APPLIED SUPERCONDUCTIVITY CONFERENCE 2000, VIRGINIA BEACH, SEP. 18{22, 2000, 5MI10

1Current-Voltage Characteristics in aSuperconducting Bi-2223 Tape in the Range ofVery Low Electric Field
Edmund So ji Otabe, Takeshi Kodama, Mitsuhiro Fukuda, Teruo Matsushita, Kikuo Itoh

Abstract | Current-voltage characteristics in the range ofvery low electric eld were analyzed from a relaxation of
the magnetization using a SQUID magnetometer in a superconducting Bi-2223 tape. It was found that the observed
current-voltage characteristics in this range were scaled wellas predicted by the vortex glass-liquid transition theory.
However, the obtained transition eld was much lower thanthat obtained from a scaling in the higher electric eld
range. At the same time, the dynamic critical index, z ,was much larger than usual values. Hence, it is concluded
that these parameters are not uniquely determined independently of the level of electric eld. The experimental
result was compared with the theoretical analysis using theux creep- ow theory in which the distribution of the e ective ux pinning strength was taken into account. It was
found that the theoretical result explains approximately theobserved result. This shows that the essential mechanism
which governs the transport property in the superconducting tape is the ux pinning.
Keywords | E-J characteristics, Bi-2223, ux creep- ow
model, very low electric eld
I. Introduction

OR practical applications of oxide superconductors, itis necessary to understand their current-voltage charF
acteristics in a wide range of the electric eld, since the elec-

the scaling of the E -J characteristics was also explained by
the ux creep- ow model[3].
In this paper, the current-voltage characteristics in therange of very low electric eld were analyzed for a superconducting Bi-2223 tape from a relaxation of the magnetization measured by a SQUID magnetometer. The scaling
was examined for the result of E -J characteristics at theelectric eld of the order of 10010 V/m. The E -J characteristics are numerically calculated using the ux creep- ow
model and the results are compared with experimental results.
II. ExperimentalSpecimen was a superconducting multi lamentary Bi2223 silver sheathed tape with 59 laments. The widthand thickness of the tape were 3.7 mm and 270 m, respectively. The average width, w, and thickness, d, of thelaments were 320 m and 11 m, respectively. The tape
was cut in a length of l = 4:2 mm for the magnetization
measurement. The temperature of the specimen was controlled in a range of 40 to 83 K and the magnetic eld
was applied parallel to the c-axis. The magnetic eld wasrst applied enough high and then reduced in certain value,
and the relaxation of the magnetic moment, m, was measured by a SQUID magnetometer (MPMS-7). The current
density, J , and the electric eld, E , are estimated by thefollowing equations:tric eld which the superconductor feels strongly depends
on the kind of application such as DC or AC equipments.
Therefore, it is necessary to measure the current-voltage
characteristics of the oxide superconductor in detail in awide range of the electric eld. However, the characteristics have not yet been clari ed, and the mechanism of ux
12m
J= 2;
motion which generates the electric eld under distributed
w df (3l 0 w)
pinning forces is still under discussion. It is well known
that the electric eld vs current density (E -J ) character0E=01 dm ;istics of an oxide superconductor is scaled in two master
2df (l + w) dt
curves as predicted by the vortex glass-liquid transition
theory[1], [2]. On the other hand, it has been shown that where f = 59 is the number of laments.
manuscript received September 18, 2000
E. S. Otabe is with Kyushu Institute of Technology, 680{4,Kawazu, Iizuka 820{8502 Japan (Telephone: +81{948{29{7683, email: otabe@cse.kyutech.ac.jp).
T. Kodama is with Kyushu Institute of Technology, 680{4,Kawazu, Iizuka 820{8502 Japan (Telephone: +81{948{29{7683, email: kodama@aquarius10.cse.kyutech.ac.jp).
M. Fukuda is with Kyushu Institute of Technology, 680{4,Kawazu, Iizuka 820{8502 Japan (Telephone: +81{948{29{7683, email: fukuda@aquarius10.cse.kyutech.ac.jp).
T. Matsushita is with Kyushu Institute of Technology, 680{4,Kawazu, Iizuka 820{8502 Japan (Telephone: +81{948{29{7663, email: matusita@cse.kyutech.ac.jp).
K. Itoh is with National Research Institute for Metals, Sakura 3{
13, Tsukuba, Ibaraki 305{0003, Japan (Telephone: +81-298-59-5081,
e-mail: itoki@nrim.go.jp).

