magnetic relaxation of highly textured bi2sr2cacu2o8+delta polycrystalline fibres

ELSEVIER Physica C 271 (1996) 133-146

PHYSICA

Magnetic relaxation of highly textured Bi 2 Sr2CaCu208 + polycrystalline fibres

E. Martinez, L.A. Angurel *, J.C. Diez, F. Lera, R. Navarro lnstituto de Ciencia de Materiales de Aragdn, CSIC Universidad de Zaragoza, Centro Polit~cnico Superior de Ingenieros,

Maria de Luna 3, E-50015 Zaragoza, Spain

Received 5 July 1996; revised manuscript received 31 August 1996

Abstract

The magnetic relaxation of Bi2Sr2CaCu2Os+ ~ superconducting highly textured polycrystalline materials (fibres) grown by laser induced floating zone melting methods have been studied using ac susceptibility and dc magnetisation techniques. Effective pinning energies, Uef f, have been derived for a wide range of current densities, J, and magnetic fields both parallel and perpendicular to the fibre axis. In agreement with the microstructure Ueff.ll(J) > Ueff, ± ( J ) and approximately follows for both orientations the phenomenology observed on single crystals for c-axis parallel fields. Near the irreversibility line Ucff is J independent, expressed as: Ueff(T,B) ~ Ueff(0 K,1 T)B-°'5(1 - T/Tc ) . Moreover, both Ueef, ll(J) and Ueff. ± ( J ) values are higher than analogous U~ff, c values on single crystals. Accordingly, for a given temperature the irreversibility line appears at larger fields, about ten times for fields perpendicular to the fibre axis and even higher in the parallel case. A careful analysis of the pinning energy distributions in fibres has been undertaken showing the presence of a high energy shoulder, absent in unirradiated single crystals.

PACS: 74.60G

Keywords: BSCCO; Magnetic relaxation; Superconductivity

1. In t roduc t ion

In order to improve the current carrying properties of high temperature superconducting (HTS) ceramics a wide set of texturing techniques have been searched. Nowadays textured HTS materials such as thin and thick films, tapes, wires, and so on have been exten- sively prepared and studied. Texturing processes are directed towards enlargement of the surface between

* Corresponding author. Fax: + 34 76 761957 e-mail: [email protected].

adjacent grains, improvement of their electric junc- tion strength and better alignment of the a -b-p lanes which contain the superconducting pairs, with the macroscopic current flow. In this way, some of the limitations related to the polycrystalline nature of HTS materials (porosity, weak inter-granular links, cracks, defects, secondary phases . . . . ) as well as to their high anisotropy may be overcome. A compari- son of the two most promising HTS families (with respect to their potential applications), follows for Y - B a - C u - O (YBCO) and B i - S r - C a - C u - O (BSCCO). The plate-like morphology of Bi-based

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134 E. MarKnez et al. / Physica C 271 (1996) 133-146

superconductors, Bi2 Sr2CaCu208 + 8 (BSCCO-2212) and (Bi,Pb)2Sr2Ca2CU3Ol0+~ (BSCCO-2223), is ideal for the development of textured bulk products by mechanical deformation and by the application of thermal gradients [1]. Nevertheless, the inherent limi- tation due to thermal activation, which strongly depends on their anisotropic characteristics ( F - 3 0 0 0 for BSCCO-2212 [2]), reduces their range of applica- bility to temperatures below the irreversibility line, Tirr(B), which occurs at lower temperatures than in YBCO (123 phase).

The vast set of experimental results on 2212 thin films and single crystals have shown the two-dimen- sional (2D) behaviour of this material [3-5]. The coherence length along the c-axis is smaller than the distance between the a-b-planes; consequently, the superconducting layers are extremely weakly cou- pled. Thus, they have been analyzed as strong superconducting 2D systems with a weaker Josephson coupling in the c-direction [6] suggesting a picture of 2D vortex pancakes. For temperatures below a crossover value, T*, (near T c for BSCCO-2212) the magnetic flux component along the c-axis is the major factor responsible for dissipation, because its projection into the a-b-plane is strongly pinned between adjacent superconducting layers (intrinsic pinning) and are energetically favoured to stay within. Consequently, the magnetic properties do not depend on B but on the effective magnetic field, Bef f, defined as: Bef f=B(F -I cos20+sin20) I/2, [7-9] where 0 is the angle between B and the a-b-plane. Because of their high anisotropy, in 2212 single crystals, except for very small 0 values Beff, is given by ~ B sin0, i.e. by the component of the field parallel to the c-axis, BiI,c.

Thermal activation processes in BSCCO-2212 single crystals, for fields along the c-axis, have been widely studied. Non-linear logarithmic time decays of the isothermal magnetisation [10,11] have been observed at high temperature while they become logarithmic at low temperatures. Moreover, power- law dependencies of the effective energy barrier with the driving current, Ueff(J ) OC J - g [11,12], are found where p, depends on J and on the pinning dimensionality. This is consistent with the predictions of collective flux creep [13] and vortex glass [14] theories for 2D systems. In the low field limit and for current densities far below the critical current density

increases of J accompanied variations in the flux bundle sizes from small through medium to large, with corresponding p, values of 1/2, 13/16 and 7 /4 , respectively [13]. When J is reduced, however, plastic creep effects take place, and Ueff(J) does not diverge; a rather weak logarithmic increase is observed instead when J approaches zero [12]. On the other hand, some experimental observations have shown a different behaviour of Uef f for fields parallel to the a-b-planes [12]. The experimental /z changes with the temperature in a similar fashion to the YBCO-123 3D system [15]. For the general case of an applied magnetic field forming an angle 0 with the a-b-plane, Uef f depends on the component perpendicular to the CuO 2 planes, that is Bef f [16].

