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Fishtails, scales and magnetic fields
Fishtails, scales and magnetic fields* L.F. Cohen, J.R. Laverty, G.K. Perkins, A.D. Caplin and W. Assmus t Centre for High Temperature Superconductivity, Blackett Laboratory, Imperial College, London SW7 2BZ, UK t Physikalisches Institut, Goethe Universit~t 6000 Frankfurt, Germany The granularity of high Tc single crystals and the cause of the secondary peak in m - H loops (known as the 'fishtail' effect) are still areas of active debate and are crucial to our understanding of the nature of the superconductivity and pinning in high Tc materials. This paper demonstrates the use of the length scale technique to rule out large scale granularity as a cause of the fishtail effect. Magnetic moment and flux creep measurements are discussed as a function of field on single crystals of YBCO; these results exclude several of the other models previously proposed to explain the origin of the fishtail feature, but support an explanation in terms of microstructural regions that are turned normal in an increasing field, and so act as additional pinning centres.
Keywords: magnetic moment; flux creep; magnetization curves
The isothermal magnetization curves of high Tc single crystals continue to be a perplexing area of research. Firstly, there have been many reports that single crystals show granular behaviour I (with evidence from subdividing crystals and observing a scaling of the magnetization signal only when the grain size has reached hundreds of microns). Granularity has been shown to occur in particular at high fields and high temperatures ( > 30 K) 2'3. Alternatively there is evidence that some crystals are fully connected 4. Secondly, anomalous features on the magnetization curve, in particular the depression of the magnetization at low fields followed by a secondary maximum, have been studied in great detail. Several mechanisms have been proposed to explain the cause of this feature, which is known as the second peak of the 'fishtail' effect. Models relating to the granularity of the crystals 1'5-7, oxygen defects ~'2'8, phase change of the flux lattice 9 and surface effects ~0 have all been advanced. Not only is it important to use a definitive, and preferably non-destructive test, to examine the connectivity of single crystals in order that the critical current density Jc of single crystals can be evaluated unambiguously from the Bean critical state model ~1, but the distinguishing of extrinsic effects from the intrinsic properties of single crystals is also essential for improving our general understanding of flux pinning in the high T~ materials. In this paper we show, using the simple and nondestructive length scale technique 12, that some YBCO
* Paper presented at the conference 'Critical Currents in High Tc Superconductors', 2 2 - 2 4 April 1992, Vienna, Austria 0011 - 2 2 7 5 / 9 3 / 0 3 0 3 5 2 - 0 5 © 1993 B u t t e r w o r t h - Heinemann Ltd
352
Cryogenics 1993 Vol 33, No 3
single crystals are well connected in fields up to and above the fishtail feature, ruling out large scale granularity as the cause of this anomaly. Enormous effort has been devoted to studying the variation of flux creep with temperature 13 and flux creep with time 14'~5 to examine evidence for nonlogarithmic behaviour. However, there is little direct reporting of the variation of flux creep with field. We have examined the flux creep variation with field through the fishtail feature and find no evidence for a flux lattice phase change, although the flux creep rate does change markedly as the field in which it is measured is increased through the fishtail feature, implying a genuine change of flux pinning properties.
Experimental procedures The measurements were carried out on flux-grown single crystals of YBCuO. The m - H loops and flux creep measurements were performed using a commercial vibrating sample magnetometer (Oxford Instruments Ltd Model 3001). The magnetic field was always parallel to the crystal c-axis and our discussion is restricted to this geometry.
Results The results presented here will be confined to one YBCO crystal, chosen from a batch of crystals showing similar effects, with dimensions w = 2 mm, l = 1.4 mm, t = 0.1 ram, and to its behaviour at 77 K ( T / T c = 0.92). The sample was zero-field cooled below To, a 0.1 mT field was applied parallel to the c-axis and
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the magnetic moment recorded (Figure 1) as the temperature was slowly increased. The double step transition is typical of oxygen-poor crystals. The magnetic moment at 77 K is shown in Figure 2a and the anomalous fishtail feature of magnitude mF is indicated on the curve, occurring at field HF.
