Competition between magnetism and superconductivity in the organic metal�-†BEDT-TTF‡2Cu†N„CN…2‡Br

David Fournier, Mario Poirier, and Kim Doan TruongRegroupement Québécois sur les Matériaux de Pointe, Département de Physique, Université de Sherbrooke,

Sherbrooke, Québec, Canada J1K 2R1�Received 10 May 2007; published 9 August 2007�

Ultrasonic velocity and attenuation measurements on the quasi-two-dimensional organic conductor�-�BEDT-TTF�2Cu�N�CN�2�Br give the first determination of the coexistence zone of the antiferromagneticand superconducting phases, which extends deep in the metallic part of the pressure-temperature phase diagramof these salts. This zone is identified from a precise control of the thermal cycle, which seems to act as aninternal pressure. The two phases are found to compete, whereas superconducting fluctuations begin to con-tribute to the attenuation at 15 K, namely, at the onset of magnetic order that is well above the superconductingtransition temperature Tc=11.9 K. Finally, the temperature profile of sound attenuation for both longitudinaland transverse phonon polarizations is found to be inconsistent with a conventional s-wave order parameter.

DOI: 10.1103/PhysRevB.76.054509 PACS number�s�: 74.70.Kn, 74.25.Ha, 74.25.Ld

I. INTRODUCTION

The physics of strongly correlated materials in the vicinityof the Mott transition has motivated much interest over thelast decade.1 Vanadium oxides, manganites, frustrated quan-tum magnetic insulators, and high-Tc and organic supercon-ductors are examples of such systems where complex ordersand quantum criticality can be found. More specifically, thecoexistence and/or competition of magnetism and supercon-ductivity near the Mott transition in high-Tc and organic ma-terials constitute fundamental issues that are widely ad-dressed in the literature �e.g., Ref. 2�. In this respect, thelayered quasi-two-dimensional �-�BEDT-TTF�2X com-pounds are of great interest. Their generic temperature vspressure phase diagram3–6 reveals that the superconducting�SC� and the antiferromagnetic �AF� insulating phases areseparated by a first order Mott transition line �MI�, where amicroscale phase separation takes place.7 The first order linepersists in the paramagnetic phase and terminates with acritical point, from which a pseudogap line emerges underpressure as a precursor of the superconducting state.�-�BEDT-TTF�2X compounds can thus be considered as pro-totype systems to study the interplay between magnetic andsuperconducting phases in the close proximity of a first orderMI transition

At ambient pressure, the �-�BEDT-TTF�2Cu�N�CN�2�Brcompound �denoted as �-H8-Br hereafter� is located on themetallic side of the MI line and shows full superconductivitybelow 12 K. A pressure shift toward the MI line is obtainedby alloying with the Cu�N�CN�2�Cl anion8 and/or deutera-tion of the BEDT-TTF molecules.9,10 These procedures pro-duce, however, an electronic phase separation dependent onthe cooling process and consisting of macroscopic metallicand insulating domains below 35–40 K.7 A slight shift onthe pressure scale can also be achieved by a fine thermaltuning of residual intrinsic disorder related to ordering ofethylene end groups of BEDT-TTF molecules occurring be-tween 200 and 60 K.10–13 In �-H8-Br, partial suppression ofsuperconductivity and simultaneous observation of macro-scopic insulating domains at the surface were observed by

fast cooling.12 However, similar to partially deuteratedsalts,14 a phase separation has been observed under a mag-netic field in slowly cooled samples.15

In this work, an ultrasonic technique and thermal cyclingare used to present a detailed study of the different phasesappearing in the vicinity of the Mott transition line in�-H8-Br. We report sound velocity and the first ultrasonicattenuation measurements to be realized on these layeredcompounds. The results clearly establish a wide domain ofthe P-T phase diagram where the phase separation occurseven in the slowly cooled samples. A fine tuning of the ther-mal cycle seems to move the system on the pressure scaleaccording to temperature at which the pseudogap anomaly isobserved, a result suggesting that structural or electronic de-grees of freedom, other than ethylene, are involved. The MIis thus reached from the metallic side where the emergenceof an ordered magnetic phase is found, which is detrimentalto superconductivity. This magnetic phase sets in around15 K in �-H8-Br and it scales with the amplitude of thepseudogap anomaly above 30 K or so.5 Below 15 K, super-conducting fluctuations start to affect both the velocity andattenuation data, a few degrees above the superconductingcritical temperature of 11.9 K. This observation of the phaseseparation, even in the slowly cooled �-H8-Br crystal, is dueto extreme sensitivity of the ultrasound technique to domainstructure and boundaries.

