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Anisotropy of the superconducting properties
of YBa 2 Cu 3 O 72x single crystals with reduced oxygen
content
V. N. Zverev, a) D. V. Shovkun, and I. G. Naumenko
Institute of Solid­State Physics, Russian Academy of Sciences, 142432 Chernogolovka,
Moscow Region, Russia
~Submitted 8 July 1998; resubmitted 14 July 1998!
Pis'ma Zh. E ’ ksp. Teor. Fiz. 68, No. 4, 309--313 ~25 August 1998!
In an investigation of the resistivity anisotropy of YBa 2 Cu 3 O 72x single
crystals with suboptimal oxygen content it is observed that the super­
conducting transition for the component r c of the resistivity tensor is
shifted to lower temperatures with respect to the transition for the com­
ponent r ab . A similar shift is also observed for the transition in the
temperature dependence of the dynamic magnetic susceptibility.
© 1998 American Institute of Physics. @S0021­3640~98!01216­X#
PACS numbers: 74.72.Bk, 74.25.Fy, 74.62.Bf
Cuprate high­T c superconductors are highly anisotropic layered compounds charac­
terized by the presence of CuO 2 planes, which are believed to be responsible for the
superconductivity.
In Ref. 1, in a study of the temperature dependences of the resistance and magnetic
susceptibility of Bi 2 Sr 32x Ca x Cu 2 O 81y single crystals, it was observed that the supercon­
ducting transition temperature was approximately 40 K higher in the case of current flow
along the CuO 2 layers (j' c, where c is the direction of the crystallographic axis perpen­
dicular to the layers! than in the case of current flow perpendicular to the layers (j i c) .
Friedel predicted theoretically a similar behavior of layered superconductors. 2 He
proposed a specific mechanism of ``growth'' of ring­shaped Josephson vortices in a
certain temperature range T f ,T,T c below T c that should suppress superconductivity in
this range in the direction perpendicular to the CuO 2 layers. According to Friedel's
conjecture, such a temperature interval should exist in any layered superconductor that is
described by a model of a stack of superconducting planes between which Josephson
links exist. The temperature T f above which these links are broken is the Friedel transi­
tion temperature.
Later, Korshunov and Rodriguez 3 pointed out an error in Friedel's calculations and
showed that such a mechanism is not realized in an ideal crystal. However, it was
recently shown theoretically in Ref. 4 that a Friedel transition can occur if the layers are
not assumed to be ideal and it is assumed that there is a random distribution over
superconducting properties of the layers. Specifically, it was assumed that two types of
layers with different parameters J i , characterizing the coupling constant inside a layer in
JETP LETTERS VOLUME 68, NUMBER 4 25 AUG. 1998
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an anisotropic 3D XY model, exist in the crystal. The Friedel transition was obtained only
when the distribution of such layers in a crystal was not periodic but random.
The reason for the observed 1 shift of the superconducting transition was not estab­
lished. In principle, any macroscopic nonuniformity of the sample can lead to a shift of
the transition, but the observed phenomenon could have been due to a Friedel transition.
In any case, such behavior is a consequence of the layered structure of the single crystals
investigated. In this connection, it is of interest to observe the shift of the transition in
other layered superconductors.
In the present work, we chose YBa 2 Cu 3 O 72x single crystals ~YBCO! for the inves­
tigations. Initially, at optimal doping x'0.05 this superconductor possesses a much
weaker anisotropy than bismuth or thallium cuprate superconductors, but as the oxygen
content decreases, the degree of anisotropy increases rapidly. The behavior of YBCO as
a function of oxygen content is reversible and has been rather well studied. For this
reason we undertook to observe the shift of the superconducting transition with decreas­
ing oxygen content in high­quality ~in the initial state! single crystals for different orien­
tations of the current relative to the CuO 2 layers.
In the experiment, the anisotropy of the electrical resistance and the dynamic mag­
netic susceptibility was measured on YBCO single crystals in the form of slabs with
dimensions of approximately 23130.05 mm, for which the crystallographic direction c
was normal to the plane of the slabs.
The YBa 2 Cu 3 O 72x single crystals were grown in a ZrO 2 crucible by the method
described in Ref. 5. The total impurity content in the samples, which was less than
0.005%, was determined by the inductively­coupled plasma method, which consisted of
a mass­spectrometric analysis of an argon plasma containing the vaporized sample and
ignited by an rf inductor.
