APPLIED PHYSICS LETTERS
VOLUME 78, NUMBER 11
12 MARCH 2001
Scanning Hall probe microscopy of flux penetration into a superconducting
YBa2 Cu3 O7À␦ thin film strip
A. N. Grigorenko,a) S. J. Bending, and J. K. Gregory
Department of Physics, University of Bath, Bath, BA2 7AY, United Kingdom
R. G. Humphreys
DERA, St. Andrew’s Road, Malvern, Worcestershire WR14 3PS, United Kingdom
共Received 8 August 2000; accepted for publication 4 January 2001兲
A high-resolution scanning Hall probe microscope has been used to measure flux profiles across one
‘‘wire’’ of a long YBa2Cu3O7⫺␦ thin-film meander line as a function of both transport current
density and applied magnetic field. Flux bundle penetration due to an applied current or magnetic
field is demonstrated to occur at the same regions at the edge of the strip. A correlation between the
surface topography of the meander line edges and the regions of penetration has been established.
Penetrating flux profiles at low temperatures are in qualitative agreement with theories of dynamical
instability of the order parameter. © 2001 American Institute of Physics.
关DOI: 10.1063/1.1352041兴
Recently, significant progress has been made in understanding flux penetration into thin superconducting strips
共‘‘wires’’兲 due to applied fields or transport currents.1–3
There is a growing consensus that flux penetration into a
strip occurs via dynamic instability of the order parameter4,5
at which points the transport or Meissner currents flowing
through it become unstable to periodic perturbations. The
behavior of the penetrating flux is usually described in terms
of a thin-film Bean–Livingston barrier,6 which is sensitive to
the surface 共edge兲 of the superconductor. In thick films and
platelets, however, a barrier of geometrical origin suppresses
flux penetration.7 Despite these insights, a microscopic picture of the onset of flux penetration into high-temperature
superconductor thin strips, which has important technological implications, is still lacking. This is due in part to the fact
that the T and H range, which is interesting for applications,
lies outside the region of validity of Ginzburg–Landau
theory, which was successfully applied to evaluate the penetration field in superconducting disks.8 On the other hand,
the London theory describing the Bean–Livingston and
‘‘geometrical’’ barriers does not account for the process of
vortex nucleation. An additional practical complication
arises due to the fact that real film wires are not ideal and
contain grain boundaries and surface/edge imperfections.
Due to the concentration of the transport and Meissner currents at the edges of the superconducting strip,1 the quality of
these regions as well as presence of vortex pinning strongly
influences the penetration field.9
In this letter, we report the use of scanning Hall probe
microscopy 共SHPM兲 to directly observe the microscopic
mechanism of flux penetration into a thin-film superconducting meander line as the applied magnetic field and/or transport current is varied. The 0.35-␮m-thick YBa2Cu3O7⫺␦
共YBCO兲 共001兲 film was grown on a MgO substrate at 690 °C
by electron-beam coevaporation of the metals. The meander
line has a total length of about 8 cm and is based on repeated
2-mm-long segments of 40-␮m-wide wires with 20 ␮m
a兲
Electronic mail: pysag@bath.ac.uk
spacings, as shown in Fig. 1. It was patterned using conventional optical lithography and Ar-ion milling, and subsequently annealed to an overdoped state in atomic oxygen.
The original film had a critical temperature of 88⫾0.1 K as
measured by magnetization. Figure 1 depicts the resistive
transition of the meander line as well as measurements of the
critical current, which yield the transition temperature 86
⫾0.1 K after annealing and a critical current of 2.2⫻106
A/cm2 at 77 K. The critical current was inferred from an
abrupt fall in d(log V)/d(log I) 共i.e., the exponent of V
⫽I n ), where I is the transport current and V is the voltage
along the meander line, which corresponds to a crossover
from creep to flux flow.
Magnetic-field maps were generated using a SHPM
based upon a custom-built low-temperature scanning tunneling microscope 共STM兲, whereby the usual microscope tip is
replaced by a microfabricated semiconductor chip.10 Two
different types of Hall probes were used: a high spatial resolution 0.3 ␮m probe with field resolution of ⬃3 ␮T/冑Hz at
77 K patterned in a GaSb/InAs/GaSb heterostructure by
electron-beam lithography, and a high-sensitivity 0.85 ␮m
probe with field resolution of ⬃30 nT/ 冑Hz at 77 K patterned
FIG. 1. 共a兲 Resistive transition of the YBCO meander line and共b兲 measurements of the critical current as a function of temperature. Optical micrographs of the meander line are shown on the right.