(1)
(2)

III. Results and Discussion

A. Experimental results
The E -J curves at 70 K evaluated from the measured
relaxation of the magnetic moment using (1) and (2) are
shown in Fig. 1(a). The range of the electric eld is of
the order of 10010 V/m and is 6 to 7 orders of magnitude
lower than that in usual measurements by the four probe
method.
According to the vortex glass-liquid theory[1], [2], E J characteristics can be scaled on two master curves by
replotting them in the form of (E=J )jT 0 Tg j (z+20D) vs.
J=jT 0 Tg j (D01) . In the above,  and z are the static

APPLIED SUPERCONDUCTIVITY CONFERENCE 2000, VIRGINIA BEACH, SEP. 18{22, 2000, 5MI102−810−910

T=70K
E (V/m)E (V/m)

900mT80mT−1010−101050mT5mT−1110

T=40K−121078101061010910210Bg=56mT
z=16.0ν=0.65

Bg=250mT
z=16.0ν=0.65ln[(E/J)/|B−Bg|

ln[(E/J)/|B−Bg|

ν(z−1)]]−10ν(z−1)

8J (A/m )2J (A/m )20

7−20−300

T=40.0K

T=70.0K
1522242620
2ν

ln[J/|B−Bg| ]2ν

ln[J/|B−Bg| ]Fig. 1. (a) Observed E -J characteristics at various magnetic elds
and at T = 70 K and (b) their scaled result in a Bi-2223 silversheathed tape wire. Solid lines in (a) represent the calculated
result using the ux creep- ow theory.

and dynamic critical indices, D is the dimension of thevortex system and Tg is the transition temperature. The
similar scaling is predicted [4] for (E=J )jB 0 Bg j (z+20D)
vs. J=jB 0 Bg j (D01) with the same critical indices,  , z ,where Bg is the transition eld.
Fig. 1(b) shows the result of the scaling of E -J characteristics, where Bg = 56 mT, z = 16:0,  = 0:65 and D = 3
are assumed. It is clear that the scaling is also obtained in
the range of very low electric eld. However, the value of z
is much larger than predicted by the glass-liquid transition
theory. That is, even if we assume D = 2, we have z = 7:5(with  = 1:3), which is still too large. The scaling is also
possible at di erent temperatures as shown in Figs. 2(b)and 3(b) at 40 K and 83 K, respectively.
On the other hand, the scaling in the range of higher
electric eld by the four probe method gives Bg = 308 mT,z = 11:0 and  = 0:5 at 70 K[5]. That is, Bg is larger andFig. 2. (a) Observed E -J characteristics at various magnetic elds
and at T = 40 K and (b) their scaled result.

z is smaller at high electric elds. This result suggests that
the E -J characteristics tend to vary from convex upwardin the higher E range to concave downward in the lower Erange.
Therefore, z and Bg are not constant but dependent on
the electric eld range. This is contradictory to the vortex
grass-liquid theory in which those parameters are considered to be intrinsically determined by the characteristic of
the ux line lattice. It should be noted that the performance of scaling of E -J curves does not necessarily meanthat the vortex glass-liquid transition theory holds. It wasshown in [6] that the thermal depinning is a transition of
the second order. This predicts the theoretical foundationthat the E -J curves can be scaled.

B. Analysis by the ux creep- ow model
These observed results are compared with the theoreticalanalysis using the ux creep- ow model[3]. According tothis model, the E -J characteristics can be calculated inAPPLIED SUPERCONDUCTIVITY CONFERENCE 2000, VIRGINIA BEACH, SEP. 18{22, 2000, 5MI10

100.0634.5mT−93E (V/m)

0.05−1010σ20.04

0.03−11100.02

1.5mT
T=83.0K−12101072J (A/m ) 100.018406080T (K)

Fig. 4. Temperature dependence of  2 .