After annealing at 500 °C in oxygen, the samples possessed a narrow superconduct­
ing transition with T c '92K and transition width less than 0.5 K. The required reduced
oxygen content was achieved by choosing the annealing temperature ~up to 820 °C! in air
at atmospheric pressure and subsequent quenching in liquid nitrogen in accordance with
the data of Refs. 6--8. The samples were annealed in a quartz ampoule and covered with
YBCO powder in order to preserve the high quality of the surface. No special measures
were taken to detwin the samples.
To measure the real part of the dynamic magnetic susceptibility x , the sample was
placed inside a pair of coaxial coils 6 mm in diameter, one of which served to excite an
ac magnetic field, while the other was for measuring. An identical pair of coils, which
was used to compensate the signal in the absence of the sample, was placed next to it.
Using the standard synchronous detection scheme, we measured the component of the
imbalance signal proportional to the real part of the induced magnetic moment M of the
sample in an ac magnetic field of frequency 10 5 Hz: M5xhV . Here h is the amplitude of
the magnetic field in the coil and V is the volume of the sample. The amplitude h of the
field was chosen to be small, so that the signal was linear in h , and equal to 0.1 Oe. The
sample in the coil was placed either perpendicular (c i h) or parallel to (c'h) to the
magnetic field. For this, the sample was glued to different faces of a sapphire rod, shaped
in the form of a rectangular parallelepiped. We denote by x ab the susceptibility compo­
nent measured in the first case, since ring currents flow only in the plane of the CuO 2
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layers, and we denote by x c the susceptibility component in the second case, since in this
case a portion of the path which the currents must follow to closure is perpendicular to
the layers.
The sample together with a thermometer and a heater arranged alongside were
placed inside a glass Dewar, which was immersed, upside down, in liquid helium. The
measuring coils were wound on the outer surface of the Dewar and were always at liquid
helium temperature during the measurements. To prevent a temperature gradient, the
sample was placed in a sapphire container.
A four­contact method was used to investigate the electrical resistance of anisotropic
single crystals. 9 In this method, two pairs of contacts were placed opposite one another
on opposite sides of the sample ~see inset in Fig. 1!. The contacts were prepared by
depositing drops of silver paste on the surface of the sample. The drops were then
``burned in'' by heating the sample in air at 400 °C. The subsequent manipulations of the
sample ~annealing, remounting! did not change the properties of the contacts. The char­
acteristic size of the contacts did not exceed 0.3 mm, and the accuracy of the placement
of the contacts opposite one another on the opposite sides of the sample was not worse
than 0.05 mm.
The components of the resistivity tensor r ab in the plane of the layers and r c normal
to the layers could be calculated numerically, using the formulas of Ref. 9, from the
results of two measurements R ab 5V 12 /J 34 and R c 5V 13 /J 24 , assuming an infinite
sample. This condition limited the applicability of this method to a large anisotropy
h5r c /r ab . In our experiments, the calculations of r ab and r z were performed only for
the initial sample with optimal oxygen content, for which h was of the order of 10 2 . For
samples with reduced oxygen content, where the anisotropy was much higher, we present
only the values of R ab and R c .
In the present work we investigated two samples in detail. Their behavior was
similar overall but different in detail. For the sample whose data are reported in the
present letter the resistivities in the state with optimal oxygen concentration were r ab
5460 mV. cm and r c 548 mV. cm at T5300 K, and the values decreased linearly with
decreasing temperature ~but not too close to T c .92 K; Fig. 1!.
Next, the sample was annealed at a fixed temperature, resulting in a lower oxygen
FIG. 1. Temperature dependence of the resistivity components r ab and r c of the initial YBCO single crystal.
Dotted lines --- extrapolations of the linear parts of the temperature dependences of the resistivity to zero
temperature. Inset: Geometry of the contacts.
334 JETP Lett., Vol. 68, No. 4, 25 Aug. 1998 Zverev et al.

concentration, after which the temperature dependences of the resistances R ab and R c and
the susceptibilities x ab and x c were measured. Then the procedure was repeated at a
higher annealing temperature, all the way up to the temperature ;820 °C at which the
sample was no longer a superconductor. 8
Figure 2 shows the temperature dependences R ab (T) and R c (T) for a sample an­
nealed at 790 °C for 35 h. As one can see from the figure, the resistances R ab (T) and
R c (T) do not vanish simultaneously as temperature decreases: first R ab vanishes at
T 1 .40 K; in the process, R c (T) increases, reaches a maximum approximately at the
point where R ab (T) vanishes, and then decreases and vanishes at T 2 .30 K, i.e., at an
approximately 10 K lower temperature. This nonsimultaneous vanishing of R ab and R c
started only when T c of the sample dropped below '60 °C, and it was observed for both
experimental samples, though the temperature interval DT where R ab 50 while R c .0
was different.
