ASC2000, Sep. 22, 2000, 5MI10Introduction
For practical applications of oxide superconductors, it is necessary tounderstand their current-voltage characteristics in a wide range of theelectric eld, since the electric 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 a wide range of theelectric eld. However, the characteristics have not yet been clari ed,
and the mechanism of ux motion which generates the electric eldunder distributed pinning forces is still under discussion. It is wellknown that the electric eld vs current density (E -J ) characteristics
of an oxide superconductor is scaled in two master curves as predictedby the vortex glass-liquid transition theory. On the other hand, it
has been shown that the scaling of the E -J characteristics was also
explained by the ux creep- ow model.
In this paper, the current-voltage characteristics in the range of very
low electric eld were analyzed for a superconducting Bi-2223 tapefrom a relaxation of the magnetization measured by a SQUID magnetometer. The scaling was examined for the result of E -J characteristics at the electric eld of the order of 10010 V/m. The E -J characteristics are numerically calculated using the ux creep- ow modeland the results are compared with experimental results.

1

ASC2000, Sep. 22, 2000, 5MI10

Experimental

 specimen

Bi-2223 multi lamentary tape wirecross section (mm)3:7 2 0:27
length of tape l (mm)4.2
number of laments f59
average lament width w(m)320average lament thickness d(m) 11
critical temperature (K)110 measurement
relaxation of magnetic moment measured bySQUID40{83 K
1.5{900 mT
B k c-axis evaluation of E -J curve
J=12mw2df (3l 0 w )

E=0

0dm
12df (l + w) dt

2

ASC2000, Sep. 22, 2000, 5MI10

3Flux creep- ow model
U0U0

flux creep

flux flow

 electric eld by ux creep

232013U(j)U
j0
67A 5; j  1
5 41 0 exp @0Ecr = Baf 0 exp 40
kB TkB T
2013U0 A5= Baf 0 41 0 exp @0;
j>1kB Tj = J=Jc0: normalized current density
Jc0:
virtual critical current density

in the creep free casepinning potential

U0 : electric eld by ux ow
E = 0;j1= f (J 0 Jc0 ); j > 1

f :ow resistivity

 total electric eld

2
E = (Ecr+ E 2 )1=2

ASC2000, Sep. 22, 2000, 5MI10

4 pinning potential, U00:835g 2Jc01=2kB
U0 =2 3=2B 1=4g 2: number of ux line in ux bundle

 scaling low of Jc02!23mT 5
Jc0 = A 41 0
B 01
TcA; m; : pinning parameter distribution of pinningforce#"2(logA 0 logAm)f (A) = K exp 02 2
Am: most probable value of A
K : constant determined by normalization
Z 1

f (A)dA = 10

 2: parameter representing a distribution width observed electric Zeld
E (J ) =10

Ef (A)dA

m, , Am, 2: adjustable parameters

ASC2000, Sep. 22, 2000, 5MI105

 number of ux line in ux bundle, g2
g 2 is assumed to be determined so that the criticalcurrent density under the ux creep mighttake a maximum value

2g =

ge2

"Baf 05kBTln2U eEc!#4=3(Ec = 10010 V=m)

ge2: g 2 for perfect triangular latticege20C66=2Jc0Baf0C66: shear modulus for perfect triangular lattice
0C66
=

Bc2B

40Bc2!

10B
2Bc2

U e = U 0 (g = g e )!

ASC2000, Sep. 22, 2000, 5MI10

6Results and Discussion
E -J curves and scaled result

E (V/m)10−9T=70K
80mT−10105mT−11107101082

ln[(E/J)/|B−Bg|

ν(z−1)]J (A/m )20

Bg=56mT
z=16.0ν=0.650T=70.0K
2224262ν

ln[J/|B−Bg| ]ASC2000, Sep. 22, 2000, 5MI107−810E (V/m)

900mT
10−1050mT
T=40K
10−121067810910210J (A/m )Bg=250mT
z=16.0ν=0.65ln[(E/J)/|B−Bg|

ν(z−1)]−10−20−30

T=40.0K
15202ν
ln[J/|B−Bg| ]ASC2000, Sep. 22, 2000, 5MI10−9E (V/m)

10834.5mT−1010−11101.5mT
T=83.0K−12107J (A/m ) 10

Bg=24.0mT]

ν(z−1)

ln[(E/J)/|B−Bg|82

1020z=16.0
ν=0.65

10T=83.0K
2223242νln[J/|B−Bg| ]25

ASC2000, Sep. 22, 2000, 5MI109

 scaling parameters at 70 Klow electric eldzBg (mT)

0.65 16.025high electric eld* 0.5 11.0308(*4 probe method by Shiraishi et al.)z and Bg are not constant but dependent on

the electric eld range. This is contradictory
to the vortex grass-liquid transition theory.

 deviation between theoretical and experimental re-sults

The deviation becomes large at low current densities especially at high temperatures. The reason for this deviation is considered to be attributed to the expression of g 2.

 parametersAmm

9:0 2 108 2.0 0.51

ASC2000, Sep. 22, 2000, 5MI1010

 distribution of Jc0, 20.06

0.05

σ20.04

0.03

0.02

0.01

40

60

80

T (K)

 The distribution width of Jc increases with tem-perature. This tendency is consistent with theusual temperature dependence of n-value, sincen becomes smaller due to the increase of thedistribution width of Jc according to increasing
temperature.

ASC2000, Sep. 22, 2000, 5MI10

11SummaryIn this paper, the E -J characteristics in the range of very low electric
eld was estimated for a superconducting Bi-2223 multi lamentarytape by analyzing the relaxation of the magnetic moment, and following results are obtained: The resultant E -J characteristics are successfully scaled in

the form predicted by the the vortex glass-liquid transition
theory even in the range of the electric eld about 6 orders ofmagnitude lower than in the ordinal four probe method.

 The dynamic critical index, z, is too large and is not consistent
with the prediction of the glass-liquid transition theory. In addition, z and the transition eld, Bg , depend on the range ofthe electric eld. Therefore, the thermodynamic phase transition of the second order in the ux line system, which ischaracterized by the scaling of E -J curves, does not originate
from the intrinsic nature of ux lines.

 The E -J characteristics are approximately explained by theux creep- ow model over wide ranges of temperature andmagnetic eld. This shows that the thermal depinning is thebasic mechanism which determines the E -J characteristics ina wide range of the electric eld.

 However, the deviation becomes large at low current densities

especially at high temperatures. The reason for this deviationis considered to be attributed to the expression of g 2 at low
current densities.