Besides the complexity of BSCCO ceramics, a series of studies has also contemplated the thermally activated dissipation of textured polycrystalline materials like c-axis 2212 thin films [17-19], Ag- sheathed 2212 wires [20] and 2223 tapes [12,21] and other compacts [22]. The similarities and differences of pinning energy distribution functions and values compared with single crystals behaviour has moti- vated the present research. The possibility to change the c-axis texture, grain sizes and secondary phase content in a continuous manner on BSCCO fibres [23] and the correlation of magnetic properties with texture have been determinant in the ultimate selec- tion of this material. Accordingly, using fibres with a well characterized microstructure, a systematic study of the magnetic relaxation has been performed to provide insights into the intergranular coupling and intragranular flux pinning. From their analysis, the effective pinning energy Ueff(J,T,B), as well as the energy distribution will be obtained and compared with the observations in single crystals.

2. Experimental

2.1. Material fabrication and characteristics

BSCCO-2212 fibres of ~ 1 mm diameter and ~ 100 mm in length with Jc(77 K) values up to 4000 A cm -2 in the self-field have been produced by the laser induced float zone melting (LFZ) method [1 ]. The action of very high thermal gradients to- gether with the anisotropic growth habit favour the

E. Martfnez et al./ Physica C 271 (1996) 133-146 135

cuts are shown. The dark lines correspond to secondary Ca -S r -Cu oxides while gray ones correspond to mixtures of BSCCO phases. Long grains, elongated along the a-axis and pointing in the growth direction, form thin platelets (c-axis) with average sizes dependent on the growth rate and laser source which, in the shown micrographs, are 100 × 15 × (0.1-0.3) p,m 3. In longitudinal cut micrographs, the a-b-plane texture of the BSCCO grains may be characterized by their distribution of angles a i with respect to the fibre axis, giving average (I c@ values which depend on the fibre growth rate. However, provided that the grains are small enough compared with the fibre diameter, they should be randomly distributed in the fibre's transversal cuts. For the fibre grown at 15 m m / h a value of (Ic~,l) = 7.7 + 1.4 °, has been estimated from digitized SEM micrographs of several polished longitudinal cuts of epoxy embedded fibres, using conventional image analysis [231.

2.2. Experimental techniques

Fig. 1. Backscattered electron SEM images of a polished transversal (a) and longitudinal (b) cut of an epoxy embedded LFZ fibre, grown at 15 mm/h with a CO 2 laser, before annealing. The dark lines correspond to secondary phases while gray ones are different mixtures of BSCCO related oxides (2201 and 2212 phases).

alignment of the grains along the fibre axis, giving rise to a conical grain distribution. Fibres grown at different rates from 5 to 70 m m / h using two different laser sources (CO 2 and Nd:YAG) have been studied. Most of the measurements here reported, however, have been performed on a representative fibre grown with a CO 2 laser at pulling rates of 15 m m / h and a rotation rate of 24 rpm in a system described elsewhere [1].

Starting with the ideal 2212 stoichiometry, as grown fibres show a mixture of superconducting and secondary phases which, upon annealing at 855°C during an optimum period, become almost single 2212 phase [23]. The microstructure of a fibre grown at 15 m m / h may be observed in the SEM micrographs of Fig. 1 where longitudinal and transversal

Cylindrically shaped samples with a diameter of ~ 1 mm and lengths of L = 5 mm have been used in the measurements here presented. Magnetic ac susceptibility, Xac, and dc magnetisation, M, measurements were performed in a Quantum Design SQUID magnetometer for fields parallel (BII) and perpendicular (B±) to the fibre axis. In-phase (X ' ) and out- of-phase (X") components of the ac susceptibility were recorded. Frequencies ranking from 0.1 Hz to 1 kHz; driving ac fields (b 0) up to 0.45 mT and superimposed parallel dc fields (B) up to 5 T were used in a wide temperature range. In the study of the magnetic relaxation in the dissipative regime and in the determination of the irreversibility line, field cooling procedures (FC) from temperatures well above T c were followed. Measurements of the magnetisation time decay M ( t ) were performed in zero field cooled (ZFC) runs up to 10 4 s. The characteristic time (dead time) required by the SQUID system to give a significant output after switching-on the field was 50 s. In addition, isothermal magnetic hysteresis loops M ( B ) between - 5 and +5 T were performed at given temperatures, in order to determine experimentally the equilibrium (M~q) and irreversible (Mir r) components of the magnetisation.

136 E. Martlnez et al. / Physica C 271 (1996) 133-146

Furthermore, comparisons of the ZFC and FC magnetisation have been performed to determine the position of the irreversibility line.

The scale of characteristic times ~- for the ac and dc measurements are different: for the ac frequencies used short ~--- 10-3-10 s are involved, while in dc experiments ~----50-104 S. Both techniques are thus complementary, allowing the study of flux dynamics in a wider range of times and current densities. Consequently, the dependence of Ueff(J , T, B ) from high to low J values has been obtained from M(t) measurements at different temperatures and fields. Nevertheless, when J is strongly reduced, for example near the irreversibility line, ac susceptibility measurements become more precise and can be used reliably to determine Uef f-

The irreversibility line Birr(T) has been derived from X~c(T,B) at different ac drive frequencies (1, 120 and 928 Hz) using small b 0 values (4 × 10 -5 (parallel) and 1 × 10 -5 T (perpendicular)). For each field value B, the temperature at which the maximum of x"(T) occurs, T 0, defines a locus of the line. Birr(T) values have also been obtained from M(T) measurements performed at fixed field values B. Considering FC and ZFC runs, the temperature at which both branches merge defines a point on the irreversibility line.

pendent on the orientation, the minor differences observed for Ton may be an experimental artifact, attributed to changes in the sensitivity of the x~(T) measurements due to the sample's shape factors. However, the higher T~ and smaller AT values found for perpendicular fields reflect the anisotropy induced by the texture, which causes higher intergranular currents to circulate through the sample for this orientation. These have been corroborated using Xac(b0) data for both, parallel and perpendicular fields. Using Bean model predictions for isotropic cylinders, in both orientations and with the dimensions of the 15 m m / h grown fibre sample, values of the inductive critical currents Jc(b0.11) = 150 A cm -2 and Jc(bo. ±) = 2500 A cm -2 at 77 K, and J~(b0,11) = 10 4 A cm -z and J~(b0,±)-- 105 A cm -2 at 5 K, have been obtained. This gives an anisotropy ratio of 17 at liquid nitrogen, which reduces upon lowering the temperature, being much smaller than the ratio of critical currents in the a-b-plane and along the c-axis, where Jc,ab/Jc.c ~ 200 found on BSCCO single crystals at 5 K [12]. It is worth mentioning that the value of Jc(bo,±) at 77 K compares satisfactorily with the self-field electric transport Jc values measured along the fibre axis [23].

