PHYSICAL REVIEW B
VOLUME 58, NUMBER 14
1 OCTOBER 1998-II
Influence of twin boundaries on the flux pinning in NdBa2Cu3Oy single crystals
A. K. Pradhan,* K. Kuroda, B. Chen, and N. Koshizuka
Superconductivity Research Laboratory, ISTEC, 1-10-13 Shinonome, Koto-ku, Tokyo 135-0062, Japan
~Received 7 April 1998!
We report on the magnetization, pinning force, and magnetic relaxation of twinned and detwinned
NdBa2Cu3Oy ~NBCO! single crystals. A double peak feature appears in the magnetization curves of the crystal
having one type of twin boundary ~TB! only in one direction, whereas a single peak is observed in crystals
either without twins, or with microtwins or mixed twins in both directions. The double peaks disappear when
the magnetic field is tilted away from the c axis of the crystal removing the influence of TB’s. In the high field
region, due to suppression of thermal fluctuations by the presence of TB’s, the relaxation rate in twinned
NdBCO crystal is small, and the pinning force density is increased compared to the YBCO and detwinned
NdBCO crystals. @S0163-1829~98!09038-9#
I. INTRODUCTION
Flux pinning by various defect structures in cuprate superconductors has attracted a great deal of attention in recent
years due to its possible applications at high temperature.
Microscopic point defects such as randomly distributed oxygen vacancies1 and twin planes2 are the effective pinning
centers in the high-T c single crystals. The interaction of vortices with twin boundaries ~TB’s! has been discussed by
many authors. The presence of TB’s leads to increased pinning at high temperature2 while they act as channels3,4 for
easier flux penetration when there are other strong pinning
centers available. However, their effective influence on the
flux line lattice is limited to a restricted angle u u u < u L ,
where u L is the lock-in angle below which the gain of free
energy from vortex capturing by a twin boundary is greater
than the energy loss by the vortex deformation. Moreover,
TB’s can act like correlated defects such as columnar defects
resulting in a strong pinning when vortices are aligned along
them. It is believed that vortices are attracted to TB’s while
remaining disordered between the planes. The most important factor as discussed by Blatter et al.5 is the intrinsic enhancement of the pinning forces acting within twin planes
due to the suppression of thermal fluctuations ~dimensionally
reduced!. At high temperatures, thermal fluctuation leads to a
renormalization of the pinning energy as well as the pinning
length. Recently much attention has been focused on the interaction of vortices with such correlated disorder.6 At the
same time, the interplay between the correlated disorder and
the generic point defects becomes important to understand
the pinning mechanism in single crystals containing both
types of disorders.
Although many studies regarding the role of point disorders and twin planes have been pursued in YBa2Cu3Oy
~YBCO! system,1–4 there still remain some controversial issues. However, at least it is clear that twin boundaries act as
pinning sites and their effect can be quantitatively
measured in a defect-free crystal.2 Recently, processed
Nd11x Ba22x Cu3Oy ~NdBCO!, which displayed a pronounced fishtail peak effect ~FTPE!, and a much higher J c
and irreversibility line7–10 than YBCO, is of technological
importance. It is believed that the source of large FTPE at
0163-1829/98/58~14!/9498~6!/$15.00
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higher field and large J c is attributed to the field-induced
pinning centers by Nd-Ba substitution sites7 rather than
oxygen-deficient regions in YBCO. The basic difference between YBCO and NdBCO is that the latter is a nonstoichiometric compound exhibiting T c at approximately 95 K when
grown in an oxygen-controlled atmosphere. These crystals
contain dense twin boundary planes. No clear attempts have
been made so far to understand the role of twin boundaries in
the pinning process for NdBCO crystals. In order to investigate the influence of such TB’s on the pinning, particularly
in the high field region, we have carried out detailed magnetization and magnetic relaxation experiments. We show the
direct influence of TB’s on the pinning in NdBCO crystal.
We have used a functional form of volume pinning force to
evaluate pinning mechanism. We have also shown clear experimental evidence that in the high field region, the magnetic relaxation is reduced by the suppression of thermal
fluctuation in the presence of TB’s.
