Supercond. Sci. Technol. 11 (1998) 821–829. Printed in the UK
PII: S0953-2048(98)93710-1
In-plane magnetoresistivity anomalies
near the average superconducting
transition in YBa2Cu3O7−δ and
Bi2Sr2CaCu2O8 crystals with
non-uniformly distributed
Tc -inhomogeneities
J Mosqueira†, S R Currás†, C Carballeira†, M V Ramallo†,
Th Siebold†, C Torrón†, J A Campá‡, I Rasines§ and Félix Vidal†
† Laboratorio de Bajas Temperaturas y Superconductividad, Departamento de
Fı́sica de la Materia Condensada, Universidad de Santiago de Compostela,
E15706, Spain
‡ Departamento de Cristalografı́a, Facultad de Ciencias Geológicas, Universidad
Complutense, E28040 Madrid, Spain
§ Instituto de Ciencia de Materiales de Madrid, Centro Superior de Investigaciones
Cientı́ficas, E28049 Cantoblanco, Spain
Received 28 April 1998
Abstract. We present detailed measurements of the in-plane magnetoresistivity,
ρab (T , H ), around the average superconducting transition in inhomogeneous
YBa2 Cu3 O7−δ (Y-123) and Bi2 Sr2 CaCu2 O8 (Bi-2212) crystals with small
Tc -inhomogeneities non-uniformly distributed in the sample volume, associated with
small oxygen-content inhomogeneities. In zero applied magnetic field, our results
confirm the presence in these inhomogeneous Y-123 crystals of sharp resistivity
peaks just above the average Tc , and they also show for the first time the presence
of similar anomalies in inhomogeneous Bi-2212 crystals. Our measurements for
magnetic fields, H , applied perpendicularly or parallel to the CuO2 (ab -) planes
show that in these inhomogeneous superconductors the so-called
magnetoresistivity excess, ρab (T , H ) − ρab (T , 0), is negative and very anisotropic
near the average Tc . By using two-dimensional electrical resistor networks, this
behaviour is explained, simultaneously and consistently for both directions of the
applied magnetic field, in terms of temperature dependent current density
redistributions associated with the presence of non-uniformly distributed
Tc -inhomogeneities in the crystals.
1. Introduction
The effects of different structural and stoichiometric
inhomogeneities, at different length scales, have been
an important subject of the physics of the low
temperature superconductors (LTSCs) [1, 2]. Due to their
small superconducting coherence length amplitude in all
directions, ξ(0), their layered structure and the complexity
of their chemistry, the copper oxide high temperature
superconductors (HTSCs) may still be more affected by
inhomogeneities than the LTSCs. Probably one of the most
common types of inhomogeneity in HTSCs are the critical
temperature (Tc ) inhomogeneities at long length scales (i.e.,
at length scales much bigger than ξ(0)), for example,
c 1998 IOP Publishing Ltd
0953-2048/98/090821+09$19.50 those produced by oxygen content inhomogeneities at
these length scales [3]. An expected but non-trivial
effect of these Tc -inhomogeneities when they are uniformly
distributed is that they round the critical behaviour of
different observables around the superconducting transition,
in competition with the intrinsic rounding effects associated
with thermal fluctuations [4]. But, in addition, it has
been recently recognized that when they are non-uniformly
distributed in the sample volume, these Tc -inhomogeneities
may deeply affect, mainly near the average superconducting
transition, the local current distributions [5]. These last
results may also provide an alternative explanation, in
terms of non-uniformly distributed Tc -inhomogeneities,
of the anomalous resistivity peaks observed above the
821
J Mosqueira et al
superconducting transition by other authors in other LTSC
[6–8] and HTSC [9, 10] compounds and that are being
attributed to different, and in some cases not well settled,
intrinsic effects.
As a further contribution to the understanding
of the transport properties near the superconducting
transition in inhomogeneous HTSCs, in this paper
we present the first measurements of the in-plane
magnetoresistivity, ρab (T , H ), in YBa2 Cu3 O7−δ (Y-123)
and Bi2 Sr2 CaCu2 O8 (Bi-2212) crystals with non-uniformly
distributed Tc -inhomogeneities associated with oxygen
content inhomogeneities.
The measurements were
performed for magnetic fields, H , applied perpendicularly
and parallel to the superconducting ab- (CuO2 ) planes,
and up to µ0 H = 1 T. To explain in terms of these
inhomogeneities the presence and the behaviour of the
ρab (T , H ) peaks, which lead in particular to a negative
(and very dependent on the magnetic field orientation)
magnetoresistivity excess, ρ(T , H ) − ρ(T , 0), we use twodimensional electrical resistor networks, that will also
allow us to visualize the corresponding electrical current
redistributions near the average superconducting transition.