3.2. Pinning energies and magnetisation decay

3. Results

3.1. Macroscopic properties

Preliminary characterization of all samples was performed using Xac(T) at 120 Hz, zero dc fields and excitation b 0 = 10 -4 T parallel and perpendicular to the fibre axis. Attention was paid to three parameters: (i) The onset of diamagnetism, Ton, defined by the temperature at which x'(T) becomes negative; (ii) the critical temperature T c, defined by the temperature at which x'(T) reaches 1% of X'(5 K) and (iii) the transition width AT, the temperature interval needed to pass from 10% to 90% of X' (5 K). For example, in the fibre grown at a rate of 15 m m / h , under parallel excitation Ton = 91.4 + 0.5 K, T~ = 85.5 __+ 0.5 K and AT = 8.8 _ 1 K. In the perpendicular direction, however, Ton = 92 _ 0.5 K, T c =90__+0.5 K and A T = 5 +0 .5 K.

AS the onset of superconductivity cannot be de-

Magnetic relaxation measurements at different fields, orientations (parallel and perpendicular to the fibre), and temperatures, (from 5 to 30 K), have been performed and some of them are shown in Fig. 2. The magnetisation data extend up to 10 4 S and, tO faci l i tate c o m p a r i s o n s , normal ized values M ( t ) / ( - M 0) and a semilogarithmic scale have been used, where M 0 correspond to the first value cap- tured by the system after a dead time t i ~ 50 S, M 0 = M (t = ti). For a given temperature the decay of the magnetisation is faster for perpendicular (full symbols) than for parallel fields (open symbols). For fields of 1 T, a logarithmic time decay as predicted by the Anderson-Kim theory, [24,25] is observed below 20 K for BI[ and 10 K for B± . Although the Anderson-Kim model is valid when J ~ Jc, M(t) logarithmic decays have been also observed when the time scale of the experiment, is not large enough to detect non-linearity in Uef f. In this case the derived barriers heights would be no longer valid.

E. Mardnez et al. / Physica C 2 71 (1996) 133-146 137

- 0 . 4 0 ~_ . . . . . . ~ . . . . . . . ~ , ~ , ~

(-M/Mo) • 3o K t

- 0 . 6 0 ~ ~ ' ~ L ,,," o / _ 20

-o.8o " ° , , ' ~ , ~ .. . . ~

- 0 . 9 0 t o . ~ ' ~ ' = ~ ~ o ' ~

t - I . 0 0 . . . . i , s s , , ' , . . . . . . I . . . . . . . . I .

1o~ 103 t (s) 10,

Fig. 2. Scaled data of the isothermal magnetisation decay M ( t ) / ( - Mo), for parallel (open symbols) and perpendicular (full symbols) fields of 1 T at different temperatures. M o corresponds to the magnetisation value measured after the dead time of the system (about 50 s).

In order to obtain the actual dependence of the effective energy barriers o n J , the procedure described by Maley et al. [26] will be used. Besides the collective pinning effects present in single grains, other contributions are expected to exist in polycrystalline samples due to intergranular effects. This has been investigated using the model proposed by Ha- gen and Griessen (HG) [27], enabling the derivation of the activation energy distribution in the material.

3.2.1. Current dependence of the effective pinning energy U~ff(J)

From the relaxation M(t ) curves measured at different temperatures and the same field, the Ueff(J) values have been calculated following the procedure described by Maley et al. [26]. The current density J is proportional to the irreversible magnetisation, Mirr(B,T,t) = M ( B , T , t ) - Meq(B,T), where Meq is

deduced from the addition of increasing and decreas- ing field magnetisation branches of the hysteresis loop. Then the effective barrier is related to the magnetisation rate by

Ueff(J) = kBT(C - lnldMirr/dtl), (1)

where C = l n (B tooa /wd) ; to o is a characteristic attempt frequency, a the fluxoid hop distance and d the sample thickness transverse to the applied field.

The value of C is fixed in such a way that the Uef f versus M~r r data should give a smooth curve at low temperatures ( < 10 K). A negligible temperature dependence of Uef f have been assumed in this range. However, at higher temperatures Uef f is corrected by a factor f (T) , that gives a smooth curve in the full temperature range [12]. In this way, Ueff(J,T) values for fixed fields are obtained and shown in Fig. 3 for parallel (1, 3.5 T) and perpendicular (0.5, 1 T) fields. In all cases fields at which complete flux penetration occurs in the sample have been used. The experimental data between 10 K and 20-30 K may be roughly fitted to a linear function, f ( T ) = 1 - T / T x, with the parameters summarized in Table 1. T x depends on the applied magnetic field and on the orientation being more similar t o Tir r t h a n t o T c . This has also been found in single crystals and BSCCO-2223 tapes [12], but with a different functional dependence f (T) = [1 - (T /Tx )2] 15. Nevertheless, considering the large error of the T x parameter it can not be con- cluded that fibres show a different behaviour.

The values of Uefe(J) for both BII and B± show a similar non-linear dependence which may be compared with the inverse power law J -~ (with /x changing with J ) predicted by 2D theories. Both upper (7 /4) and lower (1 /2) bounds have been represented in Fig. 3 by straight lines. There is a

Table 1 Characteristic data and fitting parameters obtained from the analysis of the M(t) relaxation curves using the method of Maley et al. [26]

Orientation B (T) Fitting range (K) C T x (K) Mirr(0, B) (emu/cm 3) Up( B)/k B (K) Tit r (K)

Parallel 1.0 10-30 10 58 5:3 41 217 56.5 + 0.5 3.5 10-20 9 51 5: I 29 151 44.5 5:0.5

Perpendicular 0.5 10-30 11 57.5 _+ 2 224 187 50.0 5:0.5 1.0 10-20 11 50 5:1.5 179 166 44.5 ± 1.0

Values of the irreversible magnetisation Mirr(0,B), and of the pinning energy barrier Up(B) at 0 K have been deduced assuming, below 10 K, a logarithmic Ueff(J) behaviour at high J. For comparative purposes, values of the irreversible temperature Tit r determined from ac susceptibilities at 120 Hz and the specified fields have been included.

