Physica C 332 Ž2000. 445–449
www.elsevier.nlrlocaterphysc
Scanning Hall probe microscope images of field penetration into
niobium films
S.S. James a,) , S.B. Field a , J. Seigel b, H. Shtrikman c
a
Department of Physics, Colorado State UniÕersity, Fort Collins, CO 80523, USA
Department of Physics, The UniÕersity of Michigan, Ann Arbor, MI 48109-1120, USA
Department of Condensed Matter Physics, Weizmann Institute of Science, RehoÕot, Israel
b
c
Abstract
A high resolution scanning Hall probe microscope has been used to study the penetration of magnetic flux into thin strips
of superconducting niobium as the applied field is slowly ramped. The strips, with widths w s 100 mm, and thicknesses
d f 1 mm, are thick enough such that vortices are truly three dimensional Ž d 4 l.. However, the small ratio drw implies
very strong demagnetization effects, and the relative smallness of d emphasizes the importance of the long-range force
between vortex ends over the short-range force between their bulk core currents. The microscope has 1–2 mm spatial
resolution and around 30 mG field sensitivity, allowing high-resolution imaging of flux features over its approx. 150 = 150
mm2 scan range. At low fields of a few tens of gauss, we observe Meissner screening of the external field. As the field is
increased towards several kilogauss, flux begins to enter the sample in the form of small Žf 10 mm wide. dendritic fingers.
These fingers persist over all temperatures investigated, from 0.3 to 0.95 Tc . They appear to grow in such a way as to
maximize their separation from neighbouring fingers. This suggests a growth mechanism of the flux front mediated by a
competition between long-range repulsive interactions between mesoscopic flux-containing regions, and the strong pinning
that maintains the stability of the flux front. q 2000 Elsevier Science B.V. All rights reserved.
Keywords: Hall probing; Niobium; Fluxinning; Dendrites; Pattern formation; Critical state; Field penetration
The penetration of flux into a superconductor is a
complex process, mediated by the interplay between
pinning, vortex–vortex interactions, and screening
and transport currents. The physics of this process
has been extensively studied using a variety of imaging techniques, which allow a direct investigation
into the local spatial characteristics of the flux pene-
)
Corresponding author. Interdisciplinary Research Centre in
Superconductivity, University of Cambridge, Madingley Road,
Cambridge CB3 0HE, UK.
tration. These include scanning Hall probe microscopy ŽSHM. w1x, magneto-optical ŽMO. imaging
w2x, Hall arrays w3x and electron holography w4x. A
number of characteristic behaviours have been observed in a variety of materials. Critical state models
have been verified for YBa 2 Cu 3 O 7y d ŽYBCO. films
and Bi 2 Sr2 CaCu 2 O 8q d ŽBi2212. films with artificial
pinning sites w5x. Edge barriers have been observed
in Bi2212 by MO imaging by Indenbom et al. w6x,
and using Hall arrays by Zeldov et al. w3x. Konczykowski et al. w7x have used Hall probes to investigate edge barriers in YBCO. The effects of microstructure w8x, substrate w9x and surface topology
0921-4534r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved.
PII: S 0 9 2 1 - 4 5 3 4 Ž 9 9 . 0 0 7 2 1 - 2
446
S.S. James et al.r Physica C 332 (2000) 445–449
w10x on flux penetration have been studied in various
materials.
Here, we present magnetization loops and scanning Hall probe microscope images of flux penetration into strips of niobium film. The SHM is similar
to those described elsewhere w1,11x, but has a much
larger scan range, more than 150 = 150 mm2 . This
allows us to study both the local and global characteristics of flux penetration into fairly large Žf 100
mm wide. thin film structures. We find a complex
pattern of flux penetration as the external field is
ramped, with the flux entering the sample in the
form of unusual finger-like structures. Further, during any small external field increment, the flux
increases mainly in certain highly localized regions
of the sample; these regions constantly move about
as the external field is increased.
