Volume 148,number1,2 PHYSICSLETTERSA 6 August 1990

Ultrasonicstudyof the soft phononmodein Bi2Sr2Ca1Cu2O8singlecrystals

JinWu, YeningWang,Huimin Shen,JinsongZhuDepartmentofPhysics,NanjingUniversity,Nanjing210008,PRChina

Yifeng Yan andZhongxianZhaoInstituteofPhysics,ChineseAcademyofSciences,Beijing 100080,PRChina

Received15 May 1990;acceptedfor publication 5 June1990Communicatedby D. Bloch

Ultrasonic measurementson Bi2Sr2Ca1Cu2O8single crystalshave beencarried out. The in-plane shearmoduli C66 andC’ = [~(C11+ C22)— C,2] werederivedfromthesoundvelocitydata.It wasfoundthat theC’ modeshowedanoveralltrendofsofteningovera widetemperaturerangeaboveT~andtheC~modeexhibitedthreeobvioussofteningminimaaround240—250,150and 100K. Implicationsof theseresultsfor a possiblestructuralchangearediscussed.

Before the discoveryof the high T~oxide super- moduli, i.e. the orthorhombic shear modulusconductors,mostwell-knownA- 15 superconductors C~= ~ (C11— C12), influences the effective Younghada commonprominentfeature,i.e. theexistence modulus.That is to say,the observedanomaliesinof soft phononmodes.The modesare characterized Young’s modulusmayreflect a relatedsoft phononby an elastic constantthat is decreasingwith de- mode.Similaranomaliesin Young’s modulusat 150creasingtemperatureand they can lead to elastic and 250 K in Bi2Sr2Ca1Cu2O8singlecrystalshaveanomaliesandstructuralphasetransitions[1]. It is beenfoundby Xiang et al. [9], but they attributedwell known that ultrasonicmeasurementis a very theseto the vacuumgreaseandsilver paints. How-sensitiveprobefora subtlestructuralchangeora lat- ever,in ourpreviousultrasonicinvestigations[10],tice instability. Therefore,sincethediscoveryof high we found that therewasa clearsofteningminimumT~oxide superconductors,therehavebeenmanyre- in a longitudinal wave velocity around240—250Kports of ultrasonicmeasurementsin thesematerials, andtwo otheranomaliesnear 100 and 150 K coin-which showed the existenceof elastic anomalies cident with three attenuation peaks inaroundor aboveT~[2—5]. In order to further un- Bi2Sr2Ca1Cu2O8single crystals. Detailed analysesderstandthe natureof theseanomalies,it is impor- confirmedthat theseanomalieswerenot causedbytant to find the exact soft phononmode in super- vacuumgreaseor silver paints.conductingcrystals.In an earlyultrasonicstudyof In this Letter we report the results of ultrasonicYBa2Cu3O7singlecrystals,Saint-Paulet al. [6] ob- measurementsin Bi2Sr2Ca1Cu2O8singlecrystals.Atservedthe softeningof both the shearmode C44 at first, four velocitiesVLL, VL2, VL3 andV~1weremea-108 K andthelongitudinalmodeCL alongthe [110] sured.Thedirectionof thewavevectork andthepo-direction at 100 K. In contrastto ultrasonicmea- larizationvectore for thesesoundwaveswerekalongsurements,a vibrating reed method hasalso been the [010] longitudinal mode for VU, k along theused to measureYoung’s modulusin YBa2Cu3O7 [010] ande alongthe [100] transversemodefor V~1,singlecrystals, which showedsteplike changesnear k along the direction at 100 of the [100] longitu-100, 130 and 200—240 K (hysteretic) [7,8]. As dinal modefor VL2, k alongthe directionat 100 ofmentionedby Hoenet al. [7], the in-planeelastic the [010] longitudinalmodefor VL3. Thenthe in-

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Volume 148, number1,2 PHYSICSLETTERSA 6 August 1990

planetransversemodulusC66 and the kM [110] and Thus, the valueof C’ at 260 K is nearly2.3x 10’’e~I[110] shearmodulusC’ werecalculatedbasedon dyn/cm

2.thesevelocity data. Fig. 1 showsthetemperaturedependenceof C’ for

The singlecrystalsof Bi2Sr2Ca,Cu208with a T. of theBi2Sr2Ca,Cu208singlecrystal,which presentsan

