well lower, e.g., $m_c/m_0 = 0.1, 0.25$ and $0.3$ for $KMo_6O_{17}$ [24], $(TSeT)_2Cl$ [25] and $NbSe_3$ [26], respectively. The measured medium values of the cyclotron mass in (BEDO-TTF)$_2$ReO$_4 \cdot H_2O$ could be due to the antagonist effects of the DW and of the strong electron correlations which respectively decrease and increase the cyclotron mass.

It can also be remarked that the competition between SDW state and superconductivity in this compound is strongly influenced by pressure, leading to a low pressure sensitivity of the superconducting transition temperature ($T_c$) and the cyclotron mass as well. Indeed, $dT_c/dP = 0.2 \text{ Kbar}^{-1}$ which is one order of magnitude lower than in the case of, e.g., $\kappa$-(ET)$_2$Cu(SCN)$_2$ [22]. In addition, when compared to the predictions of weak-coupling BCS theory [22], the measured cyclotron masses of both orbits are very low with respect to the values of $T_c$, which can also be related to the presence of the SDW state.

*Conclusion.* – The reported magnetoresistance experiments evidence that under moderate pressure (greater than 3.5 kbar) an applied magnetic field stabilizes a SDW state in $(BEDO-TTF)_2ReO_4 \cdot H_2O$. In that ground state, the parameters related to the two observed oscillation series are surprisingly in qualitative agreement with the FS calculations, derived from room temperature and ambient pressure crystallographic data, which yield electron and hole tubes. The pressure-induced increase rate of the extremal cross-section area of both these tubes as well as the pressure-independent ratio between these areas suggest that this field-stabilised state shares some similarities with the SDW state stabilised under magnetic field at ambient pressure. On the other hand, the strong pressure decrease of the hole-to-electron SdH oscillation amplitude ratio as well as the variance between the pressure dependence of the hole and electron cyclotron mass require further investigations.

***

We would like to thank Prof. E. B. YAGUBSKII for his interest and encouragement and to acknowledge INTAS for financial support within the contract No. 932400. VNL is grateful
to CNRS for associated researcher position in Toulouse under Contract No. ID 41/31. The work was supported in part in the framework of the project # 93030 within the Russian Program "Topical Aspects of the Condensed Matter Physics" and supported by Scientific Council "Superconductivity".

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