PHYSICS OF THE SOLID STATE
VOLUME 41, NUMBER 6
JUNE 1999
Magneto-optic study of spatial magnetic-field distribution relaxation in an HTSC film
strip after transport current turn-on
M. E. Gaevski , D. V. Shantsev, and A. V. Bobyl’*)
A. F. Ioffe Physicotechnical Institute, Russian Academy of Sciences, 194021 St. Petersburg, Russia
Yu. M. Gal’perin,†) T. H. Johansen, and H. Hauglin
Physical Department, University of Oslo, 0316 Oslo, Norway
~Submitted September 28, 1998!
Fiz. Tverd. Tela ~St. Petersburg! 41, 965–968 ~June 1999!
The paper provides the first demonstration of the efficiency of applying the magneto-optic
method to studies of the spatial and temporal magnetic-field relaxation in an YBa2Cu3O7 film strip
after the transport current is switched on. It is shown that the evolution of magnetic flux
distribution is adequately described in terms of a modified Bean model with time-dependent critical
current. At a time 50 ms after the current is switched on, the critical current of the samples
studied decreases by '15%. This proves the significance of thermally activated magnetic flux
motion ~creep! in the regime investigated. The magnetic vortex pinning energy has been
estimated as
U 0 '20 kT. © 1999 American Institute of Physics. @S1063-7834~99!00706-6#
to study the evolution of the spatial magnetic-field distribution in a YBa2Cu3O7 film strip following current turn-on
with resolutions of 4 ms and 5 mm. It was stimulated by our
previous study11 of the B(r) distribution in a film strip with
a transport current close to the critical value. It had been
found that the results obtained cannot be described in terms
of the Bean model12 for a static magnetic-flux distribution at
a constant current. The agreement was reached only by including the thermally activated magnetic-flux motion ~creep!
after the current is switched on, which was done by computer
simulation. The objective of the present work was to search
for direct evidence for the significance of the creep.
The YBa2Cu3O7 films were grown on a LaAlO3 substrate by magnetron sputtering.13 X-ray diffraction and Raman scattering measurements showed the c axis of the films
to be perpendicular to the substrate. The films exhibited a
high degree of orientation and a perfect crystal structure. The
strips measuring 500310030.2 m m were prepared by photolithography. The transport properties of the samples were
investigated with a standard four-probe arrangement. The superconducting transition temperature of the strips was
T c 591 K, the transition width was less than 1 K, and the
critical current density was j c 5106 A/cm2 at T577 K. The
strip with the most uniform current-density distribution below the superconducting transition point was selected by
means of low-temperature scanning electron microscopy.14
The MO method of visualization of magnetic flux distribution is based on the Faraday effect, i.e., rotation of the
plane of light polarization by a magneto-optical indicator
film placed directly on the superconductor surface. The angle
of rotation increases with increasing magnetic-field component perpendicular to the surface of the HTSC sample. A
bismuth-doped YIG film with in-plane magnetization served
as indicator.15 The indicator film was coated with a thin
A number of studies have recently been devoted to describing the spatial distribution B(r) of the magnetic field
and that of the current, j(r), in superconducting samples of
different shapes.1–6 Investigation of the relaxation of these
distributions in time, B(r,t), following a change in the external magnetic field or the current through the sample is also
of considerable interest.7
This work reports on a combined study of B(r,t) ~relaxation evolution in space and time! after switching on of the
current made by the magneto-optic ~MO! method. This approach has the following merits:
~1! It is known7 that B(t) relaxation exhibits logarithmic
behavior, so that the relevant experiments should be performed over a broad range of times. The disadvantage of
using an external magnetic field, which can be changed to an
appreciable extent only on the scale of a few seconds, is that
in order to obtain reliable results one has to carry out observations over several days. An experiment making use of current pulses and an MO image-recording camera is capable of
covering a wider and more interesting time range extending
from a few microseconds to a few hours. Note that further
development of this method may be useful also in studies of
such processes as macroscopic magnetic-flux jumps, annihilation of vortices and antivortices in the Meissner region,
etc.8–10
~2! Substantial penetration of a magnetic flux into a superconductor takes place only at currents close to the critical
threshold. Because the critical current density in high-quality
HTSC films j c (T!T c );107 – 108 A/cm2, one has to use narrow strips with a width &100 m m to pass current pulses of
up to 10 A. This imposes constraints on the required spatial
resolution of &1 – 3 m m, which is well within the capabilities of the MO method.
In this work, the magneto-optical method was employed
1063-7834/99/41(6)/4/$15.00
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© 1999 American Institute of Physics
878
Gaevski et al.
Phys. Solid State 41 (6), June 1999
FIG. 1. Schematic representation of current pulse profile. Portions 1–3 correspond to different instants of magneto-optic image recording.
specular aluminum layer providing double rotation of the
plane of polarization of incident light. The images were recorded with an 8-bit digital DCS420 Kodak camera. After
the recording the temperature was raised to 95 K, and the
indicator film was calibrated. This was done by determining
the dependence of the brightness of the indicator film image
obtained by the camera on the strength of the applied external magnetic field. To exclude the effect of nonuniformities
in both the indicator film and the light intensity, the calibration was performed independently at different points with a
step of 20 mm.
