PHYSICAL REVIEW B VOLUME 44, NUMBER 22 1 DECEMBER 1991-II

Anisotropic thermal conductivity of T12BazCaCu2Os and &BazCu307 single crystals:Anomaly in both in-plane and out-of-plane directions

Cao Shao-Chun, Zhang Dong-Ming, and Zhang Dian-LinInstitute of Physics, Chinese Academy ofSciencies, Bejiing I00080, China

H. M. Duan and A. M. HermannDepartment of Physics, Uniuersity of Colorado, Boulder, Colorado 80309

(Received 3 December 1990; revised manuscript received 26 March 1991)

The anisotropic thermal conductivity of T12Ba2CaCu20, and YBa2Cu307 single crystals have beenmeasured. In contrast to some earlier measurements on YBa2Cu307, we found both an in-plane and anout-of-plane anomaly for these two compounds. We argue that phonon-phonon scattering may also playsome role in the phenomenon.

All the oxide superconductors with T, ~90 K show apronounced enhancement in thermal conductivity whenthe samples enter superconducting state. ' A straight-forward way to understand the phenomenon is to ascribeit to the reduction of phonon-electron scattering due tosuperconducting pairing, which greatly increases thephonon contribution to thermal conductivity. ' Thisexplanation was then supported by experiments on singlecrystals, for which no anomaly was found in the c axis. '

This is a natural consequence of the fact that thephonon-electron interaction in the c axis is overshadowedby defect scattering. We have carried out careful thermalconductivity measurements on single crystals ofT12Ba2CaCu20, as well as YBa2Cu307 In contrast toearlier measurements, we have clearly observed thethermal conductivity anomaly in both in-plane and out-of-plane directions for both materials. We argue that,while the phonon-electron scattering may be important inthe phenomenon, we need to take some other possiblemechanism into account for the understanding of theout-of-plane anomaly.

T12BazCaCu208 crystals were grown by a method de-scribed in detail elsewhere. ' '" The YBa2Cu307 singlecrystals were grown by the usual Aux method in the fol-lowing procedure: Y203, BaCO3, CuO in the ratio 1:4:10,were thoroughly mixed, and heated to 870'C. After stay-ing there for 12 h the material was reground and heatedagain to 1000 C. The material was cooled at a rate of3—5'C/h and kept at 680'C for 5 —6 h before cooling to450—480 C, where it was treated in oxygen atmospherefor 3 days. It was a common experience that the qualityof small YBa2Cu307 single crystals is better than biggerones. In our measurements we always chose small crys-tals, the size of which usually was about 0.3X0.3X0.05mm .

Thermal conductivity was measured using a sweepingcomparative technique schematically shown in Fig, 1.Sapphire 1 was heat sunk to the cryostat, while sapphire2 was isolated from the cryostat to build between the twoplates a sweeping temperature differential which wasmeasured by thermocouple 3 composed of thin silver tape

and Constantan wire of diameter about 20 pm. A secondthermocouple 4 from the same materials but with thejoint in the middle of the silver tape separated the tapeinto two sections whose length ratio simply equals the ra-tio of their temperature differentials in the configurationof Fig. l (but with 4 directly stuck onto 2) because thethermal conductance of Constantan was negligible incomparison with that of silver tape. The superconduct-ing single crystal was then inserted between 2 and 4,which yielded a new ratio of temperature differentials.The thermal conductivity of the sample can be easily de-duced from the change of temperature differentials andthe thermal conductivity of silver. On the back of sap-phire 2 a third sapphire 5 deposited with Cr film wasstuck as a heater which provided a very homogeneoustemperature throughout the plate. To get the optimisticminimum error in measurement the conductance of thesilver tape should be adjusted comparable to the conduc-tance of the sample. In the comparative method it wasalso essential to minimize the contact thermal resistanceon both sides of the sample. This was rather easy to real-ize in our measurement because we need not have stuckthe thermocouple joint on the sample, and we found itdifBcult not to make good contacts of the crystal with the

FIG. 1. Schematic diagram of the setup for thermal conduc-tivity measurements (see text).

