INSTITUTE OF PHYSICS PUBLISHING
SUPERCONDUCTOR SCIENCE AND TECHNOLOGY
Supercond. Sci. Technol. 16 (2003) 199–204
PII: S0953-2048(03)55754-2
Quantitative magneto-optical analysis of
macroscopic supercurrent flow in MgB2
L Gozzelino1, F Laviano1, D Botta1, A Chiodoni1, R Gerbaldo1,
G Ghigo1, E Monticone2, C Portesi2 and E Mezzetti1
1
INFM - U.d.R Torino-Politecnico, INFN - Sez. Torino, Department of Physics, Politecnico
di Torino, C.so Duca degli Abruzzi, 24 10129 Torino, Italy
2
Istituto Elettrotecnico Nazionale ‘G. Ferraris’, strada delle Cacce, 91 10135 Torino, Italy
E-mail: enrica.mezzetti@polito.it
Received 8 November 2002
Published 3 January 2003
Online at stacks.iop.org/SUST/16/199
Abstract
Magnetic flux penetration and trapped flux patterns formed into a MgB2 film
during the increase and the subsequent decrease of the applied external
magnetic field were studied using magneto-optical imaging. The film was
grown by electron-beam evaporation and exhibits a granular structure. The
non-homogeneous fan-like shaped penetration, already pointed out in the
literature, was observed. To investigate the origin of this kind of penetration,
a quantitative approach was chosen. The induction magnetic field map and
the corresponding contour map of a framed zone show many isolated loops
originating from the granular nature of the sample. Inside such loops, an
estimation of the local current density was made through the inversion of the
Biot–Savart law. All the results point towards the conclusions that the
fan-like shaped patterns do mirror the percolation of dissipation paths.
Along these paths, some interfaces, distributed in a hierarchical order, play
the role of either pinning barriers or easy-flow channels.
(Some figures in this article are in colour only in the electronic version)
1. Introduction
The discovery of superconductivity at 39 K in the intermetallic
compound MgB2 [1] has stimulated the development of a new
class of superconducting materials, possibly suitable for power
[2–5] as well as for small-scale electronic applications [6–11].
In this respect, the correlation between local flux
penetration patterns and local current density for a given
microstructure of MgB2 films is a crucial step towards basic
understanding and process optimization. Actually, in most
experiments, the critical current densities are evaluated by
means of measurements integrated over the whole volume
[12] and the local information is someway shadowed. A
technique suitable for local investigations of the microscale electromagnetic properties is the magneto-optical (MO)
technique. This kind of analysis offers the advantage of
parallel measurements on each point of the analysed sample
surface, so that it can be successfully employed to study the
actual flux penetration paths as well as the local current values
and related parameters.
0953-2048/03/020199+06$30.00
Aiming at these issues, we applied this technique to the
study of a MgB2 thin film, chosen among a set of films
having the same microstructure. Magnetic flux penetration
and trapped patterns, formed during the increase and the
subsequent decrease of the applied external field, are shown.
A quantitative approach was chosen to obtain a deeper insight
into the flux dynamics. Namely the topographic distribution
and the in-field behaviour of the local current density, J (x, y),
are presented and discussed.
2. Experimental details
MgB2 films were synthesized by means of an ex situ two-step
synthesis process.
At first, amorphous boron precursor film was grown
directly on an oriented sapphire substrate, at ambient
temperature, by using electron-beam evaporation. The boron
film thickness was about 500 nm. Then, the precursor was
wrapped in Ta foils with Mg metal and encapsulated in an
evacuated quartz tube. The amount of the Mg provided a
© 2003 IOP Publishing Ltd Printed in the UK
199
L Gozzelino et al
(a)
(b)
(d )
Counts
Counts
(c )
Grain size (µm)
Channel width (µm)
Figure 1. (a) and (b) SEM images at different length scales showing that the film consists of uniformly distributed grains. The distributions
of the grain sizes as well as of the width of the visible channels between grains are reported in (c) and (d), respectively.
Mg vapour pressure sufficient to form MgB2 at the annealing
temperature. Finally, the tube was heated in argon atmosphere
(100 Torr), first at 600 ◦ C for 5 min and then at 890 ◦ C for
10 min.
In this paper we report on measurements made on a MgB2
film, chosen in a set of twin samples. Film dimensions are
8.36 mm × 3.66 mm × 0.35 µm and its resistive transition
temperature is 36 K. The transition width is less than 1 K.
Though their sizes were too large with respect to the frames
grabbed by our MO equipment, we chose not to cut the film in
order to avoid spurious scratches and boundary modulations
due to the cutting process. These scratches would result
in spurious MO patterns [13] that, in the framework of the
particular patterns observed, could be more misleading than
the features brought up along the current density evaluation
procedure by the chosen film geometry (see the discussion
below).