To examine the connectivity of the crystal, the length scale technique 12 was applied. On samples with large aspect ratios (i.e. with large demagnetizing factors for the usual geometry of plate-like YBCO crystals with H parallel to the c-axis) this technique can be used to obtain independent estimates of both the length scale A, on which the screening currents flow, and the sheet critical current density Kc=Jct. To use this technique accurately, the applied field at which the connectivity is to be examined must be large compared with the critical state penetration field AH = Kc, so that the field within the sample is almost uniform everywhere and nearly equal to the applied field. On reversal of the direction of field sweep, the circulating screening currents will have changed sign everywhere after the field has been reduced by a few times AH. The initial slope during the reversal, (dm/dH)i, is a direct measure of A. Consequently, small field steps of the order of AH/IO were applied over the field reversal region of the m - H loop to ensure enough resolution to determine the initial slope. Figure 2b shows the field reversal curves at several fields around the fishtail feature. The size of the magnetic moment varies slightly between these curves because the loops were performed at slightly different .
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Figure2 (a) Change of magnetic m o m e n t with applied field at 77 K f o r F R A 3 A . T h e f i e l d w a s s w e p t at a r a t e o f O . 2 r o T s 1. The a r r o w marks the a n o m a l o u s fishtail peak at field HF on the f o r w a r d leg of the hysteresis loop. (b) Length scale analysis at 77 K for FRA3A, s h o w i n g field reversal region at fields o f 0.1, 0.3, 0 . 5 and 1 T. (c) Length scale analysis for FRA3A; variation of screening current scale length A with field. (d) U n d e r e s t i m a t i o n of (dm/dH) caused by too large a field step
Cryogenics 1993 Vol 33, No 3
353
Fishtails, scales and magnetic fields: L.F. Cohen et al. field sweep rates (the signal is smaller at slower field sweep rates because of flux creep). The details of the length scale analysis for this sample are to be published elsewhere 3. From these calculations the critical current density at zero field Jc(0) = 6.4 × 107 A m-Z and the penetration field #oz~H = 6.4 mT. Figure 2c shows the results of the length scale measurement. The average length scale is A = 0.5 mm, which corresponds well with the smaller dimension of our crystal. At 1 T field there may be evidence that the pattern of current flow is starting to break up, but this measurement of A is less accurate, because the field step of 2 mT used in this case is only three times smaller than /~oAH, leading to a possible underestimation of A (Figure 2d shows how, if the field steps are too large, the slope will be underestimated). Overall, however, the crystal is fully connected up to fields well above the anomalous feature in the magnetic moment. Flux creep Prior to a flux creep measurement the applied field was cycled so as to ensure full penetration of the screening currents in the sample, yielding a well defined initial state. Creep rates were measured on both increasing and decreasing legs of the m - H loop. The decay of the magnetic moment was monitored over three decades of time, starting 8 s (to = 8 s) after the set field had been reached. The magnetic moment creep at different fields is shown in Figure 3. At fields between 0.1 and 1 T the creep behaves almost logarithmically with time. Also, the creep rate S=dm/dlog~o(t+to) is noticeably slower at fields below the fishtail feature compared to those above. Figure 4 plots together the magnetic moment curve, the rate of flux creep S and the normalized rate of flux creep NS, where NS = -S/m and m is the value of the magnetic moment taken from curve (a). A peak in S is visible at 0.6 T field, somewhat higher than the fishtail peak at 0.3 T. However, since the creep rate changes with field, the observed position of the magnetic moment peak depends on the sweep rate. From Figure 3, the creep rate at 0.6 T implies that the magnitude of
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the magnetic moment drops by = 20%, and at 0.3 T by = 5%, in the first few seconds. That is, if at time t = 0, m were constant in the field range between 0.3 and 0.6 T, at t = 10 s the measured m would decrease over this field range. Consequently, the observed increase in m at fields below the peak, accompanied as it is by an increasing creep rate, cannot be merely an artefact of creep rates, but must represent an intrinsic magnetic moment and critical current density that are increasing with field in this field range. The measurements were repeated on the decreasing field leg. Figure 5 shows the creep rate at different fields and Figure 6 plots the magnetic moment, together with the creep rates S and NS. The overall similarity of Figures 5 and 6 (decreasing field) to Figures 3 and 4 (increasing field) demonstrates that the main features of the behaviour of the creep rates above and below the fishtail peak are independent of the direction of field sweep. Discussion
Firstly in this section we give a brief description of the models most commonly suggested to explain the fishtail
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354
Cryogenics 1993 Vol 33, No 3
Fishtails, scales and magnetic fields: L.F. Cohen et al.
