Analysis of fluctuation conductivity of polycrystalline Er1-xPr xBa2Cu3O7-δsuperconductors

Analysis of fluctuation conductivity of polycrystalline Er_1-xPr_xBa₂Cu₃O_7-δsuperconductors

A.R. Jurelo; R. Menegotto Costa^*; A.V.C. de Andrade; P.R. Júnior; G.K. da Cruz; C.S. Lopes; M. dos Santos; W.T.B. de Sousa

Departamento de Física, Universidade Estadual de Ponta Grossa, Av. Gen. Carlos Cavalcanti 4748, 84.030-000, Ponta Grossa, Paraná, Brazil

ABSTRACT

In this work we report on conductivity fluctuation measurements in polycrystalline samples of the Er_1-xPr_xBa₂Cu3O_7-δsuperconductor (x = 0.00, 0.05 and 0.10). Samples were prepared by a standard solid-state reaction technique. The results were analyzed in terms of the temperature derivative of the resistivity and of the logarithmic temperature derivative of the conductivity that allowed the identification of power-law divergences of the conductivity. The results show that the transition proceeds in two stages: pairing and coherence transition. Also, our results, from the critical exponent analysis, show a two-peak splitting at pairing transition, indicating possibly a phase separation. On approaching the zero resistance state, our results show a power-law behavior that corresponds to a phase transition from paracoherent to a coherent state of the granular array.

Keywords: High-TC Superconductor, Erbium, Praseodymium, Critical Phenomena.

1. INTRODUCTION

It is well known that rare earth (RE) substitution for Y in YBa₂Cu₃O_7-δ (Y-123) has little effect on superconductivity, except for Pr, Ce, Tb and Pm [1]. Pr forms a compound that is isostructural with Y-123, however it is not a superconductor [2]. On the other hand, Ce and Tb do not form the compound RE-123 [3-5], and Pm is radioactive with a short half life. In particular, RE_1-xPr_xBa₂Cu₃O_7-δ compound has become one of the most studied subjects in the field of high temperature superconductivity. From these studies, it has been observed that increasing Pr substitution in RE_1-xPr_xBa₂Cu₃O_7-δ , causes a monotonically decrease in the critical temperature (T_C) [6]. Some mechanisms such as hole localization [7,8], hole filling [9], magnetic pair breaking [10] and percolation [11] have been proposed to explain the degradation of superconductivity. Also, it was observed an ion-size effect in experiments on the RE_1-xPr_xBa₂Cu₃O_7-δ system for RE = Nd, Eu, Gd, Y, Er and Yb, indicating an approximately linear T_C decrease with increasing the RE-site ions radius for a fixed dopant amount x [12]. Yet, some of REBa₂Cu₃O_7-δ compounds (such as for RE = Nd, Sm, Gd, Ho and Er) exhibit antiferromagnetic ordering below T_C [13], showing that investigations about the interplay between superconductivity and magnetism can be of particular interest in this system.

Despite the large amount of research on this system, considerable controversy still persists over the mechanisms of T_C suppression by Pr in RE_1-xPr_xBa₂Cu₃O_7-δ . Careful studies of the conductivity in the neighborhood of the critical temperature can yield information about the nature of the superconducting state [14-16] as well as on the influence of the granularity at microscopic and mesoscopic levels on the fluctuation regimes [17-19]. In this paper, we report on fluctuations conductivity measurements in polycrystalline samples of the Er_1-xPr_xBa₂Cu₃O_7-δ (0 < x < 0.10) superconductor. The structural characterization of the samples was obtained through Rietveld analysis of the XRD patterns and the results revealed that all samples were nearly single-phase, without dependence on the Pr concentration. Also, using the temperature derivative of the resistivity, dρ/dT, and the logarithmic temperature derivative of the conductivity, -dln( Δσ)/dT, we observed the evolution of the critical regimes as a function of praseodymium concentration.

2. EXPERIMENTAL DETAILS

Polycrystalline samples of Er_1-xPr_xBa₂Cu₃O_7-δ (x = 0.00, 0.05 and 0.10) were prepared by solid-state reaction technique, using Er₂O₃, Pr₆O₁₁, BaCO₃, and CuO. Appropriate amounts were mixed and calcinated in air at 850, 880 and 920ºC for 24 hours, and then slowly cooled through 700ºC. Finally, the samples were heated in flowing oxygen at 400 ºC for 48 hours. The resistivity measurements were performed with a low-frequency-low-current AC technique that employs a lock-in amplifier as a null detector. The measurements current density was up to 600 mA/cm². To provide electrical contact to the sample, four stripes of silver paste were painted onto the surface. The silver paint was fixed to the sample by heating it in flowing O₂ for 4 h at 400 ºC. Then, copper wires were attached to the samples with silver paste, resulting in contact resistance of less than 1 ohm. Temperature was measured with a Pt sensor, allowing a resolution better than 1 mK, and the resistivity measurements were performed at a 3 K/h rate or lower.

