INSTITUTE OF PHYSICS PUBLISHING
SUPERCONDUCTOR SCIENCE AND TECHNOLOGY
Supercond. Sci. Technol. 19 (2006) 980–985
doi:10.1088/0953-2048/19/9/014
Measurements of the Meissner fraction as
a function of oxygen ordering for oxygen
deficient YBa2Cu3O7−δ single crystals
K G Vandervoort1 , T T Nguyen1 , M A Demine1 and W K Kwok2
1
2
Physics Department, California State Polytechnic University, Pomona, CA 91768, USA
Materials Science Division, Argonne National Laboratory, Argonne, IL 60439, USA
E-mail: [email protected]
Received 20 June 2006, in final form 21 July 2006
Published 14 August 2006
Online at stacks.iop.org/SUST/19/980
Abstract
The influence of oxygen ordering on the Meissner fraction (the ratio of field
cooled to zero field cooled magnetization) on a number of YBa2 Cu3 O7−δ
single crystals over a wide range of oxygen deficient states
(15 K Tc 60 K) has been investigated. The Meissner fraction increases
in almost all cases with an increase in oxygen ordering. In only a few cases
where the change in transition temperature is very small (Tc < 2 K)
following ordering is no discernible increase measured. We attribute these
results to both intrinsic parameters that change with the ordering
phenomenon, for example the lower critical field, and extrinsic effects such
as the redistribution of oxygen vacancies.
1. Introduction
Since its discovery in 1990 [1–3], the oxygen ordering
phenomenon has been extensively studied in the YBa2 Cu3 O7−δ
system. Examples of investigations include studies into the
variation of transition temperature as a function of oxygen
deficiency and ordering for various ordered phases [4],
x-ray diffraction measurements to probe the extent of
long-range ordering of oxygen defects [5] and search for
exotic superstructures [6], high pressure measurements to
determine activation energies for oxygen diffusion [7], and
studies of photoinduced switching between oxygen disordered
metastable states [8], to name just a few. How oxygen ordering
relates to variations in flux pinning is of fundamental and
practical importance. Studies have been performed on ordering
effects in relation to the peak in magnetization hysteresis loops
and its implications for the critical current density [9, 10].
These experiments involved measurements on crystals with
oxygen concentrations near the optimal doping level. To our
knowledge, however, no one has studied oxygen ordering and
pinning effects over a wide range of oxygen deficiencies.
To address this issue, we report measurements of the
Meissner fraction as a function of oxygen ordering on a variety
of oxygen deficient states with transition temperatures in the
range 15 K Tc 60 K. This range of oxygen deficiencies
0953-2048/06/090980+06$30.00
encompasses states where the enhancements in transition
temperature (and therefore superconducting properties) with
ordering are most significant. The Meissner fraction represents
the ratio of the field cooled magnetization to the zero field
cooled magnetization and is a way of probing the relative
pinning of vortices that occurs upon cooling through the
superconducting transition. We find that for all crystals
measured, and for all oxygen deficiencies, the Meissner
fraction either increases or does not change with increase in
oxygen ordering. Only in cases where there is a very small
change in Tc , following ordering, do we see no change in the
Meissner fraction within the resolution of the signal. This
work is a corroboration of our earlier results which showed
the same effect for one oxygen deficient crystal, with a Tc that
changed from 10 to 25 K following ordering [11]. Our findings
imply a reduction of pinning with ordering which we attribute
to a change in intrinsic parameters, such as the lower critical
field, and extrinsic effects, such as the formation of periodic
superstructures.
2. Experimental details
Magnetization versus temperature data were obtained using
a low-field, home-built SQUID magnetometer, similar to
an instrument described elsewhere [12]. The instrument
© 2006 IOP Publishing Ltd Printed in the UK
980
Meissner fraction for YBa2 Cu3 O7−δ single crystals
is equipped with a µ-metal shield and a copper-wound
electromagnet so that the background magnetic field at the
location of the sample is <1 mG. The sample remains
stationary in the pick-up coils as its magnetization is measured
as a function of temperature. Flux exclusion magnetization
(shielding effect) was measured by cooling in zero field
to a temperature well below Tc , applying a field at low
temperatures, and recording data as the sample warmed. Flux
expulsion magnetization (the Meissner effect) was measured
by cooling in a field from above to below Tc and again on
warming to above Tc .