138 E. Martlnez et al./ Physica C 271 (1996) 133-146

Uer/(ksf(T)) (K)

1000 [ ~ - . . . ¥ ~ , ~

" ~ N . Nk ,g="

T \1 \ \ \

100.0 Mirr(emu/cm3) ~ \ ~

10 "1 100 101 102

Fig. 3. Temperature corrected values for the effective pinning energy Ueff(J)/f(T) obtained from magnetisation measurements for Bii = 1 and 3.5 T (open symbols) and for B z = 0.5 and 1 T (full symbols). The temperatures of the measurements which are indicated by bars correspond to 5, 6, 8, 10, 12.5, 15, 17.5, 20, 25 and 30 K (from left to righ0 for Bli = 3.5 T and B± = 1 T, M(t) at T = 30 K has not been measured. The continuous lines are theoretical predictions for 2D systems.

3.2.2. Distribution of activation energies The HG model of thermally activated flux motion

[27], which enable the evaluation of the distribution of activation energies m(U * ), would be followed and only a few main points needed for the discussion will be recalled here. The fraction of the pinning regions with energy between U* and U * + dU* would be m(U * )dU *. In the following analysis, the different orientations of the fibre's grains are taken into account in U *. Moreover, under the assumption that the field and temperature dependence of the activation energy is independent of the strength U * its actual value may be written as U(T,B)= b(T,B)U*, where by definition b(0,0)= 1. Further- more, if the superconducting material is formed by regions or domains characterized by U *, which relax independently, their contribution to the total magnetic moment M(t,T) will be

b(T) r~ M( t'T) = Moa- '~ Jgo,(t,r)m( U* )

decrease of the slope (i.e. of p,) with J which agrees with 2D collective creep theory as well as with single crystal observations. At low temperatures, however, slopes higher than 7 / 4 are observed. In all measured cases, a logarithmic (or quasi-logarithmic) dependence is found in the high current density regime:

Ueff (J ,B) / f (T) = Up(a ) ln ( Jc / J ) , (2)

which is often observed [28,29]. In the BSCCO compounds the above dependence is typical of the single vortex pinning regime [13]. The slope of the linear extrapolation of Uefr(J,B) v e r s u s In M i r r ( B ) at

high Mir r values enable to derive the Up(B) values given in Table l, along with the intercept of the axis Mirr(0,B). Assuming that those values are due to intergranular currents, for B = 1 T it would correspond to Jc(Bii)= 3 x l04 A cm -2 and Jc(B±) ~- 105 A c m - 2 , which are somewhat higher than the values deduced from Xac in zero dc field. In the measurements here presented only two magnetic fields are used for each orientation, thus it has not been possible to analyze the field dependence of Up(B). Nevertheless, assuming a power-law variation Up(B) at B - ' , a rough estimation of n -~ 0.2-0.3 is obtained in both cases.

[ y ( t ) ] X 1 - U b(T) ln l + - r dU*, (3)

where M 0 is the magnetic moment at 0 K; r is a characteristic time related to the attempt frequency of the flux lines; the ratio b(T)/a(T) describes the temperature dependence of the maximum current and the lower limit U0* = [b(T)]-lkBTln(1 + t /r) dis- card regions fully relaxed.

The distribution of pinning energies are obtained from M(t,T) using

m[U0* (tb,T)]

= d-~ Moo~-BTdln, 7 d-T '

(4)

while r is obtained from

[ b(T) d (M(tb'T) )] ln(tJr)=[r-~((~-~ dT b(T) a(T)

× ~ 1 dlnt (5)


and the functions a(T) and b(T) are chosen such that ~" becomes temperature independent [27]:

b(T) = (1 - e2)2[(1 + e 2 ) / ( 1 - e2)] q/2,

with 0 < q _< 3; and • = T/T c ,

a ( T ) = [ ( 1 + • 2 ) / ( 1 - e 2 ) ] p / 2 , 0 < p < _ 4 . (6)

logarithmic Mirr(t) behaviour which may be fitted to a power-law time dependence

M(t,T,B) = M( T,B )( t / z ) -k,r/Vp(r,a)

corresponding to an effective barrier, Ueff =

Upln(Jc/J) [11]. For example, for B 1 = 1 T, the values obtained at 5 and 8 K are Up/k s = 151 and 158 K, respectively.

The Mirr(tb,T) measurements and the derived ( - d M i r r / d l n tXtb,T) values at t b = 100 s have been represented in Fig. 4. A fourth order polynomial function has been used in the analysis to fit the M~r~(tb,T) results, while cubic spline was needed for the ( - dMirr/dln t)(tb,T) values (dashed and continuous lines of Figs. 4(a) and 4(b)). Furthermore a(T) and b(T) have been determined by trial and error with Eq. (6) giving a best choice for q = 0 and p = 0, in agreement with similar analyses in the literature [30,31]. This yields average values of ( ln(tb/~')) between 19 and 20, depending on the field and orientation, with standard deviations of 2.5-4.2 and z = ( 2 - 6 ) × 10 - 7 S. Although a mini- mum temperature dependence of ~- is obtained for p = 0, q = 0 with a non-negligible standard devia- tion, its influence in the energy distribution function is not very large because of its logarithmic dependence.

