High temperature crossover in paraconductivity of granular Y 1 Ba 2 Cu 3 O 7-y

Z. Phys. B - Condensed Matter 84, 13-16 (1991)

Condensed Matter

Zeitsohrift for PhysikB

9 Springer-Verlag t991

High temperature crossover in paraconductivity of granular Y1Ba2Cu307_y M. Ausloos 1, F. Gillet 2, Ch. Laurent 2' *, and P. Clippe 3 S.U.P.R.A.S. Institut de Physique B5, Universit~ de Liege, Sart-Tilman, B-4000 Liege, Belgium z Institut d'Electricit6 Montefiore B28, Universit6 de Li6ge, Sart-Tilman, B-4000 Liege, Belgium 3Institut de Physique B 5, Universitd de Libge, B-4000 Liege, Belgium Received November 29, 1990; revised version March 4, 1991

We have examined the deviation from linearity of the temperature dependence of the electrical resistivity of a YBaCuO ceramics. We have observed at high temperature a crossover behavior toward a logarithmic temperature dependence at lower temperature. It seems relevant to attribute the origin of such a term to a pair breaking mechanism contribution, thus to give a lower bound to the existence of superconductivity fluctuations onset temperature. Our findings also implies that carriers are bosons above Tc.

The linearity of the electrical resistivity of high temperature superconductors with respect to temperature T is one of the puzzling features of such materials. Recently Enz [1 ] gave a sound interpretation of such a behavior based on H,_ a coupling between two types of carriers with anisotropic masses and a spin flip dominant mechanism. On the other hand, the drop in the electrical resistivity in the vicinity of the critical temperature T~ is attributed to coherent superconductivity fluctuations in the (a, b) plane of the orthorhombic units forming the basic structure of such materials [2]. The origin of such fluctuations is not at issue here. However, the superconductivity mechanism is much thought to originate in the formation of some type of carrier pairs. These would disappear at high temperature due to various types of pair breaking mechanisms. Lawrence and Doniach [3] have written a phenomenological theory for anisotropic (layer-like) superconductors extending the work of Aslamazov and Larkin [4]. However both cases neglect the life time of the pairs which is short away from the "critical temperature" T~ but maybe sensible as soon as the "onset temperature" is reached. Maki [5] and Thompson [6] calculated an * Now at Automation & Robotics, Parc Industriel de Lambermont, B-4800 Verviers, Belgium

extra term of the Aslamazov-Larkin theory by considering the decay of superconducting pairs into quasiparticles, and vice versa. The enhancement of the conductivity is hindered by inelastic scattering and by pair breaking mechanisms resulting from lattice imperfection, magnetic impurities, a.s.o. Their theory contributes in three dimensional systems (3 D) to a log (7'/T~)like dependence. It seems interesting to examine whether the departure from linearity and a logarithmic contribution can be observed. In order to do so precise measurements must be made because a logarithmic law is usually hard to extract (by subtraction) from any data. In so doing we expect to shine some light on the temperature interval over which such superconductivity fluctuations take place, and to better quantify the rough notion of "onset temperature". Our study will be limited to the case of granular materials, but the results deserve some further study on single crystals. In (granular ceramics) superconductors so called "onset temperatures" are sometimes reported as being quite high [7-8]. These temperature values (or temperature intervals) refer to weak features on various properties without any clear cut relationship to a physical phenomenon. "Onset temperatures" are sometimes defined when a peak is found above the rapid drop in R ( T ) . Such a peak is the signature of interpenetrating grains with different crystalline phases [7]. The "onset" can also be attributed to fluctuations in superconducting wave functions [2]. More often than not an onset temperature is just some point measuring a 10% drop of the electrical resistivity. Data analysis is usually performed by observing the excess conductivity A a = a - a o, where the conductivity is a = l / p , and a0 = 1 / p o where P0 has the temperature dependence corresponding to the linear extrapolation of the room temperature R (T) [7-10]. Another method consist in the analysis of the temperature derivative of the excess resistivity d (A p ) / d T [ 11-13 ]. We first briefly argue here that such a latter method is more correct. Eventhough theoretical works predict A a behavior, they only give the most singular term and are thus strictly valid at the critical temperature Tc. On the other hand