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Equivalently, the field change required to reverse completely the screening current direction when the field is reversed also increases. This implies that either the core pinning or the surface pinning/surface barrier has increased. Kopylov et al. merely speculate that the latter is the cause and cannot eliminate the former from suspicion.
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effect. Then we outline aspects of the measurements described in the previous section relevant to the models, and discuss the likelihood of that particular model accounting for the behaviour observed.
Models (1) Josephson junction model. The Josephson junction model ~'5'6 suggests that the sample contains large regions separated by oxygen-poor material, which effectively create a granular material. It then follows that the magnetization is made up of several current contributions. Inter-regional currents dominate at low fields, and the minimum in the magnetization is attributed to the start of phase decoupling between the regions. The maximum in the magnetization is the signature that all the regions have decoupled and the regions are acting independently. Immediately beyond the field at which the maximum occurs, the magnetization is dominated by intraregional currents. These flow on a length scale corresponding to the size of the regions. (2) Microstructural model. Another model 2'8 related to the oxygen deficiency 6 suggests that there are microstructural regions in the material which are superconducting, but with a significantly lower Hc2 than the bulk. These regions start to turn normal at the field corresponding to the minimum in the magnetization, and have all done so by the field corresponding to the maximum. These microstructural normal regions then act as pinning centres and increase the critical current, and hence the magnetization also. (3) Flux lattice phase change. It has been suggested 9 that the fishtail peak in the magnetization is related simply to a change in flux creep dynamics, by analogy with low field behaviour ~5 at fields much lower than those we are concerned with here. Evidence for the phase change would be apparent in the first few decades of flux creep decay~6. (4) Surface barrier effects. Kopylov et al. ~0, using a length scale type of argument, pointed out that dM/dH, the reverse leg susceptibility, is the same for all fields, yet the magnetization M increases with increasing field.
If the breaking up of the critical current path outlined in the Josephson junction model (1) were occurring in our samples, the length scale analysis would reveal it. Instead, our length scale measurements show that the sample is fully connected up to fields well beyond the anomalous peak in the magnetic moment. This is in agreement with previous reports 4. On the other hand, the length scale analysis would not detect microstructural normal regions associated with model (2), which are probably created by oxygen-poor material*. There is no solid evidence for a surface barrier/surface pinning model. The observed increase of magnetic moment with field implies that the pinning strength is increasing, but this could result just as well from an increase in core pinning as outlined in the microstrucrural model t. Moreover any surface mechanism should introduce asymmetry in the magnetic moment between increasing and decreasing fields in the sample. At low temperatures some differences in the size of the magnetic moment signal between the two sweep directions have been observed j4. We have seen some small shifts of the peaks with field sweep direction (care must be taken to avoid experimental artefacts), but they tend to be in the opposite direction from the shift expected from a surface barrier. We do not observe any distinctive change in the form of the flux creep as the field changes through the fishtail peak. Although the creep is not strictly logarithmic with time, the deviations from logarithmic behaviour are not more marked on one side of the peak than the other. Therefore, we can infer that no pronounced change in the flux lattice occurs at the fishtail peak. The steady increase in the flux creep rate [Figure 6, curve (c)] at fields approaching the fishtail peak is significant. In fact, it looks plausible that at time t = 0, the peak in the magnetization is coincident with the peak in S (see Figure 7). The simple flux creep theory of Anderson and Kim ~7 implies that U~,, the pinning energy (to be understood here as representing some appropriately weighted average), is decreasing as the field increases toward the fishtail peak. We suggest that more pinning centres are being added (hence an increase in m), but that they are ones that are rather shallow (so that the average value of U,, decreases).
