Fluctuation-enhanced conductivity in YBa2Cu2Ox (6.5 <= x <= 6.95) and Tl2Ba2Ca2Cu3O10 +/-delta

www.elsevier.nlrlocaterphysc

Fluctuation-enhanced conductivity in YBa Cu O

_{2 3 x}

ž

6.5 F x F 6.95 and Tl Ba Ca Cu O

/

_{2 2 2 3 10 " d}

superconducting

thin films

J.Y. Juang

)

, M.C. Hsieh, C.W. Luo, T.M. Uen, K.H. Wu, Y.S. Gou

Department of Electrophysics, National Chiao-Tung UniÕersity, 30047 Hsin-chu, Taiwan

Received 14 September 1999; accepted 20 October 1999

Abstract

Ž Ž .. Ž .

The fluctuation-induced conductivity D s T near T of a sole YBa Cu O_{c 2 3 x} YBCO film with various precisely

Ž .

controlled oxygen contents 6.5 F x F 6.95 was studied and compared with those obtained from its Tl-based counterparts. Ž .

For YBCO films with x ) 6.7, Ds T displays a distinct 3D to 2D crossover as the temperature approaches T . On the otherc

Ž .

hand, as T ™ T , D s T_c of both Tl-based and YBCO film with x F 6.7 exhibits a reversed 2D to 3D crossover. It is

suggestive that the coupling between the CuO2 layers may have changed significantly with reducing oxygen. q 2000

Elsevier Science B.V. All rights reserved.

Keywords: Fluctuation effects; Oxygen stoichiometry; Cu-chains; Coherence length

1. Introduction

Since the discovery of the high-temperature

su-Ž .

perconductors HTS , the dimensionality of the ma-terials has been one of the most pursued issues as it lays the ground for constructing the high-T super-c conductivity. Questions such as whether substantial coupling between slabs of CuO2 planes is a neces-sity for high-Tc superconductivity have received

w x

much attention. Early studies 1–3 of fluctuation-en-hanced conductivity on optimum-doped YBCO thin films and single crystals have reached the conclu-sions that the material is quasi-two-dimensional

)

Corresponding author. Tel.: 571-2121; fax: q886-3-572-5230.

Ž .

E-mail address: [email protected] J.Y. Juang

ŽQ2D in nature with very short zero-temperature.

˚

Ž . Ž .

c-axis coherence length j 0_c 0.45 ; 1.8 A and a rather scattered values of effective fluctuation

thick-˚

Ž .

ness d_eff 1.7 ; 11.7 A . Subsequent extensive stud-w x

ies 4 indicated that for fully oxygenated YBCO, the Ž . physically reasonable parameters should be j 0_c

˚

˚

; 1.5 A and d ; 11.8 A, respectively. Despite theeff above consensus, however, the issue of dimensional

w x crossover has remained as a matter of debate 5 . On the other hand, alternative approach of using artifi-cial HTS superlattices with various thicknesses and materials of superconducting and

non-superconduct-w x

ing ‘‘spacers’’ has been tried, as well 6 . From these studies, it appeared that long-range Josephson cou-pling does occur and is important in superlattices with metallic spacers. Unfortunately, most of the ‘‘peculiar properties’’ obtained in these artificial sys-0921-4534r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved.

Ž .

tems seemed to stem mainly from extrinsic factors, thus, may not reflect the intrinsic properties of HTS. A direct evidence indicating that HTS compounds are native superconducting superlattices themselves was the observation of intrinsic Josephson effects

Ž .

exhibited in Bi Sr CaCu O_{2 2 2 8} Bi-2212 single crys-w x

tals by Kleiner et al. 7 . The evidence guarantees the essential validity of the model of Josephson-coupled

Ž

Q2D superconducting slabs with a junction

thick-˚

.

ness of approximately 15 A in describing the HTS. w x However, as noted by Kleiner and Muller 8 , the

¨

fully oxygenated YBCO was an exception in their observations. This implies that either YBCO is not

Ž

Josephson-coupled e.g., the material may form S–

X

.

S –S structure or the effects may be obscured by defects. In order to explore these issues, a direct monitoring of the junction structure without encoun-tering the complications arising from the detailed microstructure and defect of the films should be of interest. In this study, a single YBCO film was used

Ž .

to investigate the D s T behavior as a function of film oxygen content. It was observed that both d_eff

Ž .

and j 0 decreased drastically with reducing film_c oxygen content. These changes are translated into the coupling strength between the CuO₂ slabs. The re-sults are compared with that obtained from the more two-dimensional single grain Tl-2223 films.

2. Experiment

The YBCO films used in this study were de-posited by a KrF excimer pulsed laser on

Ž .

