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Physica l7l ( 1990)223-230 C North-Holland

Temperaturedependence the magnetic field penetration depth in of YBa2CurOt-, measured ultra fine powder on
V.F. Gantmakher,N.I. Golovko, I.G. Naumenko,A.M. Neminsky and A.V. Petinova
Institute of Solid State Physics, Academy of Sciencesof the USSR, Chernogolovka, Moscow District, 142432, USSR Received l5 August 1990

The temperature dependenceofthe magnetic field penetration depth,l(Z) in superconductingYBarCurOT-5 has been determined by measuringthe AC susceptibility of fine powder al the frequency 105Hz. The reason lor noticeablechangesin ,t at low temperatureshas been found out: strong scatteringofcarriers by low-frequencyexcitations.The coupling constantwhich controls the superconductivity has been estimated.At low temperaturesa paramagneticgignal superimposedto the superconductivity one has been observed.It is probably due to alteration in the interaction ofthe magnetic moments near the surfaceofthe particles.

l. Introduction In spite of the large number of investigations,the electrodynamics of YBa2Cu3O7_5in a superconducting state has not been elucidatedso far. For instance,the temperaturedependence the magnetic of penetrationdepth 2(7") is still to be clarified []. Numerous measurements made by different methods (muon spin resonance12,31,magnetization in . weak [4] and strong [5] fields, surfaceimpedance'', at high frequencies [6-8], etc.) causesome doubts concerningboth the presence ofa power term in the dependence,t(Z) at"tow temperaturesand the behaviourof the function 1(T) in the vicinity of [. In particular, the measurements AC susceptibilityon of fine powders [9] gave an extremely great value of ,1(O) and a largequadraticterm at low temperatures. To get some additional information on the function 2(7") we measuredthe surfaceimpedance (AC susceptibility) of a YBa2Cu:Oz_a fine powder at the frequencies l0a- 105Hz.

2. Experimental The powder was produced by the spark erosion method [ 10] . The electrodes which electric pulses to were applied were made of YBa2Cu3Or-6ceramics and immersed into the liquid oxygen. When pulses

power, duration and shapewere chosenadequately, the substance evaporatingfrom electrodeswas condensed into almost spherical particles of the same chemical composition as that of the electrodes. The average sizeof particlesin the powder was determined by measuringthe specificsurfaceareawith the help of the polyatomic adsorption method. The particles had the orthorhombic structure with the parameters a:3.83 i\, b-3.8S A and c= I l.l6 A. No other phaseshave been observedwithin the accuracy of the X-ray phaseanalysis. The oxygen content was found by the iodometric analysisto be d= 0. 17.The parameters the powder of were stable at least during a year if the powder was kept in an argon atmosphere.When the powder was subjectedto the pressureof up to 2 kbar, solid samplesproducedwere insulating.This may be the result in of the oxygen def,rciency the surfaceiayer of the particles.In this casethe measuredd value is a mean one only. To perform the measurements,the powder was loosely settled in a cylindrical container, the filling factor being about 0.25. To make surethat there were no electric contacts between the particles, in other words, that no superconducting macroloopsexisted, which would shield the inner part of the container from the penetration of the alternating field, a test mixture of the powder under examination withZrO, powder (with 4:l weight ratio) was fabricated.A


1)^

V.F. Gantmakher et al. / The temperature dependenceof A(T) in YBa2CujO7_5

relative volume occupiedby a conductingpowder in the containerwith the mixture wasx! 120lo onlv. that is, it was below the percolation threshold x,,xl5o/0. The signal from the mixture decreased the ratio by equal to that of the weights of the conducting fraction. This means that even in an undiluted sample contactsbetweenthe particleswereof no importance [9 ]. The absolute value of the diamagnetic signal U(O) /U-"* at low temperatures, determinedbelow (seeeq. (3)), servedas an extra check. It should be noted that not all the powder samples could stand up to this setof tests.It seemsthat sometimes particles adhere into clusters at the stage of powder production. All the results presentedbelow were obtained on the powder of one batch with averageparliclessize 2r= 1920+ 40 A. After fabrication the powder was not subjectedto any additional thermal treatment. Moreover, an attempt to annealit in oxygenaI T:400'C for 10 h resultedin emergence other phasesand in broadof ening of the superconductingtransition. The samplewas placed inside one of the two identical couples of induction coils connected towards each other and the disbalancesignal was measured. To reduce the changeof the backgrounddisbalance signal,the coils were disposedin liquid helium over the external surfaceof a small overturned dewar. The sample together with a thermometer and a heater _ were placed inside the dewar in gaseous helium. To. ''' prevent temperature gradients on the sample, the container for the powder was made of sapphire,its inner diameter being I mm, the outer one 9 mm, the height about l0 mm. Signal U, arising upon introducing the container with the powder into the coil, is causedby the total magnetic moment M:H. I y.u=HXV, .

nal arisingupon introducingthe superconducting lead samplewith sizesequal to inner sizesof the powder container.This made it possibleto take into account the geometricfactors resultingfrom the ratios of the coil-to-samplesizes.Comparing the signal from the powder with that from the sample with the known susceptibility, | /4n, we get

-x :
X^u*

Lr -:
U^u*

U (t/an)V 2V U
Urut X^u* Ve 3 Vp LI.ul

(2)

Here V is the volume of a lead sample and U-u* is the magnitude of the signal, when the flux is completely extruded from the powder (r.:0) tT vm
ax-2Vvcat\

-3-vo ,, .