* There is a wealth of evidence related to the oxygen deficiency ~il 3.18. It appears probable that reducing the oxygen from a fully oxygenated crystal would first introduce microstructural pinning sites and then large scale granularity 2. But the effect of oxygen on the fishtail peak needs much more detailed measurements than have yet been performed + A specific test of whether surface or core pinning is dominant would be to examine systematically the variation of normalized penetration field with oxygen deficiency
Cryogenics 1993 Vol 33, No 3
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Fishtails, scales and magnetic fields: L.F. Cohen e t al.
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Acknowledgeme'
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W e would like to th; ductivity, in partic D . N . Zheng, for measurements on f by the Science and
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k the Cambridge I R C in Superconar A. Campbell, J. Johnson and dndly allocating time for these ~ir V S M . The w o r k was supported ~ngineering Research Council.
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References
1 Osofsky, M.S., Co_n, J.L., Skelton, E.F., Miller, M. et aL Phys Rev B (1992) 45 49t6 2 Daeumling, M., Seuntjens, J.M. and Larbalestier, D.C. Nature
Applied Field
Figure 7 Schematic field variation of the inferred 'instantaneous' magnetization Mo at time t = 0 and the measured Mt at time t; the fields at the two maxima differ because of the field dependent creep rate S/Mo
Conclusions
The length scale analysis shows that our crystals are fully connected up to fields well above the fishtail feature, so that the latter is not caused by an onset o f some kind o f large scale granularity. Our observation o f the variation o f the flux creep rate with field in the vicinity o f the fishtail suggests that the latter is associated with some m o r e microscopic aspect of the samples, for example the addition o f many shallow pinning centres as the field increases. This is in agreement with a previously suggested model, in which microstructural oxygen-deficient regions turn normal in increasing field, and so provide the additional pinning centres needed to generate the fishtail feature.
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(1990) 346 332 3 Laverty, J.R. and Cohen, L.F. Phy Rev B submitted for publication 4 Welp, U., Kwok, W.K., Crabtree, G.W., Vandervoort, K.G. et al. Appl Phys Left (1990) 57 84 5 Keller, C., Kupfer, H., Gurevich, A., Meier-Hirmer, R. et a/. J Appl Phys (1990) 68 3498
6 Kupfer, H., Apfelstedt, I., Flukiger, R., Keller, C. et aL Cryogenics (1989) 29 268 7 Campbell, A.M. and Evetts, J.E. Critical Currents in Superconductors Taylor and Francis Ltd, London, UK (1972) 193 [reprinted from Adv Phys (1972) 21 (90)] 8 Vargas, J.L. and Larbalestier, D.C. Appl Phys Lett in press 9 Chiknmoto, N., Konczykowskl, M., Motohira, N., Kishio, K. et al. Physica C (1991) 185/189 1835 10 Kopylov, V.N., Koshelev, A.E. and Sehegolev, LF. Physica C (1990) 170 291 11 Bean, C.P. Rev Mod Phys (1964) 36 31
12 Angadi, M.A., Caplin, A.D., Laverty, J.R. and Shen, Z.X. Physica C (1991) 177 479-486 13 Yeshurun, Y. and Malozemoff, A.P. Phys Rev Lett (1988) 60 2202 - 2205 14 Weir, S.T., Nellis, W.J., Daliehaoueh, Y., Lee, B.W. et al. Phys Rev B (1991) 43 3034-3041 15 Svedlindh, P., Rossel, C., Niskanen, K., Norling, P. et al. Physica C (1991) 176 336-346 16 Malozemoff, A.P. Physica C (1991) 185/189 264-269 17 Anderson, P.W. and Kim, Y.B. Rev Mod Phys (1964) 36 39
18 Angadi, M.A., Shen, Z.X., Caplin, A.D., McCartney, D.G. etal. Supercond Sci Technol (1992) 5 165-168
Keywords: magnetic moment; flux creep; magnetization curves
