Excess conductivity, critical region and anisotropy in YBa2Cu4O8

SolidStateGmmunicationa, Vol. 100,No. 9,

.615-620,1996 Cq&htQl996PubhhcdbyECviefScicnceLtd FtintcdinckellBrihin.Allfight6nauved 0038-10981% $12.cm+.al

Pergamon

EXCESS CONDUcrMTY,

CRITICAL REGION AND ANISOTROPY IN YBascUgOs U.C. Upreti and A.V. Narlikar

National Physical Laboratory, Dr KS. Krishnan Road, New Delhi 110012, India (Received 2 February 1996; accepted 7 August 1996 by B. Lumfqvist) Conductivity fluctuation effects in two YBa&_t~Os samples from different batches are studied in the light of system anisotropy. The LawrenceDoniach model is not suitable, hence the Aslamaxov-Larkin model with Anderson-Zou’s formulation p,(T) =A + BIT has been used. In the mean field region both the samples show 3D order parameter fluctuations. For the mean-field critical temperature three alternatives and their consequences are discussed. The order parameter dimensional@ remains the same in all the alternatives. To account for the anisotropy of the Y-124 samples a single-crystal-analog for ab-plane resistivity has been invoked. The Ginxburg point and theoretical and experimental critical region widths are calculated and discussed in the light of anisotropy. Small variations due to different batch synthesis do not affect the analysis. A theoretical formulation without anisotropy factor does not hold good. The experimental critical region widths lie between the theoretical values of GL and those of Fisher et al. (Phys. Rev., B42, 1991, 130). Compared to Y-123 system these widths and the fluctuations are larger. Binding energy considerations cont%m this fact. Copyright 0 1996 Published by Elsevier Science Ltd Keywords: A. high-T, superconductors, A. thin films, A. superconductors D. phase transitions.

1. INTRODUCTION High temperature superconductors (HTSC) are highly anisotropic and type II. Because of a small coherence length, low carrier densities and high T,, an excess conductivity due to the thermal fluctuations is always observed in the HT!X [l]. The possibility of fluctuation effects in HT!X have been suggested by Bednorx and Muller [2]. There have been numerous studies on excess conductivity and order parameter fluctuations in YBa2Cu307, (Y-123) [3-111, Bi2Sr2CaCu20s+y (Bi2122), Bi2Sr2Ca2Cu~Ols+,, (Bi-2223) [12-211, (‘D-2212) [22-241, HgBa2Ca2DzBa&a%Os+,, Ctr~Os+~ (Hg-1223) and HgBa$aCtt206+,, (Hg-1212) [25] systems. The studies on conductivity fluctuations suggest that the superconductors with less anisotropy [16, 17, 201 have a strong tendency for threedimensional order parameter fluctuations, whereas the highly anisotropic superconductors [22-24, 261 show two-dimensional superconducting fluctuations. Thus the anisotropy dependence suggests that the order parameter dimensionality seems to be structure dependent. Because

of low dimensionality of conduction a system has increased fluctuations, whereas higher dimensional conduction shows fewer fluctuations. Varying conclusions have been drawn regarding order parameter fluctuation dimensionality in various systems including single crystals and thin films. Some definite conclusions may, however, be drawn from the studies on anisotropic resistivities or on microscopic parameters like the coherence lengths, phase breaking time, etc. Fluctuation conductivity study may also provide information regarding the critical region close to T,. While the Y-123 system is the most widely studied one for excess conductivity (order parameter) fluctuations [3-111, the YBa&&Os (Y-124) system has not been studied so far for these effects. The Y-123 superconductor has the disadvantage of having a variable oxygen content and its single crystals have extensive twinning due to tetragonal to orthorhombic phase transition on cooling from the growth temperature. The Y-124 superconductor on the other hand has stable oxygen content and no twins, since it directly grows into orthorhombic form. Here we propose to study the