The distribution of pinning energies m(U *) has been shown in Fig. 4(c) for two orientations and different magnetic fields. A main feature of these curves is the existence of two peaks in both orientations, although the high energy one is more pronounced for fields perpendicular to the fibre. In all cases both peaks increase and shift towards lower energies upon field increases. Using the obtained m(U* ) distribution in Eq. (3), relaxation curves may be derived which, at low temperatures T < 10 K and t < 10 4 S, follow a logarithmic relaxation similar to the Mir~(t,T) measurements. The corresponding average value of (U} at low temperatures are 5% lower than the values directly determined from M~(t,T) curves. However, due to the contribution of the higher energies which have not been properly taken into account in Fig. 4(c), this difference increases with temperature. Moreover, relaxation curves deduced from Eq. (3) at low temperatures and at higher time lengths t--- 105-109 s show a non-

3.3. Effective pinning energies from ac susceptibility in the dissipative regime

Xac(T,B,f) measurements with small b 0 at different drive frequencies under FC magnetic fields have been performed to study the very low J regime. Fig. 5(a) and Fig. 5(b) show some characteristic results of the Xac(T) components for B = 1 T and b 0 = 4 × 10 -5 and 1 × 10 -5 T, respectively, parallel and perpendicular to the fibre's axis. For these small b 0 values Xac does not depend on the amplitude of the excitation which would imply the same behaviour for J. In the dissipative regime, this effect may be understood in terms of the electromagnetic skin depth, 6, which depends on the frequency and the thermal activated flux flow resistivity p [32]:

3 = [ ( 4 ~ p ) / ( tzof)] ,/2 (7)

The X"(T) maximum takes place at some temperature Tp when t~ is of the order of the sample size, giving a constant p(Tp,B)/f value. As in the resis- tive region

p(T,B) = p 0 e x p [ - Neff( B,T) /kBT ] ,

the shift of Tp as a function of the frequency would enable to derive Ueff(B,T) values [32].

As deduced from the semilogarithmic Arrhenius plots of Fig. 6, there is an exponential dependence of f with 1/Tp, indicating that the energy dissipation is due to thermal activation of vortices across pinning barriers, that it does not depend on J:

l n f = l n f o - Ueff(B,T)/kBT.

When the temperature dependence of Ueff(B,T) is neglected, f0 values are too large and do not have physical meaning. From the observed linear behaviour of In f versus l/Tp realistic f0 values can only be obtained assuming appropriate Ueff(T,B) dependencies. In the simplest case Ueff(T,B)=

140 E. Martlnez et a l . / Physica C 271 (1996) 133-146

- M i r r ( tb) (emu) 10 ° , I ~ T ~ ] ~ r ~ ~ T ~ r 7 - ~ T ~ ----: ~

o.s T (a)

1 0 "t 1 T 1 T ~ ~ . , ~ !

1 0

0 5 10 15 20 25 30 35

[ d M i r r / ln t ] ( tb) ( e m u )

0.015 . . . . , . . . . , , , . . . . , . . . . . . . . , , ~ 0.004

0.~__~ (b) i

0.005 3.5 T ~- -~ "~. ~ ~

T ( K ) \ ~ ' ~ ~ 0.000 . . . . . 4 , , , T , , 0.000

0 5 10 15 20 25 30 35

0.003

0.002

0.001

m ( l / m e V ) 0 . 0 4 0 . . . . . . . . . . . . i . . . . i . . . . . . . , , v ,

!.5 T ~ \ ( 0.035 c)

0.030 1 T \

0.025 DI5

0.020 i

0.015

0.010

0.005 . . . . L . . . . . , . . . . . . . . . . . . . . . 0 10 20 30 40 50 60 70

Fig. 4. Temperature dependence of girr(t b) (a) and of (dMirr /d ln tX t b) (b) at different field values for both orientations. Continuous ( B ± ) and dashed (Bll) lines arc least-squares fits to the data used in the analysis of the distribution energies m(U * ) represented in (c) for two different fields in each orientation.

~ a c ( e m u / g )

0 . 0 0 5 . . . . i , , , . . . . , . . . . , , ~ , i . . . . (a)

° o ° ~ E ]

° o A t

-O.OO5 Btl = 1 T ° o A

° o A ~

° o ~

- 0 . 0 1 0 * ° ~ °

T (K)

- 0 . 0 1 5 . . . . I . . . . * . . . . , . . . . , . . . . * . . . . 10 20 30 40 50 60 70

~ AIA , , . v . v . . . . ; . . . . r . . . . , . . . . , . . . . , . . . .

0 . 0 0 0 n l i l l , l | [ l l I ] * [ # i . ~ * * ! [ I

...z.~=v,,vo ** *

- 0 . 0 1 0 B ± = 1 T . "

-0.015

- 0 . 0 2 0 T ( K ) -0 .025 ~ , , . . i , i l i

10 20 30 40 50 60 70

Fig. 5. Components of the magnetic ac susceptibility Xac(T) after cooling the sample inside a field of 1 T at different frequencies: 928, 120, 10 and 1 Hz (right to left) and fields (a) Bit(b o = 4× 10 -5 T)and ( b ) B ± ( b o = l × l O -5 T).

f ( s "l)

10 3 . L

102 2 ' i " \

10 i -

, . 0 3. 5.0 , i ~ , I , , , i I , , , , I , i , , , i L i i L , I i J

0.01 0.02 0.03 0.04 1 / T p ( K " l )

Fig. 6. Variation of the temperature Tp of the X" maximum with the frequency f at different magnetic fields: Eli (open symbols) and B± (full symbols). The straight lines correspond to least- squares fits of the data.

