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Excess conductivity and magneto-conductivity studies in pure and Ag-doped (La1−x Yx )2Ba2CaCu5Oz superconductors

This content has been downloaded from IOPscience. Please scroll down to see the full text. 2006 Supercond. Sci. Technol. 19 1209 (http://iopscience.iop.org/0953-2048/19/11/020) View the table of contents for this issue, or go to the journal homepage for more

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INSTITUTE OF PHYSICS PUBLISHING

SUPERCONDUCTOR SCIENCE AND TECHNOLOGY

Supercond. Sci. Technol. 19 (2006) 1209–1214

doi:10.1088/0953-2048/19/11/020

Excess conductivity and magneto-conductivity studies in pure and Ag-doped (La1−x Yx )2Ba2CaCu5Oz superconductors P K Nayak and S Ravi Department of Physics, Indian Institute of Technology Guwahati, Guwahati-781 039, India E-mail: [email protected]

Received 26 May 2006, in final form 3 July 2006 Published 18 October 2006 Online at stacks.iop.org/SUST/19/1209 Abstract The temperature variations of electrical resistivity have been measured on pure and 5 wt% Ag-doped (La1−x Yx )2 Ba2 CaCu5 Oz superconductors in the absence and presence of 1 T magnetic field. The electrical resistivity data in the absence of magnetic field were analysed in terms of fluctuation-induced excess conductivity in the mean-field regime by using the Aslamazov–Larkin (AL), Lawrence–Doniach (LD) and Maki–Thompson (MT) models. The fluctuations in the amplitude of order parameter are found to be two dimensional in nature. The magneto-resistivity data were analysed in terms of fluctuation magneto-conductivity by using the AL and MT models for layered superconductors and by taking into account both orbital and Zeeman terms. These materials exhibit a strong pair breaking effect and the typical phase breaking time at 100 K is found to be of the order of 10−16 s. The typical values of coherence lengths along the ab-plane and along the ˚ c-direction at 0 K are found to be 28.5 and 0.4 A.

transition temperature. According to the LD model for layered superconductors, the expression for excess conductivity is

1. Introduction Excess conductivity arises due to thermodynamic fluctuations of the superconducting order parameter above the transition temperature (Tc ) of high-temperature superconductors. The excess conductivity data are generally analysed based on the models proposed by Aslamazov and Larkin (AL) [1], and Lawrence–Doniach (LD) [2]. According to the AL model, the excess conductivity arising from two-dimensional (2D) and three-dimensional (3D) fluctuations are given by

e2 −1 ε 16hd ¯

(1)

e2 ε−1/2 . 32hξ( ¯ 0)

(2)

σ2D = and

σ3D =

Here ε = (T − Tc )/ Tc is the reduced temperature, d is the 2D characteristic length of the unit cell, ξ(0) is the coherence length at zero Kelvin and Tc is the mean-field 0953-2048/06/111209+06$30.00

σLD =

e2 −1 ε [1 + 2α]−1/2 . 16hd ¯

(3)

Here α = α0 /ε = (2ξc (0)2 /d 2 )/ε . The advantage of the LD expression is that it reduces to the 2D AL model for large ε values, where the coupling constant, J (T ) = (ξc (T )/d)2 , is quite small (ξc (T ) ∝ ε−1/2 ), and to the 3D AL model for small values of ε , where in some cases the coupling constant J would be quite strong. The above theoretical models are based on direct contribution to excess conductivity, i.e. due to the acceleration of Cooper pairs generated by thermodynamic fluctuations. The indirect contribution to excess conductivity (σ ) arises from the interaction of fluctuating Cooper pairs with normal electrons and was calculated by Maki [3] and later modified by Thompson [4]. The indirect contribution to excess conductivity for layered superconductors was derived by Hikami and

