Excess electrical conductivity in polycrystalline Y1Ba2Cu3O7-δ compounds: Beyond the mean-field region

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22 August 1988

EXCESS ELECTRICAL CONDUCTIVITY IN POLYCRYSTALLINE YiBa-,Cu3OT_6 C O M P O U N D S : BEYOND THE M E A N - F I E L D R E G I O N J.A. VEIRA, J. MAZA and Frlix VIDAL Laboratorio de Fisica de Materiales, Universidadde Santiago de Compostela, Santiago de Compostela E- 15700, Spain

Received 20 June 1988;accepted for publication 1July 1988 Communicatedby D. Bloch

The excess conductivity in various polycrystallineYiBa2Cu307_6single-phase (within 4%) compounds has been measured with a reduced-temperature resolution of 10-4. The full critical dynamicregion was probably penetrated for the first time, and our results admit a superconductingorder parameter of dimension two fluctuatingin three dimensions.

Thermodynamic fluctuations of the superconducting order parameter (SCOPF) are expected to play an appreciable role in bulk superconductors if

[1] kaTe > Fsn(~)~a(E) ,

( 1)

where Fs, (~) is the free energy density difference between the normal and the superconducting states, ~(~) is the superconducting order-parameter correlation length, E= ( T - T¢) / T¢ is the reduced temperature and ks is the Boltzmann constant. Tc and ~o for high-temperature superconductors (HTSC) are typically of the order of, respectively, 10 and 10- 2 times those for "low-temperature" conventional superconductors [2 ]. Thus one must expect a much more important role of SCOPF in HTSC. In fact, the presence of noticeable SCOPF effects in HTSC was first suggested by Bednorz and Miiller in their seminal work [ 3 ] as a possible explanation of the rounding of electrical resistivity observed just above To. In addition to its intrinsic interest, SCOPF will originate most of the critical behavior of HTSC near the superconducting transition. In particular, so fundamental aspects as the superconducting order-parameter dimensionality or the influence of anisotropy on the critical properties may be directly probed by studying SCOPF. The possible influence of SCOPF in HTSC has been already invoked in a considerable number of 310

works to explain the behavior near Tc of different static or dynamic magnitudes *~. For brevity, we just quote some accessible references on the excess electrical conductivity, the magnitude that we are going to study here, defined as A a ( ~ ) = 1 / p ( ~ ) - 1/pB(~), where p (~) and Ps (~) are respectively the measured and the background electrical resistivity. For references on other magnitudes near Tc in HTSC see, for instance, vols. 58-60 of Physical Review Letters and vols. 35-37 of Physical Review B. However, most of these works give in fact only very qualitative (if any) information on SCOPF, mainly as a consequence of uncertainties in the measurements, strong difficulties to separate the critical contribution from the nonintrinsic or background part, the relatively small region studied in most cases and the absence up to date of any specific theory for SCOPF in HTSC ,2. At present, Art(c) is one of the magnitudes that seems to best probe SCOPF in HTSC. It is probably fair to say that the same applies to "low-temperature superconductors" [ 1,11 ]. This is so because the relative p(~) variations can be measured very easily with high precision, but above all the background or noncritical part of it can be approximated with ~1 For references and analyses of some experimental works near Tcin HTSCsee, for instance, ref. [4]. ~2Somepreliminary theoretical results on critical phenomenain small coherencelength superconductorshave been presented by Ginzburg [ 10].

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enough accuracy (see later), which is always one of the more difficult problems in the analysis of any critical phenomenon [ 12 ]. Aa has already been studied in a wide variety of polycrystal [ 5-8 ] or single-crystal ~3 HTSC. However, all these measurements spanned only the reduced-temperature range e > 5 × 10- 3 and, therefore, they covered probably only the mean-field or Ginzburg-Landau (GL) like region for fluctuations, or even only part of it. Such a restricted temperature range does not allow for an unambiguous characterization of SCOPF in HTSC, even in the mean-fieldlike region. For instance, previous Aa data have been presented as evidence for two-dimensional [6] or three-dimensional [ 5,7,8 ] superconductivity. More recently, a crossover from 2D to 3D has also been proposed in the same ¢ region [9]. In this Letter we report measurements of the exess electrical conductivity, Aa, in various polycrystaUine YIBa2Cu307_~ single-phase (within 4%) compounds with a reduced-temperature resolution of 10 -4, which allows us to extend previous data at least one order of magnitude closer to To. Although we cannot exclude the presence of nonintrinsic effects, we analyze these results in terms of thermodynamic fluctuations of the amplitude of the order parameter. On the grounds of such an analysis the full critical dynamic region for Ae was probably penetrated for the first time in any superconducting transition. Our results seem to be consistent with a superconducting order parameter of dimension two fluctuating in three dimensions. Three series of samples were cut from three YBCO pellets sintered by A. Recovlevschi and coworkers (samples A), M.A. Alario and coworkers (B) and I. Rasines and coworkers (C). The pellets preparation and their general characteristics were presented elsewhere [ 15]. At 300 K, p°e = 108, 9.8 or 0.9 m ~ cm for, respectively, samples A, B and C. Also, according to X-ray diffraction analysis all samples are singin-phase (within 4%) and polycrystallines. Although scanning electron microscopy indicates that the typical grain diameter (ds) varies, as expected, from one series of samples to another, in all cases ds>~(T) (either parallel or perpendicular to the Cu-O planes) ~3