The current through the sample was supplied in 50 mslong rectangular pulses, with the leading and trailing edges
shorter than 1 ms. The operation of the camera was synchronized with the current supply, which permitted obtaining images a fixed time after application of the current pulse. The
images were obtained several times during a current pulse,
which is illustrated by Fig. 1. The camera exposure time was
4 ms. To reduce the distance between the MO indicator and
the HTSC film, the film with the smoothest surface was chosen. Besides, the distance between the contact pads and the
strip was larger than the indicator size. The indicator was
9 mm distant from the strip. The magnetic field generated in
the magneto-optic indicator by an I'1.4 A current was 1–5
mT, which is close to the sensitivity limit of the method.
Therefore all measurements were repeated five times with
accumulation to increase the signal/noise ratio.
Figure 2 presents an MO image of the HTSC strip recorded at the end of a current pulse of amplitude I51.4 A at
a temperature of 15 K. The bright areas correspond to a
higher absolute magnetic field. The image is fairly uniform
along the bridge, which evidences the absence of weak
bonds and other macrodefects. The experimental magneticfield profile averaged over the strip length and corresponding
to this MO image is shown in Fig. 3. The magnetic flux is
screened by the HTSC sample, which results in field maxima
near its edges. The left- and right-hand parts of the profile
relate to magnetic fluxes of opposite signs. The magnetic
flux does not penetrate into the central part of the sample,
and, as a consequence, one observes a field minimum at the
FIG. 2. ~a! Schematic representation of current-carrying YBa2Cu3O7 strip
and ~b! its magneto-optic image for a current of 1.4 A obtained at 15 K.
center. The minimum is smoothed out, because the magnetic
field is probed not in the superconductor plane but at the 9
mm height of the MO indicator.
We shall use the Bean model for a quantitative analysis
of the experimental data. The current distribution in a thin
strip calculated within this model can be written1,2
J~ x !
5
Jc
H
2
arctan
p
1,
SA
D
w 2 2a 2
,
a 2 2x 2
u x u .a,
~1!
a, u x u ,w,
where a5w A12(I/I c ) 2 , I c 52wd j c is the critical current, d
is the thickness, and w is the halfwidth of the strip. The
Gaevski et al.
Phys. Solid State 41 (6), June 1999
FIG. 3. Profiles of the magnetic-field component perpendicular to sample
surface at a height of 9 mm above a strip carrying 1.4-A current. Circles are
experimental data, and the solid line is a plot of a calculation made within
the Bean model using as parameters h59 m m and I c 51.8 A.
magnetic-field component perpendicular to the film plane at
height h can be calculated using the Biot–Savart–Laplace
equation
B~ x !5
m0
2p
E
w
2w
x 8 2x
J ~ x 8 ! dx 8 .
h 1 ~ x 8 2x ! 2
2
~2!
The B(x) profile calculated from these equations is shown in
Fig. 3 by a solid line. The best-fit parameters used in the
calculations are I c 51.8 A and h50.18 w.
Let us turn now to the relaxation of the B(x) profile
during a current pulse. Figure 4 presents the profile of the
quantity DB(x)5 u B 1 (x) u 2 u B 3 (x) u , where B 1 (x) and B 3 (x)
are the profiles obtained in the beginning and at the end of a
current pulse, respectively ~see Fig. 1!. We readily see that
the change in the field is the largest at the strip edges, while
at the center the field practically does not change at all. The
reason for the profile relaxation is magnetic flux creep,7 as a
result of which the magnetic field penetrates ever deeper into
the sample after the current is switched on. Unfortunately,
the equation describing flux creep in a thin current-carrying
strip does not allow analytic solution. Previous studies11,16
show, however, that such relaxation can be described in
terms of the Bean model with time-dependent j c (t). We
shall also use this approximation here. The solid line in Fig.
4 is a plot of DB(x) calculated using Eqs. ~1! and ~2! with
the critical currents I c 52.1 and 1.8 A corresponding to the
beginning and end of the current pulse. The agreement between the experimental and calculated relations suggests the
existence of flux creep during a current pulse. An estimate of
the change in the critical current during the pulse yields 15
879
FIG. 4. Profile of magnetic-field variation during a 50-ms long current
pulse, DB(x)5 u B 1 (x) u 2 u B 3 (x) u , where B 1 (x) and B 3 (x) are the profiles
obtained in the beginning and at the end of the current pulse, respectively.
Circles are experimental data, and the solid line is a plot of a calculation
made within the Bean model using I c 52.1 A and 1.8 A as parameters for
the beginning and end of the pulse, respectively.
