Physica C 290 Ž1997. 311–316
Field induced flux pinning in Nd 1qx Ba 2yxCu 3 O 7yd single crystal
T. Mochida ) , M. Murakami
SuperconductiÕity Research Laboratory, International SuperconductiÕity Technology Center, 1-16-25, Shibaura, Minato-ku, Tokyo 105,
Japan
Received 1 August 1997; accepted 25 August 1997
Abstract
The flux pinning behavior of a Nd 1qx Ba 2yx Cu 3 O 7y d ŽNd123. single crystal, which exhibited a peak effect, has been
studied by monitoring the time decay of the magnetic moment. The apparent pinning energy ŽU0) . was deduced from flux
creep data on the basis of the Anderson–Kim model. The magnetic field dependence of U0) showed maxima at peak fields
which depended on the temperatures, in a similar manner to those of critical current densities. In addition, the temperature
dependence of U0) showed several features. To explain the increase in U0) with the field as well as its temperature and field
dependence, we made a numerical calculation by introducing an additional pinning energy which increased with increasing
field. The results are in good agreement with the experimental data, especially at temperatures above 60 K, where the
contribution of field induced pinning centers is believed to be dominant. q 1997 Elsevier Science B.V.
Keywords: Flux pinning; Fishtail effect; Flux creep
1. Introduction
Nd 1q x Ba 2yx Cu 3 O 7y d ŽNd123. superconductors,
fabricated under a low partial pressure of oxygen,
exhibit high Tc and large Jc values w1,2x. As a
common feature of such Nd123, the M–H loops
always exhibit a peak effect, which results in considerable enhancement of Jc in a field region between 1
and 5 T at 77 K w1–5x. The origin of the peak effect
is attributed to the presence of a low Tc phase with a
slight chemical variation due to the substitution of
Nd on Ba sites w3–5x. In this scenario, the low Tc
phase is superconducting at low fields, and is driven
)
Corresponding author. Tel.: q81 3 3454 9284; fax: q81 3
3454 9287; e-mail: mochida@istec.or.jp
normal in high fields producing pinning centers. In
the samples exhibiting the peak effect, the pinning
energy is enhanced effectively with increasing magnetic field by additional field induced pinning. The
purpose of the present work is to study the temperature and field dependence of the apparent pinning
energy Žor apparent activation energy. U0) of the
sample which exhibits the peak effect in the M–H
loops.
Flux creep measurements are commonly used to
estimate the pinning energy of superconductors. Several models have been proposed to study the flux
pinning of superconductors w6–12x. The simplest and
most direct way based on the Anderson–Kim model
w13,14x uses the standard analysis for magnetic relaxation due to the thermally activated motion of flux
0921-4534r97r$17.00 q 1997 Elsevier Science B.V. All rights reserved.
PII S 0 9 2 1 - 4 5 3 4 Ž 9 7 . 0 1 7 0 6 - 1
T. Mochida, M. Murakamir Physica C 290 (1997) 311–316
312
lines Žor flux creep. out of the potential wells aided
by the Lorentz force. The simplest assumption of a
linear J-dependent form for the U0) gives
J
ž /
U0) s U0 y JBVa s U0 1 y
Jc
Ž 1.
where U0 is pinning energy at J s 0, V is the
volume of the flux bundle, a is the hopping distance
and Jc s U0rBÕa is the critical current density at
which the pinning energy disappears. Using the above
linear approximation and solving the flux creep
equation for the lowest order, one obtains the logarithmic decay for the irreversible magnetization, i.e.
½
MŽ t. s 1y
kT
U0)
ln
t
ž /5
t0
Ž 2.
where t 0 is the macroscopic attempting time for the
flux motion, U0) is the apparent pinning potential
and k is the Boltzmann constant. From the logarithmic form of the M Ž t . decay, one can deduce the
normalized relaxation rate S to determine the U0) :
U0) s y
kT
S
.
Ž 3.
3. Results and discussion
Ž 4.
