Anisotropy and dissipation in the mixed state of high temperature superconductors

Physica C 185-189 (1991) 297-302 North-Holland

A N I S O T R O P Y A N D D I S S I P A T I O N I N T H E M I X E D S T A T E OF HIGH T E M P E R A T U R E SUPERCONDUCTORS

Y. lYE, A. FUKUSHIMA, T. TAMEGAI Institute for Solid State Physics, University of Tokyo, Roppongi, Tokyo 106 Japan T. TERASHIMA and Y. BANDO Institute for Chemical Research, Kyoto University, Uji, Kyoto 611 Japan

Dissipative behavior of the flux line system in the mixed state of high temperature superconductors is studied. Difference in the magnitude of anisotropy between YBa2CuzOr-v and Bi2Sr2CaCu2Os+~ is manifest in the angular dependence of dissipation. An anomalous enhancement of disspation at high current densities is found for a narrow range of field angle near to the basal plane direction. Dissipation processes in the parallel and nearly parallel field configurations are discussed in the light of flux dynamics under the influence of strong pinning potential intrinsic to the layered structure. 1. I N T R O D U C T I O N The statics and dynamics of a flux line system in the mixed state of high temperature superconductors (ItTSCs) have attracted much attention recently t. Besides its obvious relevance to the HTSC applications, the behavior of the flux line system is of great interest in its own right, because a rich variety of phenomena, both equilibrium and dissipative, are exhibited flux lines interacting mutually and with various pinning centers. Many of the unusual properties of the flux lines in IITSCs arises from the unprecedentedly high operating temperatures. The complexity of the problem is further enriched by the strong anisotropy associated with the layered structure of HTSCs. Dissipation in the mixed state of a type II superconductor arising from motion of flux lines is governed by competition among forces acting on each flux line; i.e. driving force, pinning force and force exerted by other flux lines. The driving force in the traitpot i~ experiments is the Lorentz force J x / ~ . The flux pinning is usually due to extrinsic sources, i.e. various kinds of defects either unintentionally or intentionally introduced into the system. For a flux line parallel to the basal plane of a highly anisotropic layered superconductor, intrinsic pinning potential due to the layered shucture can play -- : ' - - -'~-' ,^1^2 'rh,~ ,,0",,(-t of mutual interaction among flux lines may be incorporated by elastic theory for the flux line lattice (or liquid, or glass3). The competition among these forces depends on various parameters; magnetic field, tranport current density, their directions, and temperature. In what follows, we present our recent experimental results with particular emphases on the consequences of anisotropy. The behavior of moderately anisotropic YBa2CuzOr-u (YBCO) and that of extremely anisotropic Bi2SrzCaCu~Os+y (BSCCO) are contrasted. All the O.ll

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tvtk

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experiments discussed in this paper are carried out with the transport current parallel to the ab-plane. 2. E X P E R I M E N T A L

Samples used in the present study were thin films of YBCO and BSCCO. Epitaxiai YBCO thin film samples grown by a reactive coevaporation w~thod 4 at ICR, Kyoto University. The most of the data shown in the present paper were obtaind on two samples which were 1000 ,~. in thickness, and patterned into an eight-arm ttall-bar shape with the channel width 100 9m by Ar ion dry-etching. The orientation of the channel was parallel to the a- (or b-) axis. The YBCO films were rather heavily twinned so that dense arrays of twin planes run across the sample at +45* with respect to the channel direction. Highly oriented polyerystalline BSCCO films were prepared at ISSP, Univ. of Tokyo, by a single target r/-sputtering method s. The BSCCO films were ,,~ ll~rn in thickness and patterned in a sixarm Hall-bar shape. As will be shown below, the large anisotropy of the IITSCs requires particularly high degree of precision in angular control. To this end, we built several versions of magnetotransport measurement systems including one with a capability of trip!e axis alignment with 0.02* precision 6. Temperature regulation, free from influence of magnetic field, was achieved by use of a sample holder equipped with a gas thermometer. Measurements were performed by angular sweep, field sweep and temperature sweep, so as to explore the multidimensional parameter space. The transport response generally shows strong non-Ohmicity, except at the lowest current densities and in the higher temperature range near To. The term 'resistivity' used in this paper stands for the quantity E/J-'. and does not imply an Ohmic response.