II. EXPERIMENT
The crystals investigated were grown by the travelingsolvent–floating-zone technique under a controlled oxygen
partial pressure ~0.1% O2 in Ar atmosphere! as described
elsewhere.11 We used two NdBCO single crystals having
dimensions 1.3630.7430.27 mm3 ~twinned-T-Nd123! and
0.630.530.27 mm3 ~detwinned-DT-Nd123!. Polarized light
microscopy revealed twin planes in both @110# and @1-10#
directions in T-Nd123 crystal.10 The average twin separation
in the crystal varies from 0.5 to 2 mm. However, it is noticed
that the twin spacing varies not only from crystal to crystal
but also within the crystal. Some regions in a crystal show
twin separation even less than 0.5 mm. The twinned crystal
used for angle-dependent magnetization measurements was
cut such that the crystal contains only one type of twin
planes ~i.e., @110# direction! and has a dimension of 0.74
30.7330.27 mm3. The detwinning was done under uniaxial
pressure at temperature range 400–600 °C. Both crystals
were annealed at 320 °C for 330 h. In the detwinned crystal,
no TB was observed under the polarizing microscope.
The magnetization measurements were carried out using a
SQUID magnetometer ~Quantum Design, MPMS! with a
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© 1998 The American Physical Society
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INFLUENCE OF TWIN BOUNDARIES ON THE FLUX . . .
9499
FIG. 1. Magnetic-field-dependent critical current density J c of
~a! twinned and ~b! detwinned NdBCO single crystals at several
temperatures. The J c value at T560 K of a twinned crystal containing one type of twin boundary planes ~@110#! is shown in ~a!.
magnetic field applied parallel to the c axis of the crystal.
The angle-dependent magnetization was carried out with an
angle precision ,0.5°. The c axis of the crystal was rotated
away with respect to the applied field. The field was applied
parallel to the @110# twin planes and the crystal was tilted
continuously away from the twin planes such that the plane,
which was formed by the directions of the field and the c
axis, was always normal to the @110# twin boundary planes.
The scan length of the specimen in the magnetometer was 2
cm to avoid field inhomogeneity. The magnetic relaxation
was performed on a sample after applying a large negative
field greater than the field for full penetration. The details of
the measurement procedure have been described
elsewhere.10
III. RESULTS AND DISCUSSION
First we present the magnetically determined J c of
twinned ~having twin boundary planes in both directions!,
detwinned, and twinned @having twin boundary planes in
only @110# direction, shown as 60 K @110# in Fig. 1~a!#
NdBCO single crystals at several temperatures in Fig. 1 for
H i c. The J c values were calculated using the modified Bean
model.12 The irreversibility field, H irr, was determined by
H irr;100 A/cm2 criterion at a given temperature. All curves
exhibit a well-defined peak at magnetic field H max . The most
striking differences between these two crystals are ~a! higher
irreversibility and peak field in the twinned crystal and ~b! a
slightly higher J c in detwinned crystal at its H max . The reduced magnetization at H max in the twinned crystals compared to the detwinned one may be due to the channeling of
vortices as observed for YBCO ~Ref. 3! and will be discussed later. In Fig. 2~a! we show the temperature-dependent
DM ~difference in moment for increasing and decreasing
field branches! as a function of H i c for the crystal containing only @110# twin boundary planes. All curves exhibit two
weak peaks in the intermediate field range in the temperature
FIG. 2. Field-dependent dM ~difference in magnetization for
increasing and decreasing field branches after attaining a critical
state in the crystal! of T-Nd123 crystal containing mainly one type
of TB for u 50°, 5°, and 15° at 40 K. The applied field is tilted
with respect to the c axis by an angle u.
range 30 to 60 K. The location of the first peak, P1, is nearly
temperature independent while the second peak, P2, is not. It
is observed that as the temperature increases, P2 comes
closer to P1 and above 70 K the two peaks merge. P1 disappears slowly as we tilt the c axis of the crystal away from
the magnetic field.