LaAlO 100 substrates at 7608C with an oxygen3 pressure of 0.28 Torr. The energy density and the repetition rate of the laser pulse were 2–4 Jrcm2 and 3–10 Hz, respectively. The as-deposited films typically have zero-resistance temperature of 89–90 K with c-axis oriented normal to the substrate sur-face. The oxygen content of the YBCO film was manipulated by an encapsulated bulk annealing

w x

method 9 . As will be discussed in detail below, this method is capable of controlling the oxygen content of the YBCO films precisely and reversibly. It is noted that by using this method, all the measure-ments can be performed on a single film. As a result, any changes in the superconducting properties should

arise mainly from the effects of the oxygen content and possible complications originated from individ-ual film structures are minimized. On the other hand, for the Tl-2223 samples studied, the measuring

w x

bridges were formed entirely on a single grain 10 . All the transport measurements were carried out by the standard four-probe technique.

3. Results and discussion

Fig. 1 shows the typical in-plane resistivity as a

Ž .

function of temperature r_{a b} T for YBCO films with

various oxygen contents. It is noted that at fully

Ž .

oxygenated state, ra bT is described neatly by the

Ž . Ž . Ž .

linear expression ra b T s ra b0 q a T with ra b 0 and a being y11 mV cm and 1.5 mV cmrK, respectively. These extrapolated values agree ex-tremely well with those obtained for YBCO single

w x

crystals 3 , indicating that the quality of the present films should be viable for revealing the intrinsic properties of the material. Furthermore, as displayed in the inset of Fig. 1, the Tc0 decreases from 90.3 K of the fully oxygenated state through the distinct

w x

two-plateau feature of YBCO system 11 with de-scending oxygen content. This is indicative that the oxygen content of the films was indeed varied as expected.

Ž .

Fig. 1. ra bT for a YBCO film with various oxygen contents. Curves 1 to 8 represent x s 7.0, 6.9, 6.8, 6.75, 6.7, 6.55, 6.5, and 6.45, respectively. The inset shows the Tc0 as a function of x.

To demonstrate the ‘‘reversibility’’ and the ‘‘im-Ž

munity’’ i.e., properties other than those directly . associate with oxygen content were not affected of the present oxygen controlling technique, repeated annealing at several conditions was carried out. As can be seen in Fig. 2, results for x s 7.0, x s 6.8,

x s 6.7, and x s 6.5 indeed demonstrate the viability

of the process in manipulating the oxygen content in YBCO films. We note that although slightly devia-tions in details are observable, the important features

Ž .

of the whole ra b T are evidently reproduced.

Con-sidering the sensitivity of the transport properties to

Ž .

the film oxygen content see below and the in-evitable fluctuations of the annealing facility, the present results are truly remarkable. First of all, it indicates that only the oxygen content was varied. If there were any accompanied variations in mi-crostructure or crystalline defects during each

an-Ž .

nealing scheme, a much more complicated ra b T

variation is expected. More importantly, it implies

Ž .

that the specific features of r_{a b}T are truly intrinsic

and are intimately associated with the state at each oxygen content. The question now is how to

encom-Ž .

pass all the drastic changes in r_{a b} T into a simple

picture of reducing oxygen. Clearly, by simply

at-w x

tributing it to hole concentration changes 11 would not be adequate.

Ž . Ž

The linear ra b T observed with x G 0.8 Tc0 .

f_{85–90 K has been interpreted to arise from some}

Ž .

Fig. 2. R T curves for x s 7.0, 6.8, 6.7, and 6.5 for the first

Žsolid curves and the second dotted curves annealing cycle.. Ž .

w x

kind of inelastic scattering 5,12 . On the other hand,

Ž . Ž .

a downturn S shape in ra b T is clearly observed

Ž .

when the film is significantly underdoped x F 6.7 . This downturn is now generally believed to arise from the opening of the spin gap below TU which leads to the freezing off of spin fluctuation scattering w_{13 . Optical and resistivity data indicate the devel-}x opment of a pseudogap below TU for the transport

w x

in the c-direction 13,14 . As will be seen below, this also reflects when the Cu–O chain mediated cou-pling unique to the YBCO system is completely suppressed. Apparently, in the x F 6.7 regime there

Ž . Ž .

is no direct way of deriving D s T from r_{a b} T

because of the intervening of the pseudogap effects. Consequently, in the remaining of this study, we will concentrate on analyzing fluctuation effects at states

Ž .

where ra b T remains linear. Incidentally, it was found that x f 6.7 not only represents the beginning of the T s 60 K plateau but also depicts a dimen-c0 sional crossover state of the YBCO system.

w x

As pointed out by Landau and Lifshitz 15 , for the effects of thermal fluctuations to become signifi-cant and observable experimentally, the required condition is k T 4 "rt . Here t is a time charac-B terizing the rate of change for some physical quantity to return to its equilibrium state. For a system de-scribable by the linearized time-dependent

Ž .