14 measurements give A p values. It is much safer to conclude on theoretical A p behavior from A o- theoretical prediction then to transform Ap data (into some A~) which contains unknown experimental error distribution [14]. Simple theoretical work allows anyone indeed to determine the temperature region in which a transformed theoretical law is valid by estimating correction term influence. We have shown elsewhere [ 15] under which condition (when Ao-/o'0>_l ) the same leading critical behavior is obtained for A a and A p. Notice that the precise determination of a0 is often a subject to be debated upon. Here we report data which extend our DC resistivity measurements [11] keeping the precision similar to that required in critical temperature regions in order to obtain reliable data at higher temperature and to extract relevant physical information. We show that the onset of superconductivity fluctuations occur above 170 K in this sample. We relate a crossover in d (A p ) / d Tbehavior through our data analysis method to true superconductivity mechanism, We also show an anomaly near 240 K, - a temperature at which sound, specific heat and resistivity anomaly have been seen [16-18]. The sample under investigation has been cut from a pellet synthesized from stoichiometric quantities of BaCO3, Y203 and C u O 3 . Cu(OH)2 which were finely ground and mixed under petroleum ether. The mixture remained at 900 ~ for one day. After slow cooling and regrinding, the mixture was pressed into a pellet wrapped in a Pt sheet and reheated at 900 ~ in an 02 atmosphere during one day. After cooling in the furnace at 750 ~ and maintaining it overnight the heater was turned off, and the pellet removed at 200 ~ The sample is optically considered homogeneous although weakly porous. The diffraction pattern is practically identical to that of Cava et al. (a = 3.820 A ~ b = 3.886 A ~ c = 11.673 A~ No extra peak indicating unreacted material is seen. Nevertheless rare small green microcrystals could be observed under the microscope. The minority phase concentration (5%) is however much less than any percolation threshold, the ceramics is thus considered to be single phase for electrical resistivity purposes. A DC four probe method capable of detecting changes in p of 1 part in 5 10 - 7 ~ cm has been used. Temperature stabilization is monitored at _+0.01 K at least during several minutes. The cooling and heating rates are about 2 K / h close to the critical temperature but can be increased to about 10 K / h at higher temperature without much loss in precision. Data points were taken under quasi equilibrium temperature conditions. Temperature and voltage sensitivity is of the order of a few m K and a few nV respectively. Current density was 0.3 A / c m 2 but was varied to observe any drastic influence. None was seen at such a low value. Due to such small error bars and precise definition of the temperaure axis scale, the temperature derivative of the data can be easily taken: five data points are interpolated through a 3ra power polynomial, and the derivative is calculated at midpoint. In so doing the critical temperature is estimated to be that near which d2R/d T 2 vanishes. It is adjusted such that the best (linear) fit be found on an as large as possible e range on a log log plot. This occurs here over about a hundred degrees.

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critical temperature for two granular ceramics YBaCuO samples; a cooling run, b heating run. On a (x) correspond to T < T~,data. Insert: R (T) data

Notice that in order to obtain the contribution for the "excess conductivity" from the resistivity the normal state contribution at "high temperature" has to be substracted. Such a contribution is usually found to be linear over an extended temperature range [19]. After taking the first

temperature derivative of p (T) this assumption of a linear background consists in substracting a constant from dp /dT. In so doing, the temperature value (hence the resistivity value) at which the linear fit starts is totally irrelevant for the data analysis. Only the slope of p (T) is thus important, and the magnitude of o-0 is irrelevant. From the plot of l o g ( d R / d T ) versus loge, such a constant (corresponding to the high temperature slope) can be extracted in order to obtain the best fit possible (to a power law) over the largest temperature range possible. We have found in several runs (Fig. 1 a-b) that the best fit occurs for d R / d T ~ Ce-(~ + 1)

(1)

15 with C = 0.9 (dR (250)/d T) and T~= 90.51 K. The factor 0.9 has a similar origin to that introduced by Oh et al. [20]. It takes into account the fact that in the original 2D Aslamazov-Larkin theory [4] the prefactor depends on the layer thickness d. In the case of high temperature superconducting ceramics, the coherence length perpendicular to the layer is so short that d must be replaced by ~• Such an analysis extends to higher temperature that reported in [11]. From the data analysis one ontains )~ § 1 = 1, in the e range of interest, thus )t = 0 for the theoretical expression

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It is well known that such a critical exponent value describes a logarithmic singularity in fact, since the more complete expression for Ap, i.e.