© 2006 IOP Publishing Ltd Printed in the UK

1209

P K Nayak and S Ravi

Larkin [5] and independently by Maki and Thompson [6] and is given as follows in the absence of applied magnetic field. √ δ 1 + α + 1 + 2α e2 σMT = ln (4) √ 8hd α 1 + δ + 1 + 2δ ¯ (ε − αε/δ) where δ = (16ξc (0)2 κB T τφ /(πd 2 h)) ¯ is the pair breaking parameter, κB is the Boltzman constant and τφ is the phase breaking time. The superconducting order parameter fluctuations can also be studied by measuring the magneto-conductivity, σ H = (1/ρ(H )) − (1/ρ(0)). Here ρ(H ) and ρ(0) are the measured resistivity in the presence and absence of magnetic field. The advantage of magneto-conductivity analysis over zero-field excess conductivity is that the uncertainty in the estimation of normal state conductivity is eliminated. The σ H is the sum of four different terms, namely AL-orbital (ALO), MT-orbital (MTO), AL-Zeeman (ALZ) and MT-Zeeman (MTZ). The AL terms correspond to direct contribution to σ H and the MT terms correspond to indirect contribution to σ H . The orbital and Zeeman terms result from the interactions of the magnetic field with the carrier orbital and spin moments respectively. The expressions for the orbital contribution to σ H can be written as follows [5, 6].

σALO = and

−e2 2 + 4α + 3α 2 2 h 64hdε ¯ 3 (1 + 2α)5/2

2 δ −e2 1+δ 48hd ¯ (1 − α/δ) ε3 α 2 (1 + 2δ)3/2 1+α h2. − (1 + 2α)3/2

(5)

σMTO =

(6)

2 (2eξab (0)2 /h) In the above equation, h 2 = Heff ¯ 2 , where Heff is the effective magnetic field to account for the angular average of the conducting planes in polycrystalline samples. According 2 to Matsuda et al [7], Heff = H 2 cos2 θ = H 2 /3, where H is the applied magnetic field. ξab (0) is the coherence length along the ab-plane at 0 K. According to Aronov et al [8], the contributions of Zeeman effect on the AL (ALZ) and MT (MTZ) terms can be written as 2 ωs e2 1+α σALZ = −0.526 (7) hdε ¯ 2 (1 + 2α)3/2 4πκB Tc

and

σMTZ =

−e2 1+δ 16hdε (1 + 2δ)3/2 ¯

ωs τφ 2 (8) h¯ where ωs = gμB H is the Zeeman energy, g is the Landé g factor and μB is the Bohr magneton. The excess conductivity analysis in high-Tc superconductors has been carried out by several groups. YBa2 Cu3 O7 superconductors exhibit a crossover from 2D to 3D fluctuations in the mean-field regime [9–13]. Two-dimensional fluctuations are widely reported in both Bi–Sr–Ca–Cu–O [14–17] and Tl– Ba–Ca–Cu–O superconductors [18, 19]. −

1210

1 + δ + δ/α [(1 + δ/α)(1 + 2δ + δ/α)]3/2

The fluctuation magneto-conductivity in YBa2 Cu3 O7 materials has been studied by several groups [20–25]. The typical value of τφ (100 K) is reported to be of the order of 10−13 –10−14 s. Matsuda et al [7] and Andersson et al [22] have worked on polycrystalline material and they have expressed the applied magnetic field H in terms of the effective magnetic field Heff averaged over all crystallites to account for the random directions of the conducting planes. Their estimated physical parameters are comparable to those obtained from single crystal materials. In NdBa2 Cu3 O7 thin film, significant contributions of both orbital and Zeeman terms of the MT model have been reported [26]. In Tl2 Ba2 CaCu2 Oz and Tl2 Ba2 CuO2 superconductors, the values of τφ are reported to be 10−13 s and 10−14 s respectively from magneto-conductivity analysis [27, 28]. The contribution of the MT term is reported to be negligible in the magnetoconductivity of Bi2 Sr2 Ca2 Cu3 Oz [29]. In the present work, temperature variations of electrical resistivity in zero field and in the presence of 1 T magnetic field were measured on six superconducting samples of the (La1−x Yx )2 Ba2 CaCu5 Oz series with compositions x = 0.1, 0.4, 0.5 (samples A, B, C) and x = 0.1, 0.4, 0.5 with 5 wt% of Ag (samples D, E, F). These materials are based on the parent compound La2 Ba2 Cu4 Oz [30], which are identical to the non-superconducting parent compounds La3 Ba3 Cu6 Oz and LaBaCu2 Oz [31, 32]. Superconductivity in the above series can be obtained by doping a CaCuO2 layer [30, 32, 33]. The crystal structure of the above superconducting series is similar to that of the non-superconducting tetragonal phase of YBa2 Cu3 O6+δ . So, it would be interesting to carry out fluctuation magneto-conductivity studies in the above series and compare them with the results of superconducting YBa2 Cu3 O7−δ with orthorhombic structure.