The field dependence of the Jc for temperatures
between 70 K and 86 K is shown in Fig. 1. The
sample shows a Jc value of 35 000 Arcm2 at 77 K
Here S is defined as
S'
dln M
1 dM
s
dlnt
1 dM
f
M dlnt
Mi dlnt
was decreased from 500 to 3008C over 400 h. The
sample dimensions were 1.18 = 1.38 = 0.47 mm3
with the largest cross-section perpendicular to the
c-axis. The sample showed a sharp superconducting
transition with an onset Tc of 91.5 K.
Magnetization loops were measured using a
Quantum Design MPMS-7 SQUID magnetometer
with a temperature and field range of 5 to 86 K and
0 to 7 T with the field applied parallel to the c-axis.
The critical current densities, Jc , were calculated
using the extended Bean model w18x. The magnetic
relaxation rate was obtained by measuring the time
decay of the magnetic moment for about 1 h as
described by van Dalen et al. w19x. The first data
point was taken after 200 s to avoid deviation from a
pure logarithmic decay. During the relaxation measurements, the scan length was kept at 3 cm to avoid
field inhomogeneities. In all cases, the field was
swept to a sufficiently low negative value to ensure
full flux penetration, before sweeping to the desired
target value.
where Mi is the initial magnetization. Although a
minor error is introduced by using Mi instead of M,
it is not critical as long as the variation in M during
the experiment is small. The U0) obtained by this
model corresponds to the U axis intercept of the
straight line tangent to UŽ J . at the measured temperature and current w15,16x. Although the model is
simplified, U0) values give valuable information
about the pinning characteristics of a sample because
these values are widely discussed for many high-Tc
superconductors.
2. Experimental
A single crystal of Nd 1q x Ba 2yx Cu 3 O 7y d was
fabricated by a flux method in 1% O 2 , using details
which are described elsewhere w17x. The crystal was
annealed in flowing oxygen while the temperature
Fig. 1. Field dependence of the critical current densities, Jc ,
obtained from magnetic hysteresis loops, measured at temperatures of 70, 74, 77, 80, 83 and 86 K.
T. Mochida, M. Murakamir Physica C 290 (1997) 311–316
Fig. 2. Semi-logarithmic plots of the time dependence of the
irreversible magnetization, measured at temperatures of 70, 77,
80, 83 and 86 K. The solid lines show linear regression fits based
on the Anderson–Kim model. Note that no deviation from pure
logarithmic behavior occurs.
and 1.25 T, which is comparable to the values
reported in other Nd123 crystals w1–5x. Clear secondary peak effects are also observed in Jc – m 0 Ha
curves. The peak field Hp, J that gives the maximum
Jc value becomes larger with decreasing temperature
w3–5x.
The typical time dependence of the magnetic
moment is shown in Fig. 2. For all the temperatures,
an almost linear dependence of the magnetic decay
on the logarithmic time scale was found, showing
that U is linearly dependent on J in the measured
current region. Therefore, we deduced the normalized relaxation rate S, from the curve of the M vs.
ln t. Thus the apparent pinning energy U0) , which we
define here by U0) s ykTrS, can also be determined.
The field dependence of U0) values is shown in
Fig. 3. The U0) – m 0 Ha curves show a field dependence similar to Jc – m 0 Ha curves. The peak effect is
also observed such that U0) values increase with
field up to peak fields Hp,U , and then decrease with
further increasing field. Like the Jc – m 0 Ha curves,
the peaks become broader with the Hp,U shifting to
higher fields and with decreasing temperature. The
peaks in U0) – m 0 Ha curves are almost identical to
313
the peaks in Jc – m 0 Ha curves. These results suggest
that the peak in U0) and Jc has the same origin.
In most cases, U0) values monotonously decrease
with increasing field w20–22x. This is understood by
considering the fact that the pinning energy
monotonously decreases with field. Therefore, the
enhancement in U0) with field in a Nd123 single
crystal is not commonly observed, and we believe
that the secondary peak effect is responsible for such
unusual behavior.