X-ray powder diffraction patterns were collected from 5º to 100º in the 2θ range with 0.02º step and 4 s counting time. Rietveld refinements of crystal structures were performed using the GSAS and EXPGUI software [20,21]. The X-ray powder diffraction patterns of Er_1-xPr_xBa₂Cu₃O_7-δ for x = 0.00, x = 0.05 and x = 0.10 are displayed in Fig. 1. The X-ray pattern almost completely matches the orthorhombic Er-123 structure (compared with JCPDS files), and belongs to the ErBa₂Cu₃O_7-δ orthorhombic unit cell with symmetry Pmmm. Also, all samples were found to be nearly single-phase, and show no dependence on the Pr concentration or the presence of trace impurities of BaCuO₂, PrBaO₃ and CuO. The presence of BaCuO₂ phase is a result of substitution of Pr at Ba site, while the observation of small quantities of the BaCuO₂ and PrBaO₃ impurity phases is a characteristic of Pr-rich samples [22,23].

The unit cell parameters, atomic parameters, and agreement factors for Er_1-xPr_xBa₂Cu₃O_7-δ (x = 0.00, x = 0.05 and x = 0.10) obtained through Rietveld refinements at room temperature are summarized in Table I. The value of the lattice parameter a decreases from 3.8236 (1) for x = 0.00 to 3.8165 for x = 0.10 while c also decreases from 11.6778 (2) for x = 0.00 to 11.6730 (2) for x = 0.10. Meanwhile, b increases from 3.8792 (1) to 3.8839 (2) . Also, the volume decreases from 173.213 (8) ³ for x = 0.00 to 173.03 (1) ³ for x = 0.10. In a general manner, the lattice parameters and volume derived from least squares refinement are in agreement with published results obtained in others studies [24,25]. From Table I we can observe that R_P (R-pattern), R_wp (R-w eighted pattern), R_e (R- expected) and (goodness-of-fit) systematically increase with increasing x. However, as the R_i factors are small, the results are reliable [26,27].

3. RESULTS AND DISCUSSION

It is well-known that sintered samples of high temperature superconductors show a pronounced granular character that plays an important role in their resistive transition. As the temperature decreases from the normal state, it is first observed a pairing transition and then a coherence transition. At the pairing transition, the superconductivity is stabilized in some small and homogeneous regions of the sample at a temperature which virtually coincides with the critical temperature of the bulk, T_C. These superconducting grains may not necessarily be coincident with the crystallographic grains. At a lower temperature, T_CO, the superconductivity is established among the grains. This is the coherence transition, a long-range superconducting state that is achieved through a percolation-like process which controls the activation of weak links between grains. This behavior is very common in polycrystalline samples and it is associated with disorder at mesoscopic level.

In Fig. 2 we show the superconducting transition for three Er_1-xPr_xBa₂Cu₃O_7-δ samples: x = 0.00 (open circle), x = 0.05 (open square) and x = 0.10 (closed circle). The measurements were performed with current density of J = 60 mA/cm² and the room-temperature resistivities were ρ(300 K) = 3.3 m Ω cm (x = 0.00), 6.0 m Ω cm (x = 0.05) and 2.4 m Ω cm (x = 0.10). The presented data are normalized to unity at 95 K. The results (not shown) also indicate that our samples present a metallic-like behavior at high temperatures. The panels (a) and (c) show the resistivity versus temperature plots whereas panels (b) and (d) show the plot of dρ/dT versus temperature in the corresponding temperature range. The plots of dρ/dT versus temperature, shown in panels (b) and (d), present two maxima denoted by T_P1 and T_P2. These two peaks are associated with a splitting of the pairing transition. The maxima T_P1 and T_P2 correspond approximately to the pairing critical temperatures T_C1 and T_C2, respectively. T_P1 is approximately 91.8 K (x = 0.00), 93.0 K (x = 0.05) and 88.2 K (x = 0.10) and T_P2 is about 91.2 K (x = 0.05) and 85.6 K (x = 0.10). These results indicate that the superconducting pairing transition occurs in two steps of about 1.8 K apart (x = 0.05 sample) and with about 4 K (x = 0.10 sample). It is interesting to note that for low concentration of praseodymium (x = 0.05), the value of T_P1 is higher than that for the pure system. This effect was also observed for other doped samples [28]. From panels (c) and (d) we can observe that 10 % Pr substitution in the Er sites causes a strong depression of the superconducting transition temperature and a significant enlargement of the width of the resistive transition (10 % to 90 % of the transition) of approximately 2.0 K (x = 0.00) to 6 K (x = 0.10). For the x = 0.10 sample, the whole transition broadens.

