Supercond. Sci. Technol. 11 (1998) 935–940. Printed in the UK

PII: S0953-2048(98)93406-6

Vortex decoupling line and its anisotropy in Bi2Sr2CaCu2O8+δ single crystals observed by Jc(H , T , θ) transport current measurements V F Solovyov†, V M Pan†, H C Freyhardt‡, M H Ionescu§ and S X Dou§ † Institute for Metal Physics, National Academy of Sciences of Ukraine, Vernadsky Blvd 36, Kiev 252142, Ukraine ¨ ¨ ‡ Institute for Metal Physics, University of Gottingen, Gottingen 37073, Germany § Centre for Superconducting and Electronic Materials, University of Wollongong, Wollongong, NSW 2522, Australia Received 2 February 1998 Abstract. Transport critical current densities in single crystals of the strongly anisotropic high-Tc superconductor Bi2 Sr2 CaCu2 O8+δ were measured in a wide range of temperature, applied field and angles between field direction and c -axis of the crystals, above and below the decoupling line. In the low-field region, below the decoupling line, an analysis of the field and angle dependences of the Jc allows us to assume a dominance of the collective pinning mechanism, which is similar to that found in moderately anisotropic YBa2 Cu3 O7−δ single crystals. We provide scaling analysis of the Jc (H , T , θ) dependences to probe the vortex topology and to locate the decoupling line on the H –T -θ diagram.

1. Introduction The crystalline anisotropy of the layered HTSC cuprates is known to be a factor responsible for emergence of new phases of the flux line lattice (FLL). As the superconductor’s anisotropy parameter 0 (0 = λc /λab where λc and λab are the c-axis and the a–b-plane penetration depth) is increased over some threshold value, 0 = 25 according to [1], the shielding current flowing along the c-axis direction encounters the series of intrinsic Josephson junctions formed by metallic, superconducting CuO2 planes with non-superconducting layers between them. This state is generally described by the Lawrence– Doniach model [2], which introduces the notion of point or pancake vortices: two-dimensional (2D) objects, confined to the metallic CuO2 planes with weak Josephson and electromagnetic coupling between them. Since the bonding between the point vortices is rather weak, some external factors may destroy it, thus driving the vortex ensemble from the coupled state (CS) to the decoupled state (DS). In the CS the point vortex ensemble behaves similarly to three-dimensional (3D) Abrikosov flux lines. In the DS the phase correlator between the adjacent layers falls to zero, implying independent behaviour of the pancakes in adjacent CuO2 layers. The DS onset is believed to be indicated by several experimentally observable phenomena: change of the field-induced microwave absorption anisotropy c 1998 IOP Publishing Ltd 0953-2048/98/100935+06$19.50

[3], second magnetization peak [4], loss of the vortex correlation in the c direction detected by µSR spectra [5] and divergence of primary and secondary voltages in the flux transformer experiments [6]. In this paper we use the following definition of the decoupled and decoupled FLL states: (i) at transport currents below Jc both states are a pinned vortex solid; (ii) at currents above Jc the decoupled FLL moves as an ensemble of independent point-like vortices. In the CS the point vortices preserve correlation along the external field direction and behave like 3D Abrikosov vortices. Assuming that the CS is the vortex phase consisting of the continuous 3D Abrikosov-like vortices, it is natural to ask whether the FLL in this state exhibits features similar to those found in much less anisotropic HTSCs, such as YBCO. Single-crystal samples offer a unique opportunity for such a study, since it has been shown that both moderately anisotropic YBCO [7, 8] and strongly anisotropic Bi2 Sr2 Ca1 Cu2 O8+δ (BSCCO) [9] high-quality single crystals have one common type of effective pinning centres: randomly distributed weak, but numerous, pointlike pins, i.e. oxygen vacancies. In this paper we compare the results of transport Jc (H, T , θ) measurements in BSCCO and YBCO single crystals to elucidate the role of the crystalline anisotropy in the flux pinning and related FLL phase transitions. 935

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Figure 1. Field dependences of the transport Jc of BSCCO single crystals at various c -axis–external magnetic field angles θ = 30◦ , 60◦ , 70◦ , 80◦ , 88◦ and 90◦ at 60 K. The inset shows the Jc (H , θ ) (θ = 20◦ , 50◦ , 70◦ , 80◦ and 90◦ ) curves for YBCO single crystal at 83.2 K. The lines connecting the data points are guides for the eye.