In Figs. 2~b!–2~c!, we show temperature-dependent
DM (cos u)21 as a function of field, and H cos u for tilt
angles u 55° and 15°. When the applied magnetic field H is
tilted away from the c axis, the measured magnetization M
arises from the projection of the component along the c axis
of the magnetization, M (cos u)21.3,13 Though we find a
small P1 for u 55°, it completely disappears for u 515°
displaying a very broad P2 at all temperatures. However, for
both u 55° and 15°, DM values become larger at H max in
comparison to u 50° (H i c). This is consistent with the phenomenon of vortex channeling3 through TB’s for H i c. Furthermore, the much reduced J c value at H max in the twinned
crystal having one type of twin boundary as shown in Fig.
1~a! for T560 K support the above phenomenon. In Fig. 3
we show the angular dependence of the normalized magnetization at three indicated temperatures for an applied field of
3 T. Two features are noticed. First, DM increases as the
field is tilted away from the c axis and second, the slope of
the curve decreases with increasing temperature. These observations suggest that the vortex channeling occurs more
significantly at lower temperatures. The field value, at which
P1 in YBCO crystal3 is observed, is nearly the same as those
in our NdBCO crystal and in that of Koblischka et al.14 This
consistent value of P1 is assigned due to the matching
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A. K. PRADHAN, K. KURODA, B. CHEN, AND N. KOSHIZUKA
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FIG. 3. Angular dependence of the normalized magnetization at
a fixed applied magnetic field m 0 H cos u53 T at indicated temperatures.
effect4 at TB’s. The twin planes go all the way through the
present crystal with their average separation of 0.5 to 2 mm.
Such a large twin spacing will not allow one to assign P1
due to the matching effect, because the observed field value
of P1 ~;2 T! corresponds to the twin spacing of a few tens
of nm only considering the relation a v ;( f 0 /B P1 ) 1/2, where
a v and f 0 are the average vortex spacing and the flux quantum, respectively. However, the observation of P1 is dependent on the types of twin boundaries in a given specimen. A
crystal having twin planes predominantly in one direction
exhibits two peaks while a crystal with microtwins or mixed
twin planes in both directions shows one peak in the intermediate field range. The influence of TB’s depends on the
average twin spacing, formation of twin complexes such as
microtwins, the integrity of the twin walls, and defect concentration in between the twin boundaries. In view of the
above observation, the origin of P1 may be due to the vortex
rearrangement as the flux pattern is disturbed by the presence
of twin planes.14 The results of our angle-dependent magnetization suggest that the vortices experience the influence of
TB’s not only in the intermediate field region but also in the
high field region as well.
In order to gain insight into the magnetic relaxation near
the peak effect regime, we show the M -H curves for the
field increasing case with magnetic relaxation for u 50°, 5°,
and 15° at T540 K in Fig. 4. The relaxation measurement at
each field was carried out for about t;3500 s. The peaks,
P1 and P2, are very prominent for u 50°, a small feature
exists at u 55° and finally disappears for u 515°. The normalized relaxation rate S (2M 21
0 dM /d ln t, where M 0 is the
initial magnetic moment at a characteristic time t5t b , where
t b is the initial magnetic moment at t;50 s! is given in the
inset for two angles. The relaxation rate progressively increases in the high field region as u increases from 0° to 15°.
It is observed that for u 55°, S lies in between 0° and 15°
and has not been shown here for clarity. The relaxation rate
is nearly identical for H<3 T, but diverges for H>3 T for
u 50° and 15°. This illustrates that TB’s influence the mag-
FIG. 4. MH curves ~only increasing branch of field after applying a large negative field! of T-Nd123 crystal for u 50°, 5°, and
15° at 40 K. The relaxation experiment has been done at the field
values shown for t;3500 s. The inset in ~a! shows the fielddependent relaxation rate S for u 50° and 15° at 40 K.
netization loop and the relaxation process as well, particularly in the high field region. The planar defects are known to
suppress the thermal fluctuation at high temperature, rendering its influence on the flux line lattice. The details will be
discussed later.
Much valuable information on pinning mechanisms has
been obtained from the functional form of the pinning force
density, F p (B)5J c B. The functional dependencies of pinning force densities on B have been estimated for a variety of
pinning mechanisms in high-temperature superconductors
~HTSC’s!.13,15,16 These include pinning by point defects,
twin planes, dislocations, irradiation induced defects, etc.
