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STUDY OF THE HIGH TEMPERATURE PHASE DIAGRAM OF beta-(BEDT-TTF)2!3

Denis Jerome, Wuon Kang, Patrick Batail, Christine Lenoir

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Denis Jerome, Wuon Kang, Patrick Batail, Christine Lenoir. STUDY OF THE HIGH TEMPERATURE PHASE DIAGRAM OF beta-(BEDT-TTF)2!3. Synthetic Metals, 1988. hal-05165456

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# STUDY OF THE HIGH TEMPERATURE PHASE DIAGRAM OF $\beta$-(BEDT-TTF)$_2$I$_3$

W. Kang, D. Jérôme, C. Lenoir and P. Batail

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

## ABSTRACT

The pressure-temperature phase diagram of the organic superconductor $\beta$-(BEDT-TTF)$_2$I$_3$ which plays an important role on the low temperature characteristics of this compound is investigated by differential thermal analysis and the low frequency ac conductivity measurement. The relatively good agreement between the results from the different methods justifies our phase diagram. Our results contrast with the calculated phase diagram for the absolute stability of the $\beta$-L and $\beta$-H phases in the low temperature region. Also we show that there can be an additional irreversible phase transition when cooling the virgin sample under pressure.

## INTRODUCTION

The ambient pressure organic superconductor $\beta$-(BEDT-TTF)$_2$I$_3$[1] has been studied very widely not only because of its highest transition temperature until the discovery of (BEDT-TTF)$_2$Cu(NCS)$_2$[2], but also because of its two different competing superconducting phases. The superconducting temperature originally found at $T_c \approx 1.5$K($\beta$-L state) could be increased drastically upto 7.5K($\beta$-H) by applying a modest pressure of 1.3kbar[3.4]. Moreover, a subsequent study has showed that this latter phase can be stabilized even at ambient pressure by depressurization at low temperature ($T \le 100$K)[5]. So we can have two different superconducting states depending on experimental conditions. The relative stability of the two different phases at low temperature and at ambient pressure has been of interest and has been studied by the differential thermal analysis(DTA)[6] and the electrical conductivity measurements[7]. As
far as the relative stability is concerned, it is the β-L phase that is stabilized by the normal cooling process and its stability is conserved even under pressure if the temperature remains sufficiently low. But if the sample is cooled under a moderate pressure down to a certain temperature which varies with the pressure, it is the β-H phase which is more stable at low temperature and it is conserved even on depressurization. However, the absolute stabilities of the two phases at low temperature is not yet clear. Recently, there was a microscopic study[8] taking into account the two non-symmetrical configurations of one of the two ethylene groups of a BEDT-TTF molecule, where the authors reestablished a diagram which fits fairly well with our experimental phase diagram at least at high temperature. But the problem of the absolute stability at low temperature remains unresolved.

In this paper, we reinvestigated the phase diagram of β-(BEDT-TTF)₂I₃ by electrical resistivity measurement and make comparison with the existing phase diagram[6,7,8]. We also report the possibility of the new phase transition when cooling a virgin sample under pressure.

## EXPERIMENTAL

The samples studied were prepared electrochemically and easily identified as β-phase from their morphology. The conductivity measurement was done on single crystals of typical size 1.8x0.8x0.2mm and all the electric contacts are prepared with gold evaporated pre-contacts and with the 17.5µm gold wires glued on by silver conducting paint. The resistivity measurements are performed by the standard four-probe method with a low frequency ac lock-in detection and the hydrostatic pressure is achieved by compressing helium gas in a Be-Cu pressure bessel.

## RESULTS AND DISCUSSION

Fig. 1 shows the experimentally determined phase diagram. It was first established by the DTA technique[6] and confirmed by the present electrical resistivity measurements. The typical behavior of the electrical resistivity of β-H to β-L conversion under ambient pressure is shown in Fig. 2. In Fig. 1, the line (a) corresponds with the second-order phase transition from the disordered high temperature phase to the incommensurably ordered state(β-L), the line (b) is the limit of the metastability of β-H phase which is stabilized by the pressure-temperature cycling where the closed and open circles are points from the DTA and electrical resistivity measurement, respectively. The line (c) that of the β-L phase which is stabilized without pressure where the points from DTA and electrical resistivity measurement are indicated by xs and a square, respectively. The three hexagons will be discussed below. According to the phase diagram, the three conversion or transition lines converge to a
tricritical point at ≈345bar and ≈150.5K. We can also see the distinct
resistivity jump in depressurizing at 150K after cooling from ambient
temperature under 2kbars(triangle in Fig. 1). We should point out that this
process passes near the tricritical point.

