PHYSICAL REVIEW B
VOLUME 57, NUMBER 22
1 JUNE 1998-II
Magnetic studies on the field-driven transition from decoupled to coupled pancake vortex phase
in Bi2Sr2CaCu2O81 d with columnar defects
Noriko Chikumoto
Superconductivity Research Laboratory, ISTEC, 1-16-25 Shibaura, Minato-ku, Tokyo 105, Japan
Makoto Kosugi and Yuji Matsuda
Institute for Solid State Physics, University of Tokyo, 7-22-1 Roppongi, Minato-ku, Tokyo 106, Japan
Marcin Konczykowski
Laboratoire des Solides Irradiés, Ecole Polytechnique, Palaiseau 91128, France
Kohji Kishio
Department of Superconductivity, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113, Japan
~Received 13 February 1998!
The reversible (M re v ) and the irreversible magnetization of Bi2Sr2CaCu2O81 d single crystals with columnar
defects were measured as a function of field and temperature. In contrast to the conventional lnB dependence
of M re v observed in the unirradiated sample, the field dependence of M re v for the irradiated samples exhibits
an anomalous dip, corresponding to the expulsion of vortices from the sample. We show that the coupling
transition, which, to our knowledge, has not been considered previously in analyzing the magnetization data, is
very important to understand the anomalous behavior of M re v . From the measurement, we obtain the almost
temperature-independent transition line B c p (T);B F /3, where B F is a matching field. This is in good accordance with the recent computer simulation. The anomalous peak effect is observed at the same field, B
;B F /3, in Bose-glass ~BG! regime, which accompanies the reentrant behavior of BG melting line.
@S0163-1829~98!06122-0#
Columnar defects ~CD! introduced by the irradiation with
very energetic heavy ions are expected to be the most effective pinning centers for vortices aligned to the defect structure. Indeed, many experiments1 have shown that the pinning
properties, such as the critical current density J c and the
irreversibility field B irr , are largely improved by the introduction of CD in high-T c superconductors ~HTS!.
In such systems, the vortices are expected to localize on
CD at low temperatures, forming a so-called Bose-glass
~BG! phase.2 It is also predicted that the BG phase melts into
an entangled liquid through the second-order transition at
high temperature. However, although the existence of BG
phase has been confirmed experimentally by many groups,3
the nature of the vortex liquid phase in the presence of CD
remain unclear. Recent reversible magnetization (M re v ) on
heavy-ion-irradiated ~HII! Bi2Sr2CaCu2O81 d ~BSCCO! exhibits an unusual field dependence below the matching field
B F , where the density of vortices is equal to the defect
density.4–6 These measurements demonstrate that the nature
of the vortex liquid phase changes dramatically when CD are
introduced. Although Bulaevskii, Vinokur, and Maley calculated the equilibrium magnetization accounting for the entropy associated with different configurations of pancake
vortices inside and outside of CD,7 there is still a large discrepancy between the theoretical prediction and the experimental data. This explicitly demonstrates our incomplete
knowledge of the nature of the vortex liquid in the presence
of CD.
Recent results of Josephson plasma resonance8 ~JPR!
have revealed that the introduction of CD leads to the ap0163-1829/98/57~22!/14507~4!/$15.00
57
pearance of two types of liquids with different c-axis correlations in pancake positions, the well-coupled and the decoupled pancake vortex liquids.9,10 It has also been shown that
the pancakes tend to couple with field and the transition between the two liquids occurs in the narrow field range.9 More
recently, the coupling of pancakes has been confirmed by the
c-axis resistivity measurement.11 Quite recently numerical
simulation using the Monte Carlo method suggested the existence of field-driven discontinuous transition at a critical
field of B/B F ;1/3, which extends from the liquid phase to
the BG phase.12
In this paper, we present detailed measurements of the
magnetization behavior of HII BSCCO. We show that the
coupling transition, which, to our knowledge, has not been
considered previously in analyzing the magnetization data, is
very important to understanding the anomalous behavior of
M re v . From the measurement, we obtain the almost
temperature-independent transition line B c p (T);B F /3,
which is in good accordance with the computer simulation.
We also show the anomalous peak effect observed at the
same field, B;B F /3, in the BG regime, which accompanies
the reentrant behavior of BG melting line.
The BSCCO single-crystal samples used in the present
study were the same as the samples used for JPR study in
Ref. 9. The crystals were grown by a floating zone method,
described elsewhere.13 After cleaving from the synthesized
rod, as-grown crystals were annealed at 800 °C for 3 days to
remove the structural inhomogeneity. Then the crystals were
subsequently annealed in a reduced atmosphere at 400 °C for
3 days to reduce the oxygen disorder. The irradiation with
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© 1998 The American Physical Society
14 508
NORIKO CHIKUMOTO et al.
FIG. 1. Field dependence of reversible magnetization for
BSCCO with B F 50, 0.3, and 1 T. Inset: The temperature dependence of B c p ~circles! for B F 51 T, traced from the point where
M re v deviates from lnB dependence ~the M re v becomes maximum!.