This behaviour may be clearly seen in Fig. 1,
which shows the Hall probe response measured vs.
applied field, with the Hall probe held stationary 25
mm from one edge of a 100-mm wide film. The
sputtered niobium film is 1 mm thick, and is characterized by fairly strong pinning; it had a residual
resistivity ratio ŽRRR. of about 3. As the external
field H is swept up and then down, the local field B
under the probe does not change in a smooth manner, as might be expected from a simple Bean-like
model. Rather, B increases and decreases very irregularly, sometimes changing at a much higher rate
than the external field does. We further note two
distinct types of flux change. On the upward sweeps,
and those down at higher temperature, the jumps are
small, irregular, and apparently not instantaneous.
However, particularly on the low-temperature down
Fig. 1. Magnetization loops at various temperatures for a 1-mmthick sputtered Nb film. The loops at 4.5 K and up are offset: 4.5
K, 400 G; 6.5 K, 700 G; 7.5 K, 900 G; 8.5 K, 1100 G.
sweeps we see very large, rapid changes in the local
field. Our imaging studies will suggest very different
physical origins of these two types of flux motion.
This magnetization behaviour is quite similar to
that reported by Stoddart et al. w12x, who ascribe
these jumps to the passing under the probe of ‘‘flux
bundles’’ — groups of vortices that move collectively and with a typical size scale. Our imaging
capabilities allow us to investigate these ideas in
much greater detail. We find no evidence for flux
motion in the form of bundles; rather, the flux-front
advances in a series of finger-like protrusions, which
appear at all temperatures investigated. Fig. 2 shows
SHM images taken at various temperatures and fields.
The characteristic behaviour seen at all temperatures
is the formation of dendritic finger-like protrusions
along the length of the film edge. There is a smooth
critical state front observed. The top row of Fig. 2
shows how the fingers form at the edge, presumably
at regions of weak edge pinning. As they move
further in, driven in part by the strong demagnetization currents, the fingers begin to branch out. It is
important to note, however, that there appears to be a
tendency for neighbouring fingers to avoid each
other. For instance, the finger, which is heading to
the right in panels 1 and 2 Žarrows., is evidently
pushed away by the presence of the flux structure to
the right of it and which is growing to the left in
panels 3 and 4. This implies that there is a long-range
repulsive interaction between neighbouring regions
of flux. Such an interaction exists in the form of a
1rr 2 force between vortices due to the surface
screening currents of individual vortices. In bulk
samples, this force is negligible compared to the
short-range force between vortex cores, but in a thin
Žbut still 4 l. film, these surface-mediated forces
may become crucial. We speculate that the destabilization of the flux front into these finger-like protrusions is due to this long range interaction, in a
similar manner to fingerings recently observed in
ferrofluid droplets w13x. Of course, there is no
‘‘surface tension’’ to be associated with the boundary of the flux front; instead, the flux structures are
kept from ‘‘blowing apart’’ by the strong pinning
present in these materials. Thus, this system presents
a very novel pattern-formation mechanism.
In the bottom row of Fig. 2 we show the flux
patterns at different temperatures. Panels 5–7 show
S.S. James et al.r Physica C 332 (2000) 445–449
447
Fig. 2. SHM images of the 1-mm-thick sputtered Nb film. ŽTop row. The progression of flux into the strip as the field is ramped from 200 to
500 G. The flux enters in distinctive finger-like structures. ŽBottom row. The left-most three panels show the appearance of the structures at
different temperatures, at a field of 400 G. The last panel shows a thermally activated flux jump into the film. The nature of this jump is
distinctly different from the fingering seen in the other panels.
that the fingers are present at all temperatures. The
main effect of temperature is to re-scale the field
needed to penetrate a given distance into the sample,
as expected from the strong dependence of the pinning strength with temperature. Additionally, at low
temperatures ŽT - 4 K., sudden large flux jumps are
observed ŽFig. 2, panel 8.. These jumps manifest
themselves as an instantaneous Žthey suddenly appear between one small field increment and another.
advance of the flux front across a large proportion of
the film. We believe these to be identical to the
thermally activated flux jumps observed by Duran
´ et
al. w14x: they are essentially instantaneous, have about
the same length scale, and stop when about halfway
across the sample. The very detailed structure observed by Duran
´ et al. is presumably missing here
because the small sample size does not allow for the
structure to form before the jump reaches the sample
center and stops.