The interest of our present magnetoresistivity results is
enhanced by the fact that recently different groups have reported the observation of a similar negative and anisotropic
magnetoresistivity excess in Y1−x Prx Ba2 Cu3 O7−δ and
La2−x Cex CuO4 crystals [11, 12], which these authors attribute to two-dimensional weak localization effects. A
negative magnetoresistivity excess near Tc has also been
observed in some LTSCs [6], and it was attributed to different intrinsic effects, such as superconducting fluctuations or localization effects. However, we will see in our
present paper that these different effects may be easily understood, in some cases at a quantitative level, in terms of
Tc -inhomogeneities. The presence of these inhomogeneities
may also explain other interesting experimental results, as
for instance the dependence of the anomalous ρ(T , H ) peak
on the amplitude of the electrical current density used to
measure it, an effect recently observed in superconducting
wires and attributed to phase slips of the superconducting order parameter in these quasi-one-dimensional systems [6]. Our results in Bi-2212 crystals may also provide information about the electrical current redistribution
associated with the presence of Tc -inhomogeneities in these
much more anisotropic compounds, a subject that may concern other important aspects of the Bi-2212 materials, as
the non-uniformly distributed flux-flow effects observed in
these compounds [13].
2. Experimental details and results
To measure the in-plane magnetoresistivity in Y-123
crystals having non-uniformly distributed small oxygen
content inhomogeneities, we have used two of the samples
previously studied, in the absence of an applied magnetic
field, in [5] (samples denoted Y16 and Y11). In this
reference the details of the growth procedure of the
crystals and of their general structural characterization
were presented. Let us just note here that both samples,
although quite twinned, present good structural quality,
822
and their stoichiometric homogeneity is better than 4%,
the resolution of our x-ray measurements. However, as is
well established [14], oxygen-content inhomogeneities well
within this uncertainty may originate Tc -inhomogeneities
of the order of a few degrees. In turn, as shown in [2],
these small Tc -inhomogeneities may originate anomalous
ρ(T ) peaks. In fact, the two Y-123 samples studied
here were chosen because although they are homogeneous
within 4% both present sharp ρ(T ) peaks just above their
superconducting transition, suggesting then the presence
of quite small non-uniformly distributed oxygen-content
inhomogeneities.
Details of the growth procedure and of the general
characterization of the Bi2 Sr2 CaCu2 O8 (Bi-2212) crystals
used in this work were reported elsewhere [15]. Most of
these crystals do not present any anomalous resistivity peak
near Tc . However, in one of the samples (hereafter denoted
Bi33) when the current is injected in the ab-plane at the
top face of the crystal the voltage measured at the bottom
face presents a sharp peak, just above the superconducting
transition, very similar to that we have previously observed
in oxygen deficient Y-123 crystals [5]. We are going to
study here the magnetoresistivity near Tc of this Bi-2212
sample. The analysis of these Bi-2212 crystals with a
polarized-light optical microscope shows that in general
they are very twinned. In addition, the Bi33 sample
studied here presents other important structural defects,
such as intergrowths and cracks. These defects may mix
in some parts of the sample the ab- and c-crystallographic
directions, which may explain the relatively high ρab and
low ρc values measured in that sample (see later).
The ρ(T , H ) measurements were performed by using
a conventional lock-in amplifier phase sensitive technique
(at 37 Hz) described previously [16]. The electrical contact
wires (of gold) are attached to silver coats (1 µm thickness
and 200 µm width), evaporated onto the sample through
a mask, by using silver paste (Dupont 4929), followed by
heating at 400 ◦ C for 2 h in oxygen atmosphere. In the
case of the Y-123 sample, the measurements in the abplane were performed with the contacts in line. The two
silver coats at the sample edges used to inject the electrical
current also cover the two corresponding lateral sample
faces, thus ensuring that the applied current is uniformly
injected through the sample. In this way, the intrinsic
anisotropy of the Y-123 crystals (ρc ≈ 102 ρab ) does not
directly affect our ρab (T ) measurements. In the case of the
Bi-2212 crystal, the electrical contact arrangement is also
in line, but an additional pair of contacts has been placed
on the bottom face of the sample. In this case, the contacts
used to inject the current do not cover the lateral faces.
With this geometry, the voltages measured in both sides of
the sample are affected by the intrinsic strong anisotropy
of this compound (ρc ≈ 105 ρab ) [13]. In both samples, to
study the influence of an external magnetic field, we have
made measurements for two different field orientations with
respect to the ab-planes, and up to 1 T.
Some examples of the in-plane magnetoresistivity
measured in the Y16 sample before re-oxygenation are
presented in figures 1(a) and (b). These results lead
to a negative and anisotropic (i.e., depending on the
Y-123 and Bi-2212 with Tc -inhomogeneities
120
80
(T,H):
Calculated ρth
ab
91.9 K
91.8 K
0.3 T
0.5 T
1T
-0.1
∆ρab(T,H)/ρab(T,0)
ρab (µΩ cm)
100
0
Y16 crystal before re-oxygenation
Measured ρab(T,H):
0T
91.7 K
91.6 K
-0.2
60
H ⊥ ab
40
91.5 K
-0.3
20
∆Vab
Iab
(a)
∆ρab(T,H)/ρab(T,0)
ρab (µΩ cm)
80
∆Vab
Iab
40
91.3 K
-0.1
91.7 K
91.6 K
-0.2
91.5 K
91.4 K
H // ab
H⊥I
-0.3
20
91.3 K
(b)
(b)
0
83
(a)
91.9 K
91.8 K
H // ab
60
91.4 K
-0.4
0
0
120
100
H ⊥ ab
-0.4
85
87
89
T (K)
91
93
95
Figure 1. In-plane magnetoresistivity versus temperature
of the crystal Y16 before reoxygenation for different
external magnetic fields with various amplitudes and
orientations. In (a) the field was applied parallel to the
crystallographic c -direction. In (b), it was applied parallel to
the CuO2 (ab -) layers but still perpendicular to the injected
current. The lines are the result of the simulations
performed with the electrical resistor network represented
in the inset of figure 3(b).
orientation of H with respect to the CuO2 planes) in-plane
magnetoresistivity excess which, for each magnetic field
orientation, may be quantified through
1ρ(T , H ) ≡ ρ(T , H ) − ρ(T , 0).
