Supercond. Sci. Technol. 12 (1999) 210–214. Printed in the UK
PII: S0953-2048(99)98131-9
Ultra-short time local current density
distribution in superconducting
strips: a new experimental approach
H Ferrari†, S O Valenzuela†, V Bekeris†k, V A Dediu‡ and
L Correra§
† Laboratorio de Bajas Temperaturas, FCE y N, Universidad Nacional de Buenos Aires,
Buenos Aires 1428, Argentina
‡ CNR-ISM, 40129 Bologna, Italy
§ CNR-LAMEL, 40129 Bologna, Italy
Received 3 October 1998
Abstract. We have studied the local current distribution in thin superconducting strips in the
presence of a transverse magnetic field, at very short times (∼10 µs) after the establishment
of the critical state. We used a non-conventional technique that combines the use of a pulsed
magnetic field and a synchronized pulsed laser. The high energy laser spot was directed to
irradiate different regions of the sample at controlled delays after the rising/falling edge of the
magnetic field. The time integrated photovoltaic pulse (∼10 ns) related to flux redistribution
was studied and a model is proposed that describes the measured signal in terms of the local
critical current distribution present in the sample at the time of laser irradiation.
1. Introduction
Magnetic flux penetration in high temperature superconducting thin films in transverse magnetic fields has recently received a great deal of attention. The interest is based on the
need for fundamental understanding and in the potential thin
film applications of the high temperature superconductors.
Recent theoretical work has addressed three main aspects:
(i) the understanding of the Bean critical state (CS) in thin film
geometry where the demagnetizing effect is large, (ii) the CS
response to slowly varying magnetic fields and/or applied currents and (iii) the time dependence of the spatial distribution
of magnetic field and current density governed by flux creep.
The strong demagnetizing effects for superconducting
long strips of width 2W along the x direction, and thickness
d along the z direction (d W ) with magnetic field Bz (x)
applied along the z direction, have led to static CS analytical
solutions [1–3] which show strikingly different features from
the well known Bean CS solution for slabs in parallel fields.
A detailed study of the CS behaviour of a strip in ac magnetic
fields [2, 3] and for an arbitrary sequence of applied transport
currents and transverse magnetic fields were recently
reported [3] where it is implicitly assumed that the electric
field Ey (x) is zero when current density Jy (x) obeys |Jy | 6
Jc , where Jc is the field independent CS current density, and
|Ey | 6= 0 for |Jy | > Jc but only for very short times after
changes in applied field or transport current occur [4].
Thermally activated flux creep, which is relevant in
high temperature superconducting samples [5], has been
k E-mail address: lbtuba@df.uba.ar
0953-2048/99/040210+05$19.50
© 1999 IOP Publishing Ltd
investigated and leads to non-linear, non-local flux diffusion
equations [6]. A simplified approach considering a modified
Bean CS model that incorporates a phenomenological time
dependent critical current density, Jc (t), has been reported to
describe results satisfactorily [7].
Recent experimental investigations have been supported
by modern techniques, in particular miniature Hall probes
[8–10] and magneto-optical imaging [11–14].
Both
techniques have provided a means for the experimental
study of the field distribution [15], resolving changes in flux
density over ∼10 µm scale distances. The intrinsic ms time
response of these techniques have limited their use when rapid
variations of magnetic flux density or current density need to
be investigated in detail.
In our previous work [16] we developed a nonconventional technique that combines the application of a
pulsed magnetic field and a synchronized pulsed laser for
the measurement of short time (∼10 µs) dc magnetization in
superconducting films. The experimental procedure consists
in driving the sample into critical state with a well defined
time origin by applying/removing the magnetic field at a
high rate (H = 1000 T s−1 ). After a controlled delay
td , a short laser pulse (∼10 ns) is triggered to heat the
sample above the irreversibility line. The vortex mobility is
drastically increased and the unstable distribution of vortices
at td completely relaxes in a very short time, so that the
resulting flux variation has a sufficiently high rate to be
detected with a pick-up coil. The time integrated pick-up coil
signal determines the overall magnetization of the sample at
td , M(td ).