Preliminary results on the electrical resistivity near Tc in single HTSC crystals are reported in ref. [9].

22 August 1988 I

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l_n I-( T-TcR )/'l-cR-I Fig. 1. Log-log plot of the normalized (to ao at 300 K) excess conductivity of sample A (diamonds) and C (squares) versus reduced temperature, the last being obtained using the resistive critical temperature TcR. The inset corresponds to sample A and shows the location of TcR and T~ on a p versus Tplot, with both critical temperatures defined as explained in the text.

up to ~> 10 -4. ac (up to 2 kHz) and dc electrical resistivity measurements were made with a fourprobe method also described before [7] ~4. We examined current densities from 0.01 to 5 A/era 2 and our experimental system was able to detect changes o f p of the order of 1 pfZ cm. Special care was taken to control the sample temperature stability and homogeneity and relative temperature variations were resolved to better than 10 mK by using Pt-100 and Rh-Fe sensors. Absolute temperatures above Tc were measured within 0.1 K. A typical example o f p ( T ) around TcR is shown in the inset of fig. 1. Three main features of the extraction of Aa(c) from these data are: (i) the estimate of the background or noncritical part of p ( T ) , PB(T); (ii) the choice, in the absence of any specific theory for Aa, of its functional dependence on ~; (iii) the choice and precise location of the critical temperature To, which may be different from the conventional resistive critical temperature, TcR, defined by p ( TeR ) = ½Ps( T¢R ) . For all the samples studied here, p ( T ) follows a linear temperature dependence from at least 2 TcR to room temperature [5,8]. Thus pn(T) in this work will be the resistivity linearly extrapolated from p (T) data above 2TcR (the straight line in the inset of fig. 1 ). We have checked, in addition, that eventual small ~* The improvements carried out on this experimental setup will be presented elsewhere.

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errors (less than 5%) in Pa (E) and in p(T¢) affect Atr appreciably only very close to T~ or in region I. In the absence of any specific theory for critical phenomena in HTSC, we will approximate Aa(e) by a a / a ° =A~ x ,

312

respectively, the crossover and full critical region. Since the data points in this last region are less precise (and they may be affected by specific non-intrinsic rounding effects [16] ), we have used the crossover region to impose the above indicated dynamic scaling results. A typical example of the resulting curves is presented in fig. 2. Here we have used e = ( T - Tcc) / Tc~, with T~c obtained for each sample by imposing eq. (2) with x = - 2 / 3 in each corresponding region III. The location of T~ for sample A on the p ( T ) curve is shown in the inset of fig. l, where we see that as expected Tc~- T~r~ ~(T) ) and anyhow independent of intergrain links. Another important complementary result, illustrated by fig. 2, is that on the grounds of this analysis, region IV will have a critical exponent of the order of - ½, as predicted by dynamic scaling approaches for the full critical region in 3D. To obtain this value of x, the data points closer to Tc