The Josephson plasma resonance ~JPR! field, B 0 , at 30 ~triangles!
and 45 GHz ~diamonds! shown in Ref. 9 was also plotted. Filled
and open symbols represent the JPR in decoupled-liquid ~DL! phase
and coupled-liquid ~CL! phases, respectively.
5.8-GeV Pb ions was performed at Grand Accélérateur National d’Ions Lourds ~GANIL! ~Caen, France! at room temperature. Direction of the incident beam was almost parallel
to the c axis. The resulting damage consists of amorphous
columns of ;7 nm in diameter, extending throughout the
thickness of the sample. The samples were irradiated to the
fluences of 1.5 and 531010 ions/cm2 , corresponding to a
dose-equivalent flux density of B F 50.3 and 1 T, respectively. After the irradiation, we did not see any observable
change of the superconducting transition temperature T c
~585.7 K!. Magnetization measurements were performed using a SQUID Magnetometer ~Quantum Design!, with magnetic fields applied parallel to the c axis, i.e., parallel to CD.
Figure 1 shows M re v of BSCCO before (B F 50 T! and
after the irradiation (B F 50.3 and 1 T! as a function of lnB.
In the London regime (B c1 !B!B c2 ) for high-k type-II superconductors, the equilibrium magnetization M varies linearly proportional to lnB as
2 m 0 M 5 ~ F 0 /8p l 2 ! ln~ h B c2 /eB ! ,
~1!
where F 0 is the flux quantum, l the penetration depth, B c2
the upper critical field, and h a numerical factor of the order
of unity. For HTS, near T c , the extra entropy contribution
due to the thermal fluctuation of order parameter gives an
additional term to Eq. ~1!. Particularly, if the interaction of
the pancake vortices between the layers is negligibly small,
the vortex fluctuation theory gives the same lnB dependence
of M .14 As a result, the so-called crossing point at which
magnetization becomes field independent appears. This will
be discussed later. As shown in Fig. 1, lnB dependence of
M re v of the unirradiated crystal is well demonstrated in almost the entire B region. In a striking contrast, M re v of HII
BSCCO exhibits an unusual field dependence. At low fields
B!B F , M re v increases as lnB and reaches a maximum at
B;B F /3. Afterward, M re v decreases and reaches a minimum for B F 51 T. The decrease of M re v is not discernible
57
for B F 50.3 T. At B.B F , M re v of the irradiated crystals
approaches that of the unirradiated crystal. Well above B F ,
M re v of HII BSCCO coincides well with that of unirradiated
crystal. Similar behavior has been reported in other systems,
such as Tl-based compounds4 and Bi2Sr2Ca2Cu3O81 d . 6
The observed nonmonotonic field dependence of M re v is
in part explained by considering the entropy associated with
different configurations of pancake vortices.7 Although there
is no bulk pinning from CD in the reversible regime, the
pancake vortices tend to localize on CD due to the interaction between vortices and CD. This effect gives rise to the
increase of M re v . At very low field, B!B F , where the
vortex-vortex interaction is negligible, the pancakes tend to
distribute almost independently in each layer over CD to
gain free energy by increasing the entropy for random distribution. In this range, the difference of M re v between the
unirradiated and the irradiated samples is simply determined
by the pinning energy and is independent of B F . 4–6 On the
other hand, at high field B@B F , all CD are filled with the
vortices, so that M re v of irradiated crystals should be the
same as that of the unirradiated one.
In the intermediate field regime (0.3B F ,B,B F ), Bulaevskii, Vinokur, and Maley7 have calculated M re v by taking
into account the entropy of the pancake distribution within
CD. However, the calculated M re v is much larger than the
measured M re v , as shown in Fig. 2 of Ref. 7. We point out
here that this large discrepancy arises from the coupling
transition of the pancakes. To check this scenario, we plot
the Josephson plasma resonance field (B 0 ) at 30 GHz for
B F 51 T in Fig. 1. At this temperature, the double resonance
peaks are observed as a function of H. The lower resonance
peak corresponds to the decoupled liquid, while the higher
peak corresponds to the coupled liquid phase, as discussed in
Ref. 9. The field at which M re v reaches a maximum is located between two resonance fields. This provides strong
evidence that the deviation from the lnB dependence of M re v
is caused by the coupling of the pancakes. The decrease of
M re v is in part due to the reduction in the entropy of whole
system, but a larger contribution comes from the modification of the vortex-vortex interaction caused by rearrangement
of vortices at the coupling transition. Thus we determine the
coupling field B c p via H at which M re v first deviates from
the lnB dependence. The determined B c p for B F 51 T is
plotted versus temperature in the inset of Fig. 1. The figure
indicates that the B c p line determined from the magnetization
gives the boundary between coupled and decoupled liquid. It
is very interesting to note that the B c p is nearly temperature
independent and the value is given by a certain portion
(;1/3) of B F . Near T c , however, a slight upturn of B cp is
observed. This may be due to the increased thermal fluctuation effect. This result is surprisingly in good accordance
with the computer simulation study reported by Sugano et
al.12
Other strong evidence to support the occurrence of vortex
coupling at B c p is given by the disappearance of the socalled ‘‘crossing-point’’ behavior in the temperature variation of M re v above B c p . The ‘‘crossing point’’ behavior,
namely, the temperature dependence of the magnetization
that different magnetic fields cross at some temperature T * ,
is commonly observed in the highly anisotropic HTS and has
been explained by the cancellation of logarithmic field de-
57
MAGNETIC STUDIES ON THE FIELD-DRIVEN . . .
