RAPID COMMUNICATIONS
PHYSICAL REVIEW B
VOLUME 58, NUMBER 14
1 OCTOBER 1998-II
Experimental comparison of the effect that bulk pinning and surface barriers have on vortex
motion in the vortex liquid state of Bi2Sr2CaCu2O8 single crystals
A. Mazilu and H. Safar
Department of Physics, University of Illinois at Chicago, Chicago, Illinois 60607
D. López
Materials Science Division, Argonne National Laboratory, Argonne Illinois 60435
and Department of Physics, University of Illinois at Chicago, Chicago, Illinois 60607
W. K. Kwok, G. W. Crabtree, P. Guptasarma, and D. G. Hinks
Materials Science Division, Argonne National Laboratory, Argonne Illinois 60435
~Received 23 June 1998!
We perform electrical transport measurements in the mixed state of Bi2Sr2CaCu2O8 single crystals by using
a Corbino disk geometry. In this configuration, vortices are forced to move in closed circular trajectories,
without crossing the sample’s edge. By comparison with conventional four-probe transport experiments we can
contrast the role that bulk pinning and surface barriers have on vortex motion in the vortex liquid state of this
material. Our Corbino and conventional experiments give the same temperature and field dependence for the
electrical resistivity in the vortex liquid state, activation energies for vortex motion and irreversibility lines.
Thus, we conclude that in these crystals, flux motion in the vortex liquid state is governed by bulk effects.
@S0163-1829~98!51338-0#
Research performed over the past ten years has uncovered
the richness of the equilibrium phase diagram of type II
superconductors.1,2 One important feature is that the traditional Abrikosov vortex lattice is melted into a vortex liquid
over a wide portion of the magnetic field-temperature plane.
In the vortex liquid phase, easy vortex motion produces a
finite, Ohmic electrical resistivity that is detected in fourprobe measurements.3
Early experiments found that in Bi2Sr2CaCu2O8 ~Bi2212!
single crystals the electrical resistivity in the vortex liquid
state is well described by a thermally activated temperature
dependence4 of the form r (T)5 r 0 3exp@2U0(H)/kT#. The
activation energy U 0 was found to be approximately 700 K
at H50.5 T. 4 Within a single-particle scenario, this thermally activated behavior was understood as arising from the
jump of vortices between pinning centers in the bulk of the
superconductor.4 Later, other considerations included vortexline crossing and cutting as possible contributors to the activation energy.5 All of these models assume that vortex motion is controlled by bulk effects, while surface and sample
edge effects are disregarded.
Recent measurements of the magnetic field generated by
the transport current suggest6 that in the conventional fourprobe experiments the electrical current flows mainly along
the edges of the sample instead of being uniformly distributed throughout the sample. This is apparently the case in
both the vortex solid and in the Ohmic, highly resistive vortex liquid states.6 This unexpected current distribution was
taken to indicate that the electrical resistivity of the edges of
the sample is several orders of magnitude lower than that of
the bulk.6 The edge’s lower resistivity in the mixed state
could imply that vortex motion is considerably slowed down
at the edges, while easy vortex motion is achieved in the
bulk. Such a scenario is possible if in this material the bar0163-1829/98/58~14!/8913~4!/$15.00
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riers for vortex penetration ~or exit! into the sample are more
effective than the bulk effects in reducing vortex motion. A
candidate for these barriers is the Bean-Livingston7,8 mechanism that results from the competition between the vortex
attraction to the surface and its repulsion with the Meissner
current. A second possibility is provided by the geometrical
barriers9 that come from creating a vortex of finite length
inside the bulk of the superconductor. Both these mechanisms could affect the entry or exit of vortices in the conventional four-probe experiments, since in this configuration
the Lorentz force acting on the flux lines forces them to
move across the edges of the sample. In the present paper,
we will use the terms entry-exit or surface barriers for both
the Bean-Livingston and geometrical mechanisms, since our
experiments will address both simultaneously.
In this work we report on electrical transport experiments
in the vortex liquid phase of Bi2212 single crystals. We devised a series of experiments that can clearly distinguish
whether bulk or surface effects dominate the vortex motion.
More precisely, we compare measurements of the electrical
dissipation produced by vortex motion in a standard fourprobe arrangement with that of a Corbino disk geometry.10 In
this latter geometry, vortices follow circular orbits without
crossing the edges of the sample, thus only bulk pinning will
control vortex motion. In the standard four-probe arrangement vortices will experience both surface and bulk pinning.