0921-4534/91/503.50 © 1991 - Elsevier Science Publishers B.V. All rights reserved.

298

E Iye et aL / Ani~otropyand dissitx~onin the mixed sa~e

3. A N I S O T R O P Y Difference in the magnitude of anisotropy between YBCO and BSCCO is manifest in the anglax dependence of resistivity as the direction of a magnetic field of fixed intensity is swept from the ab-plane (0 = 0 °) to the e-axis (0 = 90°). Figures I and 2 are such traces for YBCO and BSCCO, respectively. It is clearly seen that the overall angular dependences axe quite distinct between the two systems. The anisotropy of YBCO can be phenomenologically fitted to the anisotropic Ginzburg-Landau model (effective mass model). The anisotropy ratio of the coherence lengths, which is related with the effective mass anisotropy, is (~/~e) = (me/ma) ½ ~ 5 for a fully oxygenated YBCO t. The anisotropy ratio in YBCO increases with oxygen deficiency, as the CuO chain layer becomes more insulative. 60,,

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In contrast to YBCO, the angular trace for BSCCO shows a cusp at 0 = 0, similar to the behavior observed in a thin film superconductor. In fact, BSCCO comes very dose to the two-dimensional (2D) limit s. A flux line piercing through a layered superconductor with very weak interlayer coupling may be viewed as a stack of 2D vortex discs, or "pancake" vortices. In the 2D limit, the vortex discs in adjacent layers are completely decoupled, so that the only scaling parameter is the areal density of the vortex discs in each layer, which is given by the normal component of the applied magnetic field, H s i n 0. The inset of Fig. 2 is a replot of the data in the main panel with the abscissa scaled by the normal field component. It is seen that such a scaling makes all the d a t a collapse into a single curve, demonstrating that the 2D limit model works quite well. Namely, the parallel field component contributes very little to the dissipation. It should be added, however, that if one looks more closely at the behavior in the immediate vicinity of 0 = 0 in a logarithmic scale, one discerns deviation from the 2D model 9. Having a more three-dimensional character, YBCO does not obey such a simple scaling. A somewhat better scaling for YBCO is obtained by employing a reduced field / / ~ / s i n 2 0 + ~cos20 inspired by the effective mass model. The inset of Fig. 1 shows such a plot by choosing c- t = 5. Still, the scaling is only approximate, as expected, because the flux pinning strength varies with 8. 4. D I S S I P A T I O N A T H I G H C U R R E N T

FIGURE I Angular dependence of resistivity in Y B C O zz a low current density. T h e inset shows a replot of the same data as

a function of reduced magnetic field defined in the text.

The transport behavior at elevated current densities is drastically different from that in the low current density limit. Figure 3 shows examples of the 0 dependence of resistivity in YBCO at high current densities.

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°I-' . . . . . iT -+.20 -90 -60 -30 30 60 so 120 0 (deg) FIGURE 3 Angular dependence of resistivity in YBCO at a high current density. The field is rotated in a plane perpenaiculal to the current direction. Compare this figure with Fig. 1. l