84K and a density of 6.6 g/cm3 were grown by a flux abnormal behaviour: (a) its value is small (in re-

method [11]. The superconductingpropertiesand lation to theotherelasticconstants),and (b) it de-crystallinestructureof singlecrystalspreparedby the creaseswith decreasingtemperatureover a widesamegrouphavebeenreportedelsewhere[12,13]. temperaturerange(220—95 K). This is very similarThe samples were oriented with X-rays and then poi- to the shear modulus ~ (C,, — C,

2) of the A- 15 su-ished. MATEC6600 series equipment was used for perconductor, which undergoes a structural trans-both longitudinal and transverseultrasonic mea- formationat a temperaturenot far aboveT~[1]. In-surements.A 7.5 MHz PZTlongitudinalmodeand terestingly, Murakami et al. [15] have alsoa 5 MHz ac-cutquartzshearmode transducerwere independentlyobserveda similar elastic softeningbondedto the samplewith Nonaqstopcockgrease. behaviourin Bi2Sr2Ca,Cu208singlecrystalsusingtheThe soundvelocity was measuredby the standard measurementsof the elastic resonancefrequenciespulse-echooverlap technique. For each measure- (1=34.05kHz, at 78 K). Thesofteningminimumisment, at leastfive echoescanbe clearly observedat also around 100 K. Unfortunately,they could notroom temperature.Temperaturewas changedat a determinethe exact mode. It is worth mentioningrate of 0.5 K/mm. the interesting work of Dmowski et al. [161. From

For the orthorhombic structure of Bi2Sr2Ca,Cu208 their neutron scattering on Tl2Ba2Ca,Cu208 at lowsingle crystal and the sound waves propagating only temperature, Dmowski et al. proposed a model ofalong the c-plane, we can deduce the relation of the short-range ordering due to displacements of Tl andin-plane elastic constants and the sound velocity (V) 0 atoms. They suggested that, at low temperature,from the elastic wave equation [14]. The general both TI (or Bi in our case) and 0 atoms are dis-expression is placed along the [110] direction, resulting in local

order. The ordering, however, remains very muchC~ff—(l

2C,,+m2C22+C66) Ceff

+(12C,, +m2C

66)(12C

66+m2C

22) I2C IXIO’ dyn/cm’l ________ __________________

—12m2(C,

2+C66)2=0 (1)

and 5.3

CeffPV2, (2)••*

where Ceff is defined as the effective elastic modulus 4.9 ••

of sound propagation along the k direction, p is thesample density, / and m are the direction cosines ofkin the a—bplane, and C,,, C,

2, C22 and C66 are four •

independent elastic constants in the a—b plane. • ••Based on the four measured velocities VL,, VL2, VL3

andV~,and eqs. (1) and (2), the values of the elas- •tic constants C,,, C,2, C22andC66 were obtained as 4.1 .

follows: at 260 K, C,,=l.3xlO’2 dyn/cm2, __________ _____________________

C22= 1.1x 1012 dyn/cm

2, C,2=7.2x10’’ dyn/cm

2 80 120 160 2110 240and C

66=5.lx10” dyn/cm2. Since C,,—C

22 T(k)~ C,2+ C66, C’ canapproximatelyberepresentedby

Fig. 1. The I [~(C,, +C22) — CL2] shear modulus as a function ofC’ = ~[~(C,, + C22) — C,2] . (3) temperature for Bi2Sr2Ca,Cu20, single crystal (kIt [110],

eli [ITO]).

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Volume148, number1,2 PHYSICSLETTERSA 6 August 1990