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polycrystalline Y-124 bulk system for excess conductivity and order parameter fluctuations. Comparative studies in Y-123 and Y-124 superconductors have helped in gaining some insight into the change of Fermi surface (FS) with dopant concentration variation [27,28]. Also since Ca substitution for Y in Y-124 raises its T, [29], it is inferred that the CuOZ planes in Y-124 are under doped. These observations are expected to make the Y-124 superconductor more important for tmderstanding the mechanism of superconductivity. We feel this study, perhaps the first on thermal fluctuations in Y-124 phase, will help understand the nature and extent of fluctuations in this system which is viewed as an under doped phase. 2. EXPERIMENTAL The bulk YBa2Cu40s samples were prepared by the conventional solid state reaction process [30]. Stoichiometric quantities of highly pure (99.99% purity) YzOs, Ba(NO& and CuO were thoroughly mixed with 0.2mole fraction of Na&04 added as rate enhancer. This loose mixture was pre-reacted for 30 min at 900 K and allowing it to cool to the ambient. The pre-reacted mixture is then subjected to grinding pelletizing by die-pressing, and reacting for at least 24 h at 900K in flowing oxygen at the atmospheric pressure. After furnace cooling it was reground and pelIetized and kept at 815 Kin flowing oxygen, under atmospheric pressure, for 3-4 days with several intermediate heating and cooling processes carried out in the flowing oxygen with repeated grinding and pelletizing. The pellets were finally furnace cooled. The resistivity-temperature measurements on these pellets were made by the usual four probe method, using silver paint for making the contacts. A nano-voltmeter and a current source hooked with an IBM-PC, were used for automatic data acquisition and control. The critical, T, (R = 0), temperatures of samples Sl (S2) are 79 K and 79.5 K respectively (Fig. 1). 3. RESULTS AND DISCUSSION The excess conductivity contribution in the HTSC may be analysed by the Aslamazov-Larkin (AL) model [31], the Maki-Thomson (MT) model [32], or the Lawrence-Doniach (LD) model 1331. In this study we have used the AL model. Semba et al. [12] have also pointed out that high T, models which assume strict two dimensionality camrot be applied to the YBCO system. In fact the applicability or otherwise of the LD model can be decided using the relation &(T *) = s/ J2 between the c-direction coherence length [, and s (c-direction unit cell length/number of CuOz layers). If EC< s/ J2 the system dimensional@ is two, and if [, > s/ JZ it is three. For the Y-124 system, since ,& > s/ J2, the LD

model does not seem to be suitable.

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0.2 0.1 0.0 75

(a) ' loo

125

150

175

200 T(K)

225

250

WI

03

0 0.0 -a 75

275

-

' loo

125

150

175

MO T(K)

Fig. 1. Resistivity vs temperature samples.

225

250

275

300

for YBaZCu40s

The excess conductivity (Au) correction due to thermal fluctuations is defined as the deviation of the measured conductivity (a,) from the normal conductivity (a,). The normal conductivity is extracted from normal resistivity (pJ which is generally calculated using either of the two relations: p,(T) = AI + BIT or that suggested by Anderson-Zou [34], p,(T) = AzT + B21T. In this study p,, has been obtained from the measured resistivity at temperatures >2T, by applying the method of least squares to the Anderson-Zou relation [34]. Significance of both the terms in this relation has been explained by Anderson-Zou [34]. For sample Sl the absolute value of Bz is about two times that for a sample S2 - the difference being about 15, probably this causes a larger deviation of normal state resistivity in sample Sl. The extrapolated conductivities at T =

300K (u3& for samples Sl and S2 are l.l078(mBrespectively. Near T, Cm)_’ and 0.8549(m&mr)-’ sample Sl has a higher excess conductivity compared to sample S2. In the Aslamazov-Larkin theory [31] the excess conductivity for 2D and 3D is given by Au&T) = (e?/16M)e-‘, Au30(T) = [e2/32h[(0)]e-

(I) lL? ,

(2)