II. EXPERIMENT

Although difficult to adapt to thin organic crystals, pulsedultrasonic velocity experiments have already been carried outon few compounds of this family.5,16,17 It consists in measur-ing the phase shift and the amplitude of the first elastic pulsetransmitted through the crystal and a delay line;17 this is whythe technique yields only velocity and attenuation variations.Because of the platelet shape of the selected �-H8-Br crys-tals, only elastic waves propagating perpendicularly to theplane �direction �010�� could be generated with small piezo-electric transducers. Longitudinal waves polarized along theb axis L�010� and transverse waves polarized along the a

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axis T�100� could be generated over the 30–450 MHz fre-quency range. The crystals were submitted to the followingthermal cycles from 200 to 2 K: the standard slow cool �SL�process, 10 K/h, and a fast cool �FT� process for 10 min,followed by a FT process, a 24 h annealing at 85 K�A-85 K� or 70 K �A-70 K�. According to theliterature,11,18,19 maximum order of the ethylene end groupsis obtained when annealing is performed at a temperaturebetween 60 and 80 K for a period of 24 h. All the ultrasonicdata presented in this paper were obtained when sweepingthe temperature up from 2 K. A magnetic field up to 16 Tcould be applied perpendicularly to the plane in order tocompletely eliminate the superconducting state.

III. RESULTS AND DISCUSSION

We report in Fig. 1 the temperature profile of the relativevelocity variation � �v

v� of the L�010� mode at 100 MHz over

the 2–80 K range for different thermal cycles. No frequencydependence is observed over the 30–450 MHz range; onlythe signal to noise ratio increases with frequency. The pro-files reveal two distinct anomalies: �i� a huge dip �3%–6%�just above 30 K previously associated with a compressibilityincrease driven by the magnetic fluctuations of the electronicdegrees of freedom at the pseudogap5 and �ii� a much smalleranomaly around 12 K likely related to the onset of supercon-ductivity. Both the amplitude and the position of the com-pressibility anomaly are highly dependent on the amount ofdisorder: FT �maximum disorder� yields the maximum am-plitude �6%� at the lowest temperature �33 K�, whereas SLfollowed by annealing at 70 K �minimum disorder� reducesby half the anomaly and shifts it to higher temperature�39 K�. Other cooling rates give intermediate disorder and,in turn, intermediate results. As far as the pseudogapanomaly is concerned, the process of ordering the ethyleneend groups seems to mimic an increase of the effective pres-sure: indeed, it has been previously shown that this anomalymoves to higher temperature with a reduced amplitude as

hydrostatic pressure is applied to this compound.17 The effectof disorder on the small 12 K anomaly is shown in the insetof Fig. 1. Fast cooling �maximum disorder� produces a merechange of slope just above 11 K, while a small dip growsprogressively with increasing order together with a smallshift to higher temperatures. This dip signals the onset of thesuperconducting state in agreement with what is expected fora longitudinal mode.20 Here, if we define the critical tem-perature as the temperature at which the positive slope ismaximum �confirmed by superconducting quantum interfer-ence device magnetization measurements�, the decrease of Tcwith increasing disorder �see inset of Fig. 1� is fully consis-tent with previous studies.10,13

It is tempting to associate the process of minimizing dis-order to an increase of effective pressure. Indeed, it has beenpreviously shown that the pseudogap anomaly is reduced inamplitude and moves to higher temperature when hydrostaticpressure is applied to this compound,17 as observed in Fig. 1.However, Tc is known to simultaneously decrease with hy-drostatic pressure,17 a trend that could not be reconcile withthe inset of Fig. 1. Nevertheless, our ultrasonic results seemto indicate that disorder shifts the compound toward the firstorder MI line where inhomogeneous phases have beenshown to coexist at low temperatures in severalcompounds.4,5,7 Indeed, a hysteretic behavior, consistent withan inhomogeneity region, is clearly observed when the tem-perature is swept up and down between 2 and 20 K. Anexample of this hysteresis on the longitudinal velocity at160 MHz is shown in Fig. 2 for the SL �A-70 K� and FTprocesses. Hysteretic effects are clearly observed between 8and 16 K for the FT process; surprisingly, similar effects,although reduced in amplitude, can also be observed for theSL �A-70 K� one over the same temperature range �see insetof Fig. 2�. Similar hysteretic effects were first noticed for theCu�N�CN�2�Cl under hydrostatic pressure for the same lon-gitudinal mode,5 being the largest near the first order MI lineand decreasing with increasing pressure. Then, such hyster-etic effects together with the modifications of the pseudogapanomaly above 30 K seem to confirm a downward shift onthe pressure scale when disorders is maximized. What ismeant by maximum and minimum disorders in relation tointernal pressure is still a highly debated question. The im-

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FIG. 1. �Color online� Relative variation of the longitudinalL�010� velocity at 100 MHz as a function of temperature for differ-ent thermal cycles. Inset: zoom around the 12 K anomaly; thecurves have been shifted for a better view. The arrows indicate themaximum slope that determines Tc.

