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Critical current density and flux pinning in vortex liquid regime for YBa 2 Cu 3 O 7yd epitaxial thin films X.W. Cao a , Z.H. Wang a

b,)

, K.B. Li

c

High Magnetic Field Laboratory, Institute of Plasma Physics, Chinese Academy of Sciences, PO Box 1126, Hefei 230031, China b Shanghai Institute of Metallurgy, Chinese Academy of Sciences, Shanghai 200050, China c Institute of Solid State Physics, Chinese Academy of Sciences, Hefei 230031, China Received 9 June 1998; accepted 19 June 1998

Abstract The critical current density Jc for epitaxial YBa 2 Cu 3 O 7y d thin films as a function of applied magnetic field, temperature and angle between the magnetic field and the ab plane has been measured in detail. We observed an evidence for the dramatic change of the critical current density Jc above and below the vortex–glass transition line. In the vortex solid state, the field dependence of Jc follows an exponential dependence was argued to be from the intrinsic pinning in layered structural superconductors. But in the pinned vortex–liquid state, the Jc decreases more rapidly with increasing magnetic field. It was suggested that the nonlinear temperature dependence of Jc ŽT . near Tc was from the vortex–liquid pinning. The temperature dependence of the critical current density exhibited an exponential law, Jc A expŽyTrT0 ., in the pinned vortex liquid regime. q 1998 Published by Elsevier Science B.V. All rights reserved. PACS: 74.60.Jg; 74.60.Ge; 74.76.-w. Keywords: Critical current density; Flux pinning; YBa 2 Cu 3 O 7y d

1. Introduction It was well known that there exists an ‘irreversibility line’ ŽIL. separated the mixed state into two regions in the H–T diagram for high-Tc cuprate oxide superconductors. The vortex lattice melting w1x and the vortex–glass transition w2,3x have been proposed to identify the property and origin of such an IL. It has been recognized, so far, that the low

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Corresponding author. Fax: q86-21-62513510; E-mail: [email protected]

temperature phase below the IL is in a vortex lattice state with long-range positional order and the high temperature phase above the IL is in a vortex liquid state for a clean sample, such as untwined single crystal of YBa 2 Cu 3 O 7y d ŽYBCO.. The transition is theoretically w4–6x and experimentally w7–10x found to be the first-order phase transition from the vortex-lattice state to the vortex–liquid state. Recently, Carruzzo and Yu w11x proposed an alternative possibility of a two-step processes, in which there is a first order transition from an ordinary vortex lattice to a soft vortex solid, followed by a second order melting transition from the soft vortex solid to a

0921-4534r98r$ - see front matter q 1998 Published by Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 3 4 Ž 9 8 . 0 0 3 0 5 - 0

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vortex liquid. However, in the presence of strong disorder such as in YBCO thin films, the IL showed a phase transition from the vortex glass in low temperature to the vortex liquid in high one, a second order phase transition w3,12,13x. For the vortex liquid, one can distinguish two different regimes w14–19x: pinning and unpinning vortex liquid regimes. The suggestion predicted the existence of a genuine critical density in the pinning vortex liquid regime. However, it is open to differentiate the behaviors of the critical current density such as their field and temperature dependencies in the vortex solid state from that in the pinned vortex liquid state. The critical current density Jc is a crucial parameter of high-Tc superconductors for a variety of possible applications. The field and temperature dependencies of the critical current density may provide important information for identifying the flux pinning mechanism. However, the investigations of the dependence of critical current density on applied magnetic field and temperature have not yet resulted in a consistent pinning model either for low- or for high-Tc superconductors. In order to describe these behaviors for high-Tc superconductor, the critical state models introduced for low temperature type-II superconductors, such as Bean model w20x, Kim– Anderson model w21,22x, Kramer scaling law w23x and the exponential model w24x etc., in recent years, have been applied extensively. In this paper, the critical current density Jc for the epitaxial YBCO thin films as a function of applied magnetic field, temperature and the angle between the magnetic field and the ab plane has been measured. It was observed that above and below the vortex–glass line there was an evidence for the dramatic change of Jc and the field and temperature dependencies exhibited the distinct behavior.

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is 2.1 = 10 6 Arcm2 at 77.3 K and zero magnetic field.