(1)
The data points in figures 2(a) and (b) correspond to the
measured 1ρ(T , H ) for H perpendicular and, respectively,
parallel to the ab-planes. Only the 1ρ(T , H )-values
corresponding to temperatures above the ρ(T , 0) peak have
been represented. These important 1ρ(T , H ) values cannot
be explained in terms of thermal fluctuations (see [4]
and references therein). These results also show that,
as may be expected from the ρ(T , H )-data, 1ρ(T , H )
is very anisotropic. In particular, for H parallel to the
c-direction the 1ρ(H )T saturation value is reached, at
each temperature, for smaller field amplitudes than for H
parallel to the ab-planes. This behaviour of 1ρ(T , H )
is quite similar to that observed by other groups in other
HTSC and LTSC compounds having ρ(T , H )-peaks near
the superconducting transition and attributed by these
authors to intrinsic effects [6, 8–12] (compare, in particular,
figures 2(a) and (b) with figure 2 of [11]).
0
0.2
0.4
0.6
0.8
µ 0H (T)
1
1.2
Figure 2. Normalized magnetoresistivity excess of the
crystal Y16 before reoxygenation at temperatures above
but near the maximum of the anomalous ρ(T , H ) peak.
(a) For H applied parallel to the c -direction. (b) For H
applied parallel to the ab -planes and perpendicular to the
injected current. The solid lines are the result of the
simulation performed with the electrical resistor network
represented in the inset of figure 3(b).
The experimental results for the Y16 sample after its
reoxygenation are presented in figures 3(a) and (b) for H
applied parallel and, respectively, perpendicularly to the
CuO2 planes (see inset in figures 1(a) and (b)). In this
new oxygen annealing the crystal was again placed in a
boat within a tubular furnace with O2 flowing. The furnace
was then heated up to 600 ◦ C (at a rate of 100 ◦ C h−1 ),
kept at this temperature for 2 h, cooled to 400 ◦ C in 1 h
and held at this temperature for four days. These latter
processes were repeated three times. We see in figure 3(a)
that the anomalous peak has completely disappeared from
this ρab (T ) curve. As, in addition, no structural changes
were observed after these new annealings, these results
confirm that the peak observed before is related to the
presence in the sample of small (much less than 4% of the
average oxygenation, the resolution of our x-ray diffraction
measurements) oxygen-content inhomogeneities, that are
strongly reduced by successive O2 annealings. Let us
note here that these results fully confirm the behaviour
observed before in other Y-123 crystals with resistivity
peak anomalies [5] and, therefore, they provide new
support to the explanation of the anomalous resistivity
peak in terms of non-uniformly distributed oxygen-content
inhomogeneities. One of the new central aspects of the
823
J Mosqueira et al
140
~ab (T,H) after re-oxygenation:
Measured ρ
~
Calculated ~
ρab (T,H):
I
∆V
ab
ρ a b(µΩ cm)
100
80
0T
0.3 T
0.5 T
1T
Bi33 crystal
0.3
Rtop (Ω)
120
0.4
0T
0.3 T
0.5 T
1T
Lz
Ly
60
0.1
Y16 crystal
H ⊥ ab
(a)
(a)
0
120
∆Vab
0
0.15
~
Rab
Measured
Rbottom(T,H):
~~
Rc
Iab
Rbottom (Ω)
ab
ρ a b(µΩ cm)
100
80
60
40
~~
0.1
0.3 T
0.1 T
0.05 T
0.025 T
0.01 T
0T
Calculated
th
(T,H):
Rbottom
I
H ⊥ ab
0.05
Rab
20
∆V bottom
H // ab
(b)
85
H=0
I
∆Vtop
20
(b)
87
89
91
93
0
0.15
95
T (K)
present paper is to study how these anomalies affect the
measured magnetoresistivity.
Our results for the resistivity peak observed near Tc in
the Bi33 crystal studied here are summarized in figures 4(a),
(b) and (c). In these figures, which show for the first time a
resistivity peak near Tc in a Bi-based HTSC, the measured
top and bottom resistances are defined as V /I , where V
is the top (Vtop ) or bottom (Vbot ) measured voltage (the
voltage corresponding to the leads placed in the same or,
respectively, in the opposite crystal face to the electrical
current contacts), and I is the total injected current. As can
be seen in figure 4(a), the resistive transition in the absence
of an applied magnetic field measured in the top face of
the crystal is very wide and also it is somewhat deformed
(it presents a small step), but it does not present any peak.