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FIG. 2. �Color online� Relative variation of sound velocity as afunction of temperature: L�010� mode at 160 MHz. �a� FT process�maximum disorder� and �b� A-70 K process �maximum order�.

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portant cooling-rate dependence of the ultrasonic velocityobserved here, similar to the resistivity data,13,21 is difficultto explain with a small residual level of disorder of terminalethylene groups. It has been recently suggested22 that otherstructural or electronic degrees of freedom �in relation to thepolymeric chains� should be considered to resolve the issueof relevance of disorder and intrinsic sample properties; thiscould explain the different variation of Tc when hydrostaticpressure or disorder is varied. Our velocity data strongly sug-gest a shift on the pressure axis following different coolingprocedures. The persistence of inhomogeneities even whenthe sample is slowly cooled, minimum disorder, is puzzlingsince it has never been observed by other techniques up tonow. This is surely due to the high sensitivity of the ultra-sonic technique to these inhomogeneities as it will now bepresented.

As superconductivity is easily quenched by a field perpen-dicular to the highly conducting planes �Hc2

� �12 T�, a mag-netic field investigation of the low temperature anomaly ap-pears appropriate to identify the different phases. Thelongitudinal L�010� mode and a transverse mode, T�100�,which appears to couple more strongly to the superconduct-ing state, are used for this investigation. We compare in Fig.3�a� the �v

v �T� data at 0 and 16 T for the FT process �maxi-mum disorder�. In zero field, the velocity of the L�010� modeshows a plateau around 15 K before increasing further below11 K, where a marked softening of the mode is produced bythe magnetic field. For the T�100� mode, the velocity showsrather a maximum around 15 K, followed by an importantdip centered at 11.5 K. The dip almost disappears in a 16 Tfield and the maximum appears now more like a plateau. Wethus conclude that the 11.5 K dip in zero field is predomi-nantly due to superconductivity and that the other anomalyaround 15 K at 16 T could signal another ordered phase.This is confirmed by the 6 T curve of Fig. 3�a�, which showstwo separate anomalies, one around 5 K consistent with adownward shift of the superconducting anomaly and theother one around 15 K which appears to be practically insen-sitive to the magnetic field. When maximum order �A–70 K

process� is achieved, the temperature profile of the anomalyis greatly modified �Fig. 3�b��. For both modes, when thetemperature decreases from 20 K in zero magnetic field, amaximum is observed around 13.5 K followed by a sharpdrop till a minimum is achieved at 11.5 K; at lower tempera-tures, the velocity increases smoothly. The amplitude andtemperature profiles of the anomaly are, however, differentfor the two acoustic modes, being more pronounced for theT�100� one. As expected, if the anomaly is due to supercon-ductivity, a 16 T field appears to completely suppress theanomaly centered at 11.9 K �maximum positive slope�. Thevelocity increases smoothly with decreasing temperatureand, in contrast to the FT process, no residual anomalyaround 15 K is observed; only a weak variation of slopeoccurs around 8 K for both modes. Minimizing disorder thenfavors the superconducting phase as signaled by the sharpdrop centered at 11.9 K, consistent with the �v /v data �insetof Fig. 1�. We cannot, however, discard contributions ofother phases over this 2–20 K range, since the temperatureprofile of the 16 T curve still shows slope variations. Thesevelocity data have been reproduced several times on thesame crystal for the different thermal processes mentionedhere. The same temperature profiles were obtained withoutany indication of possible relaxation process. The presenceand nature of another phase coexisting with superconductiv-ity over this temperature range are most easily revealed bythe attenuation measurements whose sensitivity increaseswith frequency. We report now the ultrasonic attenuationmeasurements realized on this family of layered conductorsfor the A–70 K process, which favors superconductivity.

We present in Fig. 4 the variations of the attenuation���T� obtained simultaneously with the �v

v �T� data. The ze-roth value is arbitrarily chosen by extrapolating the zero fieldcurve at 0 K. For both ultrasonic modes over the 2–20 Ktemperature range, ���T� is a rapidly increasing function oftemperature; this is due to a large attenuation peak accompa-nying the huge velocity dip near 40 K �Fig. 1�, which domi-nates the whole temperature range. When the temperature isincreased from 2 K in zero magnetic field, the rate of in-creasing attenuation appears reduced at the superconducting

( )( )

FIG. 3. �Color online� Relative variation of sound velocity as afunction of temperature at fixed magnetic field values: L�010� modeat 160 MHz and T�100� mode at 100 MHz. �a� FT process �maxi-mum disorder� and �b� A-70 K process �maximum order�.