3. Experimental The electrical measurements were performed in a variable temperature insert by a four-probe method. The sample was held on a rotatable sample holder, where the angle between the film surface and the magnetic field direction could be varied with 0.18 resolution. The applied magnetic field up to 10 T was supplied by a water-cooled solenoid magnet

2. Sample The c-axis oriented YBCO epitaxial thin film used in this study was prepared by DC sputtering technique w25x. The thin film with a thickness of 200 nm was patterned into a narrow bridge with 60 mm in width and 200 mm in length. The zero resistance temperature is 90.4 K. The critical current density Jc

Fig. 1. The dependence of the critical current density Jc on the applied magnetic field H at several temperatures, Ža. for H 5 ab plane and H H J, Žb. for H 5 c and H H J.

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X.W. Cao et al.r Physica C 305 (1998) 68–74

system. The temperature was measured by a calibrated Rh–Fe resistance thermometer and corrected for the effect of magnetic field. The critical current density Jc was determined in a criterion of 5 mVrcm. This criterion was chosen to obtain a good signal to noise. Fig. 1 plots the critical current density, Jc , as a function of applied magnetic field, H, in various temperature for H 5 ab plane and H H J, as shown in Fig. 1a, and for H 5 c and H H J, as shown in Fig. 1b. It can be seen that Jc reduces monotonously with increasing magnetic field H and the reduce of Jc for H 5 c is faster than for H H c, as reported in many papers, showing that the intrinsic pinning plays a dominate role. Fig. 2 plots the angle dependence of Jc at 80 K and in several applied magnetic fields. It can be seen that the critical current density, Jc , decreases with the increase of the angle u , where u is the angle of the direction of magnetic field relative to the ab plane, as defined in the inset of Fig. 2. But a small peak of Jc appears near u s 908, as predicted by Tachiki and Takahashi w26x in the intrinsic pinning model and as observed by Roas et al. w27x and Cao et al. w28x in YBCO thin film. The appearance of the peak of Jc near u s 908 implies the existence of the two-dimensional defects along the c-axis orientation such as twins and stacking faults etc. In Fig. 3a,b, we plot the temperature dependence of Jc in various applied magnetic fields for H 5 ab plane and H H J and for H 5 c and H H J, respecFig. 3. Temperature dependence of Jc at several magnetic fields, Ža. for H 5 ab plane and H H J, Žb. for H 5 c and H H J.

tively. A flux creep model w21,22x can describe the linear relationship exhibited in the low temperature range far from Tc . However, for the nonlinear relationship near Tc in Fig. 3a, there exists a distinct explanation, and it will be discussed later.

4. Analysis and discussion 4.1. Field dependence of critical current density Fig. 2. Angular dependence of Jc for several magnetic fields at 80 K.

From Fig. 1, it can be seen that the functional form of the field dependence of the critical current

X.W. Cao et al.r Physica C 305 (1998) 68–74

density, Jc , may be described as a polynomial and discussed in the framework of flux pinning, as noted by Hampshire and Chan w29x. In order to discuss the field dependence of Jc , here, the data in Fig. 1 are replotted in Fig. 4. A linear behavior of ln Jc vs. H can be observed in the magnetic field region below a transition field, Ht , and described by an expression of type Jc s Jc 0 exp w yHrH0 x

Ž 1.

where Ht was defined as a field at which the relation of ln Jc vs. H started to deviate from linearity and decreased with increasing temperature, as shown in

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Fig. 4. H0 in Eq. Ž1. is a characteristic field and can be extracted from the slope of the relationship of ln Jc vs. H for a constant temperature. As shown in Fig. 4, H0 decreases with increasing temperature and is related to orientation of magnetic field H relative to the c-axis. For example, H0 for H 5 c is a factor of 5 than that for H H c at same temperature. The similar field dependence of Jc has been observed in BiŽPb. –Sr–Ca–Cu–OrAg tape w30–32x. Senoussi et al. w33x also observed a similar dependence in the magnetization measurement of the YBCO single crystal. The result is in agreement with the exponential model w24x in the critical state. It is suggested, here, that the exponential dependence of Jc on the magnetic field may be from the intrinsic pinning w24x in YBCO superconductor. In the other hand, a dramatic drop of Jc can be observed above the transition field, Ht , as shown in Fig. 4. We thought that the distinct field dependence of Jc above and below Ht might be associated with the vortex solid–liquid transition. In order to verify this idea, the data on the vortex–glass transition line measured for the identical sample w34x was plotted in Fig. 4, as shown by the dashed line in Fig. 4. It can be seen that the transition field Ht ŽT . was approximately consistent with the vortex–glass line. Above and below the vortex–glass transition line, the dramatic change and the distinct field dependence of Jc show the existence of distinguishable mechanism of the flux pinning: the vortex–solid–state pinning below the vortex–glass transition and the vortex– liquid-state pinning above one. 4.2. Angular dependence of critical current density

Fig. 4. The field dependence of ln Jc at various temperatures, Ža. for H 5 ab plane and H H J, Žb. for H 5 c and H H J. The dashed lines are the vortex–glass lines.