(3)

Here rr is the volume of a separateparticle, Vp:P/ 4 is the volume of the powder determined through its weightP and the "ideal" density4:6.3 g/cm3,H is the external magnetic field and I is the susceptibility of a particle with its demagnelization factor being taken into account. For a spherical particle when the penetration depth ,l=0 the value of X is: X:X^u*= -3 /8n . (l)

and the factor ] ariseson assumption of sphericity of the particles. Susceptibility entering eqs. (l) and (2) de/ scribes the magnetic moment produced by the superconductingcurrents.Ifthe ionic lattice in the surfacelayerA has magneticsusceptibility.{-e,10, then being accessible the alternating field it provides to contribution to the magneticmoment of the sample, which comes both from the susceptibilityitself and through its influenceon,t. (For instance,under normal skin-effectconditions the thicknessof the skinlayer d is 6- p-t/2; herep- ll4ny^" .) The dependenceof ,t on the susceptibility of the ionic lattice has not been investigatedadequatelyso far. However, such a dependence, at all, should afif fect the value of the magnetic flux passingthrough the sample only when )< our case we had ,1. r. Under these conditions one may take account only of alteration in the AC field amplitude by a factor | 1-4n(l - n)X^"n ( n is the demagnetizationfactor). As a result, the magneticflux @(T), cophased with the external field and normalized over the initial unperturbedflux through the volume occupied by the sample, can be expressed rather precisely the form (insteadof eq. (2) ): in Q: (I *lnX^",) - (l -X/X^u*)

:(U^u*-U/U^^*).

(4)

For calibration we usedthe quantity U"' of the sig-

It can be seenfrom the next section that the exper-


V.F. Gantmakher et al. / The temperature dependenceof ),(T) in YBa2CujO7 5

225

iment proves the existenceof the magnetic contribution to @. The amplitude of the AC field in the main experimentswas about 0.08 Oe, the frequency al2n=l}s Hz. Some special experiments confirm that there were no nonlinear effectsat theseamplitudes. Measurementsin a magneticallyshielded dewar showed that the earth's magnetic field did not matter.

3. Results Figure I depicts an experimentalline iD(T) characterizing the magnetic flux passingthrough the assemblyof the powder particles.Moving toward lower temperatures one can separate the line up into three domains: ( 1) Increase the vicinity of Z" (seeinset). in (2) A descending part wherethe penetrationdepth gradually. ,t( Z) decreases ( 3 ) Increase
tainty arising from the lack of independent measurements the 4 position. A similar vagueness of exists on the ordinate axis: the uncertainty of the position of the point @: I on the axis is comparable to the height of the maximum, that is, it is not clear whether the maximum exceedsthe shielding diamagnetic signal induced by the skin-currentsin the normal state. Earlier a similar maximum @(7") was observed upon transition to the superconducting state of fine lead powder with particles of r: 3pk in radii I I I ]. As was the casein our experiment,the width of the maximum had beenLTlT.x0.0I and its heightA@ had been also about 0.01. This indicatesthat the maximum is not relatedto magneticmoments in the lattice of a superconductor. The most reliable statementthat can be done is as follows. The arising of the maximum is conditioned by small sizesof the particles.No analogousobservations on films or massive superconductorsare available.The absence maximum in the measureof ments of X( Z) on aluminium powdersperformed by SQUID magnetometer ll2l shows that this phenomenon is related to existence of the AC field. However, no successive calculations of the impedance of small particles have been made for the fluc-

0(r)
1.00

o.97

u.v b

Fig. l. Temperature dependence ofmagnetic flux through the powder. Dashed line: the result of dividing by "paramagnetic" factor (see eqs.(4) and (5)).


226

V.F.Gantmakher al. / Thetemperature et dependence ).(T)in YBa2Cu jO7_5 of

tuation region. Therefore, this problem is still to be investigatedboth theoretically and experimentally. It is easyto separatethe contributions to @ from X and X^"n, since they changein different temperature ranges. Plotting @as a function of ?t-t, one may seethat at 7"< 15 K the Curie law takes place X^gn:CfT, C=1.1x10-3[Ksm-3]. (5)

served on vanadium powders I l3 ]: the susceptibility of powder obeyed the Curie law with the coefficient inversely proportional to the mean particle size r. Detailed experiments are required to draw final conclusionson the origin of the paramagneticsignal.

