IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 5, NO. 2, JUNE 1995

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Anisotropic flux pinning in YBa2Cu30,G single crystals Vladimir M. Pan, Vjacheslav F. Solovjov, Vasili L. Svetchnikov Institute for Metal Physics, 252142 Kiev, Ukraine Herbert C. Freyhardt Institute for Metal Physics,University of Goettingen, 37073 Goettingen, Germany Abstract--Direct transport measurements of the critical currents as well as their angular and field dependencies in YBa2Cu307~single crystals were performed. The role of *in planes as extended defects, which provide a vortex locking, is studied and their contribution to the Jc anisotropy is analyzed. The angular dependence of the critical current i s represented as a combination of a contribution from extended defects and a point-like-defect-induced anisotropic background. The latter is responsible for the major part of the measured Jc anisotropy. The obprved Kramer-like scaling law concerning the dependencies of the volume pinning force versus the applied magnetic field component along the c-axis indicates a threedimensional flux line lattice behavior and excludes vortex decoupling as a possible mechanism of the "fishtaileffect".

I. INTRODUCTION It has been recognized recently that the anisotropy of the critical current density in YBaZCu3074 CyBCO) superconductors may result from the ''intrinsic" anisotropy of the superconducting parameters Bc, h, 5- and from contribution of extended (i.e., non-point-like) defects, in particular of those which lead to a "locking" of the vortices. In YBCO specimens with a higher degree of disorder, such as epitaxial films and melt-textured samples, the J, anisotropy is dominated by dislocation loops, confined in abplanes. The models of dislocation-mediated or/and "intrinsic" pinning [ 11-[2] satisfactorilyexplain the observed JC angular dependencies in these samples at high temperatures. At lower temperatures, below 40K, the JC anisotropy in thin films is described within a twodimensional (2D) model [3] and the JCangular dependence appeares to be governed by the projection of the applied field on the c-axis direction. But for clean and comparatively defect-& single crystals the situation seems to be quite different. In our previous investigations [4]-[5] we reported on a comparative study of melt-textured and singlecrystalline samples and found that a qualitatively new approach should be worked out to explain the angular and field J, dependencies for moderately anisotropic YBCO single crystals. It was argued that in the single crystals a major role in pinning and its anisotropy is played by twin boundaries (TB) and oxygen vacancies, that is, pinning centers, which give a minor contribution to the Jc values in epitaxial films and melt-textured YBCO. The competition between the flux line lattice (FZL) interaction with the

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Manuscript received October 18,1994. This work was supported in part by the InternationalScience (G. Soros) Foundationunder the Grant U4TOOO and by the State Committee of Science & Technology of Ukraine as the Project "Supercurrent".

correlated disorder (i.e. extended defects) and with the distributed point-l&e pinning sites in the anisotropy and n o ~ o n o t o n u ofield ~ dependence of the JC in single crystals(i.e., in the socalled "fishtail" effect).

11. EXPERIMENTAL A pulse technique was used for the recording of the I-V curves. The experimental setup and the sample preparation were described in detail elsewhere [5]. The crystals were obtained by a self-flux crystallization technique in YSZ crucibles. Current pulses with IOW duration and with amplitudes up to 10 Amp. were applied to the current leads of a singlecrystalline (melt-textured) strip. A voltage criterion of 10 pV/cm was adopted as a definition of the transport critical current density, Jc. This was made possible by developing a special ampllfylng unit which allowed damping of the noise level to below of 0.2pV. DC magnetic fields up to 2T were produced by an iron-yoke solenoid, which was mounted on a rotating support. The rotation angle @wascounted from the c-axis, i.e., 8=Oo at Hl(c-axis.

111. RESULTS AND DISCUSSION

A . Twin boundary contribution

The angular dependencies of Jc for several single crystals at various temperatures and external field magnitudes are shown in Fig.l. To analyze the curves one has to separate contributions from the following sources: twin boundaries (TB), oxygen vacancies and dislocations. We will not consider here the well-studied "intrinsic" peak at &90° and assume it to be a result of the FLL-lock-in by the dislocations

t 13. The Hllc minimum of the JC(@curve is ascribed to the locking property of the TB structure, which creates a FLL state with correlated disorder [6]-[7], resulting in a FLL c&) tilt modulus enhancement. To prove the assumption of the origin of the minimum, a set of tests were performed, aimed to reveal the specific twin plane influence upon the flux pinning in the YBCO single crystals. (a) A strip was clef&from a crystal at 30' with respect to the a-axis (sample A l l in Fig.l), so that the direction of the transport current flow was close to perpendicular, and the direction of the Lorentz force was close to parallel, with respect to the TB. We regard theincreaseof thelocking .OO 0 1995 IEEE