After preliminary scanning electron microscopy (SEM)
and x-ray diffraction analysis as well as a coarse MO check
of the entire film surface, we focused our analysis on a part of
the sample, as specified below.
The flux density distribution in the film was visualized
using MO imaging based on the Faraday effect in ferrite
garnet indicator films. A description of our experimental setup can be found elsewhere [14]. MO images were converted
to magnetic induction field maps, Bz (x, y), by means of a
suitable calibration curve obtained in a zone of the indicator
film far enough from the sample to not detect the field induced
by the sample itself. The local current density values were
calculated from the Bz (x, y) maps using the inversion of the
Biot–Savart law [15, 16]. This inversion is made through the
200
convolution theorem, taking into account the finite thickness
of the sample and the distance between the superconductor
surface and the measurement plane.
All MO characterizations were performed in zero-field
cooling, at temperatures ranging from 4.5 K to 18 K. The
maximum external applied field was µ0 Hext = 15 mT. The
field was applied perpendicular to the film surface.
The spatial resolution (pixel width) of the MO images
reported in this paper is 1.65 µm. Correspondingly, the
spatial resolution of the current density reconstruction process
depends only on the actual resolution of the magneto-optical
image, because the k-space samples are calibrated to yield
the correct quantitative values. The original spatial resolution
in real space can be down-sampled to filter high-frequency
noise; in our work, such filtering process was not applied,
so the current density maps have the same resolution of the
magnetic field images and high-frequency noise could affect
our distribution. Although it seems that the macroscopic
features are not affected by high-frequency noise, for local
quantitative evaluation we made a two-dimensional average
over zones 10 × 10 µm2 wide (6 × 6 pixels), average
equivalent to low-pass filtering in k-space (see section 3).
3. Experimental results and discussion
SEM images show a rather homogeneous grain structure
(figures 1(a) and (b)), characterized by MgB2 grain average
dimensions lower than 1 µm (see histogram in figure 1(c)).
The MgB2 grains, embedded in a smoother matrix, are oriented
with the c-axis normal to the substrate as detected by the θ–2θ
Quantitative magneto-optical analysis of macroscopic supercurrent flow in MgB2
(a)
(f)
(b)
(g)
Figure 3. Magnetic induction flux map at T = 4.5 K and µ0 Hext =
4 mT. The flux penetration is characterized by fan-like shaped
patterns and the flux penetration front can be interpreted as a
wrapper of these patterns. The dotted line indicates the sample edge.
(a)
(c)
(h)
(d)
(i)
(b)
(e)
( j)
Figure 2. MO images of the magnetic flux distribution in a selected
zone of the film at T = 4.5 K. (a)–(e) Images of the flux penetration
into the virgin state. The external magnetic fields are µ0 Hext = 3, 6,
9, 12 and 15 mT, respectively. ( f )–( j) Images at µ0 Hext = 12, 9, 6,
3 and 0 mT, respectively, during the subsequent field reduction. The
bright regions correspond to high values of the flux density, while
the fully dark areas are Meissner state regions. The dark scratches,
which do not change their colour when the external magnetic field is
changed, are defects of the ferrite garnet indicator films.
x-ray diffraction pattern where only substantial (0001), (0002)
and (0003) MgB2 peaks are present. The average width of
the channels among the grains, visible at SEM resolution, is
0.20 µm (figure 1(d)).
Figure 2 shows MO images of the magnetic flux
distribution in the sample at T = 4.5 K for a sequence of
Figure 4. Magnetic induction flux maps at T = 4.5 K: (a) flux
penetration at µ0 Hext = 15 mT, (b) distribution of the trapped
magnetic flux after the applied field was turned off. The
black/white dotted lines indicate the sample edge. The dotted frame
in (b) indicates the considered region in the Bz (x, y) and J (x, y)
maps shown below in figures 5 and 6, respectively.
field-increasing (µ0 Hext = 3, 6, 9, 12, 15 mT) and fielddecreasing (µ0 Hext = 12, 9, 6, 3, 0 mT) steps. The flux
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L Gozzelino et al
(a)
(b)
Figure 5. (a) Magnification of the part of the Bz (x, y) map framed in figure 4(b). The full/open circles put in evidence regions where the
field gradient is maximum/minimum. (b) Bz (x, y) contour plot corresponding to the map shown in (a). For the sake of readability, only the
contour lines ranging between the values Bz (x, y) = −1.2 mT and Bz (x, y) = 18 mT are plotted. The white/black dotted lines indicate the
sample edge.
front advances from the edge of the sample towards the
centre. However, there is no direct evidence of global
film connectivity. Fan-like shaped patterns modulating the
flux front penetration are clearly observed from the field
map reported in figure 3. This kind of pattern is similar
to that reported in [17, 18]. However, in the considered
range of temperature (4.5–18 K) we never observed dendritic
nucleation ahead of the flux front. Such particular patterns
were attributed in [17, 19] to thermomagnetic instabilities.