In contrast, as it can be seen in figures 4(b) and (c), the
bottom resistance presents a very sharp peak preceding
the superconducting transition. This peak, as well as
its reduction by a magnetic field applied perpendicularly
(figure 4(b)) or parallel (figure 4(c)) to the ab-planes, is
very similar to that observed in the in-plane resistivity in
the case of the inhomogeneous Y-123 samples, although the
Measured
Rbottom(T,H):
Rbottom (Ω)
Figure 3. In-plane magnetoresistivity versus temperature
of the crystal Y16 after reoxygenation for different magnetic
fields applied normally (a) and parallel (b) to the ab -planes.
The lines are the resistivities used in the electrical resistor
network for the less oxygenated domains. Inset in (a):
schematic diagram of the Tc -inhomogeneities of the crystal
Y16. The shadowed parts correspond to the highest Tc
domains and the dashed areas are the silver-coated
electrical contacts. Inset in (b). two-dimensional electrical
network for the sample schematized in (a).
824
Calculated Rtopth (T)
Lx
40
0
0.2
Measured Rtop (T)
0T
0.1 T
0.3 T
1T
0.1
Calculated
th
(T,H):
Rbottom
I
H // ab
0.05
∆Vbottom
0
60
70
80
T (K)
90
(c)
100
Figure 4. Resistance versus temperature of the crystal
Bi33 for different magnetic field strengths and orientations.
(a) Obtained with the voltage terminals located on the
upper face. (b), (c) Obtained by using the voltage terminals
on the bottom face. The lines are the result of the
simulations performed with the electrical resistor network
represented in the inset of figure 6(b).
influence of H is appreciable at much lower values than for
these last samples. Moreover, the important temperature
width of the resistive transition of this Bi-2212 sample is a
clear indication of the existence of important stoichiometric
inhomogeneities. Finally, note two points: (i) In all
the measurements we have observed that the resistivities,
including the peak amplitude, do not depend appreciably on
the electrical current densities used, from 1 to 15 A cm−2 .
Above 15 A cm−2 , some simultaneous decrease of the
peak amplitude and of the transition temperature has been
detected. However, these small effects could be spurious
Y-123 and Bi-2212 with Tc -inhomogeneities
and due to the sample heating by the Joule effect produced
in the electrical contacts between the samples and the
current leads (see also next section). (ii) Due both to
the spatial smallness of these inhomogeneities (less than
10% of the sample volume fraction) and to their small
amplitude (the oxygen-content variations are less than 5%
of the total oxygenation) any direct measurement of these
inhomogeneities (such as x-ray diffraction) will be quite
difficult to make. We have, however, performed some local
measurements of the distribution of the inhomogeneities in
the samples by adding additional voltage probes. Due to
the smallness of the crystals, these new lead arrangements
were quite difficult to implement and our corresponding
measurements are not very conclusive. Some qualitative
information about the inhomogeneity distribution in the
samples could also be obtained by performing threelead measurements and using then successively two of
the different leads as voltage probes. We have also
made this type of measurement, which have allowed
us to observe some appreciable variations of the peak
anomalies. These last results provide further qualitative
support to our present analyses.
Moreover, direct
observations of microscopic inhomogeneities in different
HTSC crystals, performed by other authors with energydispersive diffraction of synchrotron-produced x-rays,
fully confirm that the presence of small oxygen-content
inhomogeneities localized in the sample borders is quite
common in these crystals [17].
3. Data analysis
The central aim of this section is to explain at a
quantitative level, in terms of non-uniformly distributed
Tc -inhomogeneities, the experimental data on the negative
and anisotropic magnetoresistivity excess presented before.
For that, we will use two-dimensional electrical resistor
networks, as first proposed in [5] in the case of the
resistivity peaks. A new central aspect of the present paper
is to simultaneously and consistently analyse with this type
of resistor network the magnetoresistivity anomalies for
the magnetic field applied perpendicular and parallel to
the ab-planes. These inhomogeneities will be small (of
the order of two degrees or less, i.e., less than 3% of the
average Tc ) and they may be due to small stoichiometric
inhomogeneities (mainly of the oxygen content) extending
over 10% or less of the sample volume. So, we are not able
to directly determine these small local inhomogeneities. In
addition, due to the oxygenation process, it is reasonable
to expect that the best oxygenated parts of the crystal
will be the edges of the sample domains. An example
of an inhomogeneity distribution capable of generating
the anomalous ρab (T , H )-behaviour observed in the Y16
crystal is the one schematized in the inset of figure 3(a).
In this figure, the shadowed domains at the upper edges of
the crystal are better oxygenated and they have a higher Tc
than the rest of the crystal. The dimensions of each high-Tc
domain are 13 Lx , Ly , 17 Lz , where Lx , Ly and Lz are the
sample’s dimensions. To study how this inhomogeneity
distribution affects the measured ρab (T , H ) and generates
the anomalous peak, we simulate the measurement through
an equivalent electrical network. The geometry of the
inhomogeneity distribution and the contact arrangement
allows us to reduce the equivalent electrical network, in
principle three dimensional, to the bi-dimensional one
represented in the inset of figure 3(b). The resistances
≈
≈
denoted as R ab (T , H ) and R c (T , H ) correspond to the
less oxygenated domains (with lower Tc ), while R̃ab (T , H )
corresponds to the domains with higher Tc . Each resistance
in the network is related to the corresponding resistivity in
the crystal by
R̃ab (T , H ) =
Lx (N + 1)
ρ̃ab (T , H )
Lz Ly N
(2)
≈
this relationship applying also to R ab (T , H ) (with
≈
ρ ab (T , H )), and by
≈
R c (T , H ) =
≈
Lz (N + 1) ≈
ρ c (T , H ).