It is difficult to completely rule out the possibility
that these protrusions of field are due to surface
scratches. Indeed, in several studies, flux is shown to
penetrate preferentially along surface imperfections
w10x. An inspection of the sample under an optical
microscope does reveal several scratches; two of
these were large enough to preferentially channel
flux along the left and right edges of the images Žthe
strip itself continues large distances to the left and
right.. However, there were no scratches visible
under the central area under discussion here. Furthermore, if flux were penetrating along randomly ori-
Fig. 3. Images and difference images at 6.5 K. Panel 1 is at
212.05 G and panel 2 at 312.95 G. Panel 3 is the difference
between the image taken at 212.05 G and an image taken at
201.83 G. Panel 4 is the difference between images at 312.89 and
302.95 G.
448
S.S. James et al.r Physica C 332 (2000) 445–449
Fig. 4. Images at 6.5 K in a clean 1-mm-thick epitaxial Nb film.
Panel 1 is a direct image at 81.86 G and panel 2 is the difference
between images at 63.67 and 54.58 G.
ented scratches, then the flux would be expected to
cross where scratches pass across each other. This
kind of behaviour is not seen; as discussed earlier,
the individual fingers avoid each other and are never
seen to cross over.
In order to better understand the penetration behaviour, we have made a series of images at closely
spaced applied fields. We investigate the areas of
greatest flux change by examining the differences
between consecutive images. As was also noted in
the magnetization data, the flux front is seen to
advance by a series of very nonlocal increases, as
shown in Fig. 3. We show direct images Žtop row.
and difference images Žbottom row., for fields near
200 and 300 G; the field increment over which the
differences were calculated was about 10 G. The
difference images are white where there has been an
accumulation of flux. The advancement of the flux
front is seen to be highly localized, with accumulation only in isolated areas, which may generally be
correlated with the tips of the finger structures.
However, certain fingers have grown during these
field increments by rather more flux than others
have; in a run of f 100 difference images, the white
spots appear to dance around the flux front in a
random manner as the external field is ramped. This
behaviour appears not to be compatible with a simple model in which the flux is being channeled by
surface imperfections. In that case, one might expect
the flux to flow in along these channels at a relatively uniform rate.
Finally, we present images of a cleaner niobium
film, epitaxially grown on sapphire. The RRR of this
film was 45, implying a very clean film with fewer
crystal defects, and thus lower pinning. Fig. 4 shows
a typical flux penetration image for this film. The
structure, about a third of the way in from the top
right of panel 1, is an extension of the Nb film
forming a voltage contact. The diagonal flux structure crossing the film just below the voltage contact
is due to a surface scratch. The temperature here is
near 6.5 K. The flux front does not appear as crisp as
those shown in Fig. 2, but there is still clear evidence
of dendritic penetration. The relative smoothness of
the flux front is possibly due to lower pinning in this
film. The difference image shows localized flux
accumulation similar to that seen in Fig. 3, though
this accumulation appears to be somewhat more
evenly distributed.
In summary, we have imaged flux penetration
into niobium films over a temperature range of 3.5 K
up to the critical temperature. We found that field
penetrates in the form of dendritic fingers of flux,
which advance by a series of irregular, spatially
localized bursts at all temperatures studied. At temperatures below 4 K, thermally activated flux jumps
are also seen, whereby, the flux front advances catastrophically across a large fraction of the film for a
small increase in applied field. We suggest that the
destabilization of the uniform flux front we observed
may be due to a long-range interaction between the
surface currents of individual vortices.
Acknowledgements
We wish to acknowledge the assistance of L.
Greene with the niobium sample fabrication.
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