The absence of this phenomenon could be ascribed either
to different sample characteristics or to a better local heat
dissipation in our equipment.
In figure 4, a comparison between two field maps
representing the flux penetration at µ0 Hext = 15 mT and
T = 4.5 K (figure 4(a)) and the trapped flux after the field
removal (remnant state, figure 4(b)) is shown. First of all, it
is worthwhile to note that some more penetrated zones, when
the field is increasing, are penetrated by flux of opposite sign
in the remnant state. It means that the magnetic flux abandons
these regions when the field is decreased, and successively the
same regions are penetrated by flux of opposite sign, which
represents the stray field of the inner supercurrents. In contrast,
the cyan–green–yellow–red zones in the remnant state
(figure 4(b)) indicate zones where part of the penetrated
flux remains pinned and coarsely corresponds to the less
penetrated regions in figure 4(a).
This comparison is
useful to put in evidence the flux pinning at interfaces
between not penetrated/penetrated zones.
This nonhomogeneous penetration/pinning could be due to a hierarchy
of grain boundaries, some of them exhibiting weak-link
202
behaviour, whose nature is probably superconducting-normalsuperconducting [20, 21].
In figure 5(a) a magnification of the zone framed in the
Bz (x, y) map of figure 4(b) is shown. The corresponding
contour map is plotted in figure 5(b). In this chosen zone
many isolated loops originating from the granular nature of
the sample [22] show up and the paths are disrupted by several
defects so that the typical electromagnetic non-locality of thin
samples is greatly reduced. Therefore, these Bz (x, y) maps
enable, through the inversion procedure of the Biot–Savart
law, one to obtain a quite conservative estimation of the local
current density. The J (x, y) map related to the Bz (x, y) maps
of figure 5 is plotted in figure 6. It must be further stressed out
that, due to the granular nature of our sample put in evidence
by the Bz (x, y) contour plot, in figure 6 no spurious current
closure loops ascribed to the J (x, y) reconstruction process
are exhibited.
The non-homogeneous current distribution mirrors the
fan-like shape flux penetration. In particular, the full/open
circles in figures 5(a) and 6 put in evidence the correspondence
between zones where the field gradient is maximum/
minimum and regions where the current is higher/lower,
respectively.
The current density dependence on the local field
(calculated in correspondence of a typical zone labelled
by a square in figure 6) is shown in figure 7 at different
temperatures. It turns out that for Bz higher than the first critical
magnetic field, the beginning of a vortex entrance is revealed
by the increase of J towards the critical value. As soon as the
critical value is reached, the current density starts decreasing
and shows a Bz−α trend. By fitting the curves with the law
Quantitative magneto-optical analysis of macroscopic supercurrent flow in MgB2
on B is weaker, likely due to the fact that the grain boundaries
provide better pinning than at higher temperatures.
All the results point towards the conclusions that the fanlike shaped patterns, generally observed in MO, do mirror
the percolation of dissipation paths. Along these paths, some
interfaces distributed in a hierarchical order play the role of
either pinning barriers or easy-flow channels. Notwithstanding
the low current density of our films with respect to films
produced by other kinds of preparation [24], we believe that
the conclusion related to the role of fan-like shaped patterns
can be extended to all similar systems.
Acknowledgments
This work was partially supported by INFM, and by INFN
under Ma.Bo project.
References
Figure 6. Current density map referring to the Bz (x, y) maps shown
in figure 5. The full/open circles put in evidence regions where the
current density is higher/lower. The dotted line indicates the sample
edge.
Figure 7. Field dependence of the local J in the zone indicated by
the black square in figure 6. The zone is 10 µm × 10 µm wide and
the Bz and J are obtained by averaging the value of the pixels inside
the chosen zone in the Bz (x, y) and J (x, y) maps, respectively.
Dashed lines indicate fits with the law J = J0 (Bz )−α .
J = J0 (Bz )−α , with J0 and α as fitting parameters, we obtained
α values of about 0.2 at all the temperatures with an exception
of 4.5 K. In the high-temperature superconductor framework,
this dependence is correlated to weak-link behaviour at the
grain boundaries [23]. At T = 4.5 K the observed J dependence
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