PHYSICAL REVIEW B VOLUME 36, NUMBER 4 1 AUGUST 1987

Anomalies in the internal friction and sound velocity in the high-temperaturesuperconductor La t SSro 2Cu04

P. Esquinazi, J. Luzuriaga, C. Duran, D. A. Esparza, and C. D'OvidioCentro Atomico Bariloche, Instituto Balseiro, 8400 Bariloche, Argentina

(Received 4 May 1987)

The internal friction Q' and the Young's-modulus sound velocity vE have been measured in

Lal SSrp2CUO4 using the vibrating-reed technique. Measurements were performed at a frequencyof 700 Hz at temperatures between 0.2 and 100 K. A drastic change of slope in the internal fric-tion versus temperature curve is observed at T=44 K just above the superconducting transitiontemperature T, =40 K. A plateau in Q

' is observed between 44 and 5 K. The sound velocityshows a decrease with decreasing temperature between 100 and 20 K and remains almost con-stant between 2 and 0.2 K.

The recently discovered ' high- T, superconductingceramic compounds have raised a number of questionsconcerning the nature of the interaction responsible forsuperconductivity. Measurements of internal friction andsound velocity could supplement those of other propertiesand help to understand the mechanisms that bring aboutthe superconducting transition.

In the present work, the vibrating-reed technique hasbeen used to obtain the Young's-modulus sound velocity(t~) and the internal friction (Q ') of a sample ofLa~ 8Sr02Cu03, which has a critical temperature of 40 K.The compound was prepared following the methods de-scribed by Cava, van Dover, Battlogg, and Rietman andwas then oxygen annealed for 6 h at 1000'C. The samplewas clamped at one end between copper flats and drivenelectrically by applying a sinusoidal voltage at a frequencyv/2 between a fixed electrode and the sample. Measuringcapacitively the amplitude of vibration at the free end as afunction of frequency v, the resonance curve was ob-tained, from which the attenuation Q '=d, v/v can bededuced. If 4 is the maximum amplitude, correspond-ing to the resonance frequency v, Av is defined as thewidth of the peak between the points where the amplitudefalls to A /2 '~ . Subsequently the sample was made to os-cillate at the resonance frequency by means of a trackingcircuit, and changes in this frequency and amplitude weremeasured as a function of temperature.

The sample is a slab 1.43 cm long, 0.297 cm wide, and187 pm thick. Its measured mass density is approximate-ly 6.0 g/cm, and the resonance frequency was found to be690 Hz. From these values a Young's modulusE =1.9X10'2 g/cmsec is obtained, which in turn givesfor the Young's modulus sound velocity vz =5.6 x 10cm/sec. The longitudinal sound velocity cL can be de-duced from this, provided the corresponding Poisson's ra-tio is known. No such data are available for this com-pound, but for reasonable assumptions of Poisson's ratiobetween 0.17 and 0.35, one obtains cL =v~x1.04 andci, =v~ x 1.27, respectively.

In a Debye solid, the sound velocity obtained from thespecific heat cD is given by

(3/cD ) = (2/cT') + (1/cL ),

2.5—

Lo, 8Sro2 Cu 0700 Hz

I

C)—2.0I

C3

OI—

LL

1.5UJ

+ 1.7

C3

1.5

3Q 4pT(K)

pp popopp pp

0.1

oppp

pooo po 0po 08p

I I I I

1 10

TEMPERATURE ( K )

100

FIG. l. Internal friction as a function of temperature. Theinset shows the point at which the plateau starts. The supercon-ducting critical temperature is 40 K for this compound.

where cT is the transversal sound velocity. Nieva et aI.have measured cD =3.4X10 cm/sec from specific-heatdata and Brun et al. have obtained cT=3.2X10 cm/secfrom Brillouin scattering of surface waves for this samecompound. These numbers are all consistent with cL ob-tained above and Eq. (1).

The internal friction data, deduced from the amplitudemeasurements, are plotted in Fig. 1 as a function of tem-perature. There is a decrease in g ' with decreasingtemperature which follows an approximate T depen-dence from the highest measured temperature of 90 K,until a drastic change in slope is seen at around 44 K. A

36 2316 1987 The American Physical Society

36 BRIEF REPORTS 2317

0.5

La~8 Sro2 Cu 0&

700 Hz0 OOO

0O0

0O0

I

C)

C3

z 0.2DC3

CLU

~ 0.1

CLUJ

0.05

0.02 '

0.1I I

1 10

TEMPERATURE ( K )

100

FIG. 2. Logarithmic plot of the internal friction, where thecontribution due to the clamping at the sample holder has beensubtracted.

plateau of almost constant attenuation is observed be-tween 44 and 5 K, and then there is a further drop in Quntil a new plateau is reached at approximately 2 K. Thisfinal plateau could be explained as due to the fact that atthese low values, attenuation from the clamping at theholder starts to be important. If a constant is subtractedto account for this and a logarithmic plot of Q

' is drawn(Fig. 2) it can be seen that the internal friction follows anapproximate T' dependence at low temperatures.