14 509
FIG. 3. The magnetic hysteresis loops showing peak effect for
~a! B F 50.3 T and ~b! B F 51 T samples.
FIG. 2. The temperature dependence of M re v measured in various applied fields for a BSCCO crystal irradiated to a dose of B F
51 T.
pendence of the mean-field magnetization @Eq. ~1!# by the
same logarithmic field dependence in the entropy contribution of a ‘‘decoupled’’ pancakes.14–16 Figure 2 displays the
M re v vs T curves for the B F 51 T sample in the field range
B,B c p , B cp ,B,B F , and B F ,B. At B,B cp , a clear
crossing behavior is observed at T * ;82 K, suggesting that
the decoupled pancakes are placed randomly ~do not form a
line! within CD at low fields. On the other hand, at B c p ,B
,B F , the crossing-point behavior disappears. Similar observation has been made by van der Beek et al.5 They explained
the disappearance in terms of the inhomogeneity introduced
by the heavy-ion irradiation. However, we point out here that
the suppression of entropy contribution by the vortex coupling gives rise to the disappearance of the crossing point. At
very high field, B@B F , the recovery of the crossing behavior is observed. This is quite natural because all CD are filled
with the vortices and interstitial vortices can be decoupled.
We now turn to the magnetization behavior below B irr
where the vortices form a BG phase. Figures 3~a! and 3~b!
show the magnetization hysteresis loops of B F 51 T and 0.3
T samples, respectively. In both samples, a so-called peak
effect with the peak field B pk ;B F /3 is observed. There are
various mechanisms that lead to the appearance of peak effect, such as ‘‘matching effect,’’17 ‘‘synchronization
effect,’’18 second-phase model ~field-induced peak effect!,19
and decomposition of the three-dimensional ~3D! flux lines
into 2D pancake vortices.20 The one that is frequently observed in HTS is the field-induced peak effect. However, we
can exclude this possibility since we confirmed that the observed peak effect does not depend on the sample quality and
only depends on CD density.
In order to get further insight, we plot the temperature
dependence of B pk together with B irr and B c p in Fig. 4. The
B irr is defined from the temperature at which the difference
in the magnetization between zero-field-cooled and fieldcooled branches becomes indistinguishable, using a criterion
FIG. 4. Magnetic phase diagram of heavy-ion-irradiated
BSCCO with B F 51 T ~circle! and 0.3 T ~square!. The closed symbols show the irreversibility field, B irr (T), while the coupling field
B c p @above B irr (T)# and the peak field B pk @below B irr (T)# are
plotted as open symbols. We also indicate the B irr (T) for the pristine sample by the dashed line.
14 510
NORIKO CHIKUMOTO et al.
roughly corresponding to J c ,100 A/cm2 . It is found that
the B pk is almost independent of temperature and smoothly
connects with B c p , suggesting that the peak effect in the BG
phase is relevant to the coupling of the pancakes. The observation of the peak effect is consistent with the computer
simulation that predicts a discontinuous jump of trapping
rate of pancake vortices below B irr . 12 It is also interesting
that the irreversibility line exhibits a reentrant behavior at
B;1/3B F , which is evident from the disappearance of magnetization hysteresis in a narrow intermediate field region
observed at T553 K in Fig. 3~b!.
Now the question is why the coupling of pancakes occurs
at a certain portion (;1/3) of B F . According to the computer simulation, the discontinuous jump of the trapping rate
of the pancakes occurs even in the 2D superconducting sheet
without interlayer coupling.12 This implies that the matching
effect occurring in a 2D CuO2 sheet, which is caused by the
competition of the vortex-vortex interaction and the vortexdefect interaction, causes the three dimensional coupling
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57
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B;1/3B F . In the liquid phase, we observed a deviation
from a conventional lnB behavior that is caused by the decrease of entropy and by the occurrence of the vortex coupling. On the other hand, in the Bose-glass phase, we observe a peak effect and reentrant of a irreversibility line at
the critical field.
We gratefully acknowledge C. J. van der Beek, L. N.
Bulaevskii, K. Hirata, X. Hu, T. Onogi, J. Shimoyama, and
R. Sugano for discussions. One of us ~Y.M.! was supported
by a grant-in-aid for scientific research from the Ministry of
Education, Science, Sports, and Culture of Japan and by
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10