Supercond. Sci. Technol. 11 (1998) 1017–1023. Printed in the UK
PII: S0953-2048(98)94302-0
Visualization of magnetic flux
distribution in Bi(Pb)-2223/Ag
multifilamentary tapes
Z W Lin†, J W Cochrane†, G J Russell†, S X Dou‡ and H K Liu‡
† Advanced Electronic Materials Group, School of Physics, University of New South
Wales, Sydney, NSW 2052, Australia
‡ Centre for Superconducting and Electronic Materials, University of Wollongong,
Wollongong, NSW 2522, Australia
Received 2 February 1998
Abstract. The high-resolution magneto-optical technique has been used to
visualize the magnetic flux distribution in Bi(Pb)-2223/Ag multifilamentary tapes.
Topographies of the magnetic flux will be presented for a seven-element x -array
filamentary distribution which has both exposed and silver-sheathed filaments. This
study was over the temperature range 40–80 K for applied magnetic fields in the
range 0–560 G and direct currents up to 60 A. Analysis of the visual patterns will
be presented and in the case of the x -array compared with the work of Mawatari
(1996 Phys. Rev. B 54 13 215) and Müller (1997 Physica C 289 123).
1. Introduction
Several methods are used to obtain the flux density
distribution in superconducting materials, e.g. scanning
Hall probe [1, 2] and electron spin resonance probe [3]
microscopies. However, the magneto–optical(MO) Faraday
effect is a powerful method that can provide high-resolution
information on the local flux distribution and critical current
in high-Tc superconductors over a range of important
temperatures.
Bean’s critical state model [4, 5] is widely used to
describe the magnetic field distribution in a slab, cylinder,
strip, disk and rectangular geometries. Magnetization
studies of Yba2 Cu3 O7−δ thin film disks in the critical
state, in perpendicular magnetic fields, have confirmed
the theoretical work for magnetic field distribution [6].
Also, for strip- and rectangularly shaped superconductors
in perpendicular magnetic fields, using the MO technique,
good qualitative agreement has been found between
experiment and theory [7].
Recently, the magnetic properties of high-Tc superconductor thin films in strip form arranged in a z-stack and
an x-array were investigated analytically using a transformation method proposed by Mawatari [8]. Mawatari calculated the magnetic field distribution of periodically arranged
superconducting strips in perpendicular fields while Müller
investigated the case where a transport current was passed
through the strips [9].
In this paper, the topographical distribution of the
magnetic flux for silver-sheathed Bi(Pb)Sr2 Ca2 Cu3 Ox
(Bi(Pb)-2223/Ag) multifilamentary tapes with both exposed
and silver-sheathed filaments when external perpendicular
c 1998 IOP Publishing Ltd
0953-2048/98/101017+07$19.50 fields and currents are applied will be presented. The
experimental data will be compared with the theoretical
results of Mawatari [8] and Müller [9].
2. Experimental details
The MO system used in this study consisted of an air-cooled
electromagnetic coil, an optical cryostat and a polarization
microscope that has a CCD camera, as shown in figure 1.
The image is transferred to a computer system. The
microscope was installed on an x–y stage to observe the
flux distribution of large specimens as most specimens
exceed the field of view of the microscope. Two leads
were welded to the ends of the specimen for applied
currents up to 60 A. The specimen was positioned on an
insulating sapphire substrate which was placed on a cold
finger inside the cryostat. The temperature of the specimen
was measured by a thermocouple which was cemented to
the sapphire next to the specimen. The Faraday indicator
film was placed on the specimen with the film facing
downwards. The specimen was cooled by a cryocooler
with the lowest temperature being 40 K. The magnetic field
produced by the electromagnet was applied perpendicular to
the specimen surface and had a maximum value of 560 G.