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corresponds to a logarithmic behavior for ~ ~ 0, e.g. [21]. This puts Aslamazov-Larkin [4] and Maki-Thompson [5-6] theories on the same footing regarding to the log T dependence. In (3) it can be thought that B contains the Maki-Thompson leading term as well. Notice that a log T dependence is strictly valid near T~ but is found here for a temperature range up to almost 2 T~. This is only an apparent paradox. In fact the log T dependence results from an e = I T--T~I/T~ expansion for ~ going to zero. In mathematical sense, this expansion is strictly valid for e __ 170K the logarithmic ( s l o p e = - 1) behavior of Ap disappears, and is replaced by a linear one (since the slope of dA p/d T vanishes, see Fig. 1 (a-b)). The logarithmic behavior corresponds to the above mentioned pair breaking mechanisms [5-6]. Extrinsic origins, like grain boundaries, crystals imperfections, as well as intrinsic scattering mechanisms by well known or exotic collective modes and inherent twin features cannot be distinguished at this time. It is also worth noting that in anisotropic superconductors elastic (as well as inelastic) scattering of electrons can contribute to pair breaking [22-231. At such temperature, minority phases do contribute to the overall p behavior as long as they are not short circuited by superconductivity paths. One could imagine that such a log behavior essentially originates in a minority (semieonducting) phase. However the sign of the contribution would be the opposite of that predicted by the above theories and would result in a peak near T~ which is not observed here, (see insert of Fig. 1). Notice that closes to T~, a crossover is expected, i.e. in the range (95; 100 K), thus near ln e = ( - 3, - 2 ) . Indeed this crossover is seen for systems with rather size homogeneous a n d / o r well aligned grains [20, 24]. However in our systems the grains are far from being of the

same size and apparently (from SEM pictures) not well aligned [25]. Thus as usual at phase transitions in systems containing impurities or in inhomogeneous systems there is some (usually much) rounding near the transition. This is the case expected here. The crossover is masked by such a rounding. This also shows that it would be interesting to extend fine measurements on good samples away from 2 Tc. Notice finally that our data (well below 2T~) are not in disagreement with those of Freitas et al. [9]. However the data analysis is made differently and leads to an interpretation in terms of a Maki-Thompson pair breaking mechanism up to 2 Tc rather than to an Aslamazov-Larkin formula which neglects the pair life time. That is why it seems more correct to use the former away from Tc. Such a fact is indeed accepted in the literature [26-27] eventhough data analysis differs from authors to authors. On the other hand the temperature at which the behavior changes from log to linear, (the so called "onset temperature") depends though midly on whether a heating or cooling run is performed. The break is also slightly rounded off. These are normal features if it is admitted that there is no specific reason for temperature fluctuations to begin or to stop at a definite temperature, - except if they are strictly controlled by an intrinsic superconductivity onset mechanism, like oxygen vacancies ordering at a given temperature. Thus our "onset temperature" is a lower bound measure. On Fig. 1a-b, a small but apparent anomaly is also seen near In e = 0.457 corresponding to T = 233 K. It can be related to previously discussed structural instability [16, 28, 29], to a magnetic transition [30], or to true superconductivity [18] in a minority phase. There is no possibility to tell whether those phenomena are the signature of a basic cause or whether they result from each other and are peculiar to the studied compound. However we have observed that different curvature behaviors exist at e > 0.66. They depend on the sign o f the temperature sweeping rate. These have been thus connected to sample ageing at high temperature. A consequence of our observations implies that in YBaCuO ageing effects can be made to occur above the onset of superconductivity fluctuations. Notice that linear as well as log behaviors (on rougher data) have also been found in single crystals [19, 31] thus likely eliminating spurious "minority phase" interpretation here. It will be of great interest to further check whether such a test can yield similar information on the superconductivity onset temperature in other ceramics e.g. on Bi-based or Tl-based compounds. In thin films of YBaCuO it was also found recently that to include a Maki-Thompson term is essential at high temperature to interpret paraconductivity data [27]. On the other hand it will be useful to correlate the onset temperature as observed here with oxygen redistribution mechanisms in bulk materials [32]. Finally, as pointed out by Mukhin et al. [33] an important question on whether the carriers obey Fermi statistics (above T~ itself) or whether the carriers are bosons in an appreciable temperature range above T~ (so that superconductivity is Bose like condensation of preexisting local pairs of carriers) seems to receive an answer from

16 o u r findings. T h e latter cause seems to be favored. This has implications on the t e m p e r a t u r e dependence of the excitation spectrum gap. O u r fit shows that it has to remain very small and quasi constant d o w n to T~. In conclusion we have shown an u n a m b i g u o u s crossover b e h a v i o r at high t e m p e r a t u r e on a finely m e a s u r e d physical p r o p e r t y o f a granular superconducting ceramics ( Y B a C u O ) . This is attributed to superconductivity fluctuation onset since at "low t e m p e r a t u r e " ( T > T~) the (log) t e m p e r a t u r e b e h a v i o r can be u n d e r s t o o d in terms of pair breaking m e c h a n i s m [5-6] while at "high temp e r a t u r e " ( T > 2T~) the linear t e m p e r a t u r e dependence o f R(T) corresponds to 2D metal b e h a v i o r [1].

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