The same effect was also observed in the temperature dependences of the dynamic
magnetic susceptibility, which were measured for two different orientations of the ac
magnetic field h --- parallel (x ab ) and perpendicular (x c ) to the c axis ~Fig. 3!. We note
FIG. 2. Temperature dependences R ab (T) (j' c) and R c (T) (j i c) in the absence of a magnetic field (s) and
in a 5 T field (n) .
FIG. 3. Comparison of the temperature dependence of the normalized dynamic susceptibility ~solid curves! and
the resistance ~dashed curves! near a superconducting transition.
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JETP Lett., Vol. 68, No. 4, 25 Aug. 1998 Zverev et al.

that Fig. 3 shows the temperature dependences normalized to the susceptibility at zero
temperature. In the experiment the ratio x ab (0)/x c (0)529, which reflects the anisotropy
of the demagnetizing factor of the sample.
As one can see from Fig. 2, applying a magnetic field B i c decreases the values of
the characteristic temperatures at which each of the measured quantities R ab (T) and
R c (T) vanishes, but the difference between them remains approximately the same as for
B50 .
The experimentally observed shift of the superconducting transition means that there
exists a temperature interval below T c where the superconducting current exists only in
the plane of the CuO 2 layers and equals zero in the perpendicular direction. As we have
said, such behavior could be a manifestation of a Friedel transition but it could also be
due to the nonuniformity of the sample. There are two types of nonuniformities which
can lead to the effect that we observe:
1! the presence of layers with a higher value of T c which are separated by layers
with a lower value of T c ;
2! the presence of planar defects, playing the role of weak links between layers,
where a supercurrent arises ~on account of thermal fluctuations! at temperatures less than
T c of the layers ~a similar mechanism is realized in granular superconductors 10 !.
The effect which we observed cannot be due to defects of the second type. This
follows from the experiment in a magnetic field. Actually an external magnetic field
should destroy the weak links and therefore shift the transition in R c (T) more strongly
than in R ab (T) .
An additional argument supporting the fact that the observed defect is not due to
defects of the second type follows from the behavior of the dynamic magnetic suscepti­
bility. The point is that in the geometry h' c, i.e., when the field is parallel to the layers,
planar nonsuperconducting defects make virtually no contribution to the susceptibility
~provided that their total volume is small compared with that of the sample!. For this
reason, even though the presence of defects can lead to the phenomenon that we observed
in the resistance, it cannot explain the behavior of the susceptibility. For this reason, the
nonuniformities of the first type can lead to the observed phenomenon only in the case
that the fraction of the higher­temperature layers is small compared with that of the
low­temperature layers. In the limiting case, one narrow high­T c layer can exist in the
sample. Although we cannot rule out this variant, it seems unlikely. It would be more
natural to infer that the distribution of T c over the layers is smooth. However, in this case
the superconducting transitions should start at the same temperature for different orien­
tations of the current, in contradiction to experiment.
The magnitude of the temperature shift DT observed in the experiment depended on
the stage of annealing of the sample, and for different samples differed appreciably for
approximately equal values of T c . This shows that the nonuniformity of the sample is
still considerable. But, at the present stage of the investigations, it could not be deter­
mined unequivocally whether we are dealing with a Friedel transition ~with allowance for
the fact that the CuO 2 layers are not all identical! or whether the phenomenon is due to
a macroscopic nonuniformity of the sample.
In summary, in the present work a shift of the superconducting transition to low
336 JETP Lett., Vol. 68, No. 4, 25 Aug. 1998 Zverev et al.

temperatures was observed in oxygen­deficient YBCO single crystals in the case of
current flow perpendicular to the CuO 2 layers. This phenomenon could be due to a
Friedel transition in a nonuniform layered superconductor.
The authors are grateful to V. F. Gantmakher for his interest in this work and for
critical remarks and to V. I. Karandashev for assisting in the elemental analysis of the
samples. This work was performed as part of Project 98­02­16636 of the Russian Fund
for Fundamental Research and Projects 96­012 and 96­060 of the State Program ``Su­
perconductivity.''
a! e­mail: zverev@issp.ac.ru
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Translated by M. E. Alferieff
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