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Y. lye et al. / Anisotropy and dissipation in the mixed state T h e t r a c e s a r e quite different in s h a p e from those for low c u r r e n t densities shown in Fig, !. A local m i n i m u m at 0 = 90* is due to e n h a n c e d p i n n i n g when the flux lines are a l i g n e d with t h e twin p l a n e s t°. This f e a t u r e can b e also o b s e r v e d at low c u r r e n t densities. A p r o n o u n c e d peak a t ,~ 5* e m e r g e s at higher current d e n s i t i e s xt. This effect is m o s t distince when t h e 0r o t a t i o n axis is chosen p a r a l l e l to t h e current direction, i.e. t r a n s v e r s e m a g n e t o r e s i s t a n c e geometry, (Fig. 4). W h e n t h e field is r o t a t e d w i t h i n t h e plane c o n t a i n i n g t h e c-axis a n d the c u r r e n t d i r e c t i o n , the angular dep e n d e n c e is r a t h e r featureless even at higher c u r r e n t densities (Fig. 5). ht b o t h eases, t h e t e m p e r a t u r e dep e n d e n c e shows the a c t i v a t e d b e h a v i o r . T h e a n g u l a r d e p e n d e n c e s of the a c t i v a t i o n e n e r g y e x t r a c t e d from these d a t a for t h e two 0 - r o t a t i o n m o d e s are p l o t t e d in t h e inset o f Fig. 6. T h e d i p of t h e activation energy

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FIGURE 4 Angular dependence of resistivity in YBCO at a high current density for different temperatures. The fieldis rotated in a plane perpendicular to the current direction. I0 0

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Inset: Angular dependence of the activation energy Ior the two modes of field rotation. The 0-dependence of the activation energy can be decomposed into two contributions, as schematically shown in the main panel• at around 5 ° c o r r e s p o n d s to the a n o m a l o u s enhancement of d i s s i p a t i o n seen in Figs. 3 a n d 4. A similar effect is also o b s e r v e d in B S C C O as shown in Fig. 7 9. It is noted t h a t t h e characteristic angle is as small as ,,, 0.1 ° for B S C C O . Before d i s c u s s i n g its physical origin, we summarize the salient f e a t u r e s of the a n o m a l o u s dissipation peak: (i) The c h a r a c t e r i s t i c angle for the m a x i n m m enhancement is t y p i c a l l y 0 ,,, .5° for Y B C O and 0 ,-- 0.1 ° for BSCCO. (ii) T h e enhancement is most clearly observed in the transverse m a g n e t o r e s i s t a n e c geometry for YBCO, i n d i c a t i n g that the effect is caused by macroscopic Lorentz force. (iii) T h e c h a r a c t e r i s t i c angle appears to b e i n d e p e n d e n t of t e m p e r a t u r e , and only weakly d e p e n d e n t on c u r r e n t density. (iv) T h e peak posi-

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Y. lye et at ] Angotropy and dissipation in the mixed state

300

tion shifts towards higher angles with decreasing field strength. As stated earlier, a flux line piercing through a layered superconductor may be viewed as being composed of 2D vortices (pancakes) localized in individual layers and lateral segments (strings) in the interlayer spacings which connect the pancakes. As 0 is decreased, the pancakes in adjacent layers become laterally separated, i.e the length of the strings increases, and the density of the pancakes decreases, as illustrated schematically in Fig. 8-a In order to simplify the argument, we assume that the contributions to dissilzation from the motion of the pancakes and from the motion of the strings can be treated separately to a first approximation, as illustrated in Fig. 8-b. This assumption obviously becomes invalid for larger 0, but is convenient in considering the situation at small 0. With the transport current in the basal plane, the pancakes are always subject to the Lorentz force irrespective of the relative direction of J and macroscopic H. Therefore, this part of dissipation is more or less the same for the two modes of 0-rotation corresponding to Figs. 4 and 5. By contrast, the Lorentz force on the strings depends on the angle between a~ and H in the usual way. The main pinning mechanism for the strings is the intrinsic pinning. On the other hand, the pancakes are pinned by twin boundaries and by point defects. At the low current densities the vertical motion of the strings is prohibited by strong intrinsic pinning, so that the dissipation is mostly due to the lateral motion of the pancakes. This yields a monotonic angular dependence as seen i:~ Fig. 1. The angular dependence remains monotonic even at high current densities, if the 0 is rotated in the plane containing the current direction (Fig. 5). However, if the O-rotation is done in the plane