The summation of the elementary pinning force densities,
either discretely or within the framework of collective pinning, leads to the definition F p 5J c 3B. In conventional superconductors, a scaling approach using the model of Yamafuji and Irie, and Kramers model,17
F P 5Cb p ~ 12b ! q ¯
~1!
is generally followed, where b is reduced field, b
5B a /B c2 , p and q are the parameters describing the pinning
mechanism, b peak5 p/(p1q), and C is a numerical parameter. Therefore all the temperature-dependent curves of
F p /F p,max versus b would collapse to a single curve if the
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INFLUENCE OF TWIN BOUNDARIES ON THE FLUX . . .
FIG. 5. Normalized pinning force as a function of reduced field
for a twinned YBCO, detwinned Nd123 ~DT-Nd123!, and twinned
Nd123 ~T-Nd123! single crystals. Curves for OCMG Nd123
~shown schematically!, detwinned Nd123 after high pressure annealing in O2 (HP-O2), and oxygen-annealed ~ann! YBCO at
500 °C are also shown.
primary pinning mechanism was not changed. In HTSC’s,
such a polynomial appears useful if B c2 is substituted by the
irreversibility field13,15 B irr . We have adopted a similar approach to explore the pinning behavior of twinned and detwinned NdBCO single crystals. The results are compared to
a flux-grown YBCO crystal as well. In Fig. 4, we show
F p /F p,max versus reduced field b for detwinned and twinned
~containing single and both types of TB’s! single crystals,
and melt-textured NdBCO @oxygen-controlled melt-grown
~OCMG! as shown in Fig. 5# and twinned YBCO crystal at
various temperatures for H i c.
The pinning forces at different temperatures were found
to collapse to a single curve and were scaled well for all
crystals. It may be noted that all crystals exhibit pronounced
temperature-dependent peak effect. The remarkable differences between these crystal are ~i! the progressive shift of b
from YBCO crystal to twinned NdBCO crystal and ~ii! reduction in tail feature of F P /F p,max versus b curves in high
field region of a twinned NdBCO crystal in comparison to
the detwinned one. As discussed below, the peak position of
b, b peak in the region of 0.4 to 0.5 clearly demonstrates that
the pinning centers are of superconducting type with reduced
order parameter or d T c change and become normal with increasing field. In order to test this, we have done the following scaling analysis using Eq. ~1!. In Fig. 6 we show the
different scaling of F p curves for twinned crystal where a is
for p50.5, q52, b for p51, q52, c for p51.45, q52, and
d for p5q52. The best fit was found for p51.5 and q52 in
the twinned crystal. The speculated pinning center in this
material is the presence of Nd-substituted Ba sites. In fact,
scanning tunneling microscopy studies revealed Nd-rich sites
with dimension of several tens of nm.18 In the detwinned
crystal the peak in b was found to be more than 0.33. It is
noted that b peak in the detwinned crystal is not affected much
upon high pressure oxygenation (HP-O2 curve in Fig. 5!. In
the YBCO crystal in which the oxygen-deficient regions play
9501
FIG. 6. Normalized pinning force as a function of reduced field
of twinned crystal and its scaling using Eq. ~1!. The notations of the
scaled curves are a for p50.5, q52, b for p51, q52, c for p
51.45, q52, and d for p5q52. The curve for the twinned sample
after optimum annealing ~Nd2! is also shown.
a role for pinning, b peak is less than 0.3. In the twinned
NdBCO crystal, b peak is remarkably higher. Compared to the
usual normal type of nonsuperconducting pinning centers
~with p51 and q52, and b peak50.33 for an ideal case!, the
pinning centers in NdBCO seem to be of the superconducting type that is consistent with either d T c ~Ref. 17! or dk
pinning.19 Furthermore, the emergence of the peak in magnetization at high temperature with increasing field suggests
that the pinning centers are field induced.
Within the range of lock-in angle where TB’s act as pinning centers, a state of correlated disorder is formed. The
correlation volume, V c (5R 2c L c , where R c and L c are the
average bundle sizes for perpendicular and parallel field vector H, respectively! increases with increase of C 44 modulus.