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FIG. 4. �Color online� Variation of the sound attenuation as afunction of temperature for the A–70 K process �maximum order�at fixed magnetic field values: L�010� mode at 160 MHz and T�100�at 100 MHz. See text for the description of the ENS curve.

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temperature around 12 K; this trend is more pronounced forthe T�100� mode, where it almost appears as a discontinuityin the slope. When a 16 T field is applied, a substantial in-crease of �� is produced below Tc �11.9 K� for both acous-tic modes but with a larger amplitude for the T�100� mode;such an increase of attenuation is expected when supercon-ductivity is quenched. Above Tc, a decrease of ���T� israther observed up to 20 K, which is likely due to a reduc-tion of the pseudogap anomaly. Surprisingly, a change ofslope persists below 15 K on the temperature profile of���T�, which could be consistent with the coexistence of asecondary phase with superconductivity even when disorderis minimized. To get an insight into this secondary phase andto ultimately isolate the superconducting contribution to theattenuation, we now examine precisely the field dependenceof the attenuation.

We have plotted in Fig. 5 the variation of the attenuation�� at 428 MHz for the longitudinal mode at different tem-peratures as a function of H2. As long as H�Hc2

� , �� varyquadratically with field at all temperatures between 2 and20 K, since straight lines are observed. Such a H2 depen-dence, which is observed for both modes at all frequencies,proceeds from the first correction term to transport and mag-

netic properties to which ultrasonic waves couple.23–27 If wewrite ���T� in zero field as a sum of two contributions, onedue to the superconducting �SC� state and another one to anexotic normal state �ENS�, ���T�=��SC�T�+��ENS�T�, wecan isolate the SC contribution by modeling the field effectson the ENS phase in the following way: ��ENS�T ,H�=��ENS�T ,0�+���T�H2. Thus, plots of �� as a function ofH2 at fixed temperatures yield ���T� as the slope and��ENS�T ,0� as the extrapolated value toward the zero fieldlimit. The contribution of the SC phase ��SC�T� can be ob-tained after substracting the ENS contribution. The velocityvariations at fixed temperatures vary also quadratically withthe magnetic field and a similar model can be used for ENScontribution: �v

v ENS�T ,H�= �vv ENS�T ,0�+�v�T�H2. It is thus

possible to extract a coefficient �v�T� that can help reveal,together with the ���T� coefficient, the nature of this ENSphase.

The ��ENS�T ,0� curves deduced from the precedingmodel are compared to the zero field data in Fig. 4. Theirtemperature profiles do not appear monotonous. When thetemperature is decreased from 20 K, the ENS curves for bothmodes coincide with the zero field one, but they departabruptly from each other around 15 K. For T�15 K, apartfrom the 12–15 K temperature range for the T�100� mode,the ENS attenuation is higher than in zero field, in agreementwith larger sound attenuation in the normal state compared tothe superconducting one. Anomalous behaviors beginning at15 K are also revealed by the ���T� and �v�T� coefficients.Examples of such coefficients for the L�010� mode are pre-sented in Fig. 6 at two frequencies, 160 and 428 MHz. Be-low 20 K, the ���T� coefficient increases with decreasingtemperature until an abrupt downward transition occurs at15 K; the transition is much more pronounced at 428 MHzsince the attenuation increases rapidly with frequency. The�v�T� is constant below 20 K, but it increases steeply at 15 Kwith a quasilinear variation at lower temperatures; here, thiscoefficient appears practically frequency independent. Thesefeatures of the ENS phase mimic the onset of an antiferro-magnetic order parameter at 15 K that is 3 K above the su-perconducting transition. This is consistent with studies

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FIG. 5. �Color online� Variation of the sound attenuation as afunction of the magnetic field for the A–70 K process �maximumorder� at fixed temperature values: L�010� mode at 428 MHz.

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FIG. 6. �Color online� Param-eters �v�T� and ���T� of the ENScontribution as a function of tem-perature for the L�010� mode at160 and 428 MHz.