12 571 1991 The American Physical Society

I2 572 BRIEF REPORTS

1.20

1.00C)C)

G.eo

G.BO

0.40

T48a~CaCu~OI

oi+o~~&De ~

0 g~g~ ~ IIso

~ ~ 0~ r rrrQ+ g*

sample1a2 ~3agp5*

1.20

1.00

0.80

oeo ~

0.20 I

150

FIG. 2. The reduced thermal conductivity of T12Ba&CaCu208single crystals: rc,b e; &, ~ 0 Q.

silver tape as well as with the sapphire substrate. Thegood contacts were confirmed by several ways: using apiece of copper wire of comparable thermal conductanceto replace the sample we got quite a reasonable result;when a sample of good conductance was clamped in, theratio of temperature differential was not changed; and byreloading the same crystal we always obtained reproduci-ble results.

The thermal conductivity was measured between roomtemperature and about 70 K. The room-temperaturevalue of in-plane thermal conductivity, ~,b, is 1.5+0.2W m ' K ' for the Tl compound and 3.0+0.7Wm 'K ' for the Y compound. The latter value issomewhat lower than earlier reports. ' The anisotropy isabout 9 and 17 for the two compounds, respectively. Theformer is close to that observed for Bi2Sr2CaCu208. '

And the latter is close to that reported in Ref. 9, butmuch higher than found in Ref. 8. We think that in theconfiguration described in Ref. 8, the value of out-of-plane thermal conductivity, ~„could be overestimatedbecause of the inhomogeneous distribution of heatcurrent and the leak along thermocouple. The absolutevalue of ~,b and ~, are rather sample dependent. Thismay be partly due to the different sample quality andpartly due to the uncertainty in judging the effective sam-ple geometry. In fact, when we plot the data in a reducedscale, we find that most of the results are quite consistentwith each other (Figs. 2 and 3). In the normal state, K sand ~, decrease when the temperature is lowered. Butone YBa2Cu307 crystal shows a negative slope of K b.The reproducibility of thermal conductivity in Tl-2:2:1:2crystals is consistent with the measurement of thermo-power which shows much less sample dependence thanY-1:2:3crystals. " In contrast to earlier measurements onYBa2Cu307 single crystals, ' the present results showthermal conductivity anomaly across T, for both in-planeand out-of-plane directions. The out-of-plane anomaly iscertainly not caused by the poor quality of the crystalswhich might lead to some mixing between the propertiesof the in-plane and out-of-plane directions. This mixingshould increase x, and lower the anisotropy, while we

1.20

1.00

O

~ o.eo

0.60

0.40

Yaa&cu&07

~ ~ g ~ gg ~ ~ ~ ~ ~ ~ ~ /PIdddd

4 e, yo c oo 0)0+&o ~0o~ 0

yOO

sample6d7eao90

1.40

1.20

CO

1.00

O.eo

0o60 ~

0.20 I

150 250 0.40

FIG. 3. The reduced thermal conductivity of YBa2Cu307 sin-gle crystals: Ir,q 6 ~; v, 0 0.

find the anisotropy in our crystals is comparable or evenlarger than previously reported. The good quality of thecrystals has also been proven by the analysis of four-circle diffractometer as well as by the measurements ofother transport properties. ' '"