Therefore, for a low field region b,0.2, twins are effective
pinning centers and are confirmed by many direct experiments. For intermediate field range, 0.2,b,0.6, where R c
.L c , twins are capable of initiating the correlated state
through intertwin regions within the lock-in angle regime
with enhancement in V c . This occurs due to decrease in L c ,
since L c a (c 44) 1/2 and due to increase of the transverse correlation radius, R c as J c increases with increasing field in the
intermediate field range. In view of the above, the twin spacing of the present crystals ~i.e., ;1 to 2 mm on average!, the
observations of drop in J c for H i c, and a lock-in state below
u ,15° as shown previously would allow the formation of a
correlated state and the enhancement in V c . Such correlation
by TB’s has been observed in transport measurements.10,20
This correlated state spreads throughout the bulk, enhancing
the b peak to higher field region; however, a decrease in J c can
be observed ~e.g., Figs. 1 and 3! due to channeling of vortices through TB’s. In this regime, there is an interaction between the pointlike disorders and TB’s due to the formation
of the correlated state which influences the flux line lattice
interaction with the point disorders.
For higher field range, b.0.6, where the applied field
approaches the irreversibility field, B irr , two independent
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A. K. PRADHAN, K. KURODA, B. CHEN, AND N. KOSHIZUKA
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relaxation is very sensitive to the thermal activation and
hence the thermal fluctuation of vortices as well. We observe
a significant difference in S between the twinned and detwinned crystal especially in the high field region. The
twinned crystal exhibits a reduced relaxation even up to very
high field and temperature regimes. This clearly supports the
reduced tail feature in the F p curve of twinned crystals in the
high field regime. This is direct evidence of suppression of
thermal fluctuation in the presence of TB’s in the NdBCO
twinned single crystals in high field and high temperature
regions as well.
IV. CONCLUSION
FIG. 7. Relaxation rate S as a function of field for ~a! twinned
and ~b! detwinned single crystals at several temperatures.
contributions for respective pinning to J c from pointlike and
TB pinning centers occur. In this field region, the interaction
between these two separate pinning centers is minimal due to
weakness of the correlated state by TB’s. However, the resulting J c from TB’s decays only algebraically with increasing temperature as opposed to the exponential dependence
on temperature obtained for pinning by point disorders, rendering the twin boundary pinning increasingly important at
higher temperature.5 Furthermore, pointlike disorders such as
the present isotropic disorder by substitution in the NdBCO
crystal are more liable to smearing by thermal fluctuations
and the efficiency of their pinning potential falls more rapidly as the field approaches B irr than that of macroscopically
large twins. Due to reduced dimensionality of TB’s, the thermal fluctuation is greatly reduced and causes enhancement in
pinning forces intrinsically.5 In Fig. 7, we compared the relaxation rate over the whole field range for twinned and detwinned Nd123 single crystals to show the effect of thermal
fluctuation on magnetic relaxation. The process of magnetic
*On leave from Centre for Advanced Technology, Indore, India.
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In conclusion, we have shown that the double peaks of
FTPE in the magnetization curve are very much sample dependent. Double peaks appear in crystal having only one
type of twin boundary, whereas a single peak is observed in
crystals with either microtwins or mixed twins in both directions. The double-peak feature disappears when the magnetic
field is tilted away from the c axis of the crystal, suggesting
the role of twin boundary pinning in determination of the J c
values when H i c. The higher relaxation rate for larger tilt
angles compared to H i c in the high field region suggests
reduction in thermal fluctuation of vortices by TB’s in the
H i c orientation. The pinning force density in a twinned crystal increases remarkably to the high field region with a reduced tail feature in comparison to the one without the twin
boundaries. In the low field region, TB’s play a role for
pinning within the lock-in angle whereas in the intermediate
field range the correlated state of TB’s along with point disorders dominate pinning. In the high field region due to suppression of thermal fluctuations by the presence of TB’s, the
relaxation rate in twinned crystal is small and hence the reduction in the tail feature is observed.
ACKNOWLEDGMENT
This work was supported by NEDO.
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