The irreversibility line and flux creep

PHYSICA

Physica C 194 ( ! 992 ) 194-202 North-Holland

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A c o m p a r a t i v e s t u d y o f B a l _xKxBiO3_,~ a n d Y B a 2 C u 3 0 7 _ , ~ Y.Y. X u e , Z J . H u a n g , H . H . Fang, W.C. C h a n , P.H. H o r a n d C.W. C h u Department of Physics and Texas Center for Superconductivity at the University of Houston, Houston, TX 77204-5932, USA M.L. N o r t o n ~ a n d H.Y. T a n g Department of Chemistry, University of Georgia, Athens, GA 30602, USA Received 2 December 1991

The relative flux creep rate S(t) = d In M/d In t of a single crystal of Bai _xKxBiO3_,~(BKBO) was measured up to a few degrees Kelvin below the irreversibility line. It is nearly constant at low temperatures but rises sharply after a threshold temperature Tt. Above Tt, the creep changesfrom logarithmicto non-logarithmicdecay.All these are very similar to those observed in Y~BazCu3OT_,~ (YBCO) samples and suggest a flux-lattice phase sub-boundary. The ratio between the boundary field Bt and the irreversibility field B~falls between 0.15 and 0.25 for both BKBO and YBCO at various temperatures, implyinga possible close relationship between the boundary and the irreversibility line.

I. Introduction High temperature superconductors (HTS's) form one of the most effective testing grounds for vortex lattice dynamics. As a result, many unexpected phenomena have been discovered and models suggested. Among them are an irreversibility line far below [ 1,2 ]; the proposed lattice melting [ 3,4 ]; a possible vortex glass transition [ 5 ]; and the anomalous universal giant flux creep [2,6 ]. Various theoretical models have been proposed to account for the magnetic properties of HTS either by modifying the traditional individual pinning to allow for the relatively weak and dense pinning centers [7,8 ], by emphasizing the lattice softening due to the thermal entropic contributions [9-1 1 ], or by balancing the lattice distortion with the pinning energy and the %1.1 1 V l l l ~

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glass model ) [ 12-14 ]. To test these proposals, a systematic comparison of various compounds would be helpful. The recent observation [ 15 ] of a new vortex phase boundary further stimulates this investigation. Permanent address: Departmenl of Chemistry. Marshall University, Huntinglon. Wesl Virginia 25755, USA.

As part of this investigation, the respective magnetic properties of Bal_xKxBiO3_6 (BKBO) and YBaECU307_a (YBCO) have been measured and compared. BKBO and YBCO (along the a, b-plane) both have comparable short coherence lengths ~ but their anisotropy is very different. Some of the magnetic properties of BKBO have been reported before [ 16,17 ]. However, the BKBO relaxation data in ref. [17] is limited to far below the irreversibility line and is not self-consistent. It shows that the compound has a rather low irreversibility line, but a relative flux creep rate three times slower than that of YBCO. Assuming that the relaxation is a thermallyactivated process, the irreversibility line would correspond to the locus of Uerr(T, B) ~ k T with Uerrbeing the characteristic creep barrier and the relative creep rate S(t) = d In M / d In t would be proportional to k T / r_~, where M is the magnetic momen! and t is the measured time. if L½rf has similar temperature-dependence in reduced units for both YBCO and BKBO, one would instead expect a higher irreversibility line for BKBO. Such contradictory evidence makes a quantitative comparison difficult. Because the uncertainties are rather large in powder or ceramic samples, and good-quality single crystal BKBO

0921-4534/92/S05 00 ¢5 1992 Elsevier Science Publishers B.V..All rights resem'ed.

Y. Y. Xue et al. / Irreversibility /i,e and flux creep

and YBCO samples are now available, a careful investigation was carried out. The resulting irreversibility line of BKBO is much higher in line with the lower creep rate. The relative creep rate S ( t ) of BKBO at low temperatures, is temperature-independent and about three times slower than that of YBCO; however, the S(t) rises sharply as it crosses a threshold Tt. Across Tt the decay also changes from logarithmic to non-legarithmic in the given time window, which is very similar to that of YBCO, and might be identical to earlier observations in PbMo6S8 [ 18 ] and BiESrCa2Cu208 [ 19 ]. Scaling with the irreversibility field Bt at the same temperature, the reduced threshold fields Bt/B~ fall between 0.15 and 0.25 for both BKBO and YBCO at various temperatures. Fitting the relaxation data with the collective pinning/vortex glass models, the parameter /t changes from ~ 1 to ~ ~ when the temperature rises past Tt, suggesting that the low energy excitation mode of the flux lattice changes across Tt [ 12 ]. All these imply a new flux phase boundary, which is rather universal and closely related to the irreversibility line.