Lx Ly N
(3)
≈
In these equations, ρ ab (T , H ) and ρ c (T , H ) correspond
to the less oxygenated domains (with lower Tc ), whereas
ρ̃ab (T , H ) corresponds to the domains with higher Tc ,
and N × N is the number of meshes of the network
≈
(6 × 6 in this case). For ρ ab (T , H ), we used the profiles
also shown in figures 3(a) and (b), that are typical of
non-fully oxygenated Y-123. The resistivity in the cdirection is assumed to be one hundred times the inplane resistivity. We assume also that ρ̃ab (T , H ) for H
parallel and perpendicular to the ab-planes may crudely
be approximated by the resistivities measured after a new
oxygen annealing, which are presented in figures 3 (a) and
(b). However, to achieve the excellent agreement with the
experimental results observed in figure 2, for ρ̃ab (T , 0) we
have used the dotted curve represented in the same figure,
that is slightly smoother than the experimental ρ̃ab (T , 0).
Such an excellent agreement is obtained in spite of the
simplicity of our network, consisting only of 6 × 6 meshes
and two different types of domain [18].
A first example of the results of these calculations
is the solid lines in figures 1 and 2. As it can be
seen, the agreement between the experimental data and
the simulation is excellent, the anomalous behaviour of
the magnetoresistivity and of the magnetoresistivity excess
being reproduced at a quantitative level for both orientations
of the external magnetic field. In figure 5(a) is represented
the current distribution in the network at T = 95 K,
a temperature well above the superconducting transition.
This case corresponds, therefore, to the trivial situation
in which the different sample domains with different
oxygen content have almost the same (normal) resistivity,
so the current lines are parallel to the ab-plane and
uniformly distributed and no anomaly is then observed.
In contrast, the electrical current distribution shown in
figure 5(b) corresponds to T = 91.2 K, the temperature
at which the maximum of the resistivity peak occurs.
At this temperature, the domains with higher Tc are
already superconducting and, therefore, the current density
distribution is no longer uniform. There appears a higher
current density in the top face of the crystal, where the
825
J Mosqueira et al
3
120
I
(a)
µ0H = 0
Lz
Ly
ρ (m Ω cm)
∆V
60
2
~
ρ ab (T,H)
∆Vtop
∆Vbottom
Bi33 crystal
Lx
ab
ρab (µΩ cm)
T = 95 K
~
~
ρ ab (T,H)
H ⊥ ab
1
0T
0.05 T
(a)
0
120
~
~
I
(b)
Rc
ab
ρ (m Ω cm)
2
∆V
60
~
~
ρ (T,H)
ab
∆Vtop
Rab
~
~
T = 91.2 K
µ0H = 0
ρab (µΩ cm)
0.1 T
0
3
~
ρ (T,H)
ab
~
Rc
H // ab
~
Rab
1
∆Vbottom
0T
0.3 T
1T
(b)
0
0
120
ρab (µΩ cm)
µ 0H = 1 T
T = 91.2 K
∆V
0
85
90
95
100
T (K)
Figure 5. Examples of the current redistributions
originating in the electrical network corresponding to the
crystal Y16 and represented in the inset of figure 3(b).
(a) At T = 95 K, well above any superconducting transition
in the sample. (b) At T = 91.2 K the temperature at which
the anomalous peak has its maximum and the highest Tc
domains become superconducting. (c) At T = 91.2 K, with
a magnetic field of 1 T parallel to the c -crystallographic
direction. These striking differences in both the current
distributions and in the measured ρ(T , H ) are associated
just with differences of the temperature and magnetic field
dependence of ρ(T , H ) in each sample domain.
voltage contacts are placed, giving rise to the anomalous
voltage peak. Finally, in figure 5(c) is represented the
826
70
80
T (K)
90
100
Figure 6. Resistivity versus temperature curves
corresponding to the different domains in the Bi33 crystal
and for both orientations (H k ab and H ⊥ ab ) of the
external magnetic field. They were obtained by solving the
electrical network represented in the inset of (b) which
corresponds to the inhomogeneity distribution represented
in the inset of (a).
(c)
60
60
current distribution corresponding to T = 91.2 K in the
presence of the external magnetic field of 1 T applied
perpendicularly to the ab-planes. The main effect of
the magnetic field is to broaden the resistive transition,
making the differences between the resistivities of the
different domains much smaller than for H = 0. As a
consequence, the current distribution is nearly uniform and
the anomalous peak almost disappears from the effective (or
measured) ρab (T , H )-curves. Moreover, the broadening of
the resistive transition is more pronounced for H ⊥ ab than
for H k ab, and this is because the field amplitude needed
to completely quench the anomalous peak is bigger for the
latter field orientation.
A simple inhomogeneity distribution well adapted to
reproduce the results obtained for the Bi33 crystal is
that represented in the inset of figure 6(a), where the
shadowed areas correspond again to the highest Tc domains.