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width and at the Ginzburg point the excess conductivity is still a small significant correction since at eo the higher order term in the energy functional will be larger than the leading term. For Y123 system Torren et al. [38] have calculated the Ginzburg point (CC= 10e2) using the field E(T) = (T - Tcmf)/Tcmf, (3) free relation [36] ed = (1~32~2)[kB~(~~(0)~c(O)~~)12 where T,“’ is enerally determined following Oh et al. where AC is the specific heat jump at the transition. 4 [4] from (Au)- vs T plot as the temperature correspond- The size of this jump AC/k, and the X-anomaly in ing to Aam = 0. However, we observe that it is difficult specific heat with wide logarithmic divergence are to precisely determine Tcmfsince Aam2varies very slowly important evidence for a critical region wider than and though near T, it tends to zero it may not always predicted by the Ginzburg criterion. According to be exactly zero. Trf is found to be temperature range Klemm [39] and Ullah ef al. [40] the slow variation dependent and the smaller the range, i.e. the better the condition of the time-dependent GL like approach fails resolution, the lower is the Tcmf. For accurate Tcmf for determining the Ginzburg point and the order paradetermination we, therefore, propose a criteria: Tpf is meter fluctuation effect calculations are doubtful unless the temperature above which the Aas vs T curve, in the the dynamic local effects are not taken into account [31smallest possible temperature interval close to T,, devi- 33,39-441. Maza et al. f45] state that Au data close to T, ates from the temperature axis. This criterion may be may be strongly affected by even smaller stoichiometric verified by a small increase in the temperature, say 0.5 K, inhomogeneities like oxygen content, consequently in whereby the next higher temperature point lying above this region we expect uncertainty regarding the reduced the temperature axis now falls on it and thus gives a temperature also. Keeping in mind all these ambiguities and uncertainhigher value of TTf. As another alternative, if we use ties we calculate the critical region width (Ginzburg TFf as the temperature corresponding to dp/dT peak there will be no ambiguity in determining it. Using either point) for our samples. In the absence of Y-124 single of these criteria we do not find any change in the crystals it is advantageous to use the single-crystal analog of polycrystalline samples to represent their dimensionality of the samples in the mean-field-region (MFR), usually taken as -3.5 I lne 5 -1.5. However, &-plane resistivity. This analog has been utilized [46] to account for carrier-impurity potential scattering in we suggest and prefer to use the dp/dT peak temperature criteria, since in other criteria the slope of In (Au/usa,,) vs doped Y-124 samples also where it has been shown In Ecurves increases as we approach the critical tempera- that from the resistivity point of view the single-crystal ture and this indicates a behaviour similar to that at analog of Y-124 samples is justified to within a factor of higher temperatures where this slope increases very fast approximately 1.33. In this analog, since p. = 113 and hence one may possibly conclude that the super- (PO,.PO,bPO,J 7 where PO,~, PO,~ and ~0,~ are the conducting system has similar behaviour in low as well resistivities in a, b and c directions, and since the as high tern erature regions, which is impossible. anisotrop;nratio _z3= (PO,clpo, &lR we obtain pe,&, = po. Since y = 10 [47] for Y-124, we The T,J values (dp/dT peak) for samples Sl and S2 (p0,apO.b) = -i’ are 80.1 K and 80.5 K, about 1 K above the correspond- can obtain po, ab and can account for the effect of anisotropy ing T, (R = 0) values, respectively, and this Tcmf higher on excess conductivity. For sample Sl experimentally p. = 0.3495 m&cm than T, behaviour agrees with the reports on Y-123 and other systems. in samples Sl and S2 for 0.1 K change in near T,, hence po,& = 7.53 x 10m2m0-cm and consequently us&, = 13.28 (m%cm)-’ near T,. For sample S2 Tcmf values the excess conductivity shows marked deviation with e. This T,“’ dependent variation of Au with ln e experimentally p. = 0.2578 mQ-cm near T, so that is inherent and has important implications for Au and po,& = 5.55 x low2 m%cm and hence ua&, = 18 (m0makes each sample to have different mean-field like Cm>-’ near T,. Thus, using single-crystal-analog of regime - a deviation from the generally followed MFR polycrystalline Y-124 samples we obtain the ab-plane (-3.5 5 lne 5 -1.5) - and affects the critical region conductivity and consequently, po,c = y2po+b gives the quantitative out-of-plane conductivity also. widths also. To calculate the experimental critical region widths There is much ambiguity about the fluctuation dominated critical region extending to the Ginzburg point (ed) we fnst consider the Ginzburg criteria Au/u,, = 1. Experiat which the order parameter fluctuations and the order mentally, for sample Sl pn = 0.3495 m&cm, i.e. a, = parameter itself are of same order, i.e. Aala, = 1. It is 2.8811 (m&cm)-’ and for sample S2 pn = 0.2578 ml% cm, i.e. a, = 3.8795 (mf&n)-‘, at their T,“‘. Therefore, estimated [l, 35-371 that eo varies from 10e4 to 10-l. the corresponding experimental critical region widths are According to Fisher et al. [l} the standard G&burg criterion may be an underestimate of the critical region approximately 0.6 K and 0.7 K respectively. According respectively, where e is the electronic charge, d is the layer spacing, A is the reduced Planck’s constant, t(O) is the 3D coherence length at T = 0 K, and E is the reduced temperature defined as