2. Experimental A BKBO single crystal ( x = 0 . 4 ) was prepared as described in ref. [20]. The sample dimensions are 2.4× 1.6X 1.2 mm 3. A four probe resistivity measurement shows a superconductive transition onset Ted of 31.4 K and a sharp transition width AT~ 2 K, indicating the high quality of the sample. The YBCO samples used were me!t-textured ingots [21] and single crystals [22]. The ingots are laminates of highly oriented quasi-single-crystal grains with a thickness of 10 to 20 lam. Typical Ted is 92 K with AT~ 1 K. Typical room temperature resistivities are 200 ~tf~cm for the single crystals and 200 to 300 ~tf~cm for the melt-textured ingots. lkA[,acrn~ll'~t', tvJttt~aa~.,tt~,

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mercial Quantum Design SQUID magnetometer. The zero field-cooled (ZFC) and field-cooled (FC) magnetization were measured at 2 . 5 0 e . The ZFC transition width (10% to 90%) is~ 5 K [27]. After correction for demagnetization, a shielding effect of nearly 100% by volume was obtained from the ZFC data of the BKBO single crystal, but the FC moment

i 95

was only 10% of that of the ZFC, indicating strong pinning in the sample [23]. For purposes of scaling, the upper critical field Be2 and the irreversibility field Bi of BKBO have been extracted from the data. Be2 was determined as the

onset field of the diamagnetic superconductive signal and the irreversibility line (Ti, Bi) was defined as the point where the deviation between the ZFC and FC magnetization data is observable [ 27 ]. They have rather large uncertainties and depend on the measurement sensitivity. To reduce these uncertainties, the same procedures and criteria were used for BKBO and YBCO. Typical sample signals were 10-2 to 10 -3 emu. Fluctuations of the signals and 0ackground noise level were 10-5 to 10 -6 emu. The estimated repeatability of these moments was better than a few percent. Measuring the relaxation rate is a delicate job, especially at higher T and B. Artifacts were primarily caused by [ 24-26 ] ( 1 ) the sample not being in the critical state, (2) the sensor drift of the magnetometer after a change in field, and (3) magnetic field disturbances around the sample either due to the field drift or inhomogeneity along the sample scanning length. At higher )'and B, the trapped field decreases and the effect of external field disturbances become very serious. It is for this reason that most early published data is limited to lower temperatures [24,25 ]. To overcome such difficulties and extend the measurement close to the Jrreversibility line, larger samples and special measuring procedures were used, thereby increasing the trapped field and reducing the field ripple during the measuring period. Measurements were taken under the following conditions [ 26 ]: (1) we increased the sample size to ensure the trapped field would be larger than few G, (2) we used a short SQUID scanning length, normally 1 cm, (3) in the field increase branch, we suspended the sample a few cm above the center of the magnetometer and mechanically dropped the sample into the center of the magnetometer to refresh the sample's critical state, as previously successfully demonstrated [ 15 ], and (4) in the field decrease branch, we put the sample in the center of the magnetometer and, after the de-

Y. Y. Xue et al. / lrreversibility line and flux creep

196

creased field stabilized, suddenly increasing the temperature of the sample a few degrees to refresh the sample's critical state, a method suggested in ref. [ 24 ]. To check for possible experimental artifacts, a YBCO sample was measured close to the irreversibility line. First the relative flux creep rate S ( t ) = d l n M ( t ) / d l n t was measured using various scanning lengths and sample sizes. The data for scanning lengths less than 2 cm were identical (fig. 1 (a) ). Second, the data obtained from the field increase and the field decrease branches were compared (fig. l(b) ). They are within an experimental resolution -2

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of 10% after subtracting the equilibrium momentum contribution extracted from the M - H loop. That demonstrated that the measurements are reliable and the surface creep barrier is not a main factor in this case. At lower T and B the possible error would be even smaller.