Ginzburg–Landau TDGL theory, the thermal fluc-tuations are expected to become significant only

Ž .

when k T 4 "rt_{B GL}. With t_GLs_{p "r8 k T y TB c} w_{16 , one expects to observe fluctuation-enhanced}x conductivity only when T - 1.65T . In this study,c only the data between T and T < 1.65Tc c will be

Ž . Ž .

used for analyzing D s T . We define D s T s

Ž . Ž . Ž . Ž .

1rr T y 1rr T with r T and r T being them l m l Ž

measured and linearly extrapolated from room tem-.

perature in-plane resistivities, respectively.

Ž . w x

According to Aslamazov and Larkin AL 17 ,

Ž .

Ds T can have distinct functional forms depending

on the dimensionality of the system, which in turn is a strong function of the temperature range under

Ž .

discussion. Namely, when d_eff< j T and the

sys-Ž .

tem is considered as 2D, D s T becomes Ds T s e2_{r16 "d ´}y₁

, 1

Ž

.

Ž

eff

.

Ž .

Ž .

where ´ ' T y T rT is the reduced temperaturec c and the critical temperature T is inferred from thec

Ž .

maximum of d r T rdT. Whereas, when d_eff4

Ž .

j T and the system becomes 3D,

2 y1r2

Ds T s e r32 " j 0

_Ž

_.

_c

_{Ž .}

´ _.

_{Ž .}

₂

Ž . Ž .

Eqs. 1 and 2 can be rewritten as: 2 2 2 1r D s

_Ž

T ´ s 16"d re

_.

_Ž

_eff

_.

´

_{Ž .}

₃ and 2 2 2 1r D s

Ž

T ´ s 32 " j 0 re

.

Ž

c

Ž .

.

Ž .

4 for 2D and 3D cases, respectively. The apparent linear ´-dependence and ´-independent form of

w 2_{Ž . x}

1r D s T ´ in each case should allow one to locate the temperature range reflecting the dimen-sionality of the system easily. Thus, one can use the appropriate functional form to derive the correspond-ing physical parameters of the specific state. We note that this is different from the methods used by previous researchers where the dimensional crossover

w x

region usually was not well-defined 1–4 .

Indeed, as shown in Fig. 3, the plots of

w 2_{Ž . x}

1r D s T ´ vs. ´ for x ) 6.8 conditions evi-dently display distinct regions characterizing the cor-responding dimensionalities. Three regions are im-mediately identified. Starting from higher

tempera-Ž .

tures, a nonlinear region I , an essentially constant

Ž . Ž .

region II , and a linear region III are observed with decreasing temperatures. In region I, since

Ž .

r_{a b} T is no longer describable by the A–L scenario

w 2_{Ž .} x

Fig. 3. 1r D s T ´ as function of ´ for YBCO with x )6.7.

Notice the curves display clear dimensional crossover.

Table 1

Ž .

Physical parameters obtained from D s T analyses discussed in the text x f 7.0 x f6.9 x f6.8 x f6.75 x f6.7 Tl-2223 Ž . Tc K 90.6 89.6 85.9 77.2 57.9 108.4 Ž . Tcr K 91.6 90.9 88.3 80.3 – 109.2 ˚ Ž . Ž . j 0c A 2.9 2.0 1.6 1.0 0.6 0.2 ˚ Ž . deff A 60.3 39.9 21.3 11.8 – 4.4 ˚ Ž . Ž . j Tc cr A 27.6 16.6 9.6 5.0 – 1.9 Ž . deffr2 j Tc cr 1.1 1.2 1.1 1.2 – 1.2

because of the diminishing fluctuation-induced ef-Ž

fects due to t -t f_{0.4 ps t is the}

relax-GL e – p e – p

. w x

ation time of electron–phonon interaction 18 , we will not analyze it further. Nonetheless, if we take region II and III as manifestation of thermal fluctua-tion-enhanced conductivity and analyze the data

Ž Ž .

within the framework of A–L theory i.e., Eq. 3

Ž .. Ž .

and 4 , systematic variations of deff and j 0 withc the oxygen content of the YBCO film are revealed. The results are summarized in Table 1.

Ž .