Ultra-short time current density distribution
y
2W
xs
Bz
x
Figure 1. Schematic diagram of the film geometry and the
experimental array. The area delimited by the broken curve
indicates the laser spot at xs .
This technique was proven to be very efficient for
determining the time [16] and the field [17] dependence of the
film magnetic moment, but provides no direct information of
local magnetic field distribution. In this work we present
additional investigations for which we have modified the
technique, by providing two electrical contacts on the film
surface for the detection of the electric field E related
to photoinduced flux motion [18], following local laser
irradiation. We analyse the information contained in the time
integrated voltage signals and we describe future work to
further understand the behaviour of local irradiation voltage
response. Section 2 describes the experimental set-up, results
are discussed in section 3 and conclusions presented in
section 4.
2. Experiment
Epitaxial 5 × 10 mm2 × 300 nm GBCO films were deposited
onto (100) NdGaO3 by spark ablation. To avoid possible film
degradation by wet photolithography, a metallic mask in the
shape of a 2.5 × 10 mm2 strip with two voltage contact pads
(see figure 1) was carefully fixed over the film surface. The
unshielded surface of the GBCO film was removed by high
energy laser evaporation, and the film was patterned in the
form of a strip with ∼20 µm spatial definition. Gold sputtered
contacts (contact resistance below 10 ) were provided and
the films were characterized by resistivity measurements,
showing sharp transitions at 89 K.
The sample was attached to a copper–sapphire sample
holder thermally connected to a pumped liquid nitrogen
cold finger of an optical cryostat. A 25 A Oe−1 coil,
independently attached to the cold finger, was fixed with
its axis perpendicular to the film surface, and connected
to a homemade pulsed voltage source [20] to provide the
magnetic field, Ha . No current oscillations were observed
at current switch-off in accordance with the estimated
parameter (L/C)1/2 /R 1, where the self-inductance
L ∼ 1 mH, the stray capacitance C ∼ 0.1 µF and the coil
resistance R = 4 .
The magnetic field square pulse (∼1 µs rising/falling
edge, variable time width ∼10 µs–1 ms) had a stability better
than 0.05%, and the remanent field 0.5 µs after current cutoff was ∼5 Oe. Its radial variation was below 1% over the
sample area. The voltage source was designed to control the
magnetic field intensity without modifying its rising/falling
edge to investigate the photosignals as a function of applied
field.
A homemade trigger device [20] synchronized the pulsed
magnetic field and the laser and controlled the magnetic field
time width. The experiment was performed with a 0.7 Hz
repetition frequency.
An excimer laser provided 45 ns FWHM pulses at
308 nm and illuminated uniformly an area of 3 cm2 . To
investigate the effect of local optical heating a rectangular
slit 2.5 × 3 mm2 was placed between the optical source and
the film. A micrometric positioner was used to scan the slit
in the x direction without illuminating the voltage contacts.
We define the position of the laser spot, as the x coordinate of
the centre of the slit, xs , as schematically shown in figure 1.
Microcoaxial 50  cable connected the sample to a
500 MHz, 2 GS s−1 Tektronix oscilloscope with 50  input
impedance.
3. Results and discussion
In figure 2 we show a typical voltage pulse induced by local
laser heating (xs = 5/3 W) in a 68 K zero field cooled sample
(ZFC) at td = 5 µs following the application of Ha = 100 Oe.
The signal pulse has a height of about 200 mV, and a time
width of about 20 ns.