Thus, if bulk effects are dominant, the results from Corbino
and standard measurements ought to be identical. On the
other hand, if entry-exit barriers are the bottleneck for vortex
motion, there will be a substantial difference in the electrical
dissipation measured in both configurations. Our experiments show that the dissipation in the vortex liquid state is
the same, regardless of the geometry considered. Furthermore, the conventional and Corbino geometry yield the same
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© 1998 The American Physical Society
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FIG. 1. ~a! Corbino disk geometry. The electrical current is fed
into the sample using a central point contact I 1 and a circular frame
I 2 . Voltage contacts V A , V B , V C , and V D are placed in pairs along
radial lines. ~b! Standard bar geometry.
values for the activation energy and the irreversibility line.
Our results demonstrate that, in the vortex liquid state of
Bi2212, vortex motion is determined by bulk effects.
High-quality Bi2Sr2CaCu2O8 single crystals were grown
using a modified floating-zone process in a double-mirror
image furnace NEC SC-M15HD with an external home-built
control for very slow growth.11 These crystals have the onset
of the resistive zero-field transition at 95 K, and a transition
width ~10 to 90% criterion! of less than 1 K. Thin platelet
crystals of about 131 mm320 mm were selected for these
experiments. Electrical contacts of low resistance ('2 V)
were made by evaporating gold pads and attaching leads to
those pads with silver epoxy. In order to check the reproducibility of our data, a total of five crystals were prepared in the
Corbino disk geometry, as it will be detailed below, and
three in the conventional four-probe geometry. After the
measurements, two of the Corbino disks were cut in rectangular shape to perform conventional four-probe measurements, in order to compare, on the same crystal, the result of
transport experiments using the different geometries.
Shown in Fig. 1~a! is a diagram of the Corbino disk geometry used in our experiments. In this configuration, the
electrical current is fed into the sample by using a point
contact (I 1 ) located at the center of the sample and a circular
frame around it (I 2 ). This contact arrangement produces an
electrical current that flows radially between the center and
the perimeter. When the magnetic field is applied perpendicular to the plane of the figure, the resultant Lorentz force
will make vortices perform closed circular trajectories
around the center, as indicated by the thin line.10 For the
Corbino experiment, we placed voltage contacts pairs on the
ab face of the crystal along various radii of the disk, equidistant from the central current contact, as indicated in Fig.
1~a!. Multiple pairs of voltage contacts were used to check
the sample’s homogeneity and isotropy of the radial current
distribution. Thin samples were selected to minimize inhomogeneous current distribution12 along the c axis near the
central current contact. For comparison, we show in Fig. 1~b!
the conventional rectangular four-probe geometry, in which
electrical current is fed into the sample through contacts at
the ends of the sample (I 1 and I 2 ). With a magnetic field
applied perpendicular to the plane of the figure, vortices will
move along a direction transversal to the sample’s entry-exit
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FIG. 2. Electrical resistance of a disk sample versus temperature
for different magnetic fields. The electrical resistance in the mixed
state was measured by using many equivalent pairs of contacts, as
described in the text. Inset: shown is the zero-field temperature
dependence up to room temperature for the electrical resistance of
the same disk sample.
edges @thin line in Fig. 1~b!#. In order to distinguish the
effects that are dominant in the vortex motion, we performed
electrical transport measurements using both Corbino and
standard bar electrode geometry. In these experiments the
voltage arising from flux motion in the vortex liquid state
was measured using conventional ac and low-frequency dc
measurement techniques, while keeping the magnetic field
constant and slowly sweeping the temperature. All the experiments were performed with the magnetic field applied
parallel to the sample’s c axis ~perpendicular to the plane of
Fig. 1!. For all data reported in this paper, the response was
in the Ohmic regime ~linear I-V curves!.