ν(z−1)]

Bg=24.0mTln[(E/J)/|B−Bg|

20

where Am is the most probable value, 2 is a constantrepresenting the degree of deviation and K is a constantdetermined by the condition of normalization.
The value of g 2 is assumed to be determined so that thecritical current density under the ux creep might take amaximum value [7], and is given by

z=16.0ν=0.6510g =g2

T=83.0K
2223242ν25ln[J/|B−Bg| ]Fig. 3. (a) Observed E -J characteristics at various magnetic elds
and at T = 83 K and (b) their scaled result.

terms of the pinning potential:
U0 =1=20:835g 2 kB Jc0;(2 )3=2 B 1=4(3)

where Jc0 is the virtual critical current density in the creep
free case and g 2 is the number of ux lines inside the ux
bundle. The magnetic eld and temperature dependencesof Jc0 at low elds is assumed as"

Jc0 = A 1 0 T 2 #mTc

B 01 ;(4)

where A, m and are pinning parameters. It is well known
that the magnitude of Jc0 is widely distributed in oxide
superconductors. Here, for simplicity, the distribution ofJc0 is assumed to originate only from the distribution of Ain (4) of the form: (logA 0 logA )2 f (A) = K exp 02 2m;

(5)

2e

 5k T  Ba  4=3B2Uef 0lnE;(6)where ge is the value where ux lines form a perfect triangular lattice, and Ue is the value of U0 when g = ge . In
the present calculation g (B; T ) is obtained by (6), while
E = 10010 V/m is assumed as a typical value of the electric eld. Further details of the calculation are describedin [3].
The parameters Am , m and used in the numerical calculation in the whole range of temperature and magnetic
eld in the present measurement are listed in Table. 1. On
the other hand,  2 , which is used as a tting parameterat each temperature, is shown in Fig. 4. The distribution
width of Jc increases with temperature. This tendency isconsistent with the usual temperature dependence of nvalue, since n becomes smaller due to the increase of thedistribution width of Jc according to increasing temperature.
The calculated results are compared with the experimental results in Figs. 1(a), 2(a) and 3(a). It is found that thetheoretical result explains approximately the observed re-TABLE I
Parameters used in the numerical calculation.

Am9:0 2 108m

2.00.51APPLIED SUPERCONDUCTIVITY CONFERENCE 2000, VIRGINIA BEACH, SEP. 18{22, 2000, 5MI10

sults in the range of very low electric eld. Since the E -J
characteristics in the higher range of electric eld can also
be explained by the theory [8]{[10], it can be said thatthe ux creep- ow model can approximately describe theE -J characteristics in wide ranges of temperature, magnetic eld and electric eld. This shows that the essential
mechanism which governs the transport property in thesuperconducting tape is the ux pinning.
However, the present theoretical model cannot explain
the details of the observed E -J characteristics. That is,
the theoretical prediction leads to an E -J curve concave
downward with a much larger value of E at very low Jvalue. This becomes more remarkable at higher temperatures. This deviation seems to be attributed to the assumption of the constant value of E = 10010 in (6) for
simplicity. In fact, this deviation is qualitatively explainedby the electric eld dependence in (6). That is, when E
becomes small, g2 takes a larger value and the e ect ofux creep is expected to become weak. However, the estimated results at 40 K, 900 mT and 70K, 80 mT are almost
unchanged even by this treatment.
Another reason for the deviation may exist in the assumption on which (6) is derived. This equation was derived for the current density far above the TAFF region.
On the other hand, the deviation becomes large around theregion where TAFF starts to take place in the theoreticalmodel. Hence, it seems to be necessary to derive a correct
expression of g2 in such a range of low current density.
IV. Conclusions

In this paper, the E -J characteristics in the range of very
low electric eld was estimated for a superconducting Bi2223 multi lamentary tape by analyzing the relaxation ofthe magnetic moment, and following results are obtained: The resultant E -J characteristics are successfully
scaled in the form predicted by the the vortex glassliquid transition theory even in the range of the electric eld about 6 orders of magnitude lower than in
the ordinal four probe method.
 The dynamic critical index, z , is too large and is notconsistent with the prediction of the glass-liquid transition theory. In addition, z and the transition eld,Bg , depend on the range of the electric eld. There-4fore, the thermodynamic phase transition of the second order in the ux line system, which is characterized by the scaling of E -J curves, does not originate
from the intrinsic nature of ux lines.
 The E -J characteristics are approximately explainedby the ux creep- ow model over wide ranges of temperature and magnetic eld. This shows that the thermal depinning is the basic mechanism which determines the E -J characteristics in a wide range of theelectric eld.
 However, the deviation becomes large at low current
densities especially at high temperatures. The reason
for this deviation is considered to be attributed to theexpression of g 2 at low current densities.
Acknowledgments

The authors would like to acknowledge Mr. K. Shiraishi,
Drs. M. Kiuchi and T. Kiss of Kyushu University for helpful discussions.
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