--1

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FIGU RE 8 Illustration of flux lines in a strongly layered superconductor. For an arbitrary field angle, the flux line minimizes the toss of condensation energy by taking a staircase pattern consisting of the 2D vortex discs (pancakes) and tlae lateral segments (strings). The bottom figure depicts a nucleation/dissociation process of a 2D vortex-antivortex pair in the parallel field geometry.

perpendicular to the current direction (Fig. 4), the motion of the strings is triggered by a strong Lorentz force at high current densities. The experimental observation suggests that the lowering of the pinning potential by the Lorentz force occurs more strongly for the intrinsic pinning of the strings than for the extrinsic pinning of the pancakes. Thus the contribution of the motion of strings to dissipation becomes visible at higher current densities, which gives rise to the observed anomalous angular dependence of dissipation. It is expected that the anomalous disspation peak may become more pronounced if more extrinsic pinning centers are introduced into the system, because they would effectively pin the pancakes and enhance the relative importance of the motion of the strings. It should be noted that if one describes the motion of a flux in terms of flux loop nucleation, the lateral motion of a pancake corresponds to nucleation of a small loop, while the vertical motion of a string corresponds to nucleation of an elongated loop. The next question is why the anomalous dissipation due to the vertical motion of the strings has such a sharp 0-dependence. On the higher angle side, the description in terms of pancakes and strings becomes meaningless when tanO .~ 1. On the lower angle side, the activation energy is expected to increase sharply as 0 ~ 0, because the intrinsic pinning energy for a string increases with its length given by ~ = d/tanO (d being the layer spacing). In the limit of 0 --, 0, the Therefore. the dissipation due to the vertical motion of strings is expected only in a narrow range of 0. In the 0 ---* 0 limit, the vertical motion of a string will take a form of interlayer jump of a segment of a certain characteristic length, as illustrated in Fig. 8-c. This type of flux dynamics will be discussed in the next section. Although we believe that it captures an essential physics of the anomalous angular dependence, the above picture based on individual flux motion is surely a gross oversimplification. A quantitative explanation for the effect should be only attained by properly incorporating the collective nature of the flux dynamics. In fact, the dependence of the characteristic angle on the field strength suggests an importance of the interaction between the flux lines. The flux line dynamics should be more appropriately described in term~ of collective motion of highly correlated flux lines that form a flux lattice (or glass, or liquid) 1~. it should be also mentioned that possible phase transitions of a flux line lattice embedded in a strongly layered structure as a function of field angle is discussed by several authors is. The observed anomaly may be related with such phase transitions , although the Lorentz force being important implies that one has to consider not just an equilibrium structure of the flux line system but also their dynamics.

301

Y. lye et aL [ Anisotropy and dissipation in the m L r ~ state

5. P A R A L L E L

GEOMETRY

FIELD

The dissipation process in the parallel field configuration, H II a/r-plane, deserves further investigation. The most drastic case is the extremely anisotropie BSCCO. For this system, a surprising result has been obtained that d i ~ i p a t i o n i s independent of the relative angle between H and d when they are both in the ab-plane s. This is in a striking contrast with the canonical behavior of flux flow resistivity in an ordinary superconduc£ tor, for which the resistivi'.ies for d II n and J 2. H differ by many orders of magnitude, as demonstrated, for example, in amorphous MoGe ~ . The macroscopic Lorentz force independence of dissipation is attributed to the nature of flux dynamics under a strong intrinsic pinning potential. For H II abplane, each flux line finds itself most confortable by laying its core in the spacing between two adjacent superconducting layersa. Let us first consider the case of H _L J, in which the macroscopic Lorentz force is such that it drives a flux line in the c-direction. In the presense of a strong intrinsic pinning potential, uniform translation of a parallel flux line in the c-direction cost a large energy. An energetically less costly excitation can be created by a local jump of a short segment of a string, which nucleates a pair of 2D vortex (pancake) and antivortex ~2J4As, as depicted in Fig. 8<. When the jump occurs in the right direction, the Lerentz force drives the vortex-antivortex pair to dissociate, while a pair created by hopping to the wrong direction is driven to shrink. These processes result in a net motion of the original flux line along the direction of the macroscopic Lorentz force. Dissipation for H 11f (force-free configuration) may be attributed to a similar process, except p(~o) = Po + Pt sin ~ ~o+ p~(~,)