It is not clear why the anomaly in ~, was not found insome earlier measurements. ' We have checked our re-sults several times and we are sure than our results are re-liable. All the five samples for which sc, was measuredshow a similar anomaly at T„ though the anomaly forT12Ba2CaCu208 is not as pronounced as YBa~Cu307.The picture that the upturn is due to a decrease inscattering of phonons by charge carriers as the latter con-dense into Cooper pairs is so natural and the anomalywas so successfully rehearsed by using the theory of Bar-deen, Richayzen, and Tewordt' that the discovery of theanomaly in ~, is quite unexpected since the out-of-planeanomaly should have been strongly depressed by defectscattering. However, if we make a scrutiny into the pic-ture, we find it not as convincing as it seems to be. Theconclusion of strong out-of-plane defect scattering isbased on the anisotropy of thermal conductivity, assum-ing as isotropic contribution of phonon modes and pho-non velocity. While it may be true that the phonon-defect scattering is anisotropic, it may also be true thatthe effectiveness of different phonon modes to thermalconductivity and the phonon velocity are anisotropic,too. Although the anisotropic contribution of phononmodes is dificult to determine experimentally, indirectevidence is provided by our measurements showing goodreproducibility of anisotropy for the same material but amarked difference for different compounds. This meansthat the anisotropy is rather intrinsic to the definite struc-ture of the compounds, which is supported by the close-ness of anisotropy of different materials with a similarstructure. ' If, due to the quite anisotropic structure,only part of the phonon modes are active in thermal con-ductivity along a definite direction, the phonon mean freepath should be substantially larger than calculated by~= —,'cvl which assumes all phonons are equally effectiveand gives, in our case, the anisotropic mean free pathshown in Fig. 4 where c and v data are taken from Refs.

BRIEF REPORTS 12 573

30.0—

20.0o~b

0 ~ g g ~

~ o p o o I()t & 8~ ~ ~ ~ ~ ~

— 100

10.0 —&)

0.050 i50 250

-100350

FIG. 4. Anisotropic mean free path of phonons of the twocompounds calculated by ~= 3cvl. The same symbols are used

as in Figs. 2 and 3.

14 and 15. Therefore, the anisotropy of phonon velocityand phonon modes effective for heat current may enlargeI, to a value where the condensation of carriers can befairly felt by phonons for a crystal of good quality. Thusthe upturn in ~, at T, can still be understood in theframework of a phonon-electron scattering mechanism.While this explanation seems plausible, we are facing thedifficulty that the out-of-plane electron mean free path isvery short, especially for T128a2CaCu208, ' which shouldgreatly weaken the effectiveness of electrons in scatteringphonons. ' An additional puzzle concerning both ~,band ~, is that, while the carrier density in Bi and Tl com-pounds seems lower than YBa2Cu307 and the supercon-ducting transition of the the former is much broader thanthe latter, it does not lead to a weaker anomaly in Bi andTl (Refs. 17 and 18) compounds.

To result in an upturn in thermal conductivity at T, byphonon-electron scattering, some restrictions should beplaced. The electronic thermal conductivity should bedecreased to an extent that the gain of phonon contribu-tion markedly surpasses the loss of electron contribution.This can be realized by the increase of electron-defectscattering, by the decrease of carrier density, or by theshift of T, to a higher temperature. ' However, introduc-ing many defects takes the risk of inducing two negativeeffects: shortening the mean free path of electrons whichmay weaken electron-phonon scattering, ' and increasingthe relative importance of phonon-defect scattering. Thecarrier density should not be too low to ensure that theelectron-phonon scattering is not overshadowed byphonon-phonon or phonon-defect scattering. The shift ofT, to a higher temperature would increase the relativeimportance of phonon-phonon scattering. Since theelectron-phonon scattering synchronously influences boththe phonon and the electron thermal conductivity, ' aproper estimate of electronic contribution would be a use-ful approach to see if the above restrictions are fulfilled ina self-consistent way. Unfortunately, quite scattered re-sults, even some paradoxical, were obtained using theWiedemann-Franz law to estimate the electronic contri-

bution. "fhe matter is: how far we can rely. on this law ina system with many more two-dimensional characteris-tics for electrons than for phonons. Alternatively, onemay experimentally determine the electronic contributionby changing the carrier density. But it is difficult tochange the carrier density without introducing additionaldefects. Thus, when one compares the thermal conduc-tivity in the normal state of the superconductor with itsinsulating counterpart, one could find quite different re-sults: an increase, ' a decrease, or roughly the same.The comparison of La2 Sr„Cu04 with La2 „Ba Cu04does show that defects play an important role in thereduction of the phonon mean free path.