The isothermal magnetization curves of high Tc single crystals continue to be a perplexing area of research. Firstly, there have been many reports that single crystals show granular behaviour I (with evidence from subdividing crystals and observing a scaling of the magnetization signal only when the grain size has reached hundreds of microns). Granularity has been shown to occur in particular at high fields and high temperatures ( > 30 K) 2'3. Alternatively there is evidence that some crystals are fully connected 4. Secondly, anomalous features on the magnetization curve, in particular the depression of the magnetization at low fields followed by a secondary maximum, have been studied in great detail. Several mechanisms have been proposed to explain the cause of this feature, which is known as the second peak of the 'fishtail' effect. Models relating to the granularity of the crystals 1'5-7, oxygen defects ~'2'8, phase change of the flux lattice 9 and surface effects ~0 have all been advanced. Not only is it important to use a definitive, and preferably non-destructive test, to examine the connectivity of single crystals in order that the critical current density Jc of single crystals can be evaluated unambiguously from the Bean critical state model ~1, but the distinguishing of extrinsic effects from the intrinsic properties of single crystals is also essential for improving our general understanding of flux pinning in the high T~ materials. In this paper we show, using the simple and nondestructive length scale technique 12, that some YBCO
* Paper presented at the conference 'Critical Currents in High Tc Superconductors', 2 2 - 2 4 April 1992, Vienna, Austria 0011 - 2 2 7 5 / 9 3 / 0 3 0 3 5 2 - 0 5 © 1993 B u t t e r w o r t h - Heinemann Ltd
352
Cryogenics 1993 Vol 33, No 3
single crystals are well connected in fields up to and above the fishtail feature, ruling out large scale granularity as the cause of this anomaly. Enormous effort has been devoted to studying the variation of flux creep with temperature 13 and flux creep with time 14'~5 to examine evidence for nonlogarithmic behaviour. However, there is little direct reporting of the variation of flux creep with field. We have examined the flux creep variation with field through the fishtail feature and find no evidence for a flux lattice phase change, although the flux creep rate does change markedly as the field in which it is measured is increased through the fishtail feature, implying a genuine change of flux pinning properties.
Experimental procedures The measurements were carried out on flux-grown single crystals of YBCuO. The m - H loops and flux creep measurements were performed using a commercial vibrating sample magnetometer (Oxford Instruments Ltd Model 3001). The magnetic field was always parallel to the crystal c-axis and our discussion is restricted to this geometry.
Results The results presented here will be confined to one YBCO crystal, chosen from a batch of crystals showing similar effects, with dimensions w = 2 mm, l = 1.4 mm, t = 0.1 ram, and to its behaviour at 77 K ( T / T c = 0.92). The sample was zero-field cooled below To, a 0.1 mT field was applied parallel to the c-axis and
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Figure 1 M a g n e t i c m o m e n t versus t e m p e r a t u r e in a 1 mT field f o r YBCO single crystal FRA3A. The sample w a s cooled initially in zero field
the magnetic moment recorded (Figure 1) as the temperature was slowly increased. The double step transition is typical of oxygen-poor crystals. The magnetic moment at 77 K is shown in Figure 2a and the anomalous fishtail feature of magnitude mF is indicated on the curve, occurring at field HF.