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Fig. 1. Experimental phase diagram of β-(BEDT-TTF)₂I₃. (a) is the second order phase transition line detected by DTA, (b) β-H to β-L conversion line, (c) β-L to β-H conversion line. The triangle is obtained by depressurizing at 150K after cooling from 295K under 2kbars. The hexagons are the points where the resistivity changes abruptly by cooling the virgin sample. (see text)

In order to explain this rather strange phase diagram, we take the Landau
expansion of the free energy up to the sixth order with the modulation
amplitude as an order parameter η in G(η) = aη² + cη⁴ + gη⁶. This expansion can
yield one or two minimum according to the values of its coefficients which can
vary with temperature and pressure. The full information of their variation is
not yet available and we can only imagine their asymptotic behavior from the
experimentally obtained values. Firstly, g should be positive to give a
stability to the system. The coefficient a of the second order term plays a
role for creating the local minimum or maximum at η=0 and therefore it should
be positive if there is a corresponding state and negative if not. Since the
non-modulated state is possible not only at higher temperature but also at low
temperature after a temperature-pressure cycling, a should be positive in this
region and it can be negative only between ≈175K and ≈130K under ambient
pressure. Now c is related to the existence of the secondary minimum when η≈0
and α>0 and from the existence of the modulated structure at low temperature,
it should be negative at lower temperature and positive at higher temperature.
Though the absolute values are always in question, we can construct a new phenomenological diagram from the free energy behavior in Fig. 3. The above two phase diagrams correspond relatively well with each other. But the conversion (c) in Fig. 1 differs significantly from the recently calculated phase diagram of Ravy et al[8]. The latter phase diagram comes from the thermodynamical calculation of the free energy for the microscopic state of the terminal ethylene groups of BEDT-TTF molecule and gives relatively good correspondence with the experiments at least at the higher temperature.

<figure><img src="image_5.png" /><figcaption>Fig. 2. Typical behavior of the electrical resistivity for the β-H to β-L transition. The superconducting transition is at 7.65K at the midpoint.</figcaption></figure>

The line (a) in the phase diagram evidently comes from the second order structural phase transition between I and II regions. For the line (b) we can easily attribute it to phase conversion from β-H to β-L phase corresponding to the passage from III to II in Fig. 3. However, DTA curves for this transition shows that there is a discontinuous heat capacity change[6]. The small appreciable downward peak in the beginning of the transition can be related to a rather small latent heat but the major effect is the heat capacity change. In this point of view, the small downward peak can be the temperature drop of the sample junction due to the heat capacity jump rather than due to the latent heat, which returns in equilibrium by itself and/or by the small latent heat if any. Really, if we suppose that the β-H state is the same state as that at 4.5K and 1.5kbar, both β-H and β-L phases are ordered and there cannot be much entropy difference which will be responsible for the latent heat.

Now the line (c) can be attributed to the crossover from β-L to the normal state. The first order like transition was already shown by the DTA measurement. This anomaly is also clearly seen by the resistivity measurement
which appears at ≈104K by the abrupt change of the resistivity. What is interesting on this transition is the preliminary transition signal at ca. 95K from both DTA and resistivity measurement which we attribute to the dynamic effect in the region (IV) in Fig. 3. On the same basis as the conversion (b), we can understand the large latent heat in this conversion since the ambient temperature phase is totally disordered and the entropy should be much greater than that of incommensurably ordered β-L phase.

<figure><img src="image_6.png" /><figcaption>Fig. 3. Phenomenological phase diagram by using the Landau free energy polynomial and its behavior in various regions.</figcaption></figure>

Now we turn our attention to the low temperature ordered state which is reported by neutron and X-ray studies. These reveal that there is no structural modulation at 20K between 1bar and 1.4kbar[10]. It is probably due to the newly ordered structure which is responsible for the $T_c$ increase since the structural study at 4.5K under 1.5kbar[11] shows clearly the existence of the ordered phase which is totally different from that of the high temperature phase. With these point we can not be sure that the low temperature phase after the temperature-pressure cycling is exactly the same as that at ambient conditions. From the fact that the ambient temperature state is totally disordered, there should be a certain mechanism or phase transition, probably order-disorder transition between the ambient temperature and the lower temperature and a
moderate pressure. In our measurement, we notice that there is a sharp change of the resistivity at 182.6K under a pressure of 850bar and 160±1K under 700 bar when the sample is first cooled under pressure These points are marked by a hexagon on the phase diagram and can be considered as a transition from the randomly disordered high temperature phase to the ordered lower temperature state which can be β-H phase. But the problem is not yet clear because these transitions are observed only on the first cooling under pressure. Moreover, after this transition, the sample becomes much more resistive and the anisotropy between different orientation decreases significantly[13]. The observation should be studied more carefully and for the moment we think that from our results and the structural data there is a transition toward the totally ordered state by cooling under pressure and that this transition is not completely reversible.

Now we consider the absolute stability between β-L phase and β-H phase at T<125K under ambient pressure. Although there is rather good correspondence between our phenomenological and Ravy's phase diagram, there is an essential difference which comes from the low temperature absolute stable state. It is the β-L phase in the former and the β-H in the latter. In the latter phase diagram the Sq=0 state which occurs at 131.5K has the same energy as Sq≠0 state at 127K and becomes more stable at lower temperature. However, there is only a difference of seven degrees and the potential barrier should be of the same order of magnitude. In this case, this barrier can be easily overcome and all the states can be transformed to the Sq=0 state. Though it agrees somewhat with the resonance Raman studies[12] it is contrary to the present experimental outputs. Therefore it is more reasonable, we think, to say that the β-L state is more stable at low temperature. Upto now there is not much study for this and more study is anticipated and under progress.

## ACKNOWLEDGEMENT

We thank J.C. Ameline for technical assistance with the pressure experiment.

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