The short contact leads connecting the sample to the 50 
coaxial cable formed a small loop which was minimized to
reduce the voltage peak related to the combined effects of
the varying applied magnetic field during switch-on/off and
the magnetic flux diffusion into/out of the superconducting
strip (wide peak, ∼15 µs, shown in the inset). The self
inductance Lc of current paths and the 50  oscilloscope
input impedance determined a very short time constant,
estimated to be below the ns time scale. The sharp peak
(∼20 ns) in the inset is the photosignal and it should be noted
that the base line for its time integration can be taken to be
constant in time.
No photosignal is observed if the sample is irradiated
above the irreversibility line or if the magnetic field is not
applied, supporting our assumption that the photovoltaic
signal is related to rapid vortex movement driven by
metastable current distributions, as was also reported in [18].
Figure 3 shows the laser pulse intensity recorded with
a fast photodiode, and for comparison we also plot a
typical photosignal, which is shorter than the laser pulse
and much shorter than the calculated time scale of the free
surface and film–substrate interface temperature variation
[19]. With these results we can estimate the thermal diffusion
contribution to the spatial definition of the localized heating
to be of the order of the film thickness.
In our earlier work [16], we investigated the time
integrated voltage signal induced in a pick-up coil by the
relaxation of magnetic flux which followed the complete
rapid optical heating of a rectangular film. We showed
that as the pick-up coil self-inductance L and the by-pass
resistor R determined an L–R circuit analogous to a ballistic
galvanometer, the time integrated voltage signal provided the
sample magnetic moment M(td ).
In [17] we studied the overall magnetic moment as a
function of applied field in zero field cooled rectangular
samples (ZFC) where a second laser pulse was triggered
after the field was removed, to leave the sample in a clean
211
H Ferrari et al
Figure 2. Signal pulse, V (t), for a ZFC sample at 68 K, td = 5 µs following the application of Ha = 100 Oe. The inset shows in a different
time scale the wide peak related to the application of magnetic field, and the sharp signal pulse.
example [3]),
s 2
x W − a2
Jc
Jy (x) = −2 arctan
π
W a2 − x 2
(1)
for −a < x < a and Jy = ±Jc for a 6 x < W and
−W < x 6 −a, respectively, where a = W/ cosh(Ha /Hd )
and Hd (T ) = 4Jc (T )d/c is a characteristic field and d is the
film thickness. The magnetization per unit volume can be
easily calculated and is given by [3]
Mz
= − tanh(Ha /Hd )
Mmax
Figure 3. Laser pulse recorded with a fast photodiode. For
comparison the signal pulse, V (t), is also shown.
state before performing the next measurement at a higher
field. When the second laser pulse was not triggered, the
experiment corresponded to a sample in a different magnetic
condition: first the sample was field cooled (the film is
heated by the first laser pulse when the field is on, but
in approximately 1 µs the film cools down to its original
temperature while Ha is still switched on); then the field
was removed to leave the film in a field cooled reduced
state (FCR) and magnetic field was applied again in the next
repetition. We called this a FCR–ZFC condition. We showed
that results were in excellent agreement with calculations
in the framework of the Bean critical state for a disc in a
transverse magnetic field.
Here we examine samples in the shape of a strip, where
the transverse Bean critical state current density distribution
in a ZFC sample has the well known expression (see for
212
(2)
where Mmax = Jc (T )W/2c. For FCR–ZFC samples, it can
be shown that
Mz
= tanh(Ha /Hd ) − 2 tanh(Ha /2Hd )
Mmax
(3)
and Mz saturates to the same value in both conditions for
Ha Hd (T ).
Figure 4 shows the time integrated photovoltaic signal,
S, as a function of magnetic field for one and two laser pulses
at xs = (4/3)W (full and empty symbols respectively), as a
function of applied field at T = 68 K and td = 10 µs.
To examine whether the voltage signal scales with Mz (Ha ),
the data are compared to calculations. Full curves are the
calculated Mz (Ha ) for the ZFC and the FCR–ZFC conditions
following equations (2) and (3), with Hd as the only fitting
parameter. Clearly, the calculated field dependence describes
results at low fields but fails to describe experimental data at
higher magnetic fields. Moreover we have found a fairly large
discrepancy between the fitted values for Hd , which resulted
20 Oe in the ‘ZFC’ condition and 15 Oe in the ‘FCR–ZFC’
case, as compared to results reported in [16].