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that dissociation of the 2D vortex-antivortex pair involves a complex flux cutting and rejoining process in Lhis case. In either case, dissipation occurs in a twostep process: thermal nucleation of a vortex-antivortex pair and its dissociation. In the case of BSCCO, the energy barrier against the first step is the dominant factor, which accounts for the Lorentz force independence of dissipation. In the case of YBCO, dissipation does depend on the relative angle be*ween H and J, but there also exists an angular independent contribution to dissipation mA4. Figure 9 shows an example of the angular dependence of resistivity in YBCO as the magnetic field is rotated within the ab-plane. The field angle ~o is measured from the direction of J, which coincides with the a(b-) axis for this sample. The angular dependence can be decomposed in the following way: P(~') = Po + Pz sin2~o + P2(~P).

Here, Po represents an angular independent (anomalous) component. A two-fold symmetric component, pl sin ~ is due to the usual Lorentz force effect. P2(9) represents sum of four-fold symmetric and higher harmonic components associated with the ab-plane structure. The ab-plane anisotropy averaged by over twin domains gives a four-fold symmetric fe,~iure with the minima both at tp = 0 ° and 90 °. A dip at ~o = 45 ° (and 135° etc.) comes from enhanced pinning when the flux lines are aligned to the twin planes. One can also measure the transverse resistivity (i.e. electric field component perpendicular to the current). which can I_)eexpressed as p.(~)

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302

Y. lye et al. / Ar, lmtropy and dissipation in the mixed state

The transverse voltage provides a good consistency check for the Lorentz force component 14. It should be reminded that only the angular independent term P0 exists in the case of BSCCO, while only the Lorentz effect term Pt exists in the flux flow in usual superconductor such as amorphous MoGe. It is useful to investigate the anomalous term po in comparison with the ordinary Lorentz effect term p~. Figure 10 is an Arrhenius plot of p o ( T ) and pt(T) for different current densities. The inset shows the current density dependence of the activation energy extracted from the Arrhenius plot. The activation energy for P0 is systematically larger than that for pt, but they are comparable in magnitude. These observations are consistent with the above picture for the p0 process as nucleation of a 2D vortex-antivortex pair by local hop of a short segment of a string. The activation energy of the first step is dominant and is expected to be comparable in magnitude with that of the Pt process, as actually observed. We should comment on other approaches to the resistive state of HTSCs. There are attempts to attribute the Lorentz force independent contribution to dissipation to superconducting fluctuation effect is. The fact that the Lorentz force independent component shows an activated behavior similar to the Lorentz force effect component may suggest that the anomalous component should be understood in the framework of flux dynamics. At the present stage, the fluctuation model appears to encounter difficulties in extending its applicability to the low-resistance tail part of the resistive transition in IlTSCs. On the other hand, it is also clear that the fluctuation model is certainly a sound approach to the problem from the high temperature side. Especially for the case of f ][ c configuration 17, where current flows across the weakly Josephson coupled layers, the description in terms of phase fluctuation seems more appropriate. The fluctuation approach and the flux dynamics approach may be unified at a deeper level. 6. C O N C L U S I O N The dissipation in the mixed state of high temperature superconductors exhibits a rich variety of behavior as a function of magnetic field angle with respective to the crystalline axes and the transport current direction. Flux dynamics in the parallel and nearly parallel field geometries are profoundly influenced by the strong intrinsic pinning potential due to the layered structure. It is clear that much work needs to be done to elucidate the dissipation mechanism especially at higher current densities. ACKNOWLEDGEMENTS This work was supported in part by Grant-in-Aid

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