In general terms the measurements are based on the
Faraday effect which is the rotation of the plane of
polarization of a beam of linearly polarized light when the
light passes through MO material in the direction of field
lines from an applied magnetic field. In this investigation,
a ferrimagnetic iron garnet thin film with perpendicular
magnetization was utilized as the indicator film. Using
1017
Z W Lin et al
(a)
(b)
Figure 2. Relationship between domain widths and applied
fields for (a) BF and (b) YF at 70 K.
Figure 1. (a) High sensitivity MO system and (b) schematic
of the sample assembly: (1) lamp housing, (2) aperture
diaphragm ring, (3) field diaphragm ring, (4) polarizer,
(5) half-reflecting mirror, (6) objective, (7) analyser, (8)
CCD camera, (9) quartz window, (10) assembled sample,
(11) cool head, (12) electromagnet, (13) cryostat, (14) x –y
stage, (15) iron garnet film substrate, (16) iron garnet film,
(17) investigated specimen, (18) sapphire,
(19) thermocouple, (20) wire for direct current.
the MO technique, a high-contrast strip domain image is
obtained from which the flux distribution can be determined
by studying the domain structure of the iron garnet film. In
fact, two types of indicator films, which were calibrated
in applied fields, were employed in this study. A yellow
film (YF), whose domains vary in size starting from a field
of 10 G, had a very high magnetic field sensitivity but
saturated at a relatively low field of 60 G. Advantage is
taken of this sensitivity in the measurements of the fields
arising from transport currents. On the other hand, a brown
film (BF), which responds to fields from 150 G, has a
relatively high saturation field at 500 G and hence was
employed to visualize the flux density of specimens at high
applied fields. Figure 2 shows the relationship between the
domain width and applied field for the YF and BF films at
70 K. A series of calibrations were performed at a number
of different low temperatures and these showed that the
domain widths for both the YF and the BF do not vary
much at temperatures near 70 K.
The investigated specimen was a 19-filament Bi(Pb)2223 tape sheathed with silver, having a width of 3.6 mm,
length of 7.94 mm and thickness of 0.27 mm. This
specimen was then polished to a thin lamina of 0.1 mm
thickness, containing seven Bi(Pb)-2223 filaments in which
five filaments were arranged in an x-array and two filaments
were unfortunately surperfluous. This gives a situation very
similar to that theoretically evaluated by Mawatari [8] and
Figure 3. Transverse cross-section of investigated specimen along the black line shown in figure 4(c).
1018
Magnetic flux distribution in Bi(Pb)-2223/Ag
Figure 4. Variation of strip domain pattern of BF for specimen at 70 K after ZFC in applied fields of (a) 220 G, (b) 350 G,
(c) 395 G.
Müller [9]. The exposed surface of the specimen was well
polished in order to improve reflection of the polarized light
and to achieve high image contrast but there were also some
scratches on the surface which reduced the quality of the
domain pattern. After investigation, the specimen was cut
along the black investigation line AA0 shown in figure 4(c)
and the transverse cross-section is shown in figure 3. It
shows that each filament has approximately elliptical crosssection with filament widths in the range 360–600 µm and
thicknesses 20–45 µm. Three of the filaments were covered
with silver while four filaments were exposed. Thus the
x-array is far from an ideal and homogeneous structure.
3. Results and discussion
3.1. External field
Above Tc , the black and white strips have the same width
over the entire labyrinth image when the external magnetic
fields magnetize the iron garnet film homogeneously.
Figure 4 shows the variation of strip domain pattern of the
BF on the polished specimen with increasing perpendicular
applied field at 70 K after zero-field cooling (ZFC). The
amplitude of the magnetic flux distribution along the black
line shown in figure 4(c) is given in figure 5 where the
Figure 5. The flux profiles for figure 4 along the black line
shown in figure 4(c).
contour and position of the filaments are also shown. Two
wide and two narrow stripes which are much greyer than the
other areas correspond to the exposed filaments in figure 3.