2. Experimental details The single-phase compounds of (La1−x Yx )2 Ba2 CaCu5 Oz for x = 0.1, 0.4 and 0.5 were prepared by the solid state route. The stoichiometric ratios of high-purity La2 O3 , Y2 O3 , BaCO3 , CaCO3 and CuO were mixed and ground under acetone to give a uniform mixture. This was presintered at 900 ◦ C for 24 h with a few intermediate grindings at room temperature. The final sintering in pellet form was carried out at 950 ◦ C in O2 atmosphere for 24 h followed by slow cooling at the rate of 50 ◦ C h−1 to room temperature. To oxygenate the samples, these pellets were annealed at 500 ◦ C for about 24 h in oxygen atmosphere followed by slow cooling to room temperature. Ag-doped samples were prepared by adding 5 wt% of Ag to the stoichiometric ratio of the above starting compounds and by following the same heat treatments. X-ray diffraction (XRD) patterns were recorded using a Seifert 3003TT XRD machine with Cu Kα radiation at room temperature. AC susceptibility was measured as a function of temperature at an AC field amplitude of 22 A m−1 by employing the mutual inductance bridge method and using a Perkin Elmer (model 7265) dual phase lock-in amplifier. The temperature variations of electrical resistivity in zero field and in the presence of 1 T magnetic field were measured using the linear fourprobe technique. The magnetic field was generated using a Walker electromagnet. The temperature variation was achieved

Excess conductivity and magneto-conductivity studies in pure and Ag-doped (La1−x Yx )2 Ba2 CaCu5 Oz superconductors

Table 1. Parameters obtained from electrical resistivity measurements and linear fit in the normal state. Sample name

Tc (0) (K)

Tc (K)

ρ(300 K) (m cm)

a (m cm)

b (m cm K−1 )

rmsd (%)

A B C D E F

57.4 53.2 50.4 57.7 57.9 51.4

62.8 65.3 60.4 67.8 67.6 64.5

3.237 3.285 4.688 2.153 3.633 4.300

1.593 2.205 2.908 0.998 1.935 2.844

5.48 × 10−3 3.61 × 10−3 5.95 × 10−3 3.86 × 10−3 5.82 × 10−3 4.86 × 10−3

0.17 0.06 0.07 0.30 0.09 0.05

40

50

(2 0 6 )

(2 0 5 )

(2 0 3 ) (2 1 2 ) ( 1 1 6 ,2 1 3 )

( 0 0 6 ,2 0 0 )

( 0 0 5 ,1 0 4 ) (1 1 3 )

( 1 0 3 ,1 1 0 ) 30

4

Resistivity(mΩ .cm)

20

(1 0 2 )

( 1 0 0 ,0 0 3 )

Intensity (a.u.)

5

(a)

60

70

2 Θ (Degree)

′ Χ /(SI Unit)

0.0

3

Sample B

2

Sample C Sample E

1

(b)

-0.2

Fit To ρ =a+bT n

H m = 22 A/m

0

-0.4

50

100

150

200

250

300

Temperature(K)

-0.6 -0.8 -1.0 20

30

40

50

60

70

80

Temperature(K)

Figure 2. Temperature variations of resistivity of sample B (circles), sample C (squares) and sample E (triangles). The solid line represents the fit of normal state resistivity to the linear relation and its extrapolation down to low temperature.

Figure 1. X-ray diffraction pattern (a) and temperature variation of in-phase AC susceptibility, χ (b) for Ag-doped (La1−x Yx )2 Ba2 CaCu5 Oz superconductor with x = 0.4 (sample E).

0.35 0.30

Sample B

0.25

3. Results and discussions

dρ/dT(mΩ .cm/K)

0.20

using a commercial closed-cycle helium refrigerator cryostat equipped with a LakeShore temperature controller (model331). The temperature was measured using a LakeShore calibrated GaAlAs sensor with an accuracy of better than ±50 mK.