(2)

where A is a temperature independent amplitude and x is a critical exponent. A and x will depend on the critical ~-region studied and, indeed, also on the precise choice of T~ in E. As is well known, singularities near critical transitions in real physical systems cannot be always adequately described by pure power laws [ 14]. In addition, Atr is very probably influenced by various nonintrinsic effects [ 1 ]. However, the functional dependence of eq. (1) is that predicted (and already observed experimentally [5-9] ) in the mean-field region by the Aslamazov-Larkin (AL) theory for fluctuations in BCS superconductors. More importantly, very general dynamic scaling ideas suggest that, in analogy with the thermal conductivity above the lambda normal-superfluid transition in liquid 4He, eq. (2) may be also a reasonably good approximation for Air in the so-called "crossover" and "full critical" regions closer to T~ [ 12,14,15 ]. In fig. I we show two examples of In(Art/ ) as a function ofln ~, with E obtained by using the T~a of each sample (diamonds correspond to data of the inset). Comparison of these results with figs. 2 of refs. [5,6,8], regarding HTSC, or with figs. 1 to 3 of ref. [ 11 ], regarding "low-temperature" superconductors, may be a good indication of the experimental progress that the present Aa data represent. These data, which penetrate much closer to T~R than previously results, give us an unique possibility of using very general dynamic scaling results to determine Tc and to probe SCOPF. In particular, the possible existence of a crossover and of full critical dynamic regions with, repectively, x = - 2 and x = - ½ in eq. (2), for three-dimensional (3D) samples will be a consequence of only the most general characteristics of the superconducting transition, as the sample dimensionality or the order-parameter dimensionality d (here d = 2 , as in the normal-superfluid transition in 4He or in conventional BCS superconductors [ 12,14,15 ] ) and will not depend on the precise mechanisms leading to the superconductivity of these materials. The results of fig. 1 allow us to tentatively identify regions III and IV as,

22 August 1988

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Ln C ( T-Tcc ) / T c c ] Fig. 2. Log-log plot of the excess conductivity versus reduced temperature,this last obtainedby usingthe temperaturefor which the regionIII slopeis - 2/3 ("crossover").Diamondsand squares correspond to samples A and C, respectively.Trianglesand circles correspond to sample B (with j=l and 0.1 A/cm2, respectively).

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( ¢ ~ 3 × 1 0 - 4 ) , probably affected by non-intrinsic rounding effects #5, are not taken into account. These results for regions III and IV constitute, in our opinion, the strongest arguments presented up to date in favor of the existence in HTSC of important SCOPF effects, which show a 3D behavior, and are also consistent with a dimensionality of the order parameter of d=2. We will just enumerate now, for brevity, some of the remaining important aspects of (or open by) the above results: (i) The critical exponent in region II is very slightly affected by the precise choice of T~ and it is, in all cases studied here, close to x = - ½. This is, in fact, the value predicted by the AL theory for 3D fluctuations in the mean-field region [ 1 ]. Some of the AL results, in particular the critical exponents, may also be obtained on the grounds of the GL theory [ 1 ]. Then, it is probably reasonable to associate region II with the GL mean-field region, as proposed before [ 5-9 ]. However, the measured amplitudes (A in eq. (2)) strongly disagree with those derivable from the AL theory. But the reduced-temperature limits of region II coincide qualitatively with those obtained from Ginzburg-like criteria for meanfield approaches [ 1,4,15 ]. (ii) The scenario for the whole Art(e) curves may be completed by supposing region I as the result of, simultaneously, a crossover from 3D to 2D regime and of the influence of shortwavelength SCOPF, both effects being associated with the smallness of ~(E) (of the order of or less than the interplanar distances [2]) in this region. (iii) Preliminary measurements under an applied magnetic field (up to 3 T) and in other Ba2LnCu3OT_a samples (with Ln=Ho and Sm) show that the general features of Ao(e) remain as described here. Also, not appreciable qualitative influence on Aa of the oxygen deficiency of the samples was found, in contrast with that observed in superconducting fluctuation-induced diamagnetism [ 16 ]. (iv) These results are compatible with the strong anisotropy of p in YBCO single crystals [ 1,17 ]: most of the observed Air effects in our polycrystalline sampies will be originated in Pll (parallel to the a-b ~5As is well known,criticaldivergencesvery closeto Tcmay be strongly affectedby nonintrinsicroundingeffectsassociated with impurities, sample inhomogeneities,size effects (~ may becomeof the order of the grainsize) etc. See for instance,ref. [14].