In the Nd123 system, there are Nd rich clusters
which are distributed in the matrix w3,23x. Such Nd
rich clusters with depressed Tc are known to act as
field induced pinning centers: they are superconducting in a low field and driven normal in higher fields,
and thus can act as pinning centers w24x. The trigger
field for pinning is dependent on temperature. The
pinning potential thus increases with increasing field
up to a characteristic field of H ) , where all the field
induced pining centers become active. We assume
that the order of magnitude of H ) is the same as
Hp,U and Hp, J . Above H ) , where no effective
activation of the field induced pinning centers takes
place, the field dependence of U0) becomes normal
and thus shows a monotonous decrease with field.
This is the origin of the peaks in U0) – m 0 Ha curves.
It should be born in mind that for effective pinning the clusters may not necessarily be in the
normal state. There is a threshold criterion for pin-
Fig. 3. The field dependence of apparent pinning energy U0) s
yT rS at T s10, 30, 50, 60, 70, 77 and 83 K.
314
T. Mochida, M. Murakamir Physica C 290 (1997) 311–316
Fig. 4. The temperature dependence of apparent pinning energy
U0) syT rS obtained through a numerical fitting of the experimental data to the Anderson–Kim model. Results for 0, 0.25, 0.5,
1, 2 and 7 T are plotted.
ning such that the change in the order parameter
Ž DC . should exceed some critical value depending
on the size of pinning center Ž d .. This criterion can
be written as U0rd where U0 is the depth of pinning
energy. For low Tc materials it is known that the
threshold value of U0rd is around 2r3 w25x. Therefore, even when the clusters are superconducting,
they can act as pinning centers.
The temperature dependence of the value of U0)
for m 0 Ha s 0, 0.25, 0.5, 1, 2 and 7 T is shown in
Fig. 4. When the external field is zero, U0) increases
linearly with increasing temperature. An increase in
U0) with an increase of temperature has been observed in various samples without the peak effect.
Such samples include Y123 single crystals w26x,
melt-processed Y123 with Y211 inclusions w20,21x,
Pr-doped Y123 w27x and Y123 thin films w22x. The
increase in U0) with temperature has been explained
in terms of either a non-linearity of U–J relations
w7,15x or a distribution of activation energies w6,26x.
In the presence of a magnetic field, several features can be seen which reflect the unusual field
dependence of U0) . First, the U0) values are higher
than those in the remanent state for temperatures
above the deviation temperatures ŽTd .. For example,
the U0) value at 0.25 T is almost equal to the one in
the remanent state at temperatures below 50 K.
However, when the temperature is raised above 60
K, the U0) value at 0.25 T exceeds the value of the
remanent state with the difference between the two
values increasing with temperature. Second, the
U0) –T curves show maximum values at peak temperatures Tp , above which the U0) values decrease
with temperature. The peaks in U0) – m 0 Ha curves
are identical to the peaks in U0) –T curves. It is also
important to note that both the Td and Tp values shift
to lower temperature with increasing field. This suggests that U0) values can be scaled by temperature
and field.
In order to account for the unusual increase in
U0) , we assume a simple model based on the idea of
field induced pinning. In this model, the pinning
energy increases linearly with field up to the characteristic field of H ) . The H ) has, of course, a
temperature dependent value which is described in
the following discussion. Writing the pinning energy
at T s T0 and H F H ) ŽT0 . as
U0) Ž T0 , H . s U0) ,BG Ž T0 , H .
q U0) ,FI Ž T0 , H ) Ž T0 . .
H
H)
.
Ž 5.
where U0) ,BG ŽT0 , H . is the ‘background’ pinning
energy and U0) ,FI ŽT0 , H ) ŽT0 .. is the contribution
from the field induced pinning centers at T s T0 . The
general form of U0) ,BG ŽT0 , H . would be w28,29x,
ž
U0) ,BK Ž T0 , H . s U0) ,BG Ž T0 . 1 y
H
Hc 2 Ž T0 .
/
Ž 6.
where Hc2 ŽT0 . is the upper critical field at T s T0 .