shortrangeanddoesnotaltertheaveragesymmetry. pendentmeasurementsshowedthat no detectableAs mentionedby Dmowskiet al. [16], suchlocalor- shift ofthepeakpositionscouldbefound [21]. Fur-deringhasmanyimplicationswith respectto theor- thermore,the height of the peaksis approximatelyderingsuperconductivityin theseoxides.As weknow, proportionalto the squareof the frequencyaroundthis modulusC’ is conjugateto the orthorhombic 100 and240—250 K. Together,theseresultsnear100strain~= 2 (b—a)/ (a+ b).Thus,thesofteningof the and240—250K indicatethatsomekind of structuralC’ modulusis at leastin part due to orthorhombic changes exists in Bi2Sr2Ca,Cu208single crystal,sheardistortion,which shouldbeshownby high-res- which is at leastin partrelatedtothesofteningoftheolution structural data. In contrast to the shearmodeC66. For anotheroxide superconductorBi2Sr2Ca,Cu208singlecrystals,the YBa2Cu3O7has Tl—Ba—Ca—Cu—O (T~= 117 K) [221, the soft trans-beenextensivelystudied[17—201.An anomalyof versephononwith a polarizationvectorparallel totheorthorhombicstrainhasbeenreported[17,191. the [010] direction, propagatingalongthe [100],But oppositeresultsshowingno anomalyof ~have that is the C66 mode,hasalso beenobservedusingalsobeenreported[18,20]. Especially,a directmea- thermal diffuse scatteringelectron-diffractionpat-surementof the shear modulus ~ (C,,— C,2) in ternsby TEM. Similarly, in YBa2Cu3O7singlecrys-YBa2Cu3O7singlecrystalsalso showedno anoma- tals, Saint-Paulet al. [6] haveobservedthe soft-busbehaviorat T~[6]. The different behaviorof ening of the longitudinal mode CL= ~(C,, +theshearmodulusC’ betweentheBi systemandthe C,2+ 2C66) along the [110] direction at 100 K,Y systemmaybecausedby the differentmicrostruc- which mayalsobedominatedby theshearmodeC66.ture, since a [110] twining existsin the Y system All the aboveexperimentalresultsseemto becon-andnot in theBi system. sistentwitheachother, suggestingthat theexistence

Fig. 2 exhibitsthreeclearsofteningminimaof C66 of soft transversemodesaroundor not far aboveT~in Bi2Sr2Ca~Cu2O8singlecrystalsaround240—250, iscommonto severalhigh T~superconductors,which150 and 100 K. In our previousworks, threecor- mayleadto a possiblesubtlestructuralchangeor lat-respondingattenuationpeaksat the sametempera- tice instability at the sametemperature.Indeed,re-ture rangeswereobserved.Recently, frequency-de- fined neutrondiffraction measurementsof atomic

positionsin YBa2Cu3O684confirmed the existenceof structuraltransformationsaboveT~[23]. They

also found themovementof atomsto coalesceintoCon I X 10 d,n/cm2 I a coherentmotionjust above80 K anddefinitelyset

thestagefor theappearanceofthesuperconductivitystage.Otherexperimentaltechniquesalso providedevidenceof the existenceof a possiblestructural

• change.Burns et al. [24] reported an anomaly• • • • • • • aroundT~in thetemperaturedependenceof theA Ig

• • • • • • phononmode at 464 cm—‘ in a Ramanspectrum

• • studyof Bi2Sr2Ca,Cu208single crystals. A similar5.02 • • anomalyofthe B~gmodeat 340 cm—’ wasalsofound

in YBa2Cu3O7 [25]. High-resolutionspecific-heatmeasurementsshowed two anomalies in Cd-Ba2Cu3O7_~single crystal near T0 [26]; one was

• characterizedby a structuraltransitionandanother

4.98 was the superconductingtransition.Moreover,it is

00 ‘ 120 ‘ ‘0 ‘ ‘ 240 interestingto note that the resultsof YBa2Cu3O7inI ~ constantexternal magneticfields up to 8 T showed

that the elasticsoftening shifted to lower tempera-Fig. 2. TheelasticconstantC~asa functionof temperaturefor tureswith increasingfield [27], which may be evi-Bi2Sr2Ca,Cu205single crystal. dencethat thissofteningnearT~is an intrinsicprop-

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Volume 148, number1,2 PHYSICSLETTERSA 6 August 1990

erty of high T~oxide superconductorsandis closely [6] M. Saint-Pauletal., SolidStateCommun.66 (1988) 641;relatedto the superconductingtransition. 69(1989) 1161;

M. Saint-Pauland J.Y. Henry, Solid StateCommun. 72In summary, the in-plane modulus C66 and (1989)685.

C’ (kPI [110], eM [110]) of Bi2Sr2Ca,Cu208single [7] 5. Hoenetal., Phys.Rev.B 38 (1988)11949.crystals have been derived from ultrasonic velocity [8] X.D. Shiet al., Phys.Rev.B 39 (1989) 827.

data. The softening of the C’ mode at 100 K and three [9] X.-D. Xiangetal., Solid StateCommun.69 (1989)833.

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[15] S. Murakamietal., privatecommunication.[161W. Dmowski, B.H. Toby andT.Kawai,Phys.Rev. Lett.61

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