0.15 0.10 0.05 0.00 0.30 Sample E

0.25 0.20 0.15

From the XRD measurement, all samples were found to be almost in single phase form. A typical XRD pattern and temperature variation of in-phase AC susceptibility for sample E are shown in figure 1. The pattern could be indexed to a tetragonal unit cell and the lattice parameters are found to be ˚ From the AC susceptibility a = b = 3.855, c = 11.577 A. measurement, the sample exhibits a diamagnetic transition with onset temperature at around 69 K. Similar diamagnetic transitions have been observed in other samples which are not shown here. Typical plots of temperature variation of electrical resistivity for samples B, C and E are shown in figure 2. They exhibit a superconducting transition with zeroresistivity transition temperatures, Tc (0), at 53.2, 50.4 and 57.9 K respectively. Typical plots of dρ/dT versus temperature for samples B and E are shown in figure 3. We can see that they exhibit a single prominent peak followed by a low-temperature

0.10 0.05 0.00 40

50

60

70

80

90

100

110

120

Temperature(K)

Figure 3. Plots of dρ/dT versus temperature for sample B (circles) and sample E (triangles).

shoulder due to intergranular weak links. The temperature corresponding to the peak in the dρ/dT versus T plot is taken as the mean-field transition temperature, Tc . The values of Tc (0), Tc , and resistivity at 300 K, ρ(300 K) for different samples are tabulated in table 1. The normal state resistivity, i.e. resistivity in the temperature region 2Tc to room temperature, was fitted to the 1211


Table 2. Parameters obtained from excess conductivity analysis using AL, LD and LD + MT models. Fit to AL model Sample name

c (10−2 (m cm)−1 )

A B C D E F

1.74 1.53 1.59 1.00 2.38 1.54

λ

rmsd (%)

c (10−2 (m cm)−1 )

ξc (0) ˚ (A)

rmsd (%)

c (10−2 (m cm)−1 )

τφ (100 K) (10−16 s)

rmsd (%)

−1.05 −0.84 −1.04 −0.98 −0.86 −1.02

0.96 0.76 1.85 0.47 0.75 0.76

1.95 1.13 1.79 0.98 1.92 1.66

0.16 0.79 0.13 0.33 0.77 0.18

1.95 1.73 2.22 1.20 1.84 1.22

1.94 1.08 1.79 0.98 1.80 1.66

3.4 2.3 2.7 4.5 1.9 1.3

2.22 1.33 2.30 1.17 0.99 1.22

0 -1

ln( Δσ / σ0)

-2 -3 Sample B -4 -5.0 -4.5 -4.0 -3.5 -3.0 -2.5 -2.0 1 0 -1 -2 Sample C -3 -4 -5.0 -4.5 -4.0 -3.5 -3.0 -2.5 -2.0 -1.5 1 0 -1 -2 Sample E -3 -4 -5.0 -4.5 -4.0 -3.5 -3.0 -2.5 -2.0 -1.5

ln( ε )

Expt. Data AL 2D Fit LD Fit LD+MT Fit

-1.5

-1.0


-1.0

-0.5


-1.0

-0.5

Figure 4. Plots of ln(σ/σ0 ) versus ln(ε) for sample B (circles), sample C (squares) and sample E (triangles). The theoretical data corresponding to the AL-2D fit, LD fit and LD + MT fit are given as solid line, dashed lines and dash–dotted lines respectively.

linear relation, ρn (T ) = a + bT , by varying the parameters a and b. The fitted normal state resistivity by extrapolating down to low temperature are shown as solid lines in figure 2 and they closely follow the experimental data in the normal state. The fitted parameters a and b for different samples are given in table 1. 3.1. Excess conductivity The experimental excess conductivity (σ ) data were obtained from the difference between the measured and extrapolated normal state conductivity, i.e. σ = 1/ρ(T ) − 1/ρn (T ). Typical plots of ln(σ/σ0 ) versus ln(ε) are shown in figure 4 for samples B, C and E. Here σ0 is the measured conductivity at 300 K. The σ data were fitted to the AL expressions (σ = cε−λ ) as given in equations (1) and (2), by varying the parameters c and λ; the fit is shown as a solid line in figure 4. The values of critical exponent (λ) obtained from the above fit are found to be −0.84, −1.04 and −0.86 for samples B, C and E respectively in the mean-field region. These values are close to two dimensional characteristic value of −1 and thus these materials exhibit mostly two-dimensional fluctuations in the mean-field region. Similarly the fit was carried out for other samples in the mean-field region. The fitted parameters c and λ along with the root mean square deviation (rmsd) values are given in table 2. The excess conductivity data in the meanfield region were also fitted to the LD expression (equation (3)) 1212