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© 2001 American Institute of Physics
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Appl. Phys. Lett., Vol. 78, No. 11, 12 March 2001
FIG. 2. SHPM scans of the edge of the YBCO strip 共lower left, white
dashed line indicates sample boundary兲 after 共a兲 FC in ⫺0.5 Oe to 65 K
关gray scale 共GS兲 spans 0.5 G兴, 共b兲 after application of 16 Oe to the ⫺0.5 Oe
FC state at 65 K 共GS 32 G兲, after application 共to the ⫺0.5 Oe FC state兲 and
removal of 共c兲 32 Oe at 65 K 共GS 7.2 G兲, 共d兲 100 mA at 70 K 共GS 1.8 G兲,
共e兲 ⫺20 Oe 共GS 1.4 G兲, 共f兲 70 mA at 77 K 共GS 3.6 G兲. Scan size is 25⫻25
␮m2.
in a GaAs/AlGaAs heterostructure by optical lithography. To
facilitate STM tracking without shorting the meander line,
the sample 共excluding contact pads兲 was covered with 200
nm of dielectric Si3N4 and 100 nm of conducting Au. The
experiments were performed with the Hall probe about 0.3
␮m above the surface.
Several different locations on the meander line have
been studied and we have found that in all cases flux penetration 共due to an applied current or a magnetic field兲 occurs
in the form of flux bundles at specific ‘‘weak’’ spots near the
edge of the superconducting strip. Figure 2 shows SHPM
images across the edge of a superconducting strip, which
occupies the bottom-left-hand corner of the image. The
sample had been field cooled 共FC兲 to 65 K in ⫺0.5 Oe trapping about eight vortices in the scanned part of the strip 关Fig.
2共a兲兴. A magnetic field perpendicular to the meander line 共or
a transport current along it兲 has then been applied at this
temperature. Figure 2共b兲 depicts the local induction over the
sample surface after a magnetic field of 16 Oe was applied.
The subsequent image after field removal was identical to
Fig. 2共a兲. However, if the applied field 共current兲 exceeds a
critical value, flux penetrates into the sample and remains
there after the field removal. We define this critical value to
be the penetration field H p (current I p ). We note that this
definition is microscopic in nature and differs from the penetration field 共current兲 derived from macroscopic measurements. Figure 2 shows the flux distribution after the application and removal from the Earth FC state of 共c兲 32 Oe at 65
K, 共d兲 100 mA at 70 K, 共e兲 ⫺20 Oe at 70 K, and 共f兲 70 mA
at 77 K. Clearly, flux penetrates into the sample in the form
of flux bundles with a large number of flux quanta 关⬃25 in
the largest bundle and ⬃7 in the smallest in Figs. 2共d兲–2共e兲兴,
which enter the sample at the same locations at the edge of
the strip under application of I⬎I p or H⬎H p 关regions A and
B in Figs. 2共c兲–2共f兲兴. We found the same to be true at all
locations in the sample regardless of temperature, field, current, or magnetization history. Several other properties of
flux penetration should be noted. At lower temperatures flux
enters along a narrow strip at the edge of the sample, as
clearly seen in Fig. 2共c兲. At higher temperatures, when the
Grigorenko et al.
1587
effective penetration depth is larger and pinning is weaker,
flux penetration is dominated by the weakest spot at the edge
of the sample 关Fig. 2共f兲兴. Note also that the vortices trapped
inside the strip after field cooling did not move.
It is well known that the thin-film strip geometry is characterized by large demagnetization factors, and the Meissner
shielding currents 共and magnetic induction兲 are strongly enhanced at the edges of the strip. At the meander line edge the
surface magnetic field can be roughly evaluated as3 B
⬇H a 冑W/d, where H a is the applied field and W is the half
width of the strip, and should be almost 8⫻ bigger than the
applied field in our case. As a consequence, surface roughness and edge imperfections, as well as damage to the superconductor during lithographic processing, may be very important for the onset of flux penetration in such samples.
To establish whether a correlation between the distribution of penetrated flux and the surface topography exists, we
make use of gating mode of SHPM, which maps a modulation of the Hall voltage signal due to electric fields arising
near the sample when it is subject to a large sample voltage.
The local electric fields depend upon the local sample–probe
separation and, therefore, yield a map of the topography with
a resolution of about 0.3 ␮m for the high-resolution Hall
probe described above. The sample was initially cooled in
the Earth’s field and the gating image of the meander line
topography was acquired 关Fig. 3共a兲兴. This image was captured at a scan height of 0.3 ␮m above the sample surface. A
field 共or current兲 has then been applied to the strip 关Fig. 3共b兲兴
and the penetration field established by comparison of the
magnetic images before the application and after the removal
of the magnetic field 共current兲. The onset of flux penetration
after application of 22 Oe at 65 K is shown in Fig. 3共c兲.
Finally, a field higher than the penetration field was applied
to the Earth FC sample and the profile of the penetrated flux
after the removal of the field was captured 关Fig. 3共d兲兴. The
same procedure was repeated at different temperatures, as
shown in Figs. 3共d兲–3共f兲 for 65, 70, and 77 K. Clearly, flux
again enters the strip at weak spots at the edge of the sample,
see, e.g., A in Figs. 3共c兲–3共f兲. Line scans of the penetrated
flux at different temperatures and the gating image along the
edge of the superconducting strip, Fig. 3共g兲, demonstrate that
there is a good correlation between sample topography and
the penetration spots—the maxima of the magnetic induction
occur at the minima of the gating voltage, which correspond
to thinner regions of the sample 关marked by vertical arrows
in Fig. 3共g兲兴. We found the same correlation in almost all
locations studied on the meander line. We estimate that the
measured thickness variations are ⬃20 nm on a ⬃5-␮mlength scale over the meander line surface.
