PHYSICAL REVIEW B VOLUME 36, NUMBER 16 1 DECEMBER 1987

High-magnetic-field study of superconducting &Qa2Cu&Q7

J. S. Moodera, P. M. Tedrow, and J. E. TkaczykFrancis Bitter National Magnet Laboratory, Cambridge, Massachusetts 02139

(Received 27 July 1987)

The resistance of single-phase samples of YBa2Cu307 —~ has been measured as a function oftemperature in magnetic fields up to 23 T. The nearly linear temperature dependence of theresistivity characteristic of this high-T, material was observed from room temperature down toabout- 120 K. Between 120 K and T,o—92.5 K the resistivity drops more quickly. Analysisshows this behavior to be consistent with the effect of three-dimensional superconducting Auctua-tions as was shown by Tsuei et al. for zero magnetic field. A critical-field slope of 3.2 T/K is ob-tained.

INTRODUCTION

The r'ecently discovered high-T, oxide superconductors'display unusual normal-state properties and the possibleabsence of the isotope effect. Considerable theoreticalinterest in these materials has been generated. The dcresistivity of the sintered material shows a striking lineardependence on temperature from room temperature downto just above the superconducting transition. It has beennoted that if this dependence represents an intrinsictransport property of the material, that is, one not due tothe granularity, then it implies an anomalously high in-elastic scattering rate. In a temperature region above thebulk superconducting transition the resistivity deviatesfrom this behavior. The resistivity decreases below an ex-trapolation of the linear behavior and resembles the effectof superconducting Auctuations. An examination of thisdecrease in fields up to 23 T shows that this decrease canbe described by the three-dimensional (3D) Aslamazov-Larkin (AL) theory. This result was found previously byTsuei et al. in zero field and is inconsistent with the sug-gested two-dimensional character of the crystallographicand electronic structure. Recent measurements on singlecrystals by Worthington, Gallagher, and Dinger confirmthe three-dimensional nature of the superconductivity inthis material.

Although quantitative information has been difFicult toextract, the temperature dependence of the superconduct-ing critical magnetic field has in the past been used suc-cessfully to identify different electron scattering mecha-nisms in metals and to give a more complete description ofthe superconducting pairing in real metals. Critical-fieldmeasurements on high-T, oxide superconductors havebeen pub/ished, ' but analysis is di%cult due to two fac-tors. First, the enormous critical field (hundreds of tesla)is beyond the magnetic field available for its measurementexcept in the temperature region close to T,o. Second, thetransition width broadens considerably with the applica-tion of a magnetic field making the position of the phaseboundary uncertain. The broadening is universally seen insintered material and is generally attributed either to a-large critical-field anisotropy or to multiphase material.Indeed, studies of single crystals show critical field andcritical current anisotropy. " Previous measurements of

the magnetic-field behavior of sintered samples have beenrestricted to temperatures at and below the superconduct-ing transition. We now have extended these measure-ments on independently fabricated samples to tempera-tures well above the transition and to higher fields.

EXPERIMENT

Samples of YBa2Cu307 b were made by the usualmethod of solid-state reaction of the oxide powders fol-lowed by an anneal at 900'C and a slow cooling in pureoxygen. The samples were cold-pressed under 1.4X 10'psi before the oxygen anneal and were found to have adensity 75% of that theoretically predicted. X-raydiff'raction shows these samples to be single phase. Thezero-field transition widths for the best samples are lessthan a degree as measured by both their resistive and di-amagnetic response. The diamagnetism was measured us-

ing a SHE Superconducting quantum interface devicemagnetometer. Resistivity was approximately 800 pQ-cm. The resistance was measured with a dc four-pointtechnique using connections anchored with silver paint. Avariable temperature probe was provided by the facilitiesof the Francis Bitter National Magnet Laboratory formeasurements in a liquid-nitrogen dewar which fit intothe 1-in. bore of a water-cooled Bitter magnet. Tempera-ture was measured with a Pt resistance thermometerwhich was corrected for its magnetoresistance.

RESULTS AND DISCUSSION

The resistance was measured as a function of field atconstant temperature from 300 to 68 K (Fig. 1). Severalfeatures of the resistive transition appear to be common tothe high-T, oxide superconductors. The resistance doesnot rise from zero to the normal-state value in a narrowinterval of field. The so-called "transition width" is essen-tially the size of the critical field. Within a few degreesbelow T p the resistance becomes nonzero for small ap-plied fields; as the field is increased the resistance satu-rates at some small fraction of the normal-state resistance.This is shown most clearly in Fig. 2. As the field is in-creased further the resistance abruptly begins to rise again

36 8329 1987 The American Physical Society

833P J. S. MOODFRA P M TED , AND J. E. TKACZYK 36

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36 HIGH-MAGNETIC-FIELD STUDY OF SUPERCONDUCTING. . . 8331

and the resistance then continues to rise toward thenormal-state value. The low-field behavior, as exemplifiedby the cusplike resistance rise in Fig. 2, may be attributedto Josephson coupling between grains. The second fieldregion, over which the sample regains most of its resis-tance, is where the resistance of the grains is recovered.In our most recent measurements on monolithic samples,the low-field behavior is absent; the resistance remainszero until the field corresponding to the second rise de-scribed above. These samples were —1 x 1 x 0 mm piecesof material with faceted faces picked out of the reactedpowder before pelletizing.