E. Marffnez et al./ Physica C 271 (1996) 133-146 141

Ueff(0,BX1- T//T c) has been taken modifying the above equation to

l n f = ln fo + Ueff(O,B)/kBTc - Ueff(O,B)/kB T. (8)

In consequence, the slope, instead of Ueff(T,B), corresponds to Ueff(0,B) and the constant term to a(B)

= In fo + U~ff(O,B)/kBTc" Fitting the experimental value to Eq. (8) values of

a(B), f0 and T c have been obtained which correspond to f0 = 5.4 × l0 7 Hz and T c = 85 K for BI), and f 0 = 1 . 6 × 108 Hz and T~=88 K for B ± . It should be noted than the T c values, within 0.5-1.5 K, agree with the ones directly obtained from x~(T), but in addition now f0, is of the order of magnitude expected for the hopping frequency between potential wells (109-10 l° Hz). The U~fy(0,B) values obtained, shown in Fig. 7, exhibit an inverse power-law dependence represented by Ueff(B) OC B -n, where n = 0.5 for both orientations. The effective pinning energy is then

Ueff(r,B) = Ueff(O,1T)(1 - T/T~)B -°5, (9)

which for the very low J regime does not depend on J. In the range of temperatures and fields studied (25-83 K, 0 .01-5 T), Ueff.ll(0,1 T ) / k B = 2260 K while Ueff,.L (0,1 T ) / k B = 1300 K.

The above dependence of U, ff(T,B) may be con- firmed by measurements of the irreversibility line,

U e r ( 0 , B ) / k B (K) ' " 1 . . . . . . . . I ' ' . . . . . . J . . . . . . . .

l 0 4

Perpendicular - - - > " ~ ~ i , 0 ,

B (T) ) h i ) i ) J ) l l J L ~ . . . . . . . . . . . , , ~

0.01 0.1 1 10

Fig. 7. Effective pinning barriers Udf(B) as a function of B deduced from the 1/Tp versus f slopes. A power law dependence, Ueff(B) ~ B -n, with n = 0.5 is obtained for both Btl (open symbols) and B a: (filled symbols).

Bi r r (T)

101 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 ' ~ P a r a l l e l

0.1 Perpendicular • " , ~

0.01

0.001 . . . .

20 30 40 50 60 70 80 90

Fig. 8. Irreversibility lines derived from the position of the X"(T) maximum upon cooling at different magnetic fields B and fixed frequency of f= 120 Hz. For parallel fields an excitation of b o = 4× 10 -5 T (open symbols) has been used while for the perpendicular case b 0 = 1 × 10 -5 T (full symbols). The continuous lines are least-squares fits corresponding to Eq. (10) with B o = 4 + 0.1 T and T e = 85 + 0.5 K for the parallel orientation, and B 0 = 1 + 0.2 T and T c = 86 + 2 K for the perpendicular one.

Birr(T) , reached when Ueff/kBT takes specific values given by some electric-field criterion. Accordingly, the irreversibility line should have the dependence

Birr(T ) = B o ( T c / T - 1) 2. (10)

The experimental results for the irreversibility line Birr(T) derived from Xac are shown in Fig. 8. If the measurements are performed with different frequencies, Bier(T) is shifted although it shows the same dependence as with dc determinations. As we can see from Eq. (7), when T = Tp (6 is of the order of the dimensions of the sample) the higher is the frequency, the higher is the resistivity, so that the electric field criterion is more restrictive at low f and the defined irreversibility temperature Tir r =Tp de- creases with f . For a fixed value of 120 Hz, the fitting to Eq. (10) gives B 0 = 4.0 _+ 0.1 and 1.0 + 0.2 T for BII and B x , respectively. The other fitting parameter takes values of T~ = 90 + 1 K = Ton for dc measurements. For ac ones T c = 85 + 0.5 K for B)l, and 86 _+ 2 K for B i , and it does not depend on f . The small discrepancy between the T~ values obtained from dc and ac measurements could be due to the different sensitivity associated with the measure- ment techniques, or to some non-linear effects present in ac measurements.

142 E. Martlnez et al . /Physica C 271 (1996) 133-146

4. Discussion

The Ueff(J) values measured on fibres for both orientations, approximately follow the tendency observed for Bit,c in single crystals, although some noticeable differences are observed. At low temperatures ( < 8 K) and in a range which depends on the applied field and orientation, the slopes of In Ueff(J) versus In Mir r correspond to ~ values greater than the upper bound (7 /4) for 2D collective flux creep. Such high values have been observed in BSCCO- 2212 single crystals when B± ,c [12] and in other 3D systems [15]. However, in polycrystalline materials, supercurrent loops through several grains may take place affecting the system's dimensionality and the observed /x values. This is probably the case because, at higher temperatures, the Ueff(J) behaviour for fibres and single crystals for B± ,c differ com- pletely. Furthermore, at high current densities a quasi-logarithmic dependence of Ueff(J) has also been found here in fibres and single crystals [29], which may be originate from 2D single vortex depin- ning. The effective activation energy barrier dependence J - J', with a current-dependent exponent /z, may also be understood on the basis of the same phenomenology [33].

The differences between the relaxation of fibres and single crystals are evident when the full energy distribution m(U *) is used instead of the above average pinning energies. Using the HG inversion scheme [27] a m(U *) structure with two maxima (Ul* ,U2* ) has been found. Such double peak pinning distribution function has also been observed in BSCCO-2212 sintered polycrystalline samples [30] and in irradiated BSCCO single crystals [31]. More- over, the range of the lower energy peak values U¿* found here (10-20 meV (116-232 K)) is very close to the lower energy distribution peak in ceramics [30], single crystals irradiated by Pb ions [31] and neutron irradiated fibres (UI*--13 meV at 1.5 T [22]). Furthermore, those values are also similar to those found for single crystals (UI*= 22 meV in magnetic relaxation at 0.1 T [31 ], and Ul* -- 25 meV in remanent magnetisation decay [30]). Conse- quently, the lower energy peak may be attributed to the relaxation within grains, while the higher energy shoulder should be associated with intergranular pinning by precipitates, empty spaces or grain bound-

aries. The latter is more pronounced for B± than for BII one, possibly due to the worse connection between grains in the latter orientation.

Using the m(U *) distribution, the Mitt(t) curves measured at low temperature can be reproduced. In this regime, non-linear dependence of Mir r versus In t is found for longer time scales t = 105-109 s. The observed behaviour is concordant with the logarithmic dependence of Ueff(J) stated in Eq. (2) being in agreement with the results obtained by the Maley et al. method. Nevertheless the high energy barriers have to be considered in order to obtain the experimental results at all temperatures.