2. Experimental details The BSCCO single crystals were grown by self-flux and solvent floating zone techniques. Two batches of optimally doped samples from independent sources were available; we measured four samples, two from each batch, to ensure the reproducibility of the results and to eliminate sample-dependent effects. According to the DC resistivity measurements the crystals have the superconducting transition at 85–86 K and the transition width is ≤1 K. The samples were cut to the standardsized 2 × 0.2 × 0.02 mm3 stripes and silver contacts pads were made by vacuum evaporation. The transport Jc measurement method is similar to that used in our prior work on YBCO single crystals and we refer to the corresponding publication [7] for the experimental details. 3. Results Figure 1 presents results of the transport Jc measurements in YBCO and BSCCO crystals as a function of the external applied field magnitude at different field vector tilt angles θ. Here θ = 0◦ corresponds to the H k c-axis orientation. Figure 1 shows, in contrast to earlier reports [4], a welldefined peak effect in BSCCO 60 K. The Jc maximum for H k c at temperatures above 40 K corresponds to very low applied fields, thus making the effect hardly observable in this orientation. Tilting the external magnetic field with respect to the c-axis of the crystal, we can shift the field value corresponding to the Jc maximum and make the effect observable up to 80 K. We note another qualitative feature of the Jc (H, θ ) dependence: in both BSCCO and YBCO (inset in figure 1) samples, the peak effect is suppressed as the H vector is tilted towards ab plane. Figure 2 shows Jc (H ) curves for H k c and θ = 80◦ orientations recorded in the 20.0–77.6 K temperature range for BSCCO single crystal (main panel) and field dependences for a tilt angle 936

Figure 2. Variation of the Jc (H ) dependences in the temperature range 20.0–77.6 K for (a) θ = 0◦ and (b) θ = 80◦ orientations. The inset presents similar data for YBCO at θ = 50◦ in the 80.0–84.0 K range. The lines connecting the data points are guides for the eye.

θ = 50◦ in the 80.0–84.0 K temperature range for YBCO (inset). It may be inferred from figure 2 that in both cases the temperature has a considerable influence on the shape and position of the maximum; it shifts to higher fields as the temperature decreases.

Vortex decoupling line and its anisotropy in BSCCO

4. Collective pinning in BSCCO and YBCO

Figure 3. Critical current density versus tilt angle for (a) various temperature and (b) applied field values for the BSCCO sample. The curves representing low-field (5 mT) and high-field (300 mT) anisotropic behaviour of Jc are marked by bold lines. All the lines are guides for the eye. The inset demonstrates anisotropic Jc behaviour of YBCO crystal at 83.2 K for 1.0 and 0.4 T applied fields. The 1 T field under these conditions corresponds to the FLL melting, provided that H k c .

Measurements of the angular dependencies of Jc reveal specific features of the BSCCO single crystals. Figure 3(b) shows Jc (θ ) dependences for a temperature of 60 K and applied field values in the range 5–300 mT. The curves may be classified in a simple way, by two limiting cases: (i) the ‘low-field anisotropy’ (5 mT on figure 3(b), thicker line), i.e. a curve having a Jc minimum at the H k a–b orientation; (ii) the ‘higher-field anisotropy (300 mT in the same figure, thicker line), with a Jc maximum at the H k a–b orientation; intermediate curves (fields of 15, 20, 40 and 100 mT, thinner lines). Figure 3(a) demonstrates the variation in Jc (θ) curves at 0.1 T applied field as the temperature is lowered from 77.6 K to 20 K. The inset to figure 3(a) shows, for the purpose of comparison, angular variation of Jc of YBCO single crystal at two applied fields, 0.4 T, the field below Birr for H k c and 1 T ≈ Birr (H k c). Note that the transformation of the Jc (θ ) curve is a feature which is not observed in less anisotropic YBCO; in the case of YBCO we always observe a local Jc minimum at H k a–b. The following discussion is organized in two sections. In the first section we will qualitatively analyse the FLL in the coupled state from the point of view of collective pinning theory and will show how the model explains the observed Jc anisotropy in both BSCCO and YBCO single crystals. In the second section we will use a simple scaling approach to define the vortex topology in BSCCO and to locate the decoupling line.