Since H r H c 2 Ž T 0 . < 1, then changes in
U0) ,BG ŽT0 , H . as a function of H can be ignored. So
U0) ,FI ŽT0 , H . is approximated as
U0) ,BG Ž T0 , H . f U0) ,BG Ž T0 . .
Ž 7.
Then the field dependence of the pinning energy at
T s T0 and H F H ) ŽT0 . becomes
½
U0) Ž T0 , H . s U0) ,BG Ž T0 . 1 q k
H
5
)
H Ž T0 .
Ž 8.
where k is the ratio of U0) ,FI ŽT0 , H ) ŽT0 ..r
U0) ,BG ŽT0 .. Assuming that the temperature dependence of U0) ,FI ŽT, H ) ŽT .. is identical to that of
U0) ,BG ŽT ., Eq. Ž8. becomes
½
U0) Ž T , H . s U0) ,BG Ž T . 1 q k
H
)
H ŽT .
5
.
Ž 8X .
T. Mochida, M. Murakamir Physica C 290 (1997) 311–316
315
shown in Fig. 5. As no consideration has been given
to the decrease in U0) above the peak, only the data
below the Hp,U Žor below Tp in U0) –T curves. are
plotted. The calculated values are in good agreement
with the experimental results, especially in the temperature region above 60 K, where the contribution
from field induced pinning centers is supposed to be
dominant w4x. These results show that the increase in
U0) below Hp,U is well described by introducing an
additional pinning energy, which increases with
magnetic field.
4. Conclusion
Fig. 5. Results of experimental data Žpoints. and numerical calculation Žlines. of apparent pinning energy ŽU0) . at m 0 Ha s 0, 0.25,
0.5, 1 and 2 T. Experimental data obtained above the peak
temperatures Tp are not plotted. For the numerical calculation,
ms1.64, H0) s13.4 and k s 2.7.
Since our results show that the peaks in U0) – m 0 Ha
curves are almost identical to the peaks in Jc – m 0 Ha
curves, it is reasonable to assume a same functional
form between the H ) ŽT . and the Hp, J ŽT .. As the
Hp, J ŽT . is written as Hp, J ŽT . s Hsc Ž1 y TrTx . m using a scaled field Hsc with parameters m ; 1.5 and
Tx s Tc w30x, the H ) ŽT . is
T
Ž 9.
Tc
with a characteristic magnetic field H0) and a fitting
parameter m. Finally, the temperature and field dependence of the U0) at T and H - H ) ŽT . becomes
U0) Ž T , H . s U0) ,BG Ž T .
= 1qk
H
H0)
Acknowledgements
m
½ ž /5
H ) Ž T . s H0) 1 y
We have measured the magnetic relaxation of a
Nd 1q x Ba 2yx Cu 3 O 7y d single crystal with a peak
effect. The relaxation process is found to be well
described by the Anderson–Kim model in the time
window of our experiment. The apparent pinning
energy ŽU0) . showed unusual temperature and field
dependence in that an increase in U0) is observed.
Such an increase in U0) can be explained by assuming an additional pinning energy, which increases
with magnetic field.
1 y Ž TrTc . 4
m
.
Ž 10 .
Fitting the experimental data to Eq. Ž9., we obtained H0) s 13.4 and m s 1.64, which are in the
same order of magnitude as in the literature w30x. For
the U0) ,BG ŽT . values, we adopted the experimentally
obtained U0) values in the remanent state. Using
these values, we found k s 2.7, which gave good
agreement with the experimental data. The experimental Žpoints. and theoretical Žlines. temperature
dependence of U0) at different applied field are
This work was partially supported by NEDO. The
authors thank Mr. K. Sawada for preparing the sample. We thank both Dr. M.R. Koblishka and Dr.
A.J.J. van Dalen for useful advice concerning SQUID
measurements. We are grateful to Dr. N. Chikumoto,
Dr. M. Wahahiki, Mr. T. Higuchi and Dr. A. Anderson for helpful suggestions. Acknowledgment is also
due to Dr. S.I. Yoo and Mr. N. Sakai for continuous
encouragement.
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