3. Results and discussion

3. I. The irreversibility line For the single crystal of BKBO, the extracted d8~2/ dT was - 0 . 5 7 T / K near Too, which is very close to the data in ref. [ 28 ]. The irreversibility temperature was defined as the merging points of the ZFC and FC moments at the field. The extracted irreversibility line of the BKBO single crystal has been measured between H = 0 . 5 and 5.5 T (fig. 2(a) ). The resuits can be expressed as Bi = Bo ( 1 - 7"/Tc)B (fig. 2(b) ) with Bo~ 20 T andfl~ 1.5 where Tc is the critical temperature of BKBO. The Bi obtained is much higher than that of ref. [ 17 ] and is in line with a lower creep rate. The published irreversibility line data of YBCO are rather scattered and seem to depend on the measurement timescale and resolution. To make the comparison meaningful, a YBCO melt-textured ingot was also measured. The data follows Bi=Bo( 1 - T/Tc) #. Iffl is fixed at 1.5, Bo would be 70 T, both of which compare favorably with published d a t a : / / o = 5 0 T, 1/=1.48 [29] and Bo=66 T,

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The irreversibility lines of HTS's have been interpreted as depinning lines in the individual pinning model or glass transition line in the vortex glass model. Distinguishing them decisively by the position of the irreversibility line is rather difficult. However, the general trend is still very different for these two models. In the case of individual pinning

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between the pin,ring strength and thermal energy. As a result, the irreversibility line and the Jc should have a positive correlation. For the glass transitiorf/collective pinning model, no quantitative prediction of the irreversibility line is available at this moment. However, the irreversibility line would be insensitive Io the details of the pinning and follow the trend

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ing BKBO, YBCO, T! and Bi compounds, the irreve~itfility line does change widely and follow the trend of ~. and the anisotropy; the isotropic BKBO has a mu~h higher irreversibility line than YBCO. Such observations are difficult to explain in the context of isolated vortex pinning. It seems that the vortex interaction plays a role and prefers the collective pinning model.

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3.2. Flux creep near the irreversibility line

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of both ~ and the anisotropy as a result of competition among vortex lattice rigidity, thermal wandering, and pinning strength which is largely determined by the vortex thermal wandering [8 ]. Our data show that the reduced irreversibility field B~/B~2 of BKBO is three times higher than that of YBCO at !he sam__ereduced temperature T~ T~. That is in an opposite trend with the values of the J~s: the Jc is 10 3 A / c m 2 for the BKBO single crystal and 5 X 10 4 A / c m 2 for the melt-textured YBCO sample at the same reduced temperature T/T~,,,O.84 and zero external field. It seems that the irreversibility line is insensitive to the pinning strength and the critical current density. On the other hand, compar-

A more critical examination of those models involves the flux relaxation and the I - V characters. Various models give different predictions. They include the function-dependence of M(t), the temperature-dependence of the relative decay rate S(t)=dlnM/dlnt, and the temperature-dependence of the effective creep barrier U~a,(T, J). Each can be verified experimentally. For the functional-dependence of M(t), the individual pinning models [ 32,33 ] predict a logarithmic decay with an exponential tail. The collective pinning models [ 13 ] and vortex glass models [6 ] proposed a decay form of M ( t ) zc 1 / [In(t/to) ]1/,,. which is the result of an I-I" characteristic in which |xexp[- (IT/I)"]. Mathematically lhe two cases can be verified bs the time-dependence of S{ f) and the decay rate R(t) = d M / d Int. On one hand a logarithmic decay a n d / o r exponential tail mean that the S{ t) will increase with lhe increase of t. Especially in the case of logarithmic decay, the R (t) is constant over the full time range. As a result, if d M / d t can be fit as t - " , R( t ) ~: t( cL~I/dt ) = t ~-'~ which would be constant for a = 1. The deviation from perfect logarithmic decay (R (t) = constant ) should be represented by a - 1, as suggested by Safer et al. [ 19 ]. The decay form of 1/ [In(t/to) ]~/;', on the other hand, introduces S ( t ) . which decreases with t. A power law decay M ( t ) ~ t -~ is also possible between the two extreme cases. Such decay is equivalent to a power law I-V characteristic [34] where V~:I" with n = ( f l - 1 ) / b . This would also imply a logarithmic I - V dependence of the effective pinnir.g potential L½rf=l..b.(T)in(Io/I) [35]. The value of S ( t ) would be a time-independent constant in such decay. Many experimental fitting are required to check