Ultra-short time current density distribution
Figure 6. The time-integrated photovoltaic signal, S(xs ), for a
Figure 4. Normalized time-integrated photovoltaic signal, S, as a
function of Ha . The measurements were performed at 68 K and
10 µs after applying the magnetic field, for ZFC (full symbols)
and FCR–ZFC (open symbols) samples. Hd (T ) was obtained by
fitting these measurements to equation (1) and equation (2)
respectively. The full curves show the normalized fit.
Figure 5. Calculated 1φ(xs ) across an area limited by the sample
edge, x = W , and the voltage leads, x = 4W , for the magnetic
field related to the currents of equation (1) in the irradiated area of
the sample for each xs .
Assuming that the photovoltaic signal is related to vortex
movement [18], it can be written as
Z y2
E(x, y, t) dy + ∂φ/∂t
V (t) =
y1
where ∂φ/∂t is the magnetic flux time variation across the
surface defined by the measuring leads and the path where the
electric field integral is evaluated. If the path integral is zero
(for example, due to symmetry for a path at x = 0) the time
integral of the voltage signal is the magnetic flux variation
1φ.
Assuming that the laser spot degrades the local current
density in the irradiated area, we have calculated the magnetic
field generated by these currents and the flux variation after
degradation, 1φ(xs ), across an area limited by the sample
edge, x = W , and the voltage leads, x = 4W , reproducing
our experimental set-up. We have made use of equation (1)
for the current distribution, and results are presented in
figure 5, where the intrinsic asymmetry of the experiment
with the voltage contacts provided at one side of the film is
observed.
laser spot scan across the film in the ZFC condition at T = 70 K
and Ha = 100 Oe, for two time delays, t1 = 10 µs and t2 = 20 µs
(full and empty symbols respectively), showing the effect of flux
creep.
Figure 6 shows S(xs ) for a laser spot scan across the
film in a ZFC condition at T = 70 K and Ha = 100 Oe,
for two time delays, t1 = 4 µs and t2 = 40 µs (full and
empty symbols respectively), showing the effect of flux creep
which will be discussed with further detail elsewhere. The
main features discussed above for calculations are present
in the experimental results; a maximum signal is obtained
irradiating approximately half the sample and a polarity
reversal occurs upon scanning approximately across the
middle of the film, although the response is not spatially
symmetric. Further tests have to be made to study the possible
effect of transport currents induced during the establishment
of the critical state when the magnetic field is switched on/off,
and possible non-local effects.
4. Conclusions
We have described a non-conventional technique to
investigate ultra-short time local dc magnetic properties of
superconducting thin films in transverse magnetic fields.
The accessible time scale is of the order of 10 µs, and
the spatial definition is 10 µm, which makes this method
very attractive for the investigation of a variety of ultra-short
time static or dynamic magnetic properties in thin films.
We have to mention that local modern techniques have a
time window that is approximately three orders of magnitude
higher, excluding the examination of transients towards the
critical state preparation.
A very simple model has been presented to describe
our experimental results for the time integrated photovoltaic
signal related to local optical heating, which resulted
satisfactory. Future work will be focused to elucidate the
possible contribution of transient transport currents induced
by the technique and of possible non-local magnetic flux
redistribution.
Acknowledgments
We acknowledge P Ruani for technical assistance. One of
the authors (H Ferrari) undertook this work with the support
213
H Ferrari et al
of the ‘ICTP Programme for Training and Research in Italian
Laboratories, Trieste, Italy’ and acknowledges the support of
Fundación Antorchas. This work was partially supported
by Fundación Sauberán and the Programme of Bilateral
Cooperation Lamel–UBA.
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