Supercond. Sci. Technol. 13 (2000) 183–186. Printed in the UK
PII: S0953-2048(00)07485-6
Temperature dependence of
filament-coupling in Bi-2223 tapes:
magneto-optical study
A V Bobyl†‡, D V Shantsev†‡, T H Johansen†, M Baziljevich†,
Y M Galperin†‡ and M E Gaevski‡
† Department of Physics, University of Oslo, PO Box 1048 Blindern, 0316 Oslo, Norway
‡ Ioffe Physico-Technical Institute, Polytechnicheskaya 26, St Petersburg 194021, Russia
Received 1 September 1999
Abstract. Coupling through random superconducting bridges between filaments in a
multifilamentary Ag-sheathed Bi2 Sr2 Ca2 Cu3 O10+δ tape has been investigated by
magneto-optical imaging at temperatures from 20 K up to Tc . Magnetic flux distributions
have been measured on the surface of an intact tape in the remanent state on applying a strong
perpendicular magnetic field. The flux distributions observed at low temperatures reflect the
arrangement of individual filaments. At high temperatures, the distribution becomes more
similar to that for a uniform monocore tape, indicating that superconducting connections
appear between the filaments. To discuss the relative contributions of the intra- and
inter-filament currents, a simple model based on the Bean critical state was proposed and
applied to analyse the temperature dependent behaviour. The inter-filament coupling,
increasing with temperature, reaches at 77 K a point where the currents flowing in large
inter-filament loops are roughly equal to the intra-filament currents.
1. Introduction
There is great interest in making use of high-Tc superconducting multifilamentary tapes in power applications. An
important issue concerning multifilamentary tapes is the possible presence of superconducting connections between the
filaments. Such a connection may appear through formation of random inclusions of the superconducting material,
making up superconducting ‘bridges’ between neighbouring
filaments. On the one hand, the coupling between filaments
may be useful for maintaining the current flow when it encounters a structural defect within a single filament. on the
other hand, however, this also leads to a substantial increase
in ac loss, important for many applications, such as power
transmission lines or ac magnets.
Filament bridging was observed in Ag-sheathed
Bi2 Sr2 Ca2 Cu3 O10+δ (Bi-2223) tapes and its effect on the magnetization loops was analysed in [1]. For multifilamentary
samples, the measured susceptibility is considerably larger
than that in isolated filaments, being although somewhat
smaller than the value expected for a monocore tape. Studies
of ac loss in a Bi-2223/Ag tape have shown that the filaments
behave as if they were connected into bundles, a typical bundle being composed of eight filaments [2].
Although the filament bridging strongly affects the
magnetic properties of a tape, its existence can be established
unambiguously only by space-resolved studies. Indeed,
these techniques have proved to be very successful in
investigations of field and current distribution in mono- and
0953-2048/00/020183+04$30.00
© 2000 IOP Publishing Ltd
multifilamentary tapes [3–7]. Hall-probe measurements of
the remanent state after passing a transport current [5] and
magneto-optical (MO) imaging at various applied fields [4]
have both revealed the existence of superconducting bridges
between filaments in Bi-2223/Ag tapes.
In the present work we used the MO imaging method to
investigate the temperature dependence of filament coupling.
Since there are different mechanisms limiting the current
inside individual filaments and the current leaking through the
random superconducting interconnections, one would expect
different temperature dependences of the corresponding
critical currents. In order to separate the two contributions
experimentally we constructed a model which can be fitted
quantitatively to the MO images. Good agreement is
achieved over a wide range of temperatures which allows
the behaviour of both the intra- and inter-filament critical
currents to be determined.
2. Experiment
The object of study was a 55 filament Bi-2223 tape, prepared
by the powder-in-tube method with subsequent drawing and
rolling [8]. The tape width, including the Ag sheath, was
3.7 mm; the critical current was 45 A at 77 K. An optical
image of the tape cross section is shown in figure 1(a).
MO images of the magnetic field distributions were taken
using a Faraday-active Bi:YIG indicator film with in-plane
magnetization. The indicator, grown by liquid phase epitaxy
183
A V Bobyl et al
(a)
15
(b)
10
19 K
41 K
57 K
62 K
69 K
76 K
80 K
86 K
93 K
102 K
108 K
5
B (mT)
(c)
0
Figure 1. (a) Optical image of the tape cross section, with
superconducting filaments appearing black. The arrows point to
three filaments located near the tape surface, see the text.
Magneto-optical images showing trapped flux (Ba = 0) in the tape
after applying a large field at 19 K (b) and at 108 K (c). The
images were taken with uncrossed polarizers, giving a monotonic
relation between image brightness and the local flux density.