The absolutevalue of C was obtained by a comparison with signal U-u*, corresponding completeexto trusion of the flux from the volume Zo. Then dividing @ by ( I *tnX-r"), we get function (l -XlX^^,) at low temperatures. frg. I it is drawn by a dashed In line. The next sectionwill be devoted to the discussion of temperature dependence X(T) so obtained. And here we shall discussin brief the origin of the paramagnetic signal. As is known, the paramagneticsusceptibilityX-r, is related to the concentration of paramagneticcenters N-r. and to their effective moment ppsby the relation: =N-gn( pltiz l3T . ,r-gn Here ps is the Bohr's magneton;coefficient p is related to the values of spin s and of g-factor g1 p:g[s(s* I)]'/t . From the absolutevalue of ;-rn, assuming5: j and S:2, we get that the relative concentrationof paramagneticcentersin referenceto the total concentration of Cu atoms is: fr^en=N^en/N6,:0, 1 . (6) ''

4. Temperature dependence 1(7) A common difhculty in processingexperiments with powders is that there is always some uncertainty in respectto the shape and size of particles. However, at a sufficiently small value of r<2 this uncertainty does not prevent one from measuring the dependence,l(?").Indeed, the magnetic moment rn of a sphereof radius r in field ll and its susceptibility X: m I H, at r < 7 are described with a good accuracy by the quadratic function [4]: X/X^u*=*ut , y:r/l. (7)

'ffi x(r) =

Using the limiting value of X(0 ) we get from eq. ( 7 ) the relation: -_)

. _, =L-" L=1(T) Td ' Lr(r)l l1(r) l

(8)

The value obtained in eq. (6 ) is too largeto attribute the paramagneticeffect to noncontrolled defectsor phase.At to the admixture of a nonsuperconducting the sametime the value is too low to suggest exthe istence of free magnetic moments of copper ions. Also, suchfree moments should have been observed, for instance, while measuring the heat capacity. Therefore,the assumptionthat the paramagnetic signal is somehowconnectedto magneticpropertiesof the surfacelayersof the particles seemsto be the most natural one. A comparison of ,4-e, with the relative number of copper atoms in the surfacelayer of ft in thickness: n^en=3h/r givesh=32 A, that is, about 3 or 4 elementarycells.Such an effectwas earlier ob-

which involves neither quantity r, nor the numerical ceefficientsfrom eqs. (2) and (7), stipulatedby the particle shape.It can be confirmed experimentally, that in our experimentst,t 1 and that eq. ( 7 ) is ap< plicable.Indeed,from the value of l-@(0) taken from the graph in fig. I one can calculateu(O) x0.67. At this u value the value of X given by eq. ( 7 ) differs from the accurateone by 4o/oll4l. Applying the measuredvalue of r=960 A, we get ,t(0) = 1430 A. However, this value, unlike all further results,dependsboth on r and on the assumption concerningthe particle shape. Figure 2 presentsa comparison of the experimental data with three theoretical lines. It is clear that the experiment allows a choice between them. Further discussionwill be carried out separately diffor ferent regionsof variation of t=T/7.. Region t < 0.4. As a rule, the variation of ,1(Z) at low temperaturesin high-temperaturesuperconductors is discussed with aspiration to choosebetweenan exponential variation of the type


V.F.Gantmakher al. / Thetemperature et dependence ).(T)in YBarCuror_u of 1.O

227

\ i\..\..
L'
-2

1

'.. \.

tJU>

\

0.0

1.0 Fig.2. Temperature dependence ofinversedsquare ofnormalizedpenetration depthl-2. Dashed linesare calculated BCSmodet in (lineBCS)andusingEliashbergfunction withlo:2,/11:0 (tinel) andwith16=2,A,=l,ao-as/5 (line2). (13)

L)/^:A(D -AQ) llQ) 'x (/lT)t/2exp(-/ lT) (f in energy units) and a powerlaw LA/Aq.t' , u70. ( l0)

and with Q> (s and T
(e)

L1/1(0)xtal2a.
Therefore, the power law which, as a scribesQ dependence ?"leads to eq. on cording to fig. 3, at t:0.4 the changein tiation depth is N,/A(0) =0.04. Hence, it

(12)
rule, de(10). Acthe penefollows:

The latter would have given evidenceof turning the gap / to zero at some points or lines on the Fermi surface I I ]. However, Dolgov, Golubov and Koshelev (DGK) mentioned in [ 15] another possible line of reasoningin consideringthe temperaturedependence Z). As it known, the interaction of elec,t( trons with virtual phonons defines the transition temperature7"", and that with thermal phonons leads to the scattering.Provided the coupling constant is large, then with increasing of the temperature the scatteringon thermal (acoustic) phonons may gradually transfer the sample from the pure limit Q>> (o aI T=0 to the dirty one Q< (e (Qis the mean free path, (6 is the zero-temperature length). In this coherence case,tincreases a factor ( l+
e(35K)=(6/0.08=2004. To show effect the ofscattering under strong coupling DGK performed calculation applying the ' Eliashbergfunction in the form I 15]:
/,-:,2

a2F(ar : n, (:;)

outt a).