To examine the connectivity of the crystal, the length scale technique 12 was applied. On samples with large aspect ratios (i.e. with large demagnetizing factors for the usual geometry of plate-like YBCO crystals with H parallel to the c-axis) this technique can be used to obtain independent estimates of both the length scale A, on which the screening currents flow, and the sheet critical current density Kc=Jct. To use this technique accurately, the applied field at which the connectivity is to be examined must be large compared with the critical state penetration field AH = Kc, so that the field within the sample is almost uniform everywhere and nearly equal to the applied field. On reversal of the direction of field sweep, the circulating screening currents will have changed sign everywhere after the field has been reduced by a few times AH. The initial slope during the reversal, (dm/dH)i, is a direct measure of A. Consequently, small field steps of the order of AH/IO were applied over the field reversal region of the m - H loop to ensure enough resolution to determine the initial slope. Figure 2b shows the field reversal curves at several fields around the fishtail feature. The size of the magnetic moment varies slightly between these curves because the loops were performed at slightly different .
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Figure2 (a) Change of magnetic m o m e n t with applied field at 77 K f o r F R A 3 A . T h e f i e l d w a s s w e p t at a r a t e o f O . 2 r o T s 1. The a r r o w marks the a n o m a l o u s fishtail peak at field HF on the f o r w a r d leg of the hysteresis loop. (b) Length scale analysis at 77 K for FRA3A, s h o w i n g field reversal region at fields o f 0.1, 0.3, 0 . 5 and 1 T. (c) Length scale analysis for FRA3A; variation of screening current scale length A with field. (d) U n d e r e s t i m a t i o n of (dm/dH) caused by too large a field step
Cryogenics 1993 Vol 33, No 3
353
Fishtails, scales and magnetic fields: L.F. Cohen et al. field sweep rates (the signal is smaller at slower field sweep rates because of flux creep). The details of the length scale analysis for this sample are to be published elsewhere 3. From these calculations the critical current density at zero field Jc(0) = 6.4 × 107 A m-Z and the penetration field #oz~H = 6.4 mT. Figure 2c shows the results of the length scale measurement. The average length scale is A = 0.5 mm, which corresponds well with the smaller dimension of our crystal. At 1 T field there may be evidence that the pattern of current flow is starting to break up, but this measurement of A is less accurate, because the field step of 2 mT used in this case is only three times smaller than /~oAH, leading to a possible underestimation of A (Figure 2d shows how, if the field steps are too large, the slope will be underestimated). Overall, however, the crystal is fully connected up to fields well above the anomalous feature in the magnetic moment. Flux creep Prior to a flux creep measurement the applied field was cycled so as to ensure full penetration of the screening currents in the sample, yielding a well defined initial state. Creep rates were measured on both increasing and decreasing legs of the m - H loop. The decay of the magnetic moment was monitored over three decades of time, starting 8 s (to = 8 s) after the set field had been reached. The magnetic moment creep at different fields is shown in Figure 3. At fields between 0.1 and 1 T the creep behaves almost logarithmically with time. Also, the creep rate S=dm/dlog~o(t+to) is noticeably slower at fields below the fishtail feature compared to those above. Figure 4 plots together the magnetic moment curve, the rate of flux creep S and the normalized rate of flux creep NS, where NS = -S/m and m is the value of the magnetic moment taken from curve (a). A peak in S is visible at 0.6 T field, somewhat higher than the fishtail peak at 0.3 T. However, since the creep rate changes with field, the observed position of the magnetic moment peak depends on the sweep rate. From Figure 3, the creep rate at 0.6 T implies that the magnitude of
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the magnetic moment drops by = 20%, and at 0.3 T by = 5%, in the first few seconds. That is, if at time t = 0, m were constant in the field range between 0.3 and 0.6 T, at t = 10 s the measured m would decrease over this field range. Consequently, the observed increase in m at fields below the peak, accompanied as it is by an increasing creep rate, cannot be merely an artefact of creep rates, but must represent an intrinsic magnetic moment and critical current density that are increasing with field in this field range. The measurements were repeated on the decreasing field leg. Figure 5 shows the creep rate at different fields and Figure 6 plots the magnetic moment, together with the creep rates S and NS. The overall similarity of Figures 5 and 6 (decreasing field) to Figures 3 and 4 (increasing field) demonstrates that the main features of the behaviour of the creep rates above and below the fishtail peak are independent of the direction of field sweep. Discussion
Firstly in this section we give a brief description of the models most commonly suggested to explain the fishtail
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creep at fields of (a) 0.1, (b) 0.2, (c) 0.3, (d) 0.4, (e) 0.5 and (f) 0.8 T is shown here, for the increasing leg of the m - H loop
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354
Cryogenics 1993 Vol 33, No 3
Fishtails, scales and magnetic fields: L.F. Cohen et al.