Up to now all the treatments agree to a phonon-dominated out-of-plane thermal conductivity with negli-gible phonon-electron scattering. Phonons should alsocontribute a great deal to the in-plane thermal conduc-tivity, otherwise one does not expect an upturn anomalynear T, . However, while the phonon-electron scatteringmay be important in determining ~,b, it is not proved toassume a negligible phonon-phonon scattering. In fact,we notice that the temperature dependence of both ~,b

and ~, are somewhere in between the curve for a crystal-line solid and that of an amorphous material. We mayassume that this kind of temperature dependence is acompromise of phonon-phonon scattering and phonon-defect scattering at least in ~„may also be in ~,b, becausethe contribution of phonon-electron scattering dependslittle on temperature at high temperatures and decreaseswhen the temperature goes down very low. ' So we maytake the change to negative values in the slope of thethermal conductivity curves as a signal of the relative in-crease of phonon-phonon scattering. Then we plot theslope below T„d 1nz!dT~z & z, against the slope in nor-

C

mal state, d lna. ldT~T )T„ in Fig. 5. We see that all the

collected data give an obvious trend: the tendency frompositive to negative of the slope in a normal state leads toa more pronounced anomaly in the superconducting

10

-20 I I I I I I i I

-3 -2 —1 0 1 2 3(din/C jdT) (10 K )

FIG. 5. The relative slope of thermal conductivity below T,and as a function of that above T, . Y-Ba-Cu-0: ~ (Ref. 8); A(Ref. 4); + (Ref. 1); + (Ref. 5); + (Ref. 3);*present work.Bi-Sr-Ca-Cu-0: Q (Ref. 19); + (Ref. 18). Tl-Ba-Ca-Cu-0:P present work. Gd-Ba-Cu-0: 0 (Ref. 2).

12 574 BRIEF REPORTS

3.0

COCO

~~ 0

8

1,0

0.040 50 60 70

(K)90

FIG. 6. The reduced height of the anomaly against the tem-perature position. The same symbols are used as in Fig. 5.

state. The result seems to imply that the more importantthe phonon-phonon scattering, the more pronounced theanomaly is. %'e get further support to the picture byplotting the reduced height of the anomaly, ~(T )la.(300K), against the temperature position T (Fig. 6). Theshift of Ir(T ) to a lower temperature with increasing~( T ) is characteristic of phonon-phonon scattering. Re-cently the out-of-plane thermal conductivity ofBi2SrzCaCu208 was measured. ' Although the authors

claimed the lack of any anomaly in ~, near T„we can ac-tually see a clear kink at T, in their data (Fig. 1 of Ref.19), though the anomaly is not as large as in K b. '

If the anomaly below T, has some relation to thephonon-phonon scattering, how can we understand theenhancement of thermal conductivity in the supercon-ducting state? A possible explanation is the softening ofphonon modes across T, (Ref. 20), which could increasethe mean free path. This is easy to understand becausethe long wavelength phonons are less scattered than theshorter ones. Since the softening of phonon modes maybe more extended than carrier pairing, which has a veryshort coherent length, the former should be less sensitiveto the broadness of the transition. However, as at presentwe do not know much about the phonon modes responsi-ble for thermal conductivity, it is difficult to judge if thesoftening is strong enough to account for the enhance-ment in thermal conductivity.

In summary, we have measured the anisotropicthermal conductivity in T128a2CaCu20, and YBa~Cu307single crystals. Both in-plane and out-of-plane anomalieswere observed. The results together with earlier mea-surements show that, while the phonon-electron scatter-ing may be important in the phenomenon, phonon-phonon scattering may provide an additional source.

This work partly supported by the Chinese NationalCenter for Research and Development on Superconduc-tivity.

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