The point at which the high-temperature plateau startsis around 44 K (see inset of Fig. 1), which is somewhathigher than the T, of the material as measured by flux ex-pulsion and resistivity and also higher than the point TMat which the specific heat changes slope (defined in Ref.6).

In Fig. 3 the relative change in sound velocity is plottedas a function of temperature. A decrease of the sound ve-locity is seen with decreasing temperature between 90 and20 K. There is a minimum at approximately 20 K, and asthe temperature is lowered further the sound velocity in-creases until at around 2 K, and up to the lowest measuredtemperature of 0.2 K the rate of increase is very slow andthe velocity remains almost constant.

The decrease of sound velocity with temperature is seenin several amorphous dielectrics in A-15 compounds suchas V3 Si (Ref. 8) and also in martensitic transformations. 9

In amorphous materials the decrease is not completely un-derstood, although in the case of vitreous silica an anoma-lous coefficient of thermal expansion is thought to be re-sponsible. In the A-15's and in martensites it is ex-plained by a softening of the material preceding a

UJ

I—

OUJO

La& 8 Sr&2 Cu 0&

700 Hz

0 —ip

1 x 10

UDLlJ

LU

UJCL

OOOOOOOOO OOCOOOOOOOO

~o

0 00 O00 O0

O.l

I I l t

1 10

TEMPERATURE ( K )

100

FIG. 3. Relative change in sound velocity as a function oftemperature. The minimum is at 20 K. The absolute value ofthe sound velocity is VE 5.6X 10 cm/sec.

structural transformation. Jorgensen et al. ' in experi-ments with neutron scattering in a similar high-T, ceram-ic (La2-„Ba„Cu04) find no anomalies in the thermal ex-pansion. If the anomalous behavior of the sound velocityis due to the softening of the material, the phase transfor-mation present in La2Cu04 and inhibited by the additionof Ba or Sr (Ref. 10) could be responsible for the soften-ing observed. The sound velocity measured at a similarfrequency for the martensitic transformation in Cu-Zn-Alalloys has almost the same shape as that observed here, al-though of course the phase transition occurs at a highertemperature. The internal friction, on the other hand, isvery different from that measured here. In the A-15's,there is a sudden stiffening of the material below T„andthe data of sound velocity obtained here show only a verygradual change in slope at around 40 K. This could bedue to the fact that the material is a granular supercon-ductor and the transition is gradual, in which case theconstant sound velocity observed below 2K could indicatethat the transition has been completed. With such a pic-ture in mind the plateau in Q

' could be explained ifdomain walls between normal and superconducting re-gions were moving in a dissipative way. Against this in-terpretation is the fact that the plateau extends from atemperature slightly above T, to a temperature (T 4.5K) higher than that at which the sound velocity saturates.

Regarding the internal friction it is interesting to notethat the order of magnitude at the plateau Q

1.55 & 10 is similar to those reported in many amor-phous metals and insulators at the same frequency. " Theplateau in attenuation or internal friction which is usually

2318 BRIEF REPORTS 36

found in amorphous materials is interpreted by means ofthe tunneling model, in which it is assumed that tunnelingsystems (TS) exist which, through an interaction with thephonons, produce a relaxational absorption with a broaddistribution of relaxation times. The existence of TS inthis compound cannot be disregarded a priori. The highlyprobable existence of oxygen vacancies and smalltetrahedral distortions of the oxygen network in this ma-terial could lead to the formation of tunneling entities asin the case of vitreous silica. " If it is assumed that onlythe usual TS-phonon interaction is present, then a Tdependence of Q

' is expected to occur, instead of theT' dependence observed. Also, the change in relativesound velocity would show a maximum at the same tem-perature (T=4.5 K) as the plateau in Q

' starts, insteadof the saturation at low temperatures seen in Fig. 3. How-ever, it should be taken into account that the specific heatat low temperatures shows a linear behavior well belowT, and up to the lowest measured temperatures (T =1 K).This could be due to normal electron excitations whichsurvive in normal regions of the sample, and the normal

electrons are known to interact with the tunneling entitieschanging the behavior expected in an amorphous insulatoror superconductor below T,. ' It should be noted that thecoefficient of the linear term y observed in the specificheat is much greater y = 1 x 10 J/gm K than thelinear term which is observed typically in amorphous met-als [y=3x10 J/gmK for amorphous Zr7oNi3o (Ref.11)] or insulators [y=1.6x10 J/gmK for suprasil I(Ref. 11)]due to the TS.

The eAect of oxygen content in the sample should be ofimportance in the formation of these tunneling systems.It has already been established ' that it has greatinfluence in the critical temperature, and further experi-ments are underway to see whether the correlation be-tween T, and the onset of the plateau in Q

' is main-tained for different oxygen contents.

Helpful discussions with M. Nunez Regueiro, A. A.Ghilarducci de Salva, G. Nieva, F. de la Cruz, and theLow- Temperature Group are gratefully acknowledged.

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