3.1 Method of Analysis

We study the effect of thermal fluctuations to the conductivity by using a Kouvel-Fischer-type method [29]. It is assumed that the fluctuation conductivity Δσ diverges as a power-law given by

where Δσ = σ - σ_ρ , A is the critical amplitude, ε = (T-T_C )/T_C is the reduced temperature and λ is the critical exponent. From the resistivity measurements, we calculate the conductivity σ = 1/ρ . σ_R , the regular conductivity, is obtained by linear extrapolation of the resistivity data in the range from 2T_C to room temperature.

To obtain the values for λ e T_C , we determine numerically the logarithmic derivative of Δσ from experimental data and define

Combining eqs. and we obtain

Then, it is possible to determine simultaneously T_C and λ by plotting versus T [14]. Performing averages over several measurements, we obtained the mean values of the critical exponents.

3.2 Critical Fluctuation Regimes

In Fig. 3 we compare the resistive transitions of ErBa₂Cu₃O_7-δ (x = 0.00) and Er_0.95Pr_0.05Ba₂Cu₃O_7-δ (x = 0.05) measured with current density of J = 60 mA/cm². In panels (a) and (c), dρ/dT x T is plotted. In panels (b) and (d), the transition is shown as x T in the corresponding temperature interval. The figure allows the identification of the asymptotic regime of the coherence critical region (between T_CO and T_P1 for x = 0.00 sample and between T_CO and T_P2 for x = 0.05 sample) and of the pairing critical region (above T_P1 for x = 0.00 sample and above T_P2 for x = 0.05 sample). The pairing critical region has an internal structure [16], and two power-law regimes are observed in sequence when T approaches T_C1 from above corresponding to ≈ 0.34 and ≈ 0.15.

From panel 3(b) we can observe, above T_P1, a full dynamic regime dominated by genuine critical flucutations labeled by the exponent = 0.35±0.03. The value of the exponent is consistent with the predictions for the 3D-XY universality class [14]. Still closer to T_C1, it is observed a fluctuation regime beyond 3D-XY with an exponent = 0.16 ± 0.03. This scaling might represent a crossover to an ultimate weakly first-order character of the normal superconducting transition of high temperature cuprates [16]. This critical regime was previously observed in polycrystalline and single-crystal samples [16,30]. Yet, from panel 3(b), we can observe near the zero resistance state (T_CO) that the fluctuation conductivity can be described by an another power law, given by the equation Δσ ∝ (T-T_CO)^-σ, with exponent σ = 2.9 ± 0.3. The insert shows an expanded view of the asymptotic regime of the coherence critical regime. This regime is interpreted as being intrinsically related to superconducting granularity at mesoscopic level. When the disorder at mesoscopic level dominates, the fluctuation conductivity near the zero-resistance state must diverge with an exponent quite large (σ ≅ 3.0) [31]. The value σ ~ 2.9 observed for this sample is according to the expected value for critical conductivity fluctuations in artificially prepared granular arrays, s ≅ 3 [32]. The same exponent was also observed to characterize the resistive paracoherence-coherence transition of Y-123 ceramics [14,33].

In panel 3(d), it is observed in sequence, again, two power-law regimes when T approaches T_C1 from above corresponding to = 0.34±0.03 and = 0.15±0.02. The value = 0.34 reveals the effects of genuine fluctuations which belong to the 3D-XY univesarlity class. In the immediate vicinity above T_P1 we identify a genuinely critical fluctuation regime described by the exponent = 0.15, which is precursor of a weakly first-order transition [16]. Another genuinely critical regime represented by the exponent λ_P2 = 0.35±0.03 is also visible below T_P1, in the immediate vicinity above T_P2. This regime, that was not observed in the x = 0.00 sample, is in agreement with the predictions of the full dynamic 3D-XY model [14]. The splitting of the pairing transition, verified by observation of critical regimes and (above T_P1) and λ_P2 (below T_P1), could be produced by the presence of two superconducting phases with different temperature transition induced by microscopic granularity. The results displayed in Fig. 2(b) suggest that Pr doping induces a superconducting phase with higher critical temperature ( ~ 93.1 K). A genuine critical fluctuation regime in the temperature range between T_P2 and T_P1 was first observed by Barros et al. in Y_1-xPr_xBa₂Cu₃O_7-δ single crystals and polycrystalline samples [19,30], and it was associated with a peculiar phase separation related with oxygen doping. Panel 3(d) also shows that, between T_P2 and T_C0, the variation of as a function of temperature is well described by a power law regime with corresponding exponent σ = 2.9±0.3. The insert shows an expanded view of the paracoherence temperature region. This value is the same observed in the pure system and is interpreted as an indication of a paracoherent-coherent transition of the granular array [14,30].