Fit to LD + MT model

Fit to LD model

by varying the parameters αo and c (=e2 /16hd) ¯ . The fitted data are shown as dashed lines in figure 4. From the fitted values of αo and by taking d as the c-axis length of the unit cell, ξc (0) values are estimated and are found to be 0.79, 0.13 ˚ for samples B, C and E respectively. Similarly and 0.77 A the σ data of other samples were fitted to LD model and the parameters c and ξc (0) are given in table 2. In order to study the contribution of MT term to the excess conductivity, we have fitted the σ data to the combination of the LD and MT expressions, i.e. using equations (3) and (4). The fit was carried out by assuming the value of αo obtained from the LD fit and by varying the parameters c (=e2 /16hd) ¯ and δ . The fitted data are shown as dash–dotted lines in figure 4, which almost coincide with the LD model fit. From the fitted values of δ , the phase breaking times τφ (100 K) were estimated and found to be 2.3 × 10−16 s, 2.7 × 10−16 s and 1.9 × 10−16 s for samples B, C and E respectively. Similarly the LD + MT model fit was carried out for other samples. The parameters obtained from the above analysis are given in table 2. The magnitudes of τφ suggest that these samples exhibit a strong pair breaking effect and that the contribution of the MT term to σ is insignificant. 3.2. Magneto-conductivity The temperature variations of electrical resistivity for zero field and for the applied magnetic field, H = 1 T, are shown in figure 5. By the application of magnetic field, Tc (0) shifts from 53.2 to 34.1 K and from 57.9 to 49.7 K for samples B and E respectively. The experimental magneto-conductivity, σ H , was obtained from the values of ρ(0) and ρ(H ). Typical plots of ln(−σ H ) versus ln ε are shown in figure 6 for samples B, C and E. Initially, we analysed the σ H data in terms of only the direct contributions, i.e. the combination of ALO and ALZ terms (equations (5) and (7)). This is mainly to estimate the value of αo . From the fitted values of αo , the coherence length along the c direction at 0 K, ξc (0) was estimated and it was ˚ for samples B, C and E found to be 0.79, 0.16 and 0.84 A respectively. These values are comparable to those obtained from excess conductivity analysis. The fitting of σ H was repeated by taking into account the indirect contribution to σ H , i.e. they were fitted to the combination of equations (5)– (8) by taking a C -factor as follows, 1 (9) [σALO + σALZ + σMTO + σMTZ ]. C Here the C -factor is to account for inhomogeneity in the current path due to voids, grain boundaries, weak links, etc

σ H =

Excess conductivity and magneto-conductivity studies in pure and Ag-doped (La1−x Yx )2 Ba2 CaCu5 Oz superconductors -3.0

3.0 2.5

Sample B

H=0T H=1T

2.0

-4.0

Sample B

0.5

-4.5 -3.50 -3.25 -3.00 -2.75 -3.75 -2 Expt.data -3 Fit to AL -4 Fit to AL+MT -5 Sample C -6 -7 -3.50 -3.25 -3.00 -2.75 -2.50 -2.25 -2 Expt.data -3 Fit to AL -4 Fit to AL+MT Sample E -5 -6 -1.75 -3.50 -3.25 -3.00 -2.75 -2.50 -2.25 -2.0 0

0.0

ln[(T-Tc )/Tc ]

ln[-ΔσH(mΩ.cm)-1]

Resistivity(mΩ.cm)

1.5

Expt.data Fit to AL Fit to AL+MT

-3.5

1.0 0.5 0.0 2.5

Sample E

2.0 1.5 1.0

20

30

40

50

60

70

80

90

100

Temperature(K)

Figure 5. Temperature variation of electrical resistivity measured at H = 0 (triangles) and 1 T (circles) for samples B and E.