65%. Using this result, one can derive the magnetic-vortex
pinning energy. Assuming the vortex activation energy to
depend logarithmically on current density,7
U ~ j ! 5U 0 ln~ j c0 / j ! ,
~3!
one obtains a power-law relation for current density relaxation in time. For the time dependence of the critical current
density j c , which enters Eq. ~1!, one obtains the following
expression:
j c ~ t ! } ~ t/ t 0 ! 2kT/U 0 ,
~4!
where t 0 is the reciprocal attempt frequency.17 Substituting
j c (t 1 )/ j c (t 2 )51.15, where t 1 54 ms and t 2 550 ms, yields
U 0 '20 kT, which is in accord with available data18 for
YBa2Cu3O7.
Thus we have demonstrated for the first time the effectiveness of the magneto-optic method in studies of magneticfield relaxation in a YBa2Cu3O7 strip in space and time following turn-on of transport current. The observed evolution
of the magnetic-field distribution is a direct evidence of the
significant role played by creep when a magnetic flux penetrates into an HTSC strip carrying transport current. The
flux creep can be adequately described in terms of the modified Bean model with a time-dependent critical current. Estimates show that the effective critical current, which is a
parameter of the model, decreases by '15% in 50 ms after
the current is switched on. This yields U 0 '20 kT as an estimate for the vortex pinning energy. Studies over a wider
range of currents, temperatures, and times, which are
880
planned for the future, will provide more comprehensive information on magnetic flux creep parameters.
Support of the Norwegian Ministry of Science and of the
Russian program on superconductivity ~Grants 96071 and
98031! is gratefully acknowledged.
*!E-mail: bobyl@theory.ioffe.rssi.ru
†!
Permanent address: A. F. Ioffe Physicotechnical Institute, Russian Academy of Sciences, 194021 St. Petersburg, Russia.
E. H. Brandt and M. Indenbom, Phys. Rev. B 48, 12893 ~1993!.
E. Zeldov, J. R. Clem, M. McElfresh, and M. Darwin, Phys. Rev. B 49,
9802 ~1994!.
3
Th. Shuster, H. Kuhn, E. H. Brandt, M. Indenbom, M. Koblischka, and
M. Konczykowsky, Phys. Rev. B 50, 16684 ~1994!.
4
R. J. Wijngaarden, H. J. W. Spoelder, R. Surdeanu, and R. Griessen, Phys.
Rev. B 54, 6742 ~1996!.
5
T. H. Johansen, M. Baziljevich, H. Bratsberg, Y. Galperin, P. E. Lindelof,
Y. Shen, and P. Vase, Phys. Rev. B 54, 16264 ~1996!.
6
A. A. Polyanskii, A. Gurevich, A. E. Pashitski, N. F. Heinig, R. D.
Redwing, J. E. Nordman, and D. C. Larbalestier, Phys. Rev. B 53, 8687
~1997!.
1
2
Gaevski et al.
Phys. Solid State 41 (6), June 1999
7
Y. Yeshurun, A. P. Malozemov, and A. Shaulov, Rev. Mod. Phys. 68, 911
~1996!.
8
A. Vl. Gurevich and R. G. Mints, Rev. Mod. Phys. 59, 941 ~1987!.
9
R. G. Mints and E. H. Brandt, Phys. Rev. B 54, 12421 ~1996!.
10
K. H. Müller and C. Andrikidis, Phys. Rev. B 49, 1294 ~1994!.
11
M. E. Gaevski, A. V. Bobyl, D. V. Shantsev, Y. M. Galperin, T. H.
Johansen, M. Baziljevich, and H. Bratsberg ~to be published in Phys.
Rev. B !.
12
C. P. Bean, Phys. Rev. Lett. 8, 250 ~1962!.
13
S. F. Karmanenko, V. Y. Davydov, M. V. Belousov, R. A. Chakalov,
G. O. Dzjuba, R. N. Il’in, A. B. Kozyrev, Y. V. Likholetov, K. F.
Njakshev, I. T. Serenkov, and O. G. Vendic, Supercond. Sci. Technol. 6,
23 ~1993!.
14
V. A. Solov’ev, M. É. GaevskiŽ, D. V. Shantsev, and S. G. Konnikov, Izv.
Ross. Akad. Nauk, Ser. Fiz. 60, No. 2, 32 ~1996!.
15
L. A. Dorosinskii, M. V. Indenbom, V. I. Nikitenko, Yu. A. Ossip’yan,
A. A. Polyanskii, and V. K. Vlasko-Vlasov, Physica C 203, 149 ~1992!.
16
M. McElfresh, E. Zeldov, J. R. Clem, M. Darwin, J. Deak, and L. Hou,
Phys. Rev. B 51, 9111 ~1995!.
17
M. V. Feigel’man, V. B. Geshkenbein, and V. M. Vinokur, Phys. Rev. B
43, 6263 ~1991!.
18
C. W. Hagen and R. Griessen, Phys. Rev. Lett. 62, 2857 ~1989!.
Translated by G. Skrebtsov