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to Fisher et al. [1] these may be an underestimate and the critical region widths will be (25 times) 15 K and 17.5 K respectively. In fact, the critical region widths depend on the anisotropies of different systems and is larger for systems with higher jalopy [24]. According to Tech [47] the anisotropy ratio of Y-124 system is approximately twice that of the Y-123 system (its = 2yiu), and since the resistivities of Y-124 and Y-123 are almost the same near T, the ab-plane resistivity of Y-124 is expected to be relatively smaller, therefore, we expect a higher critical region width for Y-124 phase. In the critical region close to T,, where the GL theory is not expected to hold, according to Lobb 1481 the G&burg criterion yields a temperature range [49] given by IT - T,“f I/T,mf< 82/(32r2cuo)(2m*m2)3(kT~~)2, where h is the reduced Plan&s constant and k the Boltzmann constant, and CYO, /3, m* are constants as used in the field free energy density functional f = aol(T - T,mfJ/T,mlWI2 +

WWlr114

+ (lh~*Mtdi)A$4~. Then Lobb [48] derived the theoretical critical region width as jT - T,“f/ < 1.07 x 1O-9 ~4(T~~)3/~~2(0), where am* is the extrapolated value of the linear part of HC2(T) near Tc?f and is defined as H&T) = @e/2&T), (p, being the su~r~ndu~~g flux quantum (=hc/2e). In this relation K and Tpf have very strong effect on the critical region width. In the GL theory, for HTSC using K = 100 and 200, HC2= 750kG and Tmf = 95 K Lobb [48] calculated /T - TFf I < 0.12K id <1.96K respectively. The corresponding widths according to the criteria of Fisher et al. shall be Q K and <49K respectively, indicating that the value corresponding to K = 200 may be unrealistic. However, in our Y-124 samples using the theoretical formulation of Lobb [48] and taking ~(hlt) = 150, HC2(0)= 800 kG, the theoretical critical region widths corresponding to TFf values 80.1 K and 80.5 K are approximately 0.348 K and 0.353 K respectively. Thus, based on the formulation of Lobb [48] the theoretical critical region widths for Y-123 system (90K class) of superconductors are larger than those for Y-124 system. But this contradicts the observation [24] that a system with higher anisotropy should have a larger critical region width. Since the formation due to Lobb [48] does not take into account the anisotropy factor and is very strongly dependent on Ted which is crucial in deciding the critical region width for a system, it may give a wrong torsion about the comparative critical region widths in different systems.