in polycrystalline materials. The C -factor was obtained by following Oh et al [10], and according to them it is equal to the ratio of slope of the normal state resistivity (dρ/dT at T Tc ) of polycrystalline material to that of single crystals. In high-Tc single-crystal superconductors, the value of normal state dρ/dT is generally 0.5–0.6 μ cm K−1 . To reduce the number of free parameters of the fit, αo was fixed using the value obtained from the ALO + ALZ fit. The other parameters, namely P1 = e2 h 2 /(64hd) ¯ , P2 = ω Tτ e2 2 (0.526e2 /hd)(ω ( s h¯ φ )2 , ¯ s /4πk B Tc ) , P3 = δ and P4 = 16hd ¯ were varied during the fit. The fitted data in the mean-field regime are shown as dashed lines in figure 6, which closely follow the experimental data. From the fitted parameters, the theoretical data of AL (ALO + ALZ) and MT (MTO + MTZ) terms were calculated. The AL data are shown as a solid line in figure 6 and they are indistinguishable from AL + MT data because of the insignificant contribution of the MT term. Similarly, AL + MT model fitting was carried out on other samples. The estimated values of ξc (0) from magnetoconductivity analysis are given in table 3. They are quite small compared to that of YBa2 Cu3 O7 materials [9–13]. The coherence length along the ab-plane ξab (0) was estimated from the fitted values of P1 and by taking into account the effective magnetic field. The ξab (0) values are tabulated in table 3 and they are comparable to those of YBa2 Cu3 O7 materials [7, 22]. The values of τφ (100 K) were estimated using δ values obtained from σ H analysis and they are given in table 3. They are of the order of 10−16 s and are comparable to those obtained from excess conductivity analysis. The values of τφ are found to be about three orders of magnitude less than those reported for orthorhombic YBa2 Cu3 O7 superconductors. However, the τφ values obtained in the present series are comparable to those reported for Bi–Sr–Ca–Cu–O superconductors [34]. According to Aronov et al [8], τφ can be compared with the energy relaxation time due to spin–orbit and spin–spin interaction. Accordingly, the energy values h/τ ¯ φ (100 K) are given in table 3 and it is found that τh¯φ κB Tc . This

Figure 6. Plots of ln(−σ H ) versus ln ε for samples B, C and E. The experimental data are shown as symbols. The theoretical AL and AL + MT data are shown as solid and dashed lines respectively, and they merge with each other.

Table 3. Parameters obtained from the analysis of magneto-conductivity using equation (9) (AL + MT terms). Sample name

ξc (0) ˚ (A)

ξab (0) ˚ (A)

τφ (100 K) (10−16 s)

h¯ /τφ (100 K) (eV)

rmsd (%)

A B C D E F

0.46 0.79 0.16 0.27 0.84 0.27

28.5 18.7 32.1 22.8 33.5 34.0

1.2 5.0 1.2 4.3 4.3 1.4

5.22 1.32 5.46 1.54 1.54 4.60

0.81 0.68 1.63 0.24 0.44 0.10

suggests that there is a strong pair breaking effect in the present materials and that the contribution of the MT term is insignificant.

4. Conclusions To summarize, we have measured the electrical resistivity on pure and Ag-doped (La1−x Yx )2 Ba2 CaCu5 Oz superconductors in the absence and in the presence of 1 T magnetic field. The resistivity data in the absence of magnetic field were analysed in terms of fluctuation-induced excess conductivity in the mean-field regime by using the Aslamazov–Larkin (AL), Lawrence–Doniach (LD) and Maki–Thompson (MT) models. These materials exhibit two-dimensional fluctuations in the mean-field region. Thus unlike orthorhombic superconducting YBa2 Cu3 O7 , where a crossover from 2D to 3D fluctuations is observed in the mean-field region, the present materials with tetragonal structure comparable to the non-superconducting YBa2 Cu3 O6+δ exhibit only 2D fluctuations in the meanfield region. This suggests that, according to LD model, the interlayer coupling constant J (T ) = (ξc (T )/d)2 1/2 in the present materials. The rather low value of J (T ) could be mainly due to reduced ξc (T ) in the present materials compared to YBa2 Cu3 O7 because the d values are comparable in both the systems. There is a possibility of large anisotropy and hence a small ξc (T ) in the present series that leads to 2D fluctuations. It may also be noted that 1213


other high-Tc superconductors such as Bi–Sr–Ca–Cu–O and Tl–Ba–Ca–Cu–O systems exhibit tetragonal structure with large anisotropy [35, 36] and 2D fluctuations in the meanfield region [14–19]. On the other hand, well oxygenated YBa2 Cu3 O7 with orthorhombic structure exhibits relatively low anisotropy [36]. Kleiner and Müller have also reported that Bi2 Sr2 CaCu2 O8 and Tl2 Ba2 Ca2 Cu3 O10 superconductors exhibit an intrinsic Josephson effect, in which each CuO2 layer behaves like a 2D superconductor, but such an effect has not been observed in YBa2 Cu3 O7 [36]. The magnetoresistivity data were analysed in terms of fluctuation magnetoconductivity by using the AL and MT models and by taking into account both orbital and Zeeman terms. The fluctuation magneto-conductivity analysis suggests that these materials exhibit a strong pair breaking effect, and the typical phase breaking time at 100 K is found to be of the order of 10−16 s.

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