4t? 6(o - a6\ . (13)

(0(x):l when and x<0 0(x)=0 when 0).Here x>
the first term describes acousticpart ofthe specthe trum, and the secondone the optical part. Line I in fig. 2 was drawn with the parametersls=2 and lt:0.It turnedout that T"=a6f 5.In otherwords, this is strong coupling with optical phonons without scattering: at T < Tc phonons co' are not excited practically and the scatteringby them is in-essential. Accordingly, here a very low growth of/. is observed at


V.F. Gantmakher et al. / The temperature dependenceof ),(T) in YBa2CurO7,5

1.10

1.08

t.uo

L 1.04

1.00

__....#rt.
o.2
part Fig. 3. Low-temperature oflinesin fig. 2 in (4, /)-coordinates.

low temperatures(see frg. 3), as well as in the BCS theory. Line 2 was drawn with A6=2, lr:l and (Do=7.. Temperature 4 itself did not undergo any alteration when the interaction with acoustic phonons was switched on and 7l remained equal to aro/ 5 as before. However, the function 2(Z) altered. It '' becameconsistent with the experiment,evidentlydue.. to scattering on real phonons with frequencies : 0 < ctl< rr.ro ?t" at small f. It should be noted that line 2 does not practically differ from that drawn by Rammer for the case of strong coupling in the "pure" limit [ 17]. However, sincein I l7 ] the couplingconstant waslarge(A=6), and the real phonon spectrum applied involved a lowfrequency acoustic part, the phonon scatteringevidently had been taken into account automatically. In many papers(12,4,5,91, also I I ] ) the funcsee tion Z(l) was describedin the low-temperatureregion by a parabola.By comparison,the experimental data and the theoretical line 2 from hg. 3 can both be approximated to a sensibleaccuracyin the range 0
( l4)

A weaker reliable temperaturedependence, than the above one, had apparently never been observed.A

stronger one seemsto be related to the low quality of the sample.For instance,for an annealedpowder with other phasesadmixed we obtained the value of at=0.6, as had been obtainedin paper [9]. Region (I-t)<< 1. All the theories,not raking account of fluctuations, yield the finite derivative for the function L-'(t) at the point y: I (seeinset in fi9. 2).This derivative is a very convenient subject for comparison of the theory and the experiment. To illustrate the possibilitiesof such comparison, fig. 4 depicts the resultsofcalculating the derivative D=d(L-z)/d/ as a function of the coppling constant lo in the model ( l3 ) without acousticscattering, that is, at 1, = 0. The most important part of the line is 0

V.F. Gantmakher et al. /The temperature dependenceof ).(T) in YBa2CujO7_5

229

no
Fig. 4. Dependenceof a6/7. and derivative d&-2) /dt on the coupling constant16 in the model ( I 3 ) without acoustic scatrering,thal is,atl'=0.Pointmarksthevaluesof ots/T.andd(L-2)/dtwithacousticpartswitchedon(lo:2,,4r=l,oto:tos/5).

be explainedreferring to the scattering,this time, on thermal optical phonons.Thesephonons exist below the transition temperaturedue to the decrease rain tto aslT, accompanyingthe growth of ,4o | 18I (the upper curve in fig. 4).

apparently be used for estimates.In any case,2> I for sure.

Acknowledgements The authorsare grateful to A.A. Golubov and A.E. Koshelev for numerous fruitful discussionsand for in assistance applying the algorithm of calculating the penetration depth, developed by them, and to G.M. Eliashberg and D.V. Shovkun for valuable comments.

5. Conclusion

A comparison of experimental and theoretical curvesA(T) for the low-temperature region f <0.4 showsthat in YBa2Cu3O7_6 there exists strong coupling with low-frequencyexcitations,in general,not necessarily with phonons. The scatteringof carriers on theseexcitationsis so strongthat even at low temperatures l:0.4-0.5 it is the main factor limiting the mean free path l. In its turn this resultsin the power law in the behaviourof the function )(T\. The magnitude of the coupling constantA canbe obtained by measuringderivative D =d ( L-2) /dt in the vicinity of the temperatureof the superconducting transition l: 1. Though the calculatedvalue ofD dependson a particular spectrum, model ( l3 ) can

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