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Equivalently, the field change required to reverse completely the screening current direction when the field is reversed also increases. This implies that either the core pinning or the surface pinning/surface barrier has increased. Kopylov et al. merely speculate that the latter is the cause and cannot eliminate the former from suspicion.
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effect. Then we outline aspects of the measurements described in the previous section relevant to the models, and discuss the likelihood of that particular model accounting for the behaviour observed.
Models (1) Josephson junction model. The Josephson junction model ~'5'6 suggests that the sample contains large regions separated by oxygen-poor material, which effectively create a granular material. It then follows that the magnetization is made up of several current contributions. Inter-regional currents dominate at low fields, and the minimum in the magnetization is attributed to the start of phase decoupling between the regions. The maximum in the magnetization is the signature that all the regions have decoupled and the regions are acting independently. Immediately beyond the field at which the maximum occurs, the magnetization is dominated by intraregional currents. These flow on a length scale corresponding to the size of the regions. (2) Microstructural model. Another model 2'8 related to the oxygen deficiency 6 suggests that there are microstructural regions in the material which are superconducting, but with a significantly lower Hc2 than the bulk. These regions start to turn normal at the field corresponding to the minimum in the magnetization, and have all done so by the field corresponding to the maximum. These microstructural normal regions then act as pinning centres and increase the critical current, and hence the magnetization also. (3) Flux lattice phase change. It has been suggested 9 that the fishtail peak in the magnetization is related simply to a change in flux creep dynamics, by analogy with low field behaviour ~5 at fields much lower than those we are concerned with here. Evidence for the phase change would be apparent in the first few decades of flux creep decay~6. (4) Surface barrier effects. Kopylov et al. ~0, using a length scale type of argument, pointed out that dM/dH, the reverse leg susceptibility, is the same for all fields, yet the magnetization M increases with increasing field.
If the breaking up of the critical current path outlined in the Josephson junction model (1) were occurring in our samples, the length scale analysis would reveal it. Instead, our length scale measurements show that the sample is fully connected up to fields well beyond the anomalous peak in the magnetic moment. This is in agreement with previous reports 4. On the other hand, the length scale analysis would not detect microstructural normal regions associated with model (2), which are probably created by oxygen-poor material*. There is no solid evidence for a surface barrier/surface pinning model. The observed increase of magnetic moment with field implies that the pinning strength is increasing, but this could result just as well from an increase in core pinning as outlined in the microstrucrural model t. Moreover any surface mechanism should introduce asymmetry in the magnetic moment between increasing and decreasing fields in the sample. At low temperatures some differences in the size of the magnetic moment signal between the two sweep directions have been observed j4. We have seen some small shifts of the peaks with field sweep direction (care must be taken to avoid experimental artefacts), but they tend to be in the opposite direction from the shift expected from a surface barrier. We do not observe any distinctive change in the form of the flux creep as the field changes through the fishtail peak. Although the creep is not strictly logarithmic with time, the deviations from logarithmic behaviour are not more marked on one side of the peak than the other. Therefore, we can infer that no pronounced change in the flux lattice occurs at the fishtail peak. The steady increase in the flux creep rate [Figure 6, curve (c)] at fields approaching the fishtail peak is significant. In fact, it looks plausible that at time t = 0, the peak in the magnetization is coincident with the peak in S (see Figure 7). The simple flux creep theory of Anderson and Kim ~7 implies that U~,, the pinning energy (to be understood here as representing some appropriately weighted average), is decreasing as the field increases toward the fishtail peak. We suggest that more pinning centres are being added (hence an increase in m), but that they are ones that are rather shallow (so that the average value of U,, decreases).