YBa2 Cu3 O7−δ single crystals were grown by a self-flux
method [13, 14] and were rectangular solids with the short
dimension along the c-axis. In all, six crystals were used in
the study and represented samples from three separate batches
(and from three different sample growers). Original transition
temperatures of the fully oxygenated crystals were >91 K
with magnetic transition widths of <0.5 K in a field of 1 G.
Preparation of the low-Tc oxygen deficient phases consisted
of a 5 day anneal at temperatures that ranged from 470 to
530 ◦ C in pure oxygen atmospheres at pressures between 2 and
30 Torr, depending on the desired stoichiometry. Transition
widths for the oxygen deficient samples were consistently less
than 2 K in a field of 1 G.
Basal plane oxygen site disorder was introduced by
annealing the crystals in air at 150 ◦ C for 30 min. The
samples were then quenched to liquid nitrogen and transferred
within 2 min to the sample chamber of the magnetometer
to a temperature of <100 K. Shielding and Meissner curves
were recorded for this disordered state and the sample was
subsequently warmed to 38 ◦ C overnight (for a period of at
least 8 h) to induce ordering of the oxygen atoms. At 38 ◦ C,
the kinetics of oxygen ordering is sufficient [1] to produce
the equilibrium ordered state in a much shorter time than is
required at room temperature. The sample was then cooled and
shielding and Meissner curves were recorded for the sample in
its ordered state. For the two series of magnetic measurements,
for the disordered and ordered states, the sample remained
at the exact same position and orientation on the sample
probe in the magnetometer. Because of this, the difference
in data between the two states represented differences due
only to changes in the properties of the sample rather than
orientation dependent artefacts that can affect the magnitude
of the Meissner signal [15]. All measurements were obtained
with the magnetic field aligned along the c crystallographic
axis.
3. Results
Figure 1 shows Meissner data for a sample A that was
originally prepared with an oxygen deficiency and ordered
state with a Tc of 53.0 K. The sample was cooled in a field
of 7 G at various rates and the data shown are for warming in
that field. The data are displayed in normalized units in terms
of the magnetization, M , the applied magnetic field, H , and
the demagnetization factor, n . In each curve, the data reach a
constant value as the temperature is lowered, and remain at that
value to the lowest temperatures measured. The magnitude of
this constant value will be referred to as the Meissner signal.
As the cooling rate of the sample decreases, the magnitude of
Figure 1. The Meissner effect as a function of cooling rate for
sample A in a field of 7 G. The cooling rate is varied from
15 K min−1 (+) to 1 K min−1 ( ) to 0.5 K min−1 () and finally to
0.2 K min−1 ( ). For rates 0.5 K min−1 , the magnitude of the data
does not change. The method for defining Tc is indicated at the top of
the figure.
◦
•
the Meissner signal increases from 0.060 to 0.065 normalized
units. The magnitude of the signal asymptotically approaches
a limit, however, and for cooling rates of 0.5 K min−1 and
slower, the data fall on top of one another. This same property
was observed for other samples. Similar results have been
seen elsewhere [16], although in the other study significantly
higher fields were applied and no asymptotic behaviour was
ever observed. For all measurements in our study, the cooling
rate was monitored and maintained at less than 0.5 K min−1 so
that all the data were reproducible. In addition, for these slow
cooling rates the magnitude of the Meissner signal for warming
and cooling was the same. For clarity, only Meissner warming
data are displayed in the figures.
Figure 2 shows typical shielding and Meissner data for
sample A in both its disordered state (with a Tc of 51.1 K) and
in its ordered state (with a Tc of 53.0 K). As was the case for
the Meissner data, the shielding data reach a constant value as
the temperature is lowered and the magnitude of this constant
value will be referred to as the shielding signal. As displayed
in figure 2(a), the shielding signal has the same value (0.89
normalized units) for both the disordered and ordered states.
This same characteristic was observed in all applied fields and
for all samples and oxygen deficient compositions. The result
follows from the fact that the shielding signal represents the
flux exclusion that is dependent only on sample size, shape,
orientation and fraction of the sample that is superconducting.
Observation of the constancy of this value is evidence of the
fact that the sample did not move between measurements.