!98

Y.E Xue et al. / Irreversibilitylineandflux creep

the time-dependence of S(t). In some situations, the dependence would be so small that it would be hard to draw a conclusion. To make that clear, d In S ( t ) / d In t is calculated as a measure of time-dependence. For logarithmic decay, M ( t ) ~c 1 - a l n t, d In S ( t ) / d In t= ( a - a 2 1 n t) ~ a ~ S ( t = O ) . In other words, an increase of S(t) would be obvious only if the decay rate is large. At low T and B, the flux creep rates are usually rather small (a ~ 0.02 ). Within a reasonable time window, the difference between logarithmic and non-logarithmic decays, judged by d In S ( t ) / d In t is often masked by the experimental resolution. Extending the experimental region closer to the irreversibility lines to increase the decay rate and the difference would be helpful. For the vortex-glass type of decay, the situation is slightly different. In such a case, S ( t ) = l/IAn(t/Zo) [61, and d l n S ( t ) / d l n t = 1/ ln(t/zo) = ItS(t). Close to the irreversibility line, although S ( t ) is larger, but a small/z as the data suggest, makes the difference between the power law and the vortex glass rather small even near the irreversibility line. A quasi-power law decay can have various origins. It can be a result of the special shape of the pinningpotential well in the individual pinning model as suggested by Zeldov et al. [35]. It also could be a result of a very small parameter/t, as we calculated. One way to distinguish the two cases is to measure the temperature-dependence of the effective pinning potential ~ f f = Uj( T)ln (Jo/J). According to Zeldov et al. [ 35 ], the parameter Uj(T) is the real characteristic pinning strength. In their model, Uj(T) is expected to change with T and B the condensation energy roughly as [ 1 - (7"/To) ]". However, for a collective pinning/vortex glass model, the relationship is not necessary true. To compare the above predictions, a single-crystal BKBO sample and several melt-textured or single crystal YBCO samples (with HIIc) were measured up to a few degrees below the irreversibility line. The functional-dependence of the decay of YBCO and BKBO are very similar. Several typical relaxation curves are shown in fig. 3(a) (for YBCO) and fig. 4 (a). At low temperatures, the decay rates S(t ) of each sample are small. This is especially true of BKBO, where S(t) is 0.005 at 15 K and 0.5 T. Such a low creep rate is in line wflh the higher irreversibility line. In such a case, both decay quasi-loga-

rithmically within a time window of 10 to 10 4 S. To clarify this, the decay rate dM/dt is fitted at t-'~ (fig. 3(d) and 4 ( d ) ). tx is roughly 1 for both BKBO and YBCO at lower temperatures. At higher T, the current window is widened and the deviation from the logarithmic increases. For example, the persistent current density decreases 50% and the corresponding decay rate R (t) = d M / d In t (which is a constant for logarithmic decay) decreases more than two-fold within the time window of I to 500 min at 65 K and 5 T. In figs. 3(d) and 4(d), it is obvious that the parameter a increases from 1 after a threshold temperature, suggesting that the original Anderson-Kim models [32,33] cannot properly describe the decay at higher T. However, it is still impossible to distinguish the power law decay from the vortex-glass type of decay in our case. Our data for YBCO can be equally well fitted as power law or M ( t ) ~ 1/[ln(t/ro) ],/u with /z<
Y. Y. Xue et al. / IrreversibiStv line and flux creep

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Fig. 3 (a) M ( t ) us In t of a melt-textured YBCO at 77 K and 2 T: ( O ) data, ( - - ) fit with 1/ [ In ( t~ ro ) ] ~/~ with/t ~ 0.18 5 and ro = 10- ~o s, ( - - - ) fit with t ~ where fl= - 0 . 2 2 . ( b ) S ( 10 m i n ) us T a t H = 2 T for YBCO. (c) Parameter a vs T a t H = 2 T for YBCO (see text). ( d ) Collective pinning fitting parameter/t vs Tat 2 T for YBCO ( t o = 10-~o s).

The temperature dependence of S ( t ) is also very similar for YBCO and BKBO. The relative decay rate S ( t ) at a fixed time ( 10 rain in figs. 3(b) and 4 ( b ) is approximately temperature-independent at low T, which is similar to early reported YBCO results [ 6 ]. (The choice of the fixed time is not critical, a quasipower law decay suggests a roughly "ume-mu~p~n--"--'dent S ( t ) . ) Such temperature-dependence is a puzzle for the individual pinning models but rather natural in the collective pinning/vortex glass models [6]. Our results suggest that the phenomenon is rather common for oxide superconductors.