The dimensions for each high Tc domain are in this
case 13 Lx , Ly , 23 Lz . As for the Y-123 sample analysed
above, with this inhomogeneity and for this electrical
contact arrangement, the equivalent electrical circuit can
be reduced to the bi-dimensional one represented in the
inset of figure 6(b). In addition, (2) and (3) relating the
resistances to the corresponding resistivities also hold in
Y-123 and Bi-2212 with Tc -inhomogeneities
≈
this case. The corresponding ρ̃ab (T , H ) and ρ ab (T , H )
curves for the different domains used in the simulation
are represented in figure 6(a) and (b) for H perpendicular
and, respectively, parallel to the ab-planes. Also, for the
c-direction resistivity we used a factor of 103 times the
ab-plane resistivity. Note that this value is much smaller
than the commonly accepted ρc /ρab ≈ 105 for Bi-2212
crystals [13]. This last result, together with the high ρab
values shown in figure 6, suggests the existence in the Bi33
crystal of some structural inhomogeneities, in addition to
the stoichiometric ones, which may mix in some parts of
the sample the ab- and c-directions.
The results of the simulation for the effective ρ(T , H )
of the Bi33 crystal are the solid lines in figures 4(a)–(c).
As it may be seen in these figures, the experimental data,
including the peak in Vbot (T , H = 0) and the small step
in Vtop (T , H = 0), are reproduced at least at a qualitative
level. When the temperature is well above any transition
temperature in the sample, the current concentrates near
the upper face (where the current contacts are placed) due
to the intrinsic strong anisotropy (ρc ρab ) of this type
of compound. But at temperatures at which the highest
Tc domains are already superconducting and the rest still
remains in the normal state, the current deviates to the
bottom face of the crystal, giving rise to the anomalous
peak in Vbot (T ) and the step in Vtop (T ). These results
also show that the external magnetic field amplitude needed
to completely quench the anomalous peak in the Bi33
crystal is much smaller than that for the Y16 crystal. This
may easily be understood at a quantitative level by just
taking into account that the broadening of the resistive
transition by an external magnetic field is more pronounced
in Bi-2212 than in Y-123.
As already noted in the introduction, anomalous
magnetoresistivity peaks near Tc very similar to the ones
described here have been observed in some thin films and
granular samples of different LTSCs [6]. The simplicity
of the chemical structure of these compounds makes
quite improbable the presence of appreciable non-uniformly
distributed compositional inhomogeneities.
However,
another source of Tc -inhomogeneities could be related to the
well known low dimensionality effects, which appear when
the superconducting coherence length, ξ(T ), becomes of
the order of or bigger than one of the sample’s dimensions
(thickness in the case of thin films, or grain diameter in
the case of granular samples) [3]. Due to the relatively
important coherence length amplitude of the LTSC (ξ(T =
0 K) ≈ 1000 Å), these low dimensionality effects may
easily be present in the LTSC films. In addition, the
thin film edges are never completely sharp, but instead
they have an irregular thinner shape, and so having a
higher Tc than the rest of the film. When the temperature
is well above any possible Tc in the film, the electrical
current used to measure the resistivity must be uniformly
distributed. But at temperatures in which the film edges
are superconducting and the rest of the film still remains
in the normal state, the current lines must concentrate in
the edges. This current redistribution may give rise to an
increment in the signal detected by a voltmeter connected
at the film edges and, in some cases, to the anomalous
resistivity peak. A condition for that is simply that the edge
thickness should be non uniform along the film. Otherwise,
at the temperature at which the film edges are already
superconducting a continuous superconducting path would
connect both voltage terminals and no signal (and then
no peak) would be detected. The anomaly so originated
will be very dependent on the current used to perform
the measurements. In fact, due to the smallness of the
section of the highest Tc edges, it is very easy to reach the
critical current density by increasing the applied current,
making the effect to disappear. Some of the different
experimental results of [6] may satisfactorily be explained
on the grounds of these simple ideas based on the presence
of low dimensionality induced Tc -inhomogeneities, nonuniformly distributed in the films. The anomalous ρ(T , H )peaks observed in some granular LTSC samples [6] could
also easily be explained in terms of low dimensionality
effects, through the dependence of Tc on the grain diameter,
if a non-uniform distribution of grains having different
diameters exists in the sample.
4. Conclusion
In this paper we have presented detailed measurements of the in-plane magnetoresistivity, ρab (T , H ), of
YBa2 Cu3 O7−δ and Bi2 Sr2 CaCu2 O8 crystals with small
oxygen-content inhomogeneities at long length scales and
non-uniformly distributed in the crystals. These inhomogeneities deform the ρab (T , H )-curves, mainly near Tc ,
generating the appearance of giant resistivity peaks, very
sensitive to an external magnetic field. In particular, we
have reported here the observation of such a ρab (T , H )peak in a Bi-based copper oxide superconductor. Our measurements have also shown that the associated magnetoresistivity excess near the average Tc is, for both inhomogeneous superconducting compounds, negative and very
anisotropic. These different effects have been explained
simultaneously and at a quantitative level in terms of nonuniformly distributed Tc -inhomogeneities associated with
the stoichiometric ones. For that, we have used electrical
resistor networks, which have also allowed us to visualize the corresponding electrical current redistributions, that
are particularly important near the average superconducting
transition. Together with our previous findings on the resistivity and on the thermopower peaks near the average Tc
in inhomogeneous HTSCs [5], our present results open the
possibility of deeply shaping the transition of copper oxide
superconductors by just O2 doping some chosen parts of the
samples. In fact, our preliminary measurements in inhomogeneous Tl2 Ba2 Ca2 Cu3 O10 crystals indicate that it will even
be possible to introduce non-uniformly distributed inhomogeneities in HTSC crystals which will lead to an effective
negative longitudinal magnetoresistivity [19]. These different inhomogeneity effects in HTSCs could have some direct practical applications, for instance in thermal detection
(bolometers) due to the increasing of dρ(T , H )/dT around
the transition. Let us also note here that until now the reduction of the macroscopic critical current densities, Jc (T , H ),
in practical HTSCs was mainly attributed, in addition to
vortex dissipation, to structural inhomogeneities [20, 21].