Strong contrast enhancement was applied to the image (c). The
stripes along the tape, clearly seen in the image (b), reflect the
arrangement of the filaments.
on GGG substrate, was mounted in contact with the large surface of an intact Ag-sheathed Bi-2223 tape. Details of the MO
imaging technique itself are given in [9]. Contrary to the conventional procedure, we chose an angle between the polarizer
and the analyser far from 90◦ . In this case the grey level in
the MO images becomes a single-valued function of the flux
density, i.e., the brightness grows with B, rather than with |B|.
In this work we studied the remanent states obtained
after applying a magnetic field of Ba = 105 mT, which much
exceeds the full penetration field at all temperatures. MO
images of the tape at 19 and 108 K are shown in figure 1. The
major feature of the B-distribution at 19 K is a set of stripes
that correspond to a particular arrangement of filaments.
Secondly, the distribution also has common features with
that expected for a uniform strip, namely a large peak of
positive flux in the middle and regions of smaller negative
flux near the edges (cf [4]). At 108 K the stripes can hardly
be distinguished and the flux distribution is very close to that
in a uniform strip.
The flux density profiles across the tape are shown for
different temperatures in figure 2. The peaks in the profiles
correspond to the bright stripes in the MO images. It is
evident that the remanent state flux distribution is strongly
temperature dependent. Firstly, and quite as expected, the
trapped flux decreases with increasing temperature owing
to reduced pinning at elevated temperatures. Secondly,
we notice a less obvious feature, namely that the profiles
become smoother at higher temperatures. To reveal the loss
of fine structure more clearly, we can focus on the region
−0.9 (mm) < x < 0. At low temperatures one finds three
distinct peaks in B profiles. As the temperature increases,
the two minor peaks gradually vanish and finally disappear
at 70 K.
The three peaks coincide in space with three individual
filaments near the tape surface (see arrows in figure 1(a)).
Thus, we are confident that the peaks originate from current
loops within these filaments. When the peaks vanish from the
184
−5
Tape
−10
−0.5
0.0
x (mm)
0.5
1.0
Figure 2. Experimental profiles of the flux density in the
remanent state on removing a strong field at different
temperatures. The profiles are obtained from MO images as in
figure 1(b, c) by averaging grey levels over a 100 µm band across
the tape. The band is shown under the profiles. As the temperature
increases, there occurs (i) a decrease of the trapped flux, and
(ii) smoothening of the flux profiles.
flux profile, this may only be due to changes in the current
flow pattern, our configuration being fixed mechanically. We
assign the merging of the three flux maxima into one broad
peak to the creation of inter-filament current loops at elevated
temperatures. Therefore, our conclusion is that there exists a
temperature dependent redistribution of the intra- and interfilament currents in the tape.
3. Model
We propose a simple model to describe the observed
redistribution of currents.
Individual filaments are
considered to be thin infinite strips, while the inter-filament
coupling is described by an additional (fictitious) wide strip.
The positions and widths of the thin strips are taken from
the optical image, figure 1(a). The position and width of the
wide strip are determined from the B-profile at the highest
temperature, where the inter-filament currents appear to be
dominant. The spatial arrangement of the strips is shown in
figure 3 and also specified quantitatively in table 1.
We assume that all the strips behave according to the
Bean model for a fully-penetrated remanent state, i.e., the
critical current flows along the strip so that +Jc and −Jc are
the current densities in each of its halves. We allow different
critical current densities, Jcintra and Jcinter , for the narrow strips
and additional wide strip, respectively. The latter is the
critical current limiting the transport between the filaments,
and, in general, one expects it to be different from Jcintra .
Temperature dependence of filament-coupling in Bi-tapes: MO study
Table 1. Widths and centre positions of the strips used in
T = 108 K
0.2
modelling, see also figure 3. The origin of the x-axis is chosen as
in figure 2. The strips 1–3 correspond to real filaments, and their
dimensions are taken from the optical image of the tape,
figure 1(a). The wide strip, 4, models the inter-filament coupling.
0.0
Number
w (mm)
xc (mm)
−0.2
1
2
3
0.15
0.09
0.11
8
−0.79
−0.46
−0.09
4
0.6
−0.37
B (mT)
6
T = 57 K
4
2
0
15
T = 19 K
10
5
0
−1.0
−0.8
−0.6
−0.4
x (mm)
−0.2
0.0
Figure 3. Experimental profiles (symbols) of the flux density
across the tape at three temperatures. Full curves are fits by the
model (2) which assumes a fully penetrated state of the filaments.
The positions of the filaments are sketched at the bottom, and
specified in more detail in table 1. The fitting parameters are the
two critical sheet currents, Jcinter and Jcintra .
very different temperatures. It is evident that our modelling
successfully reproduces the important features of the flux
profile variation. Some deviation between the fitting curves
and the measured flux profiles can be assigned to the effect
of the field trapped in the remaining filaments of the tape.