A shielding signal of 1.00 would ostensibly indicate that
100% of the sample was superconducting. However, for the
six crystals measured in this study, values for the shielding
signal ranged from 0.8 to 1.3 normalized units. These
variations were an indication of the degree of uncertainty in
981
K G Vandervoort et al
(a)
(b)
Figure 3. Meissner fraction as a function of transition temperature
for sample A, annealed to a variety of oxygen deficient states. Pairs
of points connected by an arrow denote a particular oxygen deficient
state before and after a 38 ◦ C anneal. Applied magnetic fields include
1 G ( ), 3 G ( ) and 7 G ().
◦
Figure 2. Data for sample A in a field of 7 G for before (disordered
state) and after (ordered state) a 38 ◦ C anneal. Both (a) flux exclusion
(shielding effect) and (b) flux expulsion (Meissner effect) data are
displayed.
determining the sample dimensions, which strongly influence
the calculated demagnetization factors. The values indicate
that the samples were close to 100% superconducting, at least
within experimental uncertainty.
As displayed in figure 2(b), the Meissner signal, unlike the
shielding signal, does increase in magnitude when the sample
is annealed to its oxygen ordered state. The increase in the
magnitude of the Meissner signal reflects the decrease in the
flux pinning in the sample for the ordered as compared to the
disordered state. One can define an empirical Meissner fraction
as the ratio of the Meissner to the shielding signals. We equate
this empirical Meissner fraction to the true Meissner fraction
(the ratio of the Meissner signal to the signal for complete
flux exclusion, that is, for a sample that has 100% volume
superconductivity), since our samples exhibited 100% volume
superconductivity, within experimental uncertainty. For these
data, the Meissner fraction increases from 0.0709 to 0.0736
due to oxygen ordering.
The subtlety of the change in the Meissner fraction
allowed us to obtain reliable results for field applied along the
c-axis only, where the measured signals were much larger. For
field aligned along c, the demagnetization factors for these
crystals ranged from 0.78 to 0.91. These demagnetization
factors would have a larger effect on the shielding signal
than on the Meissner signal, since the distortion of the
field is greatest when field is completely excluded from the
sample. Therefore, our Meissner fractions are dependent
982
•
on these demagnetization values. We therefore concentrate
our study on comparison of the Meissner fractions for
disordered and ordered states of the same crystal rather than
making quantitative comparisons between different crystals
with different demagnetization factors.
Similar Meissner fraction experiments were performed
on sample A following preparations to a variety of oxygen
deficient states. Figure 3 displays these results as pairs of
data points that represent the Meissner fraction and transition
temperatures in the disordered and subsequent ordered state,
following the 38 ◦ C anneal. The arrow between points is a
guide to the eye for linking each pair and to indicate the
direction of ordering. For example, the two data points at the
farthest right-hand section of the graph, toward the bottom,
are the data from the results shown in figure 2. Two major
trends can be seen from this figure. For a given oxygen
deficient and disordered/ordered state, the Meissner fraction
always decreases as the applied magnetic field increases, as
has been seen and explained by others [17, 18]. In addition, in
all cases the Meissner fraction either increases with increase in
oxygen ordering or does not change within the resolution of the
signal. Only for the most oxygen rich state with the smallest
change in transition temperature (Tc = 1.3 K) following
annealing, from Tc = 52.1 to 53.4 K, in applied fields of
1 and 3 G, is there no measurable change in the Meissner
signal. In addition to the dependence on oxygen ordering, to
a lesser extent there is an overall trend that, for a given degree
of oxygen order, the Meissner fraction is greater for the more
oxygen rich states. For example, comparing oxygen ordered
states in an applied field of 1 G, the most oxygen deficient
state with a Tc = 30.2 has the lowest Meissner fraction of
0.127, while the most oxygen rich state with a Tc = 53.4 has
the highest Meissner fraction of 0.151. However, the trend is
not universal. Again comparing ordered states in a field of 1 G,
the more oxygen deficient state with a Tc of 35.3 has a greater
Meissner fraction of 0.136 than the more oxygen rich state with
a Tc of 41.8 and Meissner fraction of 0.130.