827
J Mosqueira et al
These inhomogeneities include connectivity defects, such
as polycrystallinity and grain boundaries, cracks and pores,
and crystallographic misorientations (which, in turn, may
strongly affect the local current densities [21]). However,
our present results on the local current redistributions due
to Tc -inhomogeneities clearly suggest that the presence of
small stoichiometric inhomogeneities, non-uniformly distributed, may also deeply affect Jc (T , H ), mainly near the
average Tc .
Acknowledgments
This work is in part based on the PhD Thesis of Jesús
Mosqueira (University of Santiago de Compostela, Spain,
1997), and it has been supported by the CICYT, Spain,
under grant No MAT95-0279. JM and CC acknowledge
financial support from Xunta de Galicia and TS from
Ministerio de Educación y Ciencia of Spain and from the
European Economic Community, grant No CHRX-CT930325.
References
[1] See, e.g., Tinkham M 1978 Electrical Transport and
Optical Properties of Inhomogeneous Media (AIP Conf.
Proc. 40) ed J C Garland and D B Tanner (New York:
AIP) p 130
[2] Some earlier works on inhomogeneity effects in low
temperature superconductors may also be seen in
Gubser D U et al (eds) 1980 Inhomogeneous
Superconductors (AIP Conf. Proc. 58) (New York: AIP)
[3] In addition to stoichiometric inhomogeneities, there are
other possible causes for Tc inhomogeneities in LTSC
and HTSC compounds, such as local strains (see, e.g.,
Schoemberg D 1962 Superconductivity (Cambridge:
Cambridge University Press) p 75
Testardi L R 1971 Phys. Lett. 35A 33) or
low-dimensionality (see, e.g., Abeles B, Cohen R W and
Walker G W 1966 Phys. Rev. Lett. 17 632
Abeles B, Cohen R W and Stowell W R 1967 Phys. Rev.
Lett. 18 902
Dickey J M and Paskin A 1968 Phys. Rev. Lett. 21 1441)
[4] Maza J and Vidal F 1991 Phys. Rev. B 43 10 560
Pomar A, Ramallo M V, Mosqueira J, Torrón C and
Vidal F 1996 Phys. Rev. B 54 7470
Pomar A, Ramallo M V, Mosqueira J, Siebold Th,
Campá J A, Rasines I, Maza J and Vidal F 1996 J. Low
Temp. Phys. 105 675
[5] Mosqueira J, Pomar A, Veira J A and Vidal F 1994
Physica C 225 34
Mosqueira J, Veira J A, Maza J, Cabeza O and Vidal F
1995 Physica C 253 1
Mosqueira J, Pomar A, Veira J A, Maza J and Vidal F
1994 J. Appl. Phys. 76 1943
Mosqueira J, Siebold Th, Pomar A, Dı́az A, Veira J A,
Maza J and Vidal F 1997 Cryogenics 37 563
[6] See, e.g., Lindqvist P, Nordström A and Rapp Ö 1990
Phys. Rev. Lett. 64 2941
Santhanam P, Chi C C, Wind S J, Brady M J and
Buchignano J J 1991 Phys. Rev. Lett. 66 2254
Spahn E and Keck K 1991 Solid State Commun. 78 69
Kwong Y K, Lin K, Hakonen P J, Isaacson M S and
Parpia J M 1991 Phys. Rev. B 44 462
Nordström A and Rapp Ö 1992 Phys. Rev. B 45 12 577
Vloeberghs H, Moshchalkov V V, Van Haesendonk C,
Jonckheere R and Bruynseraede Y 1992 Phys. Rev. Lett.
69 1268
828
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
Kleinsasser A W and Kastalsky A 1993 Phys. Rev. B 47
8361
Romanov S G, Fokin A V and Babamuratov K Kh 1993
JETP Lett. 58 824
Kim J J, Kim J, Shin H J, Lee H J, Lee S, Park K W and
Lee E 1994 J. Phys.: Condens. Matter 6 7055
Moshchalkov V V, Gielen L, Neuttiens G, van
Haesendonk C and Bruynseraede Y 1994 Phys. Rev. B
49 15 412
Park M, Isaacson M S and Parpia J M 1995 Phys. Rev.