In the very low J regime the behaviour of Ueff(T,B) observed on fibres follows the power-law dependence expressed in Eq. (9). The Uef f values obtained on fibres (collected in Table 2) are between two to six times larger than for single crystals which could be understood considering the distribution of pinning energies. Moreover the exponent n, which is equal to 0.5, is also higher than the value found on single crystals, which ranges between 0.17 and 0.5, depending on the field (the latter just for B < 0.1 T). Values of these parameters on polycrystailine sam- pies and thin films (in the overall B± range) have been summarized in the same table, and shown Ueff(0,1 T) values of the same order of magnitude as in fibres, as well as n values around 1/2.

The coincidence of the Ueff(T,B) dependencies deduced for BII and B± from the dc magnetisation relaxation and from ac susceptibility suggests that the same flux dynamics mechanisms act in both cases. Although the values of the effective energy barriers, derived from M and Xac measurements at a given field, are higher for parallel fields, the U~ff curves for BII = 3.5 T and B± = 1 T may roughly stack upon each other, as shown Fig. 9, when single scaling values Mirr(0,B) of Table 1 are used for each orientation.

Assuming that in each grain all the magnetic properties depend on the extemal field projection parallel to the c-axis, as determined for single crystals [16], and neglecting intergranular effects, the effective magnetic field on a grain will be given by Beff, i = B sin[0/(fl,Oti,t~i) ]. Here fl is the angle formed by B and the fibre's axis, and 6 i an angle which reflects the random orientation of the platelet shaped grains in the fibre's cross-section. The aver-

E. Martlnez et al./Physica C 271 (1996) 133-146 143

Table 2 Effective pinning energies Ueff(0,1 T) and exponents, n, of the power-law field dependence derived for single crystals and other textured BSCCO-2212 materials near the irreversibility line

Single crystals (nil c) Polycrystalline samples Thin films ( nil c)

Ueff(0,1 T) / k a (K) 600 [39] 1300 fibres B 3_ 890-1740 [17] 400 [34] 2260 fibres nil 1320 a [18] 530 [16] 3500 wires [20]

600 [32] ~ 650 ceramics [40] 5oo [4Ol

1 /6 (0.1-3) [34,39] 0.5 (10-3-5) fibres B 3_ 0.5 (0.01-15) [171 1 /3 (3-10) [34,39] 0.5 (0.1-4) fibres nil 0.5 a (0.3-12) [18] 1 /3 (0.1-1.6) [16] 0.47 (0.2-2.2) ceramics [40] 0.3 (0.2-2.2) [40] 0.6 a (5 × 10- 4-10) tapes [21] 0.5 (5 × 10-4-0.1) [35]

The range of fields (in T) used in the fit of experimental Uef f data have been also given. a Materials with a majority of BSCCO-2223 phase.

age effective fields acting along the c-axis of the fibre's grains would depend on the angle distribution through the whole fibre

( n e f f , i ) = B(sinl0i(/3,ai,t~i)l), (11)

which may be determined experimentally from the measured distribution of a~. Moreover, assuming field independent critical current density values (i.e. Bean model) the magnetisation of the fibre parallel to the applied field would be given by

M( T,B,/3 ) = Mo( T)(sinlOi( /3,ai,6i)[>. (12)

Accordingly, if each grain relaxes independently its contribution to the magnetisation parallel to the ap-

U t/(Ksf(T)) [K]

B =0.5T ±

1ooo . , . .~v ~ ' , ~ ~ - - - - - - - - nil= l T

,0o "'':3"ST"lb ,T

Mirr/Mirr(O,B) ~ ~ 1 , 1 . 1 i h i , i k l , I i i , i , , i b

10 "z 10 "l 1 0 °

Fig. 9. Effective pinning energy Uef f / f ( T ) as a function of the irreversible magnetisation Mir r/Mitt(0, B) for different fields and orientations. The Mirr(0,B) values of Table 1 have been used.

plied field will be additive and determined by its effective pinning energy Ueff , i = Ueff(T, neff, i). Fur- thermore, assuming a Ueff , i o['n'l/2eff.i dependence as stated in Eq. (9), and a logarithmic time decay, it is possible to derive average activation energies from the experimental fibre's magnetisation which would depend on the microstructure, as well as on the field orientation:

U e f f ( T , B , / 3 ) ' = Uo( T,B ) (sinlO,( /3,ce;,8;)1>

/([sinl0i(/3,a, ,6~)1] 3/2). (13)

In well textured fibres, for parallel fields nil = B(/3 = 0), the average effective field acting on a grain is greatly reduced to (Beff.i>llotB(tanlail). Similarly, MII(T,B)ot Mo(T)(tanlail) is diminished while Ueff, II(T,B) ~ Uo(T,B)(tanl @ )/ ( ( t an l ail) 3/2 > increases. However, for perpendicular fields B± = B(/3 = "rr/2), (Bell.i) ± at B and M± (T,B) at Mo(T) there are only minor field and magnetisation reduc- tions with Uetf, ± (T,B) CX Uo(T,B), i.e. yielding lower barriers because the proportionality constant is the same for both orientations [23].

The reduction of the effective fields may qualita- tively explain the observed improvement in flux creep resistance even in polycrystalline materials (see Table 2), since for random orientations <Beef. i) = (2/-rr)B. Consequently, this decrease would pro- duce effective energies higher than the Ueff. c observed in single grains (using the field dependence of Eq. (9) they would be ~ 25% higher). In the out-