A second set of experiments were performed for sample
B and the data for that crystal are shown in figure 4. Similar
Meissner fraction for YBa2 Cu3 O7−δ single crystals
Figure 4. The Meissner fraction as a function of transition
temperature for sample B, annealed to a variety of oxygen deficient
states. Symbols are equivalent to those defined for figure 3. It was
not possible to obtain data in a field of 7 G for the most oxygen
deficient state because the magnetization signal never levelled out to
the lowest temperature measured (4.2 K).
trends are seen for sample B as for sample A, that is, there
are only increases or no changes in the Meissner fraction due
to ordering and there is a decrease in the Meissner fraction
for increasing applied field. As for sample A, only for the
most oxygen rich state and for the smallest gain in transition
temperature upon annealing (Tc = 1.5 K), from Tc = 54.8
to 56.3 K, do no discernible changes occur in the Meissner
fraction. In addition, unlike for sample A, an increase in the
Meissner fraction is universally correlated with an increase in
overall oxygen stoichiometry.
Several other crystals were prepared and measured in
various oxygen deficient states. Data for all of these other
samples are shown in figure 5. Although there is a great
degree of sample dependence, each pair of points demonstrates
an increase in the Meissner fraction with increase in oxygen
ordering. All data display the decrease in the Meissner
fraction that is associated with increasing applied fields.
Therefore, from the results of figures 3–5, these two features
appear to be universal properties of the YBa2 Cu3 O7−δ system.
The correlation between oxygen stoichiometry and Meissner
fraction, seen partially for sample A and universally for sample
B, however, is not as apparent comparing different crystals.
This apparent ambiguity will be addressed below.
4. Discussion
The origin of the Meissner fraction has been analysed
theoretically [18] and the conclusions from that work are
consistent with our experimental results and the results of
others [17]. Through analysis of the Bean critical state
model [19] in the application of low fields, the Meissner
fraction was found to depend on the critical current density, Jc ,
the lower critical field, Hc1 , and the dimensions of the sample,
D.
More precisely, the Meissner fraction was found to be a
decreasing function of a dimensionless flux-pinning parameter,
γc1 , where,
n( 4cπ )Jc (Tc1 )( D2 )
γc1 =
(1)
.
f Hc1 (Tc1 )
Figure 5. Meissner fraction as a function of transition temperature
for all of the rest of the samples measured. Symbols are equivalent to
those defined for figure 3.
In this formula [18], f is a dimensionless factor between 0 and
1, Tc1 is the temperature at which the applied field is equal to
the lower critical field, and n is the power associated with the
temperature dependence of Jc , assumed to follow the formula
Jc (T ) = Jc (0)(1 − t 2 )n , where t = T / Tc . In addition,
the lower critical field was assumed to follow the formula
Hc1 (T ) = Hc1 (0)(1 − t 2 ).
The experimental observation that the Meissner fraction
increases with decreasing applied field is consistent with an
application of equation (1) for n > 1. For n > 1, the
critical current density decreases more rapidly with increasing
temperature than does the lower critical field, and, in addition,
their ratio (and hence γc1 ) also decreases with increasing
temperature. A decrease in γc1 (pinning) implies an increase
in the Meissner fraction. Applying equation (1) to increased
temperatures (and increased Meissner fraction) is associated
with a greater value for Tc1 , and a lesser value for Hc1 , since
the lower critical field is a decreasing function of temperature.
Since Hc1 (Tc1 ) is, by definition, equal to the applied field,
the lesser value for Hc1 is equivalent to a lesser value for
the applied field. Consequently, lower applied fields are
associated with greater Meissner fractions. Therefore, n > 1
appears to be the correct range of applicability for the Meissner
fraction analysis using equation (1), due to the qualitative
correspondence between theory and experiment.
Other studies [20, 21] have investigated changes in
the Meissner fraction as a function of oxygen deficiency,
irrespective of oxygen ordering. Similar to our results, it is
found that the Meissner fraction is reduced for the more oxygen
deficient states. One of these studies [21] compared Meissner
fractions between different oxygen rich and oxygen deficient
crystals and, as indicated by figure 5 (and from equation (1)
due to a dependence on sample dimension), results of such
studies can sometimes be ambiguous. However, the other
study [20] did look at comparisons between oxygen deficient
and oxygen rich states on the same crystal and found an
unambiguous relationship. An intrinsic reason for this effect
can be linked to the observed reduction in the lower critical
field that occurs from reduced hole doping, due to oxygen
deficiency [22, 23] or due to oxygen disorder [24]. As was
noted in those studies, reduced hole doping leads to smaller
983
K G Vandervoort et al
superconducting screening currents and, consequently, longer
penetration depths. These properties lead to reduced critical
fields (both thermodynamic and lower and upper critical fields)
and, as is consistent with equation (1), an increased pinning
parameter and reduced Meissner fraction. However, such
intrinsic properties would most likely lead to steady increases
of the Meissner fraction with increasing transition temperature.