Lett. 75 3740
Strunk C, Bruyndoncx V, Van Haesendonk C,
Moshchalkov V V, Bruynseraede Y, Burk B, Chien C J
and Chandrasekhar V 1996 Phys. Rev. B 53 11 332
Arutyunov Yu K 1996 Phys. Rev. B 53 12 304
Park M, Isaacson M S and Parpia J M 1997 Phys. Rev. B
55 9067
Burk B, Chien C-J, Chandrasekhar V, Strunk C,
Bruyndoncx V, Van Haesendonck C, Moshchalkov V V
and Bruynseraede Y 1998 J. Appl. Phys. 83 1549
Strunk C, Bruyndoncx V, Van Haesendonck C,
Moshchalkov V V, Bruynseraede Y, Chien C-J, Burk B
and Chandrasekhar V 1998 Phys. Rev. B 57 10 854. As
stressed in the main text, many of the resistivity peak
effects around Tc described in these papers and attributed
by the authors to sophisticated intrinsic mechanisms,
may be easily explained in terms of Tc inhomogeneities
non-uniformly distributed in the samples. This last
explanation was discarded by some of the authors due to
the erroneous belief that these Tc inhomogeneities do not
affect the magnetoresistivity measured with in-line
electrical arrangements (see [5]; see also the note in [7])
Vaglio R, Attanasio C, Maritato L and Ruosi A 1993 Phys.
Rev. B 47 15 302. In that paper it was concluded that the
ρ(T ) peaks observed near Tc in some low temperature
superconductors by using a Van der Paw electrical
arrangement (with the electrical leads in the sample
corners) could be due to the presence in the samples of
Tc inhomogeneities. However, it was erroneously
suggested in that paper that in the case of an in-line
electrical arrangement the Tc inhomogeneities could not
produce a ρ(T ) peak. This last type of measurements
were analysed for the first time in [5].
Attanasio C, Maritato L and Vaglio R 1993 Tunneling
Phenomena in High and Low Tc Superconductors ed
A de Chiara and M Russo (Singapore: World Scientific)
p 179
Gerber A, Grenet T, Cyrot M and Beille B 1990 Phys. Rev.
Lett. 65 3201
Fabrega L, Crusellas M A, Fontcuberta J, Obradors X,
Piñol S, van der Beck C J, Kes P H, Grenet T and
Beille J 1991 Physica C 185–189 1913
Crusellas M A, Fontcuberta J and Piñol S 1992 Phys. Rev.
B 46 14 089
Trawick M L, Ammirata S M, Keener C D, Hebboul S E
and Garland J C 1996 J. Low Temp. Phys. 105 1267
Rubin S, Schimpfke T, Weitzel B, Vossloh C and
Micklitz H 1992 Ann. Phys. Lpz. 1 492
Pradham A K, Hazell S J, Hodby J W, Chen C,
Chowdury A J S and Wanklyn B M 1993 Solid State
Commun. 88 723
Crusellas M A, Fontcuberta J and Piñol S 1994 Physica C
226 311
See, e.g., Busch R, Ries G, Werthner H, Kreiselmeyer G
and Saemann-Ischenko G 1992 Phys. Rev. Lett. 69 522
See, e.g. Chen C H 1990 Physical Properties of High
Temperature Superconductors II ed D M Ginsberg
(Singapore: World Scientific) p 199
Campá J A, Gutiérrez-Puebla E, Monge M A, Rasines I
and Ruiz-Valero C 1992 J. Cryst. Growth 125 17
Pomar A, Dı́az A, Ramallo M V, Torrón C, Veira J A and
Vidal F 1993 Physica C 218 257
Y-123 and Bi-2212 with Tc -inhomogeneities
[17] Skelton E F, Drews A R, Osofsky M S, Qadri S B, Hu J Z,
Vanderah T A, Peng J L and Greene R L 1994 Science
263 1416
[18] Let us stress, however, that in this case (which corresponds
to a typical non-uniformly distributed inhomogeneity)
th
the behaviour of the calculated (th) ρab
(T , H ) does not
depend on the number of meshes of the network,
provided that the proportion and location of the different
resistances is kept unchanged. This contrasts with the
case of uniformly distributed Tc -inhomogeneities for
which with a small number of meshes it is not possible
to represent adequately the inhomogeneity distribution.
In this case, a small number of meshes could lead to the
appearance of important spurious longitudinal and
transversal voltages, which are just an artifact of an
inadequate simulation. For instance, the calculations of
the longitudinal and transversal voltages in
superconductors with uniformly distributed
inhomogeneities presented by R Griessen and coworkers
in Physica C 235–240 1371 (1994) may be affected by
these spurious effects.
[19] Siebold Th, Carballeira C, Mosqueira J, Ramallo M V and
Vidal F 1997 Physica C 282–287 1181. By using three
dimensional electrical resistor networks, in this paper it
is shown that the presence of non-uniformly distributed
inhomogeneities may lead, for some distributions, to the
appearance of countercurrents which, when distributed
in the sample surface, may lead to negative effective
resistivities.
[20] See, e.g., Dı́az A, Maza J and Vidal F 1997 Phys. Rev. B
55 1209
[21] See, e.g., Pashitski A E, Gurevich A, Polyanskii A A,
Larbalestier D C, Goyal A, Specht E D, Kroeger D M,
DeLuca J A and Tkaczyk J E 1997 Science 275 367
829