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0.2 0.4 0.6 0.8 1.0 1.2 1.4 Applied field c-projection, bHcose(T)

Fig. 3. JdH) dependenciesmeasured at 83.2K versus c-projectionof applied field.

angle observed for the JJO) curve of sample A l l as a convincing proof of our assumption. (b) Similar test may be performed, if one would rotate the crystal around the c-axis on the sample holder, thus aligning the desired crystallographic plane along the external field rotation plane. The corresponding angle yof rotation is the angle between a basal a-ais and the magnetic field rotation plane. Thus, at 7=45" the magnetic field vector H lies in the (1 10) plane for all 6 values. By this technique a more exact alignment may be achieved, but it should be noted, that the transport currentexternal field angle changes while the field vector H is rotated. We carried out a set of such experiments and varied the angle y from 45O, i.e. TBIIH, to -45', i.e. TBIH. The results of the measurements are presented in Fig.2. The sample B8 was cleft as usual, i.e., the strip was parallel to the basal axis and the direction of the TB's was defined via direct observations in polarized light. It may be easily derived from Fig.2 that the lacking angle does not change appreciably at TJ3kI-rotation plane misorientations greater than 20'. When the planes coincide, the FLL is locked-in by twin structure. and the anisotropic features of the Jc( 4,visible at high misorientations, are suppressed. It follows, that excluding the minimum at Hllc and the maximum at Hllab (the former being contributed from twins and the latter - from the ab-plane-confined dislocation loops), the remaining strong Jc anisotropy should be attributed to the co-action of the random point-like disorder and the c~ystallographicanisotropy effects.

B. Point defects contribution In this subsection the intermediate orientations 2O0<&7O0 are considered, i.e., an angular range where the influence of

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the above mentioned extended defect may be neglected and one only has to consider the pointdefect pinning case. In this context point defects are oxygen vacancies and extended defects, acting like point defects. In this angle region the field dependencies of Jc clearly exhibit the "fishtaileffect".

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manner. It means, when a vortex intcracts with a point defect the deformation occurs basically along ab-plane and therefore the 3D pinning should depend only upon the cprojection of the applied field. However, it is important to emphasize again that the vortices are not decoupled and the Lorentz force should drag the flux line as a whole. Thus, in the 3D superconductor the volume pinning force is expected to be approximated by the Kramer's scaling law [ll]:

where b=B/Bc2(8) (for HTSC materials Bc2 should be replaced by the melting field BA. For the anisotropic case Bc2(8) is given by the anisotropic Ginsburg-Landau theory:

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Fig.4. Scaling ofthe volume pinningforce FP as a hction of the c-projectionof the applied fileld.

Here Bc2Ccorresponds to the upper critical field for O=O (cdirection). For YBCO one finds an anisotropy parameter rz6, and in the low angle region, &60°, we assumed Bczcos0 as the approximation of Eq.2. Fig.4 shows the scaling of the bulk pinning force, Fp(p&cosB), measured at

Thus, the Jc anisotropy is accompanied by the anisotropy of this effect.

For an anisotropic superconductor, such as YBCO, it would be natural to expect an 2D-3D crossover, i.e., the transition from a usual lattice of continuous Abrikosov vortices to an array of the decoupled point-like vortices. Indeed, the 2D state of the FLL is wellestablished for the highly anisotropic BSSCO-2212 superconductor (see, e.g., [SI) and is assumed to be observable in the YBCO films [3] as well. Moreover, in recent experiments on artificially layered structures, e.g., on Pb/Ge multilayers [9], the "fishtail" anomaly was observed, which was found to be suppressed by the introduction of extended pinning centers. The authors of [9] ascribe the anomaly to the 3D-2D crossover, as a consequence of the Pb-layer decoupling by the magnetic field. Thus, it seems to be interesting to check the 2D hypothesis in our case. In the 2D model, according to Kes et al. [lo], the Jc(H,8) dependencies, measured at various 0 angles should scale like Jc(H,B)=Jc(HcosB),that is, only the field projection on the caxis (c-projection) controls the magnitude of Jc. Fig.3 demonstrate an attempt to apply the 2D scaling to the present results. One derives from the Fig.3 that the Jc(H,8) curves do not obey the 2D scaling, though positions of the characteristic minima and maxima roughly coincide. It should be taken into account that for the moderately anisotropic YBCO an intermediate situation appears to be realized, where the 3D FLL of the continuous vortices interacts with the random point-like disorder in a 2D