22 August 1988

planes). (v) In agreement with general considerations on the symmetry of fluctuations around Tc [ 12,14 ], our measurements indicate that SCOPF also affects p(T) below T~. However, in contrast with T> Tc, in this region p(T) is also strongly deformed by nonintrinsic effects, as high junction disorder [ 6,18 ], or small stoichiometric inhomogeneity and it will not be commented on here. In conclusion, we have presented measurements of the electrical resistivity rounding effects above the superconducting-normal transition in different YBCO compounds which extend previous data at least one order of magnitude in reduced temperature closer to the transition. Even though the presence of nonintrinsic rounding effects, associated for instance with small stoichiometric inhomogeneities or with the polycrystallinity of the samples, cannot be excluded, we believe that the easiest explanation of the observed excess conductivity is to admit the presence of SCOPF effects, as expected on the basis of the GL-like approaches. Thus, the experimental results are analyzed in terms of SCOPF by using very general critical dynamic scaling ideas, together with the time-dependent GL approaches probably applicable to HTSC in the mean-field region. Our analysis strongly suggests that the observed effects are compatible with SCOPF in, essentially, three dimensions. It will be the first time that the full critical region is experimentally penetrated in any superconducting transition. In spite of the strong anisotropy of the order parameter in HTSC and the polycrystallinity of our samples, the general aspects of the critical dynamics near the superconducting transition of this family of HTSC seem to have close analogies with those of the normal-superfluid transition in bulk liquid 4He. In particular, the number of the order parameter components will be 2. Measurements in single-crystal HTSC can, indeed, help to answer or confirm some of the points enumerated above. However, we believe that the main general critical aspects of Aa in this family of HTSC are those we have reported here. We gratefully acknowledge Professors M.A. Alario, E. Montn, A. Recovlevschi, I. Rasines and coworkers for providing us with the different high quality YBCO samples used in this work. Even though this work was not explicitly supported by the CAICYT 313

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( S p a i n ) , we h a v e u s e d f i n a n c i a l s u p p o r t f r o m t h e project PR-84-620.

References [ 1] M. Tinkham, Introduction to superconductivity (McGrawHill, New York, 1975) ch. 7; W.J. Skoepol and M. Tinkham, Rep. Prog. Phys. 38 ( 1975 ) 1049, and references therein. [2] T.K. Worthington et al., Phys. Rev. Lett. 59 (1987) 1160; and to be published. [3 ] J.G. Bednorz and K.A. Miiller, Z. Phys. B 64 ( 1986 ) 189. [ 4 ] A. Kapitulnik et al., Phys. Rev. B 37 ( 1988 ) 537. [5] P.P. Freitas, C.C. Tsuei and T.S. Plaskett, Phys. Rev. B 36 (1987) 833. [ 6 ] M. Ausloos and Ch. Laurent, Phys. Rev. B 37 ( 1988 ) 611; Ch. Laurent et al., Z. Phys. B 69 ( 1988 ) 435. [ 7 ] J.A. Veira et al., J. Phys. D 21 ( 1988 ) L378. [8] F. Vidal et al., Solid State Commun. 66 (1988) 421; F. Vidal et ai., Physica C 153-155 (1988) 1371. [9] T.K. Worthington et al., Physica C 153-155 (1988) 32; N.P. Ong et al., Physiea C 153-155 (1988) 1072;

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R.J. Wijngaarden et al., Physica C t53-155 (1988) 1329; D.U. Gubser et al., Physica C 153-155 ( 1988 ) 1335. [ 10 ] V.L. Ginzburg, Physica C 153-155 ( 1988 ) 1617. [11 ] J.C. Garland and H.J. Lee, Phys. Rev. B 36 (1987) 3638, and references therein; W.L. Johson, C.C. Tsuei and P. Chaudhari, Phys. Rev. B 17 (1978) 2884. [12]P.C. Hohenberg and B. Halperin, Rev. Mod. Phys. 49 (1977) 435. [ 13] M.A. Alario et al., Mater. Res. Bull. 23 (1988) 313; P. Monod et al., J. Phys. (Paris) 48 (1987) 1369; J.A. Campa et al., Phys. Rev. B 37 (1988) 529; J. Amador, C. Cascates and I. Rasines, in: Proc. MRS 1987 Fall Meeting, Symposium AA, High Tc superconductors, 4.7, Boston, 1987 (to be published) and references therein; and to be published. [ 14] G. Ahlers, in: Phase transitions, eds. M. Levy, J.C. Le Guillou and J. Zinn-Justin, Nato Adv. Stud. Inst. Ser. B, Vol. 72 (Plenum, New York, 1982)p. 1. [ 15] C.J. Lobb, Phys. Rev. B 36 (1987) 3930. [ 16 ] K. Kanoda et al., to be published. [17] K. Murata et al., Japan. J. Appl. Phys. 26 (1987) L1941, and to be published. [ 18 ] M.A. Dnbson et al., Phys. Rev. Lett. 60 ( 1988 ) 1061.