The fact that j 0 of the fully oxygenated statec

˚

Žf_{2.9 A}. _{agrees well with that obtained by the} w x

upper critical field measurements 1 indicates the viability of the present analyses. Nonetheless, there are several features which needed some further dis-cussion. First of all, we note that the ‘‘width’’ of the dimensional characteristic temperature range and the crossover temperature T_cr changed systematically with the oxygen content. The widening of region III Ži.e., T y T_{c cr}. with the decreasing oxygen content clearly indicates a more 2D characteristic of the system. Second, although within the first T -plateauc Ž6.8 - x - 7.0 the T. c0 values decreased only slightly,

Ž .

both j 0 and dc eff dropped drastically with decreas-ing x. To further elucidate this peculiar trend, we

Ž . Ž . Ž .

define a parameter j Tc cr by using j T ' j 0c c

=e1r2

to determine when the system will always

w x _{Ž .}

exhibit 2D behavior 16 and plot j 0 , dc eff, and

Ž .

j Tc cr as a function of x in Fig. 4. It is interesting to observe that they are all extrapolated to intercept at

x f 6.7. The results are discussed below by

encom-passing the recent microscopic structural changes associated with oxygen depletion in YBCO system.

Right from the beginning of the HTS studies, it is known that the Cu–O chain is the most prominent sector to be affected by removing oxygen from the

w x

YBCO system 11 . The long-range order structure characterized by a metallic conduction behavior is interrupted by the depletion of the oxygen at the chain site, leading to short-range oxygen ordering

w x

structure 19 . Such microscopic rearrangements of

Ž . Ž .

the O 1 chain site oxygen have been found to give rise the non-metallic conduction and tremendous

w x

structural diffuse scattering 19–21 . The consensus reached in these studies is that the retention of the long-range order Cu–O chain is the most prominent factor of obtaining enough hole doping in the CuO2 planes and the coupling strength between them. The hole density accounts for high-T . Whereas the de-c

Ž . gree of the Cu–O chain ordering affects j 0 andc hence, the coupling interaction necessitated for the effective conducting thickness extending over sev-eral unit cells along the c-axis. Within this scenario, the dimensional crossover from 3D to 2D is

deter-Ž .

mined primarily by the divergence of j T near T ,c c as was observed here.

The above argument further implies that when

x F 6.7, the Cu–O chain mediated coupling unique

to the YBCO system is completely suppressed. Thus, the system is expected to behave more like the non-chained Bi-based and Tl-based HTS. This is indeed observed by comparing the results obtained from a single grain Tl-2223 system. As is evident

Ž .

from Fig. 5, D s T of both Tl-2223 and x s 6.7 YBCO clearly displays a 2D to 3D crossover with

Ž . Ž .

Fig. 4. Plots of deff, j 0 , and j Tc c cr as a function of x. Notice

Ž .

the dotted lines to guide the eye intersect at x ;6.7.

w 2_{Ž .} x

Fig. 5. 1r D s T ´ as function of ´ for YBCO with x s6.7

and that of a Tl-2223 film. The lines are drawn to guide the eye.

lowering temperatures. The crossover sequence is opposite to that found in YBCO with x ) 6.7, thus is not explainable by the A–L theory. Nevertheless, this is exactly what one would expect from the

Ž . w x

Lawrence–Doniach L–D theory 22 . Where the dimensionality of the system is governed mainly by

Ž .

the order parameter coupling Josephson-like be-tween the adjacent conducting layers. Since the

func-Ž .

tional forms of D s T are the same for each dimen-sionality in A–L and L–D theories, both deff and

Ž .

j 0 can also be determined and are included in_c

Table 1. For the Tl-2223 sample, the obtained deff

˚

Ž .

and j 0c are 4.4 and 0.2 A, respectively. This indicates that Tl-2223 is a highly anisotropic mate-rial and the in-plane conductivity is confined within the triplicate CuO units. For YBCO at x s 6.7, the2

˚

Ž .

calculated j 0 is 0.6 A, coinciding with the in-c

Ž . Ž .

ferred extrapolated value of j Tc cr Fig. 4 . Unfortu-nately, deff, in this case, is undetermined due to the absence of a well-defined T . Finally, as listed in thecr last row of Table 1, the ratio between deff and

Ž .

j Tc cr is the same in all cases, indicating a universal characteristic of the cuprate HTS. This suggests that there indeed exists a dimensional crossover in all HTS materials and within different regimes, one might need to use different theoretical analysis schemes to extract physically meaningful parameters.

4. Summary

In summary, we have presented a viable process to reproducibly manipulating the oxygen content of a

Ž . single YBCO film. By analyzing the D s T data with a novel functional form, the effects of oxygen

Ž . content on parameters such as deff and j 0 arec unambiguously determined. The results indicate that at x f 6.7, the prominent role of Cu–O chains in mediating the c-axis conduction in YBCO is com-pletely suppressed and the system behaves more like the quasi-2D Tl-2223 material.

Acknowledgements

This work was supported by the National Science Council of Taiwan, R.O.C. through grant: NSC88-2112-M009-21.

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