3.3. A sub-phase-boundary below the irreversibility line

We have observed a vortex phase boundary far below the irreversibility line in YBCO [15,37]. The boundary T, is characterized by the following. I ]

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Fig. 4, (a) Typical relaxation data for the BKBO single crystal: ( O ) 28 K (M: 10- 4 emu ), ( [] ) 24 K (M: 10- 3 emu ), ( A ) 15 K (M: 10-: emu ). ( b ) S( 10 rain ) vs T for BKBO at ( A ) 0.1 T and ( [--t) 0.5 T. (c) S( 10 rain ) us H at 5 K for BKBO. (d) The parameter ot us T for BKBO at 0.5 T (the parameter a is extracted from fitting dM/dt,,, fit -").

cay part f r o m the non-logarithmic part in our t i m e window ( I0 to 10 4 s; fig. 3 ( c ) ). At low T, part of the data are scattered due to smaller current density window (fig. 3 ( c ) ) but the trend is still clear in the a versus T plot. (3) The data can be fitted to the proposed vortex glass model [6,13] M ( t ) x 1 / ( l n t / r o ) ~/~'. It has been d e m o n s t r a t e d that flux creep in H T S is never exactly logarithmic [38,39]. However, the deviation from the logarithmic decay will d e p e n d on both # and Zo in a given time window. A s u d d e n increase of the deviation implies a quick change o f p a n d / o r %. An accurate regression to separate the two factors is difficult. Nevertheless, for a reasonable ro between 10-mo to 10 e s, the/a is always smaller than I above 7,. As-

suming 7:o~ 1 0 - ' o s, p will be ~ 1 at low temperature and decrease after across Tt up to ~ ~i (fig. 3 ( d ) ) . Similar b e h a v i o r has been observed in BKBO (fig. 4 (a), ( b ) , (c), a n d (d), suggesting that such a boundary might be a general p h e n o m e n o n . These observations suggest that 7", is a vortex-phase boundary in the T, B-plane (fig. 2 ( a ) ) a n d that the flux creep rate changes sharply as it rises through that plane. Using the irreversibility field Hr as the scaling factor to plot the boundary field H, as a function o f the reduced t e m p e r a t u r e (fig. 6), the new boundary seems to be a rough constant. The ratio B,/Bi for BKBO and Y B C O is not too different although they have very.' different anisotropy. This p h e n o m e n o n might be universal. Early pub-

Y.Y. Xue et al. / lrreversibilii • line and f l u x creep. 0.3

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r.e~ult of the decrease of the creep barrier, which begins at Tt. The vortex glass model does not describe the change o f / t in detail. The vortex glass state at low temperatures has been regarded as structureless. On the other hand, the collective pinning model predicts some structures in the vortex glass state, characterized by the value of/t and the dimensionality of the vortex bundle [ 13 ]. However, the predicted /1 changes from ~ ~ at low temperatures to ~ 1 at high temperatures [ 13 ] which is in conflict with our observation. Recently, our short time relaxation data [ 40 ] suggested that there is a two-plateau feature in the/t value./t ~ 0.5 near the irreversibility line, ~ ~ 2.5 at lower temperatures, and the transition between the two plateaus is coincident with the new boundary. Similar phenomena [41] has been observed in transport E - J characteristics of YBCO thin films. Dekker et al. [41 ] interpret it as a transition between the vortex-glass state and the collective-pinning lattice-state. More investigation seems necessary. In summary, a comparison of BKBO and YBCO shows that the irreversibility line is unlikely to be the simple depinning line of isolated single vortex pinning. Flux creep at high H and T suggests a new vortex-phase boundary which might be closely related to the irreversibility line.

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Fig. 6. B*/Br vs T~/T¢ for ( O ) melt-textured YBCO, ( [] ) singlecrystal BKBO, ( A ) ceramic Bi2122 [ 19 ], and ( @ ) single-crystal PbMo6S8 [ 18 ].

lications suggested that there might be a boundary in the T, B-plane separating the logarithmic from the non-logarithmic decay regions for Bi2122 [ 18 ] and PbMo6S8 [19]. These proposed boundaries scaled with the corresponding irreversibility field Bi also are plotted in fig. o. l ne data are scattered but, considering the different measuring methods and the uncertainty of these boundaries, they still fall inside a broad band and could be manifestations of the same phenomenon. Further investigation is under way. If such a guess were proved, it would suggest a close relationship between the irreversibility line and the new phase boundary, i.e. the irreversibility line is a

Acknowledgement We would like to thank R.L. Meng and Y.K. Tao for the melt-textured and single crystal YBCO sampies. This work is supported in part by the NSF Low Temperature Physics Program Grant No. DMR 86126539, DARPA Grant No. MDA 972-88-G-002, NASA Grant No. NAGW-977, Texas Center for Superconductivity at the University of Houston, and the T.L.L. Temple Foundation. The work at the University of Georgia is partially supported by the SURA/ORAU/ORNL Summer Cooperative Program i 990.

References [ 1 ] K.A. MiJller, M. Takashige and J.G. Bednorz, Phys. Rev. Lett. 58 (1987) 1143.

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Y. Y. Xue et al. / lrreversibilio, line and flux creep

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