In the framework of our approach we assume that CS of the FLL in BSCCO has elastic properties similar to the Abrikosov vortex lattice in the less anisotropic YBCO [10]. Also, taking into account the dominance of the point-like pinning due to the oxygen vacancies, it is not unreasonable to apply collective pinning theory [11] for the qualitative estimation of the CS properties. According to the collective pinning theory, disorder of the FLL, induced by the pinning potential, may be imagined as a set of domains with the Larkin–Ovchinnikov volume Vc (so-called ‘correlation volume’), where the short-range order of the FLL is preserved within each domain. The critical current density in this case is proportional to the mean square of the pinning potential within the volume −1/2 and, obviously, Jc ∝ Vc . The correlation volume is defined by the balance of the energy loss through elastic deformation of the FLL and energy gain due to better matching to the pinning potential of randomly distributed point-like defects. Therefore the Vc value depends in a straightforward way on the elastic moduli of the FLL, primarily the tilt modulus c44 and the shear modulus c66 . In anisotropic superconductors, such as the HTSC layered cuprates, the FLL tilt deformation energy is greatly reduced as compared with the isotropic case [12] and thus c44 is an important parameter, which to a great extent defines FLL pinning in anisotropic superconductors with the pointlike disorder. Moreover, the energy of short-wavelength tilt deformation, as produced by point-like pins, is lower than that of long-wavelength tilt deformation, i.e. the tilt modulus exhibits non-local behaviour and depends on the deformation wavevector. If the collective pinning scenario were realized, the non-locality would lead to a correlation volume reduction and an increase of the critical current as a function of the applied magnetic field. Such an anomalous pinning enhancement may be a mechanism for providing the discussed peak effect in YBCO and BSCCO single crystals and some low-temperature superconductors with weak pinning [13]. The anisotropy of the elastic moduli proves to be of major importance for such samples. If some external factor increases the vortex stiffness with respect to tilt deformation, the FLL responds to such an influence by increasing the correlation volume with the related Jc reduction. Taking as an example YBCO single-crystal behaviour, we may say that for the H k a–b orientation the crystalline anisotropy of the superconductor is responsible for the much higher c44 tilt modulus value [12] than for H k c, and this is a reason for the Jc (H k a–b) minimum; see inset in figure 3(a), 0.4 T Jc (θ ) curve (the sharp minimum at H k c on 0.4 T curve, inset in figure 3(a), is an effect of the crystal twinning and is not discussed here; see for example [7] for details). Indeed, the stiffer the FLL is, the more difficult it is for it to be pinned by a number of random point-like pins. This reasoning is true for fields below the irreversibility line: as the field increases, excessive elastic modulus softening finally leads to the FLL melting and zero critical current. The curve corresponding to 1.0 T applied field for YBCO (the inset in figure 3(a)) illustrates this case: the FLL melts at H k c 937

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Figure 4. The 2D scaling of the volume pinning force dependencies recorded at tilt angles θ = 50◦ , 60◦ , 70◦ , 80◦ , 81◦ , 82◦ , 83◦ , 85◦ and 87◦ using a factor α = 1 for the BSCCO crystal at 60.0 K (main panel) and YBCO crystal at 83.2 K and θ = 20◦ , 30◦ , 40◦ , 50◦ , 60◦ and 70◦ (inset). Note that the scaling applies for the whole field range in the case of YBCO and for the low-field region in the case of BSCCO. The lines connecting the data points are guides for the eye.

but is still solid for tilted orientations and we observe an intermediate Jc maximum at θ = 60◦ and local minimum at H k c, where the FLL has already melted. Thus the Jc (θ ) curve of single-crystal BSCCO, corresponding to 5 mT field on the main panel of figure 3, may be explained in terms of collectively pinned coupled vortices, analogously to the case of Abrikosov vortices in YBCO single crystal. We observe a Jc (H k a–b) minimum for 5 mT applied field, because under these conditions (below the coupling line) the FLL pinning is controlled by the tilt deformation, which is the highest for H k a–b orientation. As the external field increases, the FLL undergoes the decoupling transition with the corresponding change of the vortices topology. From a point of view of the theory the coupled pancakes behave like Abrikosov vortices which are 3D string-like objects, having non-zero tilt energy. The pinning is collective and the form of the Jc (θ ) curve is mainly defined by strong angle dependence of the tilt modulus. Above the decoupling line the FLL is composed of decoupled point vortices and has negligible tilt modulus value, being ‘transparent’ to the applied field component parallel to the a–b-plane. In this state the pinning is realized via individual point vortex–pin interactions and the critical current is a decreasing function of the point vortex density, which in turn, is proportional to cos θ. Consequently, the minimum of Jc (H k a–b) in the CS (5 mT curve in figure 3) changes to a corresponding maximum in the DS (300 mT curve in figure 3). The above model differentiates between CS and DS only by their tilt deformation energy and does not consider the actual vortex topology. In the next section we will show how a simple scaling analysis of Jc (H, θ) curves helps to discern between vortex lattices consisting of 3D and 2D vortices. 938