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We therefore, emphasize on comparing the critical region widths calculated from the experimental data alone. The criteria of Fisher et al. [I] yields the theoretical critical region widths for our samples Sl and S2 as 8.7 K and 8.825 K a~ro~mateiy. Thus, for Y-124 samples we find that: GL theoretical widtb < experimental width < Fisher et al. theoretical width. The values of Fisher et af. (“9 K) agree with the widths at E m 10m2for samples Sl and S2 both. We observe that according to Torren et al. [38] ec = 10m2 is the Giiburg point for Y-123 system also. The above analysis may well be performed on the abplane conductivity also. It may be noted that in the single-crystal-analog the ab-plane conductivity is roportional to the bulk conductivity, as as,& = (10) upa,,,. Thus due to the anisotropy the fluctuations in the abplane will be enhanced by a factor of -4.6. This becomes evident from the log/log plots of the ab-plane conductivity which get displaced with respect to the corresponding measured conductivity plots. The logilog plots of normalized excess conductivity (Adu3& with E, Fig. 2, show that both the samples have sharp (large) fall in excess conductivity near T,, and in the MFR upward from the lower bound of lne this fall with e (or T) starts stabilizing. The AC/T variation shows a steep fall for sample S2 and the change in Au stabilizes also faster than sample Sl. We a~bute this to slightly higher T, and lower p(higher Au) near T, (R = 0) of sample 52. Above about 2TC, the Au variation in both the samples is almost stabilized. In the MFR both the samples show 3D orderparameter fluctuations and there is no tendency for a crossover, in agreement with other anisotropic systems where the crossover is absent those with fewer anisotropies [16, 17, 201 having a 2D and those being highly anisotropic [20-24, 261 having 3D fluctuations of the orderparameter. At T,(R = 0) the maximum Au is 1247 (m&cm)-’ and 996 (m&cm)-’ for samples Sl and S2 respectively. In samples Sl and 52 the dpldT vs T curves peak at 80.1 K and 80.5 K thus the resistivity infection points are at almost equal temperatures and the dp/dT values 0.1007 and 0.0913 respectively are also almost equal. Differences may be identified in the (Au)-~ vs T curves wherein sample Sl shows a sublinear curvature near I;: and sample S2 a superlinear behaviour. From Fig. 2, for sample Sl (S2) the lower limit of the MPR seems to be around ine = -3.58 (-3.28). In comparison with Y-123 samples this is in slightly higher temperature regime. This is expected also in view of the higher loopy of Y-124 system. Thus, in Y-124 systems the Ginxburg point is also at a higher temperature. Hence a larger critical flu~ation regime width is expected in Y-124 systems compared to the Y-123 systems.

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1

Fig. 2. In [A&& samples.

I

619

for the anisotropy of the ~lyc~s~i~ Y-124 samples no silent difference is found in the behaviour of the samples. For samples Sl and S2 the experimental critical region widths (GIL) are 0.6 K and 0.7K, according to Fisher et aL [l] they are 15 K and 17.5 K respectively. This is in accordance with the higher jalopy of Y-124 system. The theoretical Ginxburg critical region widths for samples Sl and S2 are 0.348 K and 0.353 K respectively, which according to Fisher et al. [l] are 8.7 K and 8.825 K respectively. Thus, the experimental critical region widths for the Y-124 samples lie between the theoretical Ginxburg width and the Fisher et 02. width. It is observed that small differences in the physical properties of the samples synthesized in different batches have no si~ificant effect on the excess ~nductivi~, order parameter dimensionality, or the critical region widths. The theoretical formulation of Lobb [48] has not been found suitable. The Ginxburg point for samples Sl and S2, corresponding to the critical region widths (=9K), agrees with the G&burg point 10e2 for the Y-123 system. Compared to the Y-123 samples, the Ginzburg point for the Y-124 samples is at slightly higher temperature as expected because of higher anisotropy, and ~nsequently the critical fluc~ation regime width is also larger. Larger fluctuations in the Y-124 systems are also confirmed by binding energy considerations.

vs ln [(T - Z’~%‘,“f] for Y-124

The nature and extent of the fluctuations may be explored on the basis of binding energy considerations. The binding energy 26(O) of a Cooper pair is proportional to ks’Fc(2A(O) = 3.5ksT,) with the pro~~onality constant (3.5) depending on the coupling strength. For the Y-124 system 2A(O)&T, = 6.2 rf: 0.2 and it remains constant with respect to temperature even up to a fall of 8K in T, due to an impurity, whereas, in the case of Y-123 the 2A(O)/~~~~value falls from 5.8 at T, = 90K to 3.5 at T, = 50K [SO]. Thus, in the case of Y-124, 2A(O) remains higher with respect to T, values. We, therefore, expect larger fluctuations in a Y-124 system as compared to the Y-123 system, as is observed in our samples.

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4, CONCLUSIONS 8. Excess conductivity studies have been performed in two ~ly~s~~e bulk samples of YBa$.&Os obtained from different batches. Using the AslamazovLarkin model for the excess conductivity and AndersonZou’s formulation for the background resistivity with three alternatives for T$ dete~ation in the MFR both the samples show 3D flu~ati~~ of the order parameter in all the three alternatives. Using single-crystal-analog samples for the &plane resistivity, invoked to account

Fisher, D.S., Fisher, M.P.A. and Huse, DA., Phys. Rev. B43,1991,130.

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