MO images of the Bi(Pb)-2223/Ag multifilamentary
1019
Z W Lin et al
(a)
(b)
Figure 6. (a) The arrangement of strip lines in an x -array and illustration of the parameters. (b) Theoretical profile of
magnetic field, Hz , for an x -array arrangement at L/W = 2.2, 3, 4 and Ha /H0 = 4, 3, 2, 1, 0.5 [8].
tape clearly reveal macroscopic inhomogeneities in the
magnetic flux distribution especially at high fields.
However, in order to understand the variation of flux
and compare the results with the theoretical data, most
of the inhomogeneities are not present in the selected
section shown in figure 5. There is no doubt that these
inhomogeneities are caused by factors such as misoriented
grains, second-phase precipitates and cracks [10]. Five
bands where the domain density is higher are clearly seen;
this means that the magnetic flux density in these bands is
lower than for other regions. The magnetic field passes
straight through the silver between the superconducting
filaments; as a result, the white domains of the indicator
film over these gaps should increase with increasing
magnetic field, as shown in figure 2. In fact, the fields
in these gaps were higher than the applied field. This
phenomenon is clearly shown in figure 5 and is in accord
with theoretical calculations (see figure 6). This is caused
by the demagnetization factor. On the other hand, in the
1020
regions of the superconducting filaments the magnetic field
is shielded to some extent, the filaments being in the mixed
state, with the shielding being reduced with increasing
applied field.
Figure 6 shows a series of profiles of the z component,
Hz , of the magnetic field, derived by Mawatari [8] for a
system of thin films periodically arranged in an x-array in
perpendicular applied fields. In the figure the film is located
at 0 < x/W < 2. Figure 6(a) illustrates the parameters and
geometry where Ha is the applied magnetic field and H0 =
Jc d/π where Jc is critical current density. In comparing
the theoretical results with the experimental data, one can
observe several significant points. Firstly, the magnetic
fields in the regions of the superconducting filament gaps
are higher than the applied field, as discussed previously.
However, the theoretical sharp peak of the magnetic field
at the edges of each filament is not obvious. The reason for
this is that the real filament has an approximately oval crosssection [11] instead of a rectangular cross-section as used in
Magnetic flux distribution in Bi(Pb)-2223/Ag
Figure 7. Variation of strip domain pattern of YF for specimen at 70 K in applied direct currents of (a) 15 A, (b) 20 A,
(c) 30 A, (d) 40 A and (e) 50 A.
the theoretical investigation and that a space exits between
the brown film and specimen surface [12]. Secondly, when
the applied field increases from zero, slow penetration of
the flux front into the centre of each filament from the
edges was not clearly observed. The reason could be that
the edges of the sample were in the mixed state in a field
of 220 G at 70 K. Finally, the flux density of each filament
gradually increases instead of remaining zero in increasing
magnetic field. It means that above a certain magnetic
field, B(T )∗ , the whole filament fills with a magnetic field
and shows a characteristic spatial field distribution which
is determined by the geometry of the filament and by the
strength and distribution of the pinning forces acting on the
single flux lines. Such behaviour has also been observed by
Brawner et al [13] and Pashitski et al [10]. The latter two
phenomena are mainly explained by weak-link behaviour at
grain boundaries along which the magnetic field can easily
penetrate into the whole superconducting filament [14, 15].
1021
Z W Lin et al
Figure 8. The flux profiles for figure 7 along the black line
of figure 4(c).
3.2. External current
In this section, we study the magnetic field distribution for
the case of an applied increasing direct current. The YF is
employed to image the flux distribution because of its high
sensitivity to small magnetic fields. Figure 7 shows the
variation of the domain pattern for the YF on the specimen
with increasing direct current at 70 K. The corresponding
field distribution along the black line is shown in figure 8.