5. Vortex topology in BSCCO and YBCO In a strongly anisotropic system, as BSCCO, we expect some parameters to obey the 2D scaling law, i.e. parameter dependence on the applied magnetic field amplitude H and tilting angle θ may be reduced to a dependence on the applied field projection on the c-axis, H cos θ. The 2D scaling procedure may also be used for moderately anisotropic superconductors, e.g. YBCO, serving as a reasonable approximation for a complex Ginsburg–Landau expression [14], provided that the tilt angle is not too high, i.e. θ < 80◦ . If this parameter is the critical current Jc , such a procedure is a straightforward test for the vortex topology: successful scaling of Jc (H, θ ) as Jc (H, cos θ ) implies a DS, and lack of scaling indicates that that 3D correlation along the external field direction exists. Thus, in the case of coupled vortices, such as YBCO and low-field (below the decoupling line) FLL state in BSCCO, attempt to apply 2D scaling for Jc (H, θ ) curves would fail, since the vortices are 3D objects. If we introduce the volume pinning force as Fp = Jc H α, where H is the modulus of the applied field vector H (in our experiment Jc ⊥ H) and α is a factor reflecting the vortex topology, scaling may be successful for a ‘modified’ volume pinning force Fp . In this case the volume pinning force depends only on static parameters of the FLL, such as elastic moduli in the case of isotropic pins, and should obey 2D scaling in both YBCO (Abrikosov vortices) and BSCCO (low-field CS and high-field DS), provided that the factor α properly describes the vortex topology. Simply, α reflects the FLL interaction with the transport current. For strongly coupled Abrikosov vortices the Lorentz force acts on the whole length of the vortex and hence α = 1, Fp = Jc H , and the vortex moves as a 3D object. In the case of the decoupled FLL, where individual motion of the decoupled point vortices substitutes for the bulk flux movement and

Vortex decoupling line and its anisotropy in BSCCO

Figure 5. The 2D scaling of Jc (H , θ) at θ = 40◦ , 50◦ , 60◦ , 70◦ , 80◦ , 82◦ , 84◦ and 87◦ for the BSCCO crystal at 60.0 K (main panel) and YBCO crystal at 83.2 K and θ = 0◦ , 20◦ , 30◦ , 40◦ , 50◦ , 60◦ and 70◦ (inset). The full straight line separates regions of good 2D scaling and scaling failure. The 2D scaling for YBCO fails in the whole field range. The lines connecting the data points are guides for the eye.

the α factor is proportional to the pancakes’ density, α = cos θ , the resulting expression would be Fp = Jc H cos θ . The following plots demonstrate application of the scaling approach to the case of BSCCO and YBCO crystals: in figure 4 the volume pinning force, Fp , as defined earlier, at α = 1, is plotted versus H cos θ while in figure 5 the critical current is plotted as a function Jc (H cos θ). Thus we obtain a collapse of the Fp (H, θ) curves for YBCO single crystals as the inset in figure 4 shows. A similar procedure applied to BSCCO single-crystal data yields an expected result: we observe 2D scaling only at low fields. Although the field range of the good scaling is rather limited, we consider this result as an indication on existence of the strongly coupled vortices, which behave similarly to Abrikosov ones. Attempts to apply the H cos(θ) scaling procedure to the Jc (θ, H ) curves obtained for the YBCO single crystal, it failed as inset of figure 5 shows: the curves do not collapse; this is not unexpected for the moderately anisotropic YBCO. The similar plot for the BSCCO sample yields a successful result only above a certain applied field value, which is angle dependent; see figure 5. Note that this field coincides with the threshold between high- and lowanisotropy regimes and the same field is an upper boundary of good scaling with α = 1 factor, as shown in the main panel of figure 4. We introduce a boundary which separates the high-field area where the scaling holds true and lowfield one where the scaling fails. This separation line can be obviously identified with the phase boundary between the decoupled 2D pancakes and coupled Abrikosov-like vortices on the H –T phase diagram. In contrast, according to our data in YBCO the vortices are 3D up to 0.9Birr and the DS, if it exists, is confined to a rather narrow field range near the transition to the vortex liquid or the decoupling and melting lines practically coincide, in an agreement with results of [15].

6. Conclusion In conclusion, we have performed the transport measurements of the Jc anisotropy of BSCCO single crystals and compared the results with those ones for YBCO single crystals. We have shown that, at low applied fields, a strongly coupled 3D vortex state is realized. The pinning mechanism of the FLL in the state is similar to that in YBCO single crystals and is mainly defined by the FLL response to tilt deformation. In high applied fields the strongly CS is replaced by the DS or point-vortex state which is still in a ‘solid region’ of the H –T diagram. We have shown that these FLL phases can be discerned by scaling analysis of the critical current density field and angle dependences.

Acknowledgments The authors (VFS and VMP) appreciate the partial support of this research work by the State Foundation of Ukraine for the Fundamental Research (DFFD) under Grant 24/349.

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