Fig. 4 displays representative plots of x T for the Er_0.90Pr_0.10Ba₂Cu₃O_7-δ (x = 0.10) sample for J = 60 mA/cm². Above T_P1 , the results show the occurrence of a genuine critical regime, with exponent = 0.32±0.01 that is consistent with the predictions for the 3D-XY universality class. It is important to point out that, in this case, a scaling beyond 3D-XY precursory of a weakly first-order transition [16] was not observed, as noticed for the Y_0.95Pr_0.05Ba₂Cu₃O_7-δ and pure samples. Between T_P2 and T_P1 we can clearly observe another fluctuation regime with exponent = 1.3±0.2. This exponent does not correspond to an integer dimensionality. In this case we supose that the flucutations develop in a space having fractal topology. According to Char and Kapitulnik [34], the conductivity exponent should be written as λ = 2 - where is the fractal dimension of the flucutation network. Our exponent ≈ 1.3 is consistent with , which is the weel-known fractal dimensionality of the percolation network [35] that corresponds to a crossover regime between 1D and 2D geometry. A similar exponent was also observed in Bi based cuprates [14, 36]. We expected the presence of the 3D-XYscaling closer to T_P2 in the x = 0.10 sample, as observed for the x = 0.00 and x = 0.05 samples. The disappearance of this regime is cleary related with the increase in Pr doping. The observation of the Gaussian regime is related with its robustness against the Pr doping.Again, in approaching the zero resistance state, our results show a power-law behavior with critical exponent σ = 2.7 ± 0.1 that corresponds to a phase transition from a paracoherent to a coherent state of the granular array [31]. These results indicate that an increasing Pr concentration destroys the pairing critical regimes. On the other hand, 10% of Pr substitution does not affect the coherent transition.

Fig. 5 compares representative plots of x T for the x = 0.05 sample for two different currents density, J = 60 mA/cm² and J = 600 mA/cm². We can observe that the regimes and λ_P2 are stable against J within the studied range. This behavior is consistent with the interpretation that the observed λ_P2 regime is related with a pairing (intragrain) transition. Below T_P2, and down to the zero-resistance state, the resistivity is current dependent. The figure shows that the higher current intensity shifts T_CO to lower temperatures. Thus, the enlargement of the resistive transition induced by current in our samples is an effect directly related to granularity. Indeed, the self-field is expected to enhance the granular character of the samples by weakening the junctions between grains. The effect of increasing current for the x = 0.10 sample (not shown) is similar to that observed for the x = 0.05 sample.

The comparison of the results obtained in the pure and doped systems shows that the Pr doping (until 10 %) alters significantly the critical behavior of the Er_1-xPr_xBa₂Cu₃O_7-δ compound above T_P2. Two possible Pr doping effects can be inferred from our experiments and analysis. The first one is a phase separation, showed in Figs. 3, 4 and 5, and that is indicated by the presence of two genuinely critical regimes above T_P2. These critical regimes are not affected by the studied currents. The second effect is the weakness of the superconductivity, which can be observed by the suppression of the pairing critical regimes. The regime beyond 3D-XY (λ ≈0.13), observed above T_P1 for x = 0.00 and x = 0.05 samples, was not observed for the x = 0.10 sample. At the same time, the critical regime 3D-XY (λ ≈ 0.33) observed between T_P1 and T_P2 for the x = 0.05 sample, was also suppressed in the x = 0.10 sample. On the other hand, below T_P2, in the paracoherent regime, it was not observed any influence of the Pr doping on the critical exponents. These results indicate that Pr doping induces structural disorder at a microscopic level in the studied system.

4. CONCLUSIONS

In conclusion, our conductivity experiments on granular Er_1-xPr_xBa₂Cu₃O_7-δ (0 < x < 0.10) samples show that the superconducting transition proceeds in two stages: pairing and coherence transition. From the temperature derivative and power-law divergences of the conductivity, our results show a two-peak splitting at pairing transition, indicating possibly a peculiar phase separation associated with Pr doping. Another Pr doping effect is the weakness of the superconductivity, which can be observed through the suppression of genuine critical regimes. On approaching the zero resistance state, our results show a power-law behavior that corresponds to a phase transition from paracoherent to a coherent state of the granular array with exponents that are doping independent.

Acknowledgements

This work was partially financed by the CNPq Brazilian Agency under contract nº 475347/01-3.

(Received on 3 July, 2009)

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Publication Dates

• Publication in this collection
  11 Feb 2010
• Date of issue
  Dec 2009

History

• Received
  03 July 2009