* There is a wealth of evidence related to the oxygen deficiency ~il 3.18. It appears probable that reducing the oxygen from a fully oxygenated crystal would first introduce microstructural pinning sites and then large scale granularity 2. But the effect of oxygen on the fishtail peak needs much more detailed measurements than have yet been performed + A specific test of whether surface or core pinning is dominant would be to examine systematically the variation of normalized penetration field with oxygen deficiency
Cryogenics 1993 Vol 33, No 3
355
Fishtails, scales and magnetic fields: L.F. Cohen e t al.
I I
Acknowledgeme'
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W e would like to th; ductivity, in partic D . N . Zheng, for measurements on f by the Science and
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k the Cambridge I R C in Superconar A. Campbell, J. Johnson and dndly allocating time for these ~ir V S M . The w o r k was supported ~ngineering Research Council.
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References
1 Osofsky, M.S., Co_n, J.L., Skelton, E.F., Miller, M. et aL Phys Rev B (1992) 45 49t6 2 Daeumling, M., Seuntjens, J.M. and Larbalestier, D.C. Nature
Applied Field
Figure 7 Schematic field variation of the inferred 'instantaneous' magnetization Mo at time t = 0 and the measured Mt at time t; the fields at the two maxima differ because of the field dependent creep rate S/Mo
Conclusions
The length scale analysis shows that our crystals are fully connected up to fields well above the fishtail feature, so that the latter is not caused by an onset o f some kind o f large scale granularity. Our observation o f the variation o f the flux creep rate with field in the vicinity o f the fishtail suggests that the latter is associated with some m o r e microscopic aspect of the samples, for example the addition o f many shallow pinning centres as the field increases. This is in agreement with a previously suggested model, in which microstructural oxygen-deficient regions turn normal in increasing field, and so provide the additional pinning centres needed to generate the fishtail feature.
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(1990) 346 332 3 Laverty, J.R. and Cohen, L.F. Phy Rev B submitted for publication 4 Welp, U., Kwok, W.K., Crabtree, G.W., Vandervoort, K.G. et al. Appl Phys Left (1990) 57 84 5 Keller, C., Kupfer, H., Gurevich, A., Meier-Hirmer, R. et a/. J Appl Phys (1990) 68 3498
6 Kupfer, H., Apfelstedt, I., Flukiger, R., Keller, C. et aL Cryogenics (1989) 29 268 7 Campbell, A.M. and Evetts, J.E. Critical Currents in Superconductors Taylor and Francis Ltd, London, UK (1972) 193 [reprinted from Adv Phys (1972) 21 (90)] 8 Vargas, J.L. and Larbalestier, D.C. Appl Phys Lett in press 9 Chiknmoto, N., Konczykowskl, M., Motohira, N., Kishio, K. et al. Physica C (1991) 185/189 1835 10 Kopylov, V.N., Koshelev, A.E. and Sehegolev, LF. Physica C (1990) 170 291 11 Bean, C.P. Rev Mod Phys (1964) 36 31
12 Angadi, M.A., Caplin, A.D., Laverty, J.R. and Shen, Z.X. Physica C (1991) 177 479-486 13 Yeshurun, Y. and Malozemoff, A.P. Phys Rev Lett (1988) 60 2202 - 2205 14 Weir, S.T., Nellis, W.J., Daliehaoueh, Y., Lee, B.W. et al. Phys Rev B (1991) 43 3034-3041 15 Svedlindh, P., Rossel, C., Niskanen, K., Norling, P. et al. Physica C (1991) 176 336-346 16 Malozemoff, A.P. Physica C (1991) 185/189 264-269 17 Anderson, P.W. and Kim, Y.B. Rev Mod Phys (1964) 36 39
18 Angadi, M.A., Shen, Z.X., Caplin, A.D., McCartney, D.G. etal. Supercond Sci Technol (1992) 5 165-168