Shown in Fig. 2 are results of the Corbino disk experiment. We measured the voltage between two pairs of contacts V B 2V A and V D 2V C , as described before, and divided
that by the total electrical current to calculate the electrical
resistance. The resulting electrical resistance is plotted versus
temperature for zero magnetic field ~inset and main panel!
and 500 G and 60 G ~in the main panel!. Experiments at
other magnetic fields were performed, and their results are
omitted from the figure for clarity. It is seen that the electrical resistance measured by both contacts follows a very similar temperature dependence, indicating homogeneous current
flow and sample properties. As a matter of fact, difference
between these resistances only becomes appreciable at very
low dissipation levels. To further investigate the homogeneity of the radial current distribution, we measured the voltage
difference between crossed pairs of contacts; i.e., V B 2V C ,
and V D 2V A . The results are also shown in Fig. 2, and are
very similar to the values obtained in the previously measured contact pairs, indicative of the isotropy of the current’s
radial distribution. As can be seen in Fig. 2, there are differences in the resistance values measured by the different voltage contact pairs. Differences of the same magnitude are
observed when we compare the electrical resistances of all
the samples investigated in this work. These differences are
likely to be due to local variations of the pinning properties
within the large crystals that we used. This conclusion is in
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EXPERIMENTAL COMPARISON OF THE EFFECT THAT . . .
FIG. 3. Comparison of the normalized electrical resistance versus temperature for a Corbino disk and a rectangular sample, for
various applied magnetic fields. Inset: results from the same experiments obtained in a different sample.
agreement with recent magneto-optical observations of flux
penetration in crystals from the same source as those used in
our work.13
After completion of the above-described Corbino experiments, we carefully cut the sample so as to convert it into a
rectangular bar geometry, keeping for voltage contacts one
pair previously used in the disk experiment. For current injection we used the remaining of the disk’s frame contact.
The sample cut in this fashion is effectively arranged as
the standard rectangular geometry. Since vortices cross the
sample in their motion, edge barriers could be relevant in this
geometry. We investigate the importance of these barriers by
comparing the temperature and magnetic field dependence of
the electrical resistance measured in the Corbino experiment
with that measured in this rectangular bar geometry. It is
important to remark that both experiments are performed in
the same sample, using the same pair of voltage contacts,
thus they both measure the same underlying bulk properties.
Of course, the current density is different in both cases. For
the same applied electrical current the electrical resistance of
the rectangular sample is higher than that of the disk sample,
even in the normal state. Experimentally, we find that, for
example at T5100 K and H50, the rectangular sample’s
resistance is about four times higher than the disk’s resistance, in agreement with the value estimated from the sample’s dimensions.
Shown in Fig. 3 is a comparison between the normalized
electrical resistance versus temperature obtained in the
Corbino-disk and the rectangular bar geometry experiments
performed in the same crystal. The electrical resistance data
are normalized to their values at 100 K to account for the
different current densities. It can be seen that, for all magnetic fields, the electrical resistances in the mixed state are
practically indistinguishable. A conservative estimate indicates that our resistivity measurements could clearly show
differences between the Corbino and standard geometries if
the contribution of the entry-exit barriers to the activation
energy U 0 is at least a 20% of the bulk pinning contribution.
This estimation is reached by requiring the resistivity to
change by an amount greater than the inhomogeneous spread
shown in Fig. 2. This is a conservative estimate since our
experiment is ultimately performed on the same section of
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FIG. 4. Zero-resistance lines ~defined at 1024 of the resistance
at 100 K! for the Corbino disk and rectangular samples. Inset: magnetic field dependence of the activation energy U 0 for a Corbino
disk and rectangular samples.
the sample. Thus, the data in Fig. 3 demonstrate that in these
Bi2212 crystals the electrical dissipation produced by vortex
motion in the liquid state is dominated by bulk effects. This
is the main result of our paper. Shown in the inset is the
result of an identical set of experiments performed in a different single crystal. For completeness, we also measured
standard bar samples ~i.e., without cutting them from a disk!,
and the obtained results are identical to those shown in the
figure. For all of the investigated samples, the electrical resistances measured in the Corbino and standard experiments
were always within the same order of magnitude. No systematic differences could be detected among the different sample
geometries, with either the conventional configuration giving
slightly more dissipation than the Corbino arrangement, or
vice versa. Thus, the scatter in the data is likely to arise from
differences in the pinning properties of the many crystals
investigated, as discussed before.
In addition to the electrical resistivity, other physical parameters can be compared. Shown in the main panel of Fig.
4 are the zero-resistance lines for the rectangular and disk
samples. These lines are defined when the measured electrical resistance drops below 1024 of its value at 100 K. Again,
we find that these lines are practically identical for both
samples, which is further indication that the same mechanism is governing flux pinning in these different geometries.
At low fields, the zero-resistance lines coincide with the
vortex-lattice melting transition in this material, and also coincides with the onset of magnetic irreversibility as seen in
our preliminary superconducting quantum interference device ~SQUID! magnetization measurements performed in the
same sample, all indicative that indeed these lines separate
the vortex liquid and solid phases.