The pronounced variation in the B-profiles with temperature leads to quite different temperature dependences of
the fitting parameters Jcinter and Jcintra , as shown in figure 4.
At low temperatures, the intra-filament critical current far
exceeds the inter-filament current. This would be expected
since in this temperature range the current transport through
random interconnections between filaments is severely limited by weak links. At higher temperatures, however, Jcintra
becomes very small, and essentially all the current flows in
large inter-filament loops. These loops consist of filaments
and interconnections, both having the same critical current
Jcinter . This result is consistent with the observation that in
Bi-2223 the depinning critical current decreases with temperature much more rapidly than the critical current through
weak links does [10]. At 77 K, the operating temperature for
most tape applications, Jcinter ≈ Jcintra . Hence, at this temperature the currents flowing in the large inter-filament loops
are roughly equal to the intra-filament currents. Moreover,
larger current loops obviously give larger contribution to ac
From the Biot–Savart law it follows that the field
distribution at a distance h above such a strip of width 2w is
given by B(x) = Jc F (x, w) where
2
x 2 + h2
µ0
(1)
ln F (x, w) =
4π
(x + w)2 + h2 (x − w)2 + h2
50
with Jc the critical sheet current, and x the coordinate across
the strip with x = 0 in the centre. The total field generated
by currents in all the four strips is
30
B(x) = Jcintra
inter-filament
40
Jc (kA m−1)
3
X
intra-filament
20
F (x − xci , wi ) + Jcinter F (x − xc4 , w4 ) (2)
i=1
where wi and xci are the strip widths and centre positions,
respectively.
Equations (1) and (2) were fitted to the experimental
flux density profiles in the range −0.9 (mm) 6 x 6 0.
The height h was chosen to be 0.17 mm, which is the
separation between the MO indicator film and the top layer of
filaments, the distance primarily defined by the silver sheath
thickness. For each temperature the B-profile was fitted with
two free parameters, Jcinter and Jcintra , using the least-squares
method. The result of the fitting is shown in figure 3 for three
10
0
0
20
40
60
T (K)
80
100
Figure 4. Temperature dependence of the critical currents, Jcinter
and Jcintra corresponding to inter- and intra-filament current loops,
respectively. The data were obtained by fitting (2) to experimental
flux density profiles.
185
A V Bobyl et al
loss. Therefore, at 77 K losses due to inter-filament current
even dominate over intra-filament losses.
4. Conclusion
Magneto-optical imaging shows directly the existence
of superconducting interconnections between filaments in
multifilamentary Bi-2223/Ag tape. Using a Bean-model
approach, we have extracted from such observations the
temperature dependences of the intra-filament and interfilament critical currents. It is shown that the relative strength
of inter-filament coupling grows steadily as the temperature is
raised from 20 K to Tc . At the highest temperatures, the interfilament current becomes the dominant current component.
Acknowledgments
We thank P Vase (NST, Brøndby, Denmark) for sample
preparation. Financial support from the Research Council
of Norway, from NATO science fellowship via the
Research Council of Norway, project 131315/140, and
from the Russian National SC Program 98031 is gratefully
acknowledged.
186
References
[1] Everett J, Perkins G, Volkozub A V, Caplin A D, Dhallé M,
Polcari A, Marti F, Huang Y B and Flükiger R 1998
Physica C 310 202
[2] Gömöry F, Gherardi L, Crotti G, Bettinelli D, Martini L,
Bigoni L and Zannella S 1998 Physica C 310 168
[3] Pashitski A E, Polyanskii A, Gurevich A, Parrell J A and
Larbalestier D C 1995 Physica C 246 133
[4] Koblischka M R, Johansen T H, Bratsberg H and Vase P
1998 Supercond. Sci. Technol. 11 479
[5] Volkozub A V, Caplin A D, Huang Y, Flükiger R, Grasso G,
Eckelmann H, Quilitz M and Goldacker W 1998
Physica C 310 159
[6] Oota A, Kawano K and Fukunaga T 1997 Physica C 291 188
[7] Herrmann J, Savvides N, Müller K H, Zhao R,
McCaughey G, Darmann F and Apperley M 1998
Physica C 305 114
[8] Vase P, Skov-Hansen P, Han Z, Poulsen H F and Frello T
1997 Proc. Eur. Conf. on Applied Superconductivity (The
Netherlands, 1997)
[9] Koblischka M R and Wijngaarden R J 1995 Supercond. Sci.
Technol. 8 199
[10] Welp U et al 1995 Phys. Rev. Lett. 74 3713
Polyanskii A A, Gurevich A, Pashitski A E, Heinig N F,
Redwind R D, Nordman J E and Larbalestier D C 1997
Phys. Rev. B 53 8687