Indeed, careful studies of the dependence of the lower
critical field on transition temperature for a highly underdoped
YBa2 Cu3 O7−δ sample [24] demonstrate that Hc1 (0) increases
smoothly as a power law with Tc . Sharp increases, where a
large increase in Meissner fraction occurs with only a small
change in transition temperature, for example for sample E in
figure 5 and for the 51.1–53.0 K Tc increase in figure 3 for
sample A, are most likely due to changes in more extrinsic
properties, such as a redistribution of oxygen vacancies.
Several groups [21, 23, 25] have investigated the
dependence of the critical current density on oxygen deficiency
from measurements of magnetization hysteresis loops. These
studies show that the critical current density decreases with
increasing oxygen deficiency. Here again, changes in intrinsic
properties, for example the decrease in the condensation energy
density, defined as Fc = Hc2 /8π , and its relationship to
pinning, were offered [23] as the main contribution to the
decrease in critical current with increased oxygen deficiency.
From our results and others [20, 21], the observation that the
Meissner fraction decreases with increasing oxygen deficiency
implies, from equation (1), that the changes in critical current
density are not as significant as changes in the lower critical
field, which have the greatest impact on changes in the
Meissner fraction.
Other aspects of magnetization hysteresis loops, namely
the peak effect in the magnetization, have been studied [9, 10, 26] for samples with oxygen concentrations very
close to the optimum doping level, δ < 0.1. It was found that
the critical current increases as a function of oxygen ordering
and it was proposed that this oxygen ordering leads to the formation of oxygen vacancy clusters, increasing pinning for the
more ordered state. In our results we do not find this effect.
Increased pinning with increased oxygen ordering would lead
to decreased Meissner fractions, which we never find. As mentioned, the more significant increases in the Meissner fraction
that occur over a small change in transition temperatures we
link to changes in extrinsic properties of the material, such as
changes in the distribution of oxygen vacancies. Our results
indicate that ordering of oxygen vacancies for materials with
significant oxygen deficiencies (δ > 0.2) leads to reduced pinning in contrast to the published results for samples that are
only slightly oxygen deficient (δ < 0.1). A possible explanation for these observations would be that two different pinning mechanisms are responsible in the different oxygen deficient regimes. One mechanism, suggested from studies of
the peak effect [9, 10, 26], involves increased pinning that occurs when, upon ordering, randomly interspersed oxygen vacancies coalesce into oxygen vacancy clusters. A mechanism
for decreased pinning may be associated with the formation of
short-range superstructures that form during ordering and consist of empty chains separated by two or three fully occupied
chains, as measured in x-ray scattering experiments [27], or
empty chains separated by one fully occupied chain (ortho II
984
phase), as predicted in simulations [28]. For the samples near
optimal doping, the superstructure regions would be fairly dilute and the decreased pinning associated with this ordering
effect would be weak. For the significantly oxygen deficient
samples, however, larger domains of ordered superstructures
with significant long-range order can form [29], and the reduction of pinning due to these features might overwhelm any
increase of pinning due to oxygen vacancy clustering.
In summary, we have measured the dependence of the
Meissner fraction on oxygen ordering for oxygen deficient
YBa2 Cu3 O7−δ , on several crystals and for significant varieties
of δ . Consistent with our earlier results on a single crystal
in a particular oxygen deficient state, we find that, in almost
all cases, the Meissner fraction increases following oxygen
ordering. Only in a few instances, for small changes in
transition temperature (Tc < 2 K), do we measure no
increase in the Meissner fraction within the limits of noise. We
attribute these results to both intrinsic parameters that affect
the Meissner fraction, such as changes in Hc1 that occur due to
changes in the charge carrier density in the planes, and extrinsic
factors, such as the redistribution of oxygen vacancies. We find
that for these significantly oxygen deficient states, pinning does
decrease due to oxygen ordering, in contrast to reported results
for samples that are only slightly oxygen deficient.
Acknowledgments
Acknowledgment is made to the Donors of the American
Chemical Society Petroleum Research Fund for support of this
research. This work was also supported by the US Department
of Energy, BES, Materials Science under contract no W-31109-ENG-38 at Argonne National Laboratory.
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