In the inset to Fig. 4 we plot the activation energies for
vortex motion U 0 versus magnetic field for the disk and rectangular samples. The activation energy U 0 is calculated in
both cases from a fit to an Arrhenius expression of the low
temperature portions of the resistance versus temperature
data. Over a wide range of magnetic fields the activation
energies calculated for both samples are practically identical
in value and field dependence.
Thus, our experiments indicate that bulk pinning, and not
surface barriers, dominate vortex motion in these Bi2212
crystals. This is in apparent contradiction with the conclu-
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sions of the work by Fuchs et al.6 A possible reason for this
disagreement comes from the different relative strengths of
bulk pinning and surface barriers in the different samples.
We can expect that in samples with very weak bulk pinning
and strong surface barriers vortex motion could be dominated by the latter. However, our work shows that this would
not be a situation that can be extended to all other materials,
as suggested by earlier reports.6 Clearly, experiments where
bulk pinning and/or surface barriers are carefully controlled
are needed to exactly determine the regimes where vortex
motion is dominated by each of those factors. We should
remark that in our samples bulk pinning is not extremely
high: regardless of the geometry, our low-field resistance
versus temperature measurements show ~for example, at H
560 G in Fig. 3! the sharp drop attributed6 to the vortexlattice melting transition in this material. This indicates that
in the crystals used in this work bulk pinning is not strong
enough to destroy the order of the Abrikosov vortex lattice.
Indeed, preliminary SQUID magnetization measurements of
the critical current in our crystals yield a value of J c '3
3104 A/cm2 at T525 K and H50.1 T, a value of the same
order of magnitude to the one observed in very clean
crystals.14 Thus, our experiment also suggests that even very
G. W. Crabtree and D. R. Nelson, Phys. Today 50 ~4!, 38 ~1997!,
and references therein.
2
For a comprehensive review, see G. Blatter, M. V. Feigelman, V.
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Phys. 66, 1125 ~1994!.
3
H. Safar et al., Phys. Rev. Lett. 69, 824 ~1992!; W. K. Kwok
et al., ibid. 69, 3370 ~1992!.
4
T. T. M. Palstra et al., Phys. Rev. Lett. 61, 1662 ~1988!.
5
J. A. Fendrich et al., Phys. Rev. Lett. 74, 1210 ~1995!.
6
Dan T. Fuchs et al., Nature ~London! 391, 373 ~1998!.
7
C. P. Bean and J. D. Livingston, Phys. Rev. Lett. 12, 14 ~1964!.
1
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weak bulk pinning could overcome the effects of surface
barriers, placing a stringent limit on the regime in which
surface barriers would dominate vortex motion.
In conclusion, we have performed measurements of the
electrical resistance in the mixed state of Bi2212 single crystals. Our measurements were performed using a Corbino disk
geometry and a standard bar geometry. We find that in both
geometries the temperature and magnetic field dependence of
the flux-flow resistance, the activation energies for vortex
motion, and the irreversibility lines are identical. Our results
demonstrate that the motion of flux lines in the vortex liquid
state of these Bi2212 crystals is governed by bulk effects.
We would like to thank Vitali Vlasko-Vlasov for sharing
with us the results of his unpublished magneto-optic measurements, and Ulrich Welp for his help in performing the
preliminary magnetization characterization of our crystals.
The work at UIC was supported by a National Science Foundation CAREER Award DMR-9702535. The work at ANL
was supported by the U.S. Department of Energy, Office of
Basic Energy Science and the National Science Foundation
under Contract No. DMR91-20000 through the Science and
Technology Center for Superconductivity.
8
L. Burlachkov, A. E. Koshelev, and V. M. Vinokur, Phys. Rev. B
54, 6750 ~1996!.
9
E. Zeldov et al., Phys. Rev. Lett. 73, 1428 ~1994!.
10
R. P. Huebener, Magnetic Flux Structures in Superconductors,
Springer Series in Solid-State Sciences 6 ~Springer-Verlag, Berlin, 1979!.
11
P. Guptasarma and D. G. Hinks, Bull. Am. Phys. Soc. 42, 713
~1997!.
12
R. Busch et al., Phys. Rev. Lett. 69, 522 ~1992!; H. Safar et al.,
Phys. Rev. B 46, 14 238 ~1992!.
13
Vitali Vlasko-Vlasov ~private communication!.
14
T. W. Li et al., Physica C 274, 197 ~1997!.