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where deuteration of the BEDT-TTF molecules shifts thecompound on the pressure scale at the boundary of the phasediagram where superconductivity is replaced by an antiferro-magnetic insulating phase at 15 K.28 We suggest that the15 K anomalies observed in our velocity and attenuationdata are the result of a magnetoelastic coupling with an or-dered AF phase. The temperature at which this phase occursis TAF=15 K and appears to be very weakly field dependent�Fig. 2�a�� up to 16 T. This observation is consistent with thesymmetry of the AF phase deduced for the �-D8-Brcompound.9 Finally, we notice that the signs of ���T� and�v�T� are, respectively, negative and positive at all frequen-cies for both modes �Figs. 2 and 5�. Since the low tempera-ture profiles of the velocity and attenuation are dominated bythe giant pseudogap anomaly above 30 K, this means that amagnetic field applied perpendicular to the planes tend todecrease the attenuation and increase the velocity �or de-crease the softening�. Since this anomaly appears on thepseudogap line that joins the Mott critical point,5 this can beinterpreted as a decrease of criticality by a magnetic fieldapplied perpendicularly to the highly conducting planes.

Finally, the contribution of the superconducting state tothe attenuation ��SC�T� is presented in Fig. 7. For bothmodes, ��SC�T� is negative as expected for a superconduct-ing state. However, the temperature profile below Tc does notappear to be consistent with a conventional s-wave orderparameter for which a monotonous decrease of attenuation iswell known to be expected. For the L�010� mode, the de-crease of the attenuation at 15 K suggests the existence ofsuperconducting fluctuations, whereas the shoulder at 11.9 Kcoincides with the onset of phase coherence. Then, ��SC�T�goes through a minimum around 8 K before increasing fur-ther down to 2 K while remaining always negative. For thetransverse mode T�100�, although superconducting fluctua-tions are also effective below 15 K, they rather produce anenhancement of the attenuation followed by a sharp down-ward trend below 12.5 K and a further change of slope atTc=11.9 K. At lower temperatures, ��SC�T� decreases fur-ther and flattens below 7 K. These features around 7–9 Kcannot be reconciled with any theoretical model for the mo-ment; neither s or d wave superconducting order parameter

could yield an increase or a flattening of the attenuation atthese temperatures, although we must keep in mind the pe-culiar topology of the Fermi surface, which consists of twoparts, namely, the quasi-one-dimensional electron sheets andtwo-dimensional hole pockets. We remind that the ultrasonicL�010� mode probes the complete two-dimensional Fermisurface, while the transverse T�100� could only be sensitiveto one part. Finally, the low temperature features around 8 Kcould be the result of an interaction between the magneticand superconducting phases that could explain a secondarydissipation phase observed in the pressure transportmeasurements.3,29

IV. CONCLUSION

In conclusion, our velocity and attenuation data clearlypoint toward a competition between metallic �superconduct-ing� and insulating �antiferromagnetic� phases at low tem-peratures deep in the Fermi liquid part of the P-T phasediagram. The farther the system is from the first order bound-ary, the stronger is the superconducting phase relative to themagnetic one. This can be realized by applying hydrostaticpressure or, as demonstrated in our paper, by controlling theamount of disorder in �-H8-Br. This competition is summa-rized in Fig. 7: when magnetic fluctuations probably con-nected to an ordered AF phase disappear around 15 K, su-perconducting fluctuations grow rapidly to yield a transitionat 11.9 K. It is clearly demonstrated that disorder favors themagnetic fluctuations �huge dip at 33 K�, which is detrimen-tal to the superconducting state. However, this competitionapparently yields a phase separation over all the sample’svolume. Such a phase separation has been suggested frominfrared reflectivity data at high temperatures for fastcooling12 and the insulating regions were only found at thesurface. For slow cooling, only NMR measurements in amagnetic field revealed this phase separation15 originally ob-served in partially deuterated crystals.14 In spite of a rela-tively small portion of the volume occupied by this insulat-ing phase, the ultrasonic experiment appears highly sensitiveto it due to a domain structure �ultrasonic wavelength of theorder of 10 �m at 200 MHz�; this is confirmed by the hys-teresis observed on our velocity and attenuation data in the2–20 K range. Finally, although the attenuation data do notappear consistent with an s-wave order parameter, a thor-ough frequency and polarization analysis of the ultrasonicattenuation together with precise theoretical predictions30

will be needed to establish the symmetry of the supercon-ducting order parameter.

ACKNOWLEDGMENTS

The authors thank C. Bourbonnais and A.-M. Tremblayfor discussions and the critical reading of the paper and M.Castonguay for his technical support. This work was sup-ported by grants from the Fonds Québécois de la Recherchesur la Nature et les Technologies �FQRNT� and from theNatural Sciences and Engineering Research Council ofCanada �NSERC�.

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FIG. 7. �Color online� ��SC as a function of temperature:L�010� mode at 160 MHz and T�100� at 100 MHz.

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