Another important feature of the flux penetration, which
is clearly resolved with the submicron Hall probe, is the
quasiperiodic modulation of the transport current along the
strip edges after the onset of the penetration process. Figure
4 shows surface plots of the local induction above the edge
of the YBCO strip 共FC in ⫺0.5 Oe to 65 K兲 after 共a兲 application of 32 Oe at this temperature and 共b兲 removal of the
field. The modulation can be seen in Fig. 4共a兲 as seven peaks
along the edge with the average peak-to-peak distance of
⬃3.5 ␮m and a peak-to-valley amplitude of ⬃12 G. This
modulation was quite pronounced at temperatures well be-
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1588
Grigorenko et al.
Appl. Phys. Lett., Vol. 78, No. 11, 12 March 2001
FIG. 3. 共a兲 Gating image of the surface of the sample 共lower left, white
dashed line indicates sample boundary兲. 共b兲 SHPM image after application
of 32 Oe to the ⫺0.5 Oe FC state at 65 K 共gray scale spans 73 G兲. SHPM
scans after application 共to the ⫺0.5 Oe FC state兲 and removal of 共c兲 22 Oe
at 65 K 共GS 1.9 G兲, 共d兲 32 Oe at 65 K 共GS 12.6 G兲, 共e兲 32 Oe at 70 K 共GS
14.7 G兲, 共f兲 16 Oe at 77 K 共GS 6.3 G兲. 共g兲 Gating response and magnetic
induction close to the edge of the superconducting strip along the solid black
lines shown in 共a兲, 共d兲–共f兲 offset for clarity. The vertical arrows indicate the
maxima of penetrated flux and minima of the strip height. Scan size is
25⫻25 ␮m2.
low T c and resulted in the modulation of the penetrated flux
after field 共current兲 removal 关see Fig. 4共b兲, where about
seven white peaks of local induction along the edge of the
strip are present with peak-to-valley amplitude ⬃8 G兴. The
wavelength of the modulation decreased as the temperature
was reduced, suggesting that it is connected to the penetration depth. We speculate that the modulation may be the
precursor of the dendritic penetration structures observed in
Nb films.11,12 The measured penetration field and penetration
current were linear functions of temperature in the temperature range 65–80 K, which suggests that the penetration field
is inversely proportional to the square of the penetration
depth ␭ 共or an effective penetration depth ⌳ eff⫽2␭2/d, where
d is the film thickness兲.
FIG. 4. Surface plots of the local induction above the edge of the YBCO
strip after 共a兲 application of 32 Oe to the ⫺0.5 Oe FC state at 65 K 共gray
scale spans 82 G兲, and 共b兲 removal of the applied field 共GS 21 G兲. The
meander line is in the upper-right-hand corner. Scan size is 25⫻25 ␮m2.
Finally, we discuss our results in the light of existing
theories. The dynamic instability of the order parameter4,5
predicts that flux penetrates the superconductor in the form
of a modulated strip along the edge of the sample, which is
in qualitative agreement with the results shown in Fig. 4.
However, the penetration field evaluated from Ref. 5 is
higher (H p ⬃100 Oe for YBCO兲 and the modulation wavelength is much shorter 共⬃12 nm兲 than our measured values.
This is not surprising since Ref. 5 considers an intermediate
geometry where ⌳ effⰇWⰇ␰ 共W is the width of the strip and
␰ is the coherence length兲 and magnetic fields created by
superconducting currents are neglected, leaving the coherence length as the only important length scale in the problem. We note that accounting for the demagnetization factor
of 8 estimated for our system reduces the predicted penetration field H p from 100 to 12 Oe, which is close to the measured values. Attempts have been made to incorporate order
parameter fluctuations into a theory of the thin-film Bean–
Livingston barrier in the presence of strong pinning and edge
roughness.9 This was, however, achieved in a rather ad hoc
fashion and yields estimates of H p which are more than an
order of magnitude smaller than our measured values. We
believe that the discrepancy will be resolved if this work can
be extended to realistically account for the presence of thickness variations and edge roughness.
In conclusion, we have found that the flux penetrates
into a YBCO superconducting strip in the form of flux
bundles at weak spots near the edge and established that
these tend to correspond to slightly thinner regions of the
film. The penetrated flux is spatially modulated along the
edge of the strip with a temperature-dependent period. We
do not fully understand the origin of the thickness variations
but speculate that they may arise due to inhomogeneous distribution of crystallographic defects, e.g., growth spirals. Our
results suggest that the production of smoother films, and
probably also better control of the lithographic process so as
to avoid edge damage, should increase the working field/
current range of high-temperature superconducting devices.
This work was supported in the U.K. by EPSRC and
MOD Grant Nos. GR/J03077 and GR/L96448 as well as the
University of Bath Initiative Fund.
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