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Fig. 5. Angular dependencies of p and q exponents, derived from the scaling law (1). Inset shows Fp scaling for 50' orientation. M O , 20°, 30°, 40°, 50°, 60°, 7 0' and in Fig.5 the angular dependencies of the exponents p andq, derived from Fp(H) fitting by Eq.1, are shown. Note, that the scaling breaks down for M'and &60°. The plots in Fig.5 reveal that the indexes p and q are increasing, when the Hllab configuration is approached. We attribute the scaling breakdown to the interference of the extended defects with the point-like disorder.

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IV. CONCLUSION The angular dependence of the critical current of twinned YBCO single crystal was analysed. The Jc anisotropy arises from two sources: (i) The lock-in of vortices by extended defects, which results in a pronounced minimum at Hllc and a small maximum at Hilab. (ii) The 3D pinning by the randomly distributed isotropic point defects, which reveals the intrinsic anisotropy depdending upon the c-projection of the applied magnetic field, is responsible for the major anisotropic contribution to the Jc ( (0) dependence. ACKNOWLEDGMENT V.L.S. thanks the NWO and FOM for the financial support as well as the The TU Delft for a research opportunity. V.M.P thanks the DAAD and the Institute for Metal Physics of the University of Goettingen for the support at the time when this work was carried out. REFERENCES [l] V. Selvamanickam, M. Mironova, S. Son, and K.

Salama, "Flux pinning by dislocations in deformed melttextured Y-Ba-Cu-0," Physica C, vol. 208, pp.238-244, Febnrary 1993. [2] M. Tachiki and S. Tackahashi, "Anisotropy of critical currents in layered superconductors," Solid State Comm., vol. 72, pp. 1083-1086, September 1989. [3] R. M. Schalk, H. W. Weber, Z. H. Barber, P. Przyszlupsky, J. E. Evetts, "Anisotropic flux pinning mechanisms in YBa2Cu3074 thin films," Physica C, vol. 199, pp. 311-320, September 1992.

[4] V. F. Solovjov, V.M. Pan and H.C. Freyhardt, "Transport

critical current in singlecrystalline and melt-textured YBa-Cu-O: A comparative study",Proc. of 7th IWCC, 2427 January 1994, Alpbach, Austria; Physica C, in press. 51 V. F. Solovjov, V.M. Pan and H.C. Freyhardt, "Anisotropic flux dynamics in singlecrystalline and melt-textured YBa2Cu3O7-4,"Phys. Rev. B, vol. 50, 1 November 1994, in press. [6] D.R Nelson and V.M. Vinokur, "Boson localisation and pinning by correlated disorder in high temperature superconductors," Phys. Rev. Lett., vol. 67, pp. 23982401,1992 [7] G. Blatter, J. Phyner and V. M. Vinokur, Vortex

pinning by twin boundaries in copper oxide superconductors," Phys. Rev. B, vol. 43, pp. 7826-7830, April 1991. [SI H. Yamasaki, K. Endo, S. Kosaka, K. Umeda, S. Misawa, S. Yoshida and K. Kajimura, "Magnetic-field angle dependence of the critical current density in high quality Bi2Sr2CalCu2OX thin films," IEEE Trans. on Appl. Supercond., vo1.3, pp. 1536-1539, March 1993. [9] M. Baert, V. V. Metlushko, K. Temst, E. Rossel, C. D. Potter, J. Snauwaert, L. Hellemans, V.V. Moshchalkov, Y. Bruynseraede, "Anomalous field dependence of the critical current and flux creep rate in Pb/& multilayers," Physica C, vol. 228, pp. 42-48, July 1994. [IO] P. H. Kes, J. Aarts, V.M. Vinokur and J.C. van der Beek, "Dissipation in highly anisotropic superconductors", Phys. Rev. Lett., vol. 64, pp. 10631066, February 1990. [ l l ] E.J. Kramer, "Scaling laws for flux pinning in hard superconductors," J. Appl. Phys., vo1.44, pp. 1360-1370, March 1973.