Fig. 5 plotted the field dependence of ln Jc for various u-angles at 80 K. It can be clearly seen that for small angle of u F 108, the dependence of ln Jc on magnetic field H up to 10 T exhibits a good linearity. However, a nonlinear behavior begins to appear as the applied magnetic field exceeds a transition field Ht , as shown by the arrows in Fig. 5. With increasing u-angle, Ht decreases and as a sequence, the linear part of Jc vs. H decreases also. The linear part practically disappears for the angles of u s 758 and 908. It was well known that the Lorentz force acting on the flux line was perpendicular to the ab plane

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that the relation exhibited good linearity showing that the angular dependence of Jc may be described in terms of the intrinsic pinning model w26x. This result shows further that the intrinsic pinning plays the dominant role in our sample.

Fig. 5. The field dependence of ln Jc at 80 K for various angles between the magnetic field and the ab plane.

for a configuration of u s 08 and the component of the Lorentz force perpendicular to the ab-plane decreases with increasing u-angle. Therefore, the result in Fig. 5 shows that the exponential law of Jc Ž H . might originate from the intrinsic pinning for layered-structural superconductors. The exponential law of Jc Ž H . can be also interpreted in terms of the collective pinning theory w35x. The data in Fig. 2 were replotted as the relation of Jc vs. siny1 r2u , as shown in Fig. 6. We could find

Fig. 6. The relationship of Jc vs. siny1 r2u at three magnetic fields.

Fig. 7. The temperature dependence of ln Jc at different magnetic fields, Ža. for H 5 ab plane and H H J, Žb. for H 5 c and H H J. The dashed line was the vortex–glass line. The inset in figure showed the temperature dependence of constant T0 .

X.W. Cao et al.r Physica C 305 (1998) 68–74

4.3. Temperature dependence of critical current density near Tc The nonlinear behavior near Tc in the temperature dependence of Jc , as shown in Fig. 3, in general, can be described as a powder-law, Jc A Ž1 y t . n , as reported in Refs. w36–38x. The nonlinear variation of Jc ŽT . with n s 1.5 is in agreement with the Ginzberg–Landau theory w39x and for n s 2, can be explained in terms of formation of SNS weak links in the materials w40x. Here, we suggested that the nonlinear behavior of Jc ŽT . near Tc might be from the vortex–liquid pinning. In order to understand such a nonlinear behavior, we replot the data in Fig. 3 as a relation of ln Jc vs. T, as shown in Fig. 7. The vortex–glass transition lines measured for identical sample w33x are given in Fig. 7 to compare with the dependence of Jc in Fig. 5. We find the logarithmic decrease of the critical current density Jc with increasing temperature above the vortex–glass line, i.e., the temperature dependence of the critical current density in the pinned vortex liquid regime follows an exponential law Jc s Jc 0 exp Ž yTrT0 . .

Ž 2.

Here the constant, T0 , can be extracted from the slope of ln Jc vs. T in the linear part in Fig. 7a,b, and is a function of the applied magnetic field. A logarithmic field dependence of 1rT0 , i.e., 1rT0 A lnŽ H ., for H 5 ab plane, and a power law field dependence of 1rT0 , lnŽ1rT0 . A lnŽ H ., for H 5 caxis, are exhibited clearly, as shown in the inset in Fig. 7a,b, respectively.

5. Conclusions We have measured the field, temperature and angle dependencies of the critical current density, Jc , for epitaxial YBa 2 Cu 3 O 7y d thin films. We observed an evidence for the dramatic change of Jc above and below the vortex–glass transition lines. Below the transition line, the field dependence of Jc follows an exponential dependence, Jc A expŽyHrH0 ŽT .., and it was argued that the intrinsic pinning of flux might be responsible for the exponential behavior of Jc Ž H .. The nonlinear behavior of Jc ŽT . near Tc was pro-

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posed to be from the vortex–liquid pinning. The temperature dependence of the critical current density in the pinned vortex–liquid regime above the vortex–glass line follows an exponential law, Jc s Jc0 expŽyTrT0 ..

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