The critical-field phase boundary is generally found bychoosing for each temperature the field for which theresistance has risen to some fraction of the normal-stateresistance. In this system the severe broadening castsdoubt on the validity of this procedure. Therefore, wehave looked toward an analysis of superconducting fluc-tuations to obtain critical-field information. In bulk su-perconductors, conductance fluctuations are usually asmall fraction of the normal-state conductivity. However,due to the short coherence length and high normal-stateresistance of this material, conductance fluctuations aresignificant. An additional consequence is the failure ofthe Ginzberg-Landau description within an observabletemperature region (-0.1 K) about T,. ' The datapresented here lie outside this region.

The data presented in Fig. 1 are replotted in Fig. 3 as afunction temperature for constant applied field. Thecurve in Fig. 4 shows a comparison of the fluctuation con-ductivity to the three-dimensional AL term.

2

crAp = (T,/T T, ) '~2. —

A value for the coherence length of the order of the BCSvalue g —1 nm is obtainable from the critical-field slope. "The absence of the Maki-Thompson-type' contributionto the Auctuations is usually associated with strong pair-breaking. ' The presence of this term would increase the

magnitude of the conductance fluctuations by a factor of5. A recent theory proposes that the inelastic processesplay an important role in the superconductivity of thehigh-T, ceramic superconductors. As such, inelasticscattering may account for the absence of a contributionto the Auctu ation conductivity from the anomalous(Maki) term.

Deviations from the AL expression at higher tempera-tures are characteristic of superconductors with very shortmean free path. ' Tsuei et a/. have suggested this to bethe case for YBa2Cus07 s. It is generally believed thatthe deviation at higher temperatures is the result of theunphysical emphasis the AL term gives to short wave-length Auctuations. This failure is particularly apparentin YBa2Cu307 —b, since the normal-state conductivity isdecreasing as T ', that is, faster than the AL Auctuationconductivity at high temperatures. The AL result isequivalent to that obtained from the Ginzberg-Landaufree-energy expansion to fourth order. Near T,o thetemperature-dependent coherence length serves as a lowercutoff to the wavelength of superconducting fluctuations.At higher temperatures the coherence length decreases in-troducing a contribution from smaller wavelength fluctua-tions, a contribution which would not be favorable in ahigher-order Ginzberg-Landau free-energy expansion. Aphenomenological modification of the AL expressionwhich has been used previously introduces an ad hoccutoA' to the Auctuation spectrum at large wave number.With this modification, the Auctuation conductivity athigh temperature decreases faster than the AL result.Ami and Maki' introduced expressions, somewhat morecomplicated and involving numerical integrations, basedon the microscopic theory which reproduced the charac-teristic damping of the Auctuation conductivity at hightemperature seen in the data. In Fig. 4 the modified ALterm for a cutoA' of wavelengths less than 10 times thecoherence length is shown. In the past, ' cutoA's of the or-der of the coherence length were found appropriate for

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FIG. 5. The measured fluctuation conductivity plotted onaxis for which the intercept with the temperature axis defines

T, (H). The AL term corresponding to zero field is shown. Thesolid lines through the data measured in a field are guides to theeye.

8332 J. S. MOODERA, P. M. TEDROW, AND J. E. TKACZYK 36

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This enhancement accounts for the decrease in slope nearT, (H) of the curves in Fig. 5. The enhancement is readilyseen in thin films and is a-consequence of the fact that theenergy spectrum in a field is discrete. ' We have takenthe intercept with the temperature axis to define T, (H)giving the critical-field slope of 3.2 T/K (Fig. 6). Thisvalue is intermediate between those values obtained by theconventional method of taking the field at which the resis-tance rises to 50% and 90%%uo of the normal-state resistivityfor each temperature. This suggests a critical field at zerotemperature of just over 200 T as estimated from theGinsberg-Landau theory. However, in the absence ofspin-orbit scattering, the critical field would be limited tothe Pauli limiting field Hp 1,84X T 0 T. '

085 90

Te m pe ra ture (K )

FIG. 6. The critical field as determined from the intersectionof the curves in Fig. 5 with the temperature axis.

other materials.In Fig. 5 the data near T,o are plotted on axes for which

the AL fluctuation conductivity plots linearly and. inter-cepts the temperature axis at T,o. The zero-field data areindeed linear in accord with Fig. 4 and intercept the tem-perature axis at T,o of 92.4 K. The theoretical 3D fluc-tuation conductivity' in a field applied perpendicular tothe current direction has a square-root singularity atT, (H). However, the coefficient of the singularity is tem-perature and field dependent and has a magnitude whichis larger than that of the AL term. That is, the fluctuationconductivity is enhanced by a perpendicular applied field.

CONCLUSION

The resistance of single-phase YBa2Cu307 —q has beenmeasured as a function of field from 300 to 68 K. NearT,n the resistance becomes nonzero for very small fieldsindicating that at T,n the grains become Josephson cou-pled. The fluctuation conductivity is adequately describedby the three-dimensional AL term with a wavelengthcutofI' of 10 coherence lengths. The absence of the anom-alous (Maki) contribution to the fluctuations indicatesstrong pairbreaking possibly due to inelastic scattering.

ACKNOWLEDGMENT

We would like to thank the U.S. Department of Energyfor support under Grant No. DE-FG02-A4ER45094. TheFrancis Bitter National Magnet Laboratory is supportedat the Massachusetts Institute of Technology by the Na-tional Science Foundation.

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