Müller [9] has analytically investigated the z component of
magnetic field for a system of rectangular cross-section thin
films periodically arranged in an x-array when an external
direct current is applied; see figure 9. The field profiles
are significantly different between experiment and expected
theoretical result. In fact, the critical current at 70 K for
the seven filaments was found to be approximately 5.2 A,
that is Jc = 14 000 A cm−2 . For an ideal situation an
applied current of 5 A should produce a maximum magnetic
field of 40 G at the surface of the high-Tc filaments for
L/W = 4. However, for our experimental setup the
vertical field component at the garnet film was much lower
than the calculated 40 G and thus it was rather difficult
to detect domain changes. Increasing the applied current
resulted in the curves shown in figure 7, which indicates
that the high-Tc strips at the centre are in the normal state,
with the silver sheath taking the majority of the current, as
the resistivity of silver at 70 K is significantly less than
for Bi(Pb)-2223 material in the normal state. The two
high-Tc superconducting strips at the edges appear to be
in the mixed state and clearly show their superconducting
effect on the flux distribution up to 30 A, at which point
the whole specimen appears to be dominated by the silver
sheath carrying the current. However, even at 50 A,
the filaments still appear to have an effect on the field
distribution as shown by the field penetration through the
large gap. Detailed discussion of this experimental profile
appears to be complicated by the filament geometries and
further work on a patterned thin film with fine rectangular
strips is being undertaken.
1022
Figure 9. Theoretical profile of magnetic field, Hz , for an
x -array arrangement with L/W = 2.2, 3, 4 and Ia /Ic = 0.99,
0.8, 0.5. [9].
Magnetic flux distribution in Bi(Pb)-2223/Ag
4. Conclusion
The MO technique is a very powerful and high-resolution
technique for studying the magnetic flux distribution associated with superconducting specimens. In this study, using
a seven-element x-array filamentary distribution fabricated
from a Bi(Pb)-2223/Ag multifilamentary tape, the actual
geometry of the filaments and their shape clearly affect
the results, while inhomogeneities in the superconducting
strips are easily observed in perpendicular external magnetic fields. In fact, comparison with published theoretical
predictions shows a good deal of agreement but intrinsic
results can only be determined if well-defined superconducting arrays having a very high Jc are studied. This last
point is particularly true for the case of applied currents
as the agreement between the experiment and theoretical
prediction is shown to be rather poor.
References
[1] Xing W, Heinrich B, Zhou Hu, Fife A A and Cragg A R
1994 J. Appl. Phys. 76 4244
[2] Grant P D, Denhoff M V, Xing W, Brown P, Govorkov S,
Irwin J C, Heinrich B, Zhou H, Fife A A and
Cragg A R 1994 Physica C 229 289
[3] Khasanov R J, Talanov Yu I, Vashakidze Yu M and
Teitel’baum G B 1995 Physica C 242 333
[4] Bean C P 1962 Phys. Rev. Lett. 8 250
Bean C P 1964 Rev. Mod. Phys. 36 31
[5] Bean C P 1970 J. Appl. Phys. 41 2482
[6] Mawatari Y, Sawa A and Obara H 1996 Physica C
258 121
[7] Schuster T, Kuhn H and Brandt E H 1994 Phys. Rev. B 50
16 684
[8] Mawatari Y 1996 Phys. Rev. B 54 13 215
[9] Müller K-H 1997 Physica C 289 123
[10] Pashitski A E, Polyanskii A, Gurevich A, Parrell J A and
Larbalestier D C 1995 Physica C 246 133
[11] Theuss H, Forkl A and Kronmüller H 1992 Physica C 190
345
[12] Knorpp R, Forkl A, Habermier H-U and Kronmüller H
1994 Physica C 230 128
[13] Brawner D A and Ong N P 1993 J. Appl. Phys.
73 3890
[14] Gotoh S and Koshizuka N 1991 Physica C 176 300
[15] Dorosinskii L A, Indenbom M V, Nikitenko V I,
Ossip’yan Yu A, Polyanskii A A and Vlasko-Vlasov K
1992 Physica C 203 149
1023