144 E. Mart[nez et aL / Physica C 271 (1996) 133-146

lined approach, with independent relaxation for each grain, some quantitative relationships may be derived. S i m i l a r (Beef,/) values should be present for fields in the ratio B ± / B I I = (tan(lail))--([ai[)= 0.14 (deduced from SEM analysis [23]) while Mi~r..L/Mir~,ll, which would be field independent, also would confirm the same ratio. Moreover, assuming the field behaviour of Eq. (9), Ueff .±(T,B) would coincide with UeffI[(T,B) when ( B ± / B ) 1 / 2 = ( ( t a n l a i l ) 3 / 2 ) / ( t a n "a i ) -~ 0.37, i.e. for a similar B±/BI I = 0.14 ratio. However, from the effective energy scaling shown in Fig. 9 for BII = 3.5 T and B ± = 1 T, a higher value for the ratio B ±/BII ~ 0.29 is found. This factor corresponds to an average fibre grain misalignment of (I ail) -- 17-19 °, which is far away from the error in the determination of I~il [23]. Inasmuch, about the same ratio is obtained in the Ueff(B) cu rves of Fig. 6, deduced from the Xac measurements which may be scaled with B±/BII = 0.33. Moreover, it has been found that in the energy distribution functions m(U * ) (see Fig. 4(c)), the first maximum for BII = 3.5 T and B L = 1 T occurs at around the same energy values. On the other hand the anisotropy of the high energy peak, shows approximately the same tendency than the low energy one. Nevertheless, a quantitative analysis is difficult because of the noise in the m(U * ) function.

All experimental findings are thus in mutual agreement, discarding the theoretical prediction of B.c/BII ~ 0.14, derived from the hypothesis of iso- lated grains, and pointing out that interactions among them are not negligible. Two interaction pathways may be outlined: (i) local changes in the direction of the magnetic field, where the superconducting currents flowing inside a grain should give, in the surroundings, diminished fields in the c-axis direction, which would affect neighbouring grains adapt- ing the magnetic flux somehow to the grain's texture. (ii) The existence of intergranular currents would also affect to the actual magnetic field inside the fibre.

The smaller pinning strength observed on single crystals is also reflected in the irreversibility line, which occurs at smaller fields than in polycrystalline samples and thin films. Comparisons of the irreversibility lines obtained for fibres (even in the worse case for B±) with results of the literature on single crystals [34-36] yield values of Bit r o n e order

of magnitude higher in fibres. Assuming that in BSCCO-2212 Uef f depends on Bef f, Birr, ± should occur in fibres at fields about 1.5 times higher than in single crystals. This factor is much smaller than the observed one. Moreover, the Tirr(B) plateau that occurs in single crystals at B -- 0.1 T is not observed in fibres. This may be due to either the occurrence of a different relaxation mechanism or to the existence of a grain misalignment distribution that overlaps the plateau.

The observed n = 0.5 value and the linear dependence of f ( T ) = 1 - T I T c, also found in thin films [17], single crystals for B < 0.1 T [35] and 2223 thin films [18] and tapes [21], has been attributed to the thermally activated plastic motion of pinned flux liquid [37]. The characteristic plastic barriers have been estimated to he [38]

Uef f = ( m a b / m c ) I/2 crp2ao/8~rA 2 a ( T c - T ) B - , /2,

where mab and m c are effective masses of the charge carriers along the a-b-plane and the c-axis, respectively, a 0 the vortex lattice parameter and A the London penetration depth for Bii,c. This value of Uef f is of the order of the energy of the flux line segment of length ~ a 0, and therefore this estimate can be applied, except for an additional numerical factor, to any vortex deformation with such scale. This can occur if motion of vortices is caused by cutting and reconnecting of the vortex lines, in an entangled liquid. Kucera et al. [17] have estimated for Bi-2212 compounds the value U~ff(0,1 T ) / k B = 2710 K. This is about twice the value derived here for fibres (1300 and 2260 K), or those observed on wires [20] and thin films [17]. Nevertheless, it is 4-5 times higher than the measured one in single crystals (Table 2), where n 4:0.5 is found in most cases.

5. Conclusions

The effective energy barriers Ueff( J ,T , B ) of highly textured polycrystalline samples (fibres) have been obtained for fields parallel and perpendicular to the crystallographic c-axis by using dc magnetisation as well as ac susceptibility measurements. These enable to cover the range of small and high current densities. In all cases, dependencies similar to those of single crystals for Bii.c are found, but with higher Ueff


values and some quantitative differences arising from the broader distribution of activation energies, as well as from intergranular effects. Moreover, the observed behaviour may be understood using the predictions of collective flux pinning [13] and vortex glass [14] models for 2D systems.

The distribution of pinning m(U * ) energies have been derived using the HG inversion scheme. These functions are broader and reach higher values in

fibres than in single crystals, with the presence of two maxima. The lower energy maximum, which corresponds to intragranular pinning and is also present in single crystals, while the higher energy shoulder has been ascribed to intergranular effects. The same significant features on m ( U * ) are displayed for both field orientations although with different energy values. The observed m(U *) distribution explains the fact that higher Uef f values are found experimentally in fibres than in single crystals.

In the very low J regime, near the irreversibility line, Uee f becomes J independent. This regime has been studied by ac measurements at low excitation fields, yielding Ueff(T,B) values which, for both field orientations, follow Eq. (9) and have been attributed to the thermally activated plastic motion of pinned flux liquid [37]. Smaller effective barriers in single crystals cause the irreversibility line to occur at lower magnetic fields, about l0 times lower than in fibres for B± and even lower for B u.

In the overall J , T and B range studied here, the effective barriers for both orientations show the same functional dependence, indicating that the same pinning mechanisms are involved. In addition, the

Ueff(ff) o r Ueff(n) curves may scale one upon the other when fields in the ratio of BII /B . = 0.33 are considered. Nevertheless, this value does not correspond with the results of (tan(I a i l ) ) --- 0.14 obtained by SEM images [23] which would hold for independent grains. The intergranular currents greatly reduce the fibre anisotropy, becoming one order of magnitude lower than in single crystals and contributing significantly to higher energy pinning.

Acknowledgements

The authors are indebted to the Spanish Ministry of Education and Science (CICYT, MAT 95-0921-

C02-01 and 02) and to the M I D A S Program (CICYT-OCIDE-REE-UNESA) ( 9 4 / 2 4 4 2 ) for fi- nancial support of this research. E.M. thanks the Spanish Ministerio de Educaci6n y Ciencia for a

scholarship.

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magnetic relaxation of highly textured bi2sr2cacu2o8+delta polycrystalline fibres

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