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Dip effect and its disappearance
J.W. Lin a,*, X. Leng b, G. Liu b, H. Luo b, Y. Liu b, S.Y. Ding b
a College of Science, Hohai University, Nanjing 210098, PR Chinab National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, PR China
Abstract
Measurement was made of ac susceptibility (acs) as a function of temperature T for a YBa2Cu3O6:993 single crystal
under dc fields ðHdcÞ, and dips in the acs curves were observed in both v0ðT Þ and v0ðHdcÞ curves in the same time for the
sample. We explain the dips in the experimental v0ðT ;HdcÞ curves as bulk pinning effect in higher fields and lower
temperatures. However, the dips were weakened and finally replaced by surface barriers. Careful analysis of the data
shows that there exists evidence indicating the transition of flux pinning mechanism.
� 2002 Published by Elsevier Science B.V.
PACS: 74.60.Ge; 74.72.Bk
Keywords: Dip effect; Dip depth; Bulk pinning; Surface barriers
1. Introduction
In the investigation of flux dynamics for high
temperature superconductors (HTSC), ac suscep-
tibility (acs) is one of the most important tech-
niques. In such an experiment, a small ac field hac
is used to probe the behavior of vortex matter gov-
erned by a large dc field Hdc and temperature T[1–4]. An explanation of peak effect (PE) in mag-
netization or critical current density Jc has been an
interesting object [5,6]. The corresponding dip in v0
(real part of acs) is proved as a typical bulk pin-
ning characteristics [7].
In ideal systems, one expects to see a first-ordermelting transition. However, It is suggested that
the existence surface barriers (SB) could possibly
form new vortex matter phases in HTSC, which
is expected to see over a wide range of applied
magnetic fields. Hence, different opinions about
whether a dip effect (DE) in a HTSC sample is
governed by SB or bulk pinning appears [8,9].In this paper, we carefully measured the acs for
a YBa2Cu3O6:993 single crystal at different dc fields,
and observed a quite different DE. The measure-
ment of acs in lower dc fields shows signal indi-
cating the transition of flux pinning mechanism.
2. Experimental
The sample was a ultra-pure Ba2Cu3O6:993 crys-
tal grown in a bulk BaZrO3 crucible. The chemi-
cal and structural characterization of this crystal
confirmed that it had very low level of impu-
rity elements and high degree of crystalline order.
The sample is a perfect rectangle with dimensions
* Corresponding author. Tel.: +86-25-359-3661/378-6636;
fax: +86-25-359-5535.
E-mail addresses: [email protected] (J.W. Lin), syding@
netra.nju.edu.cn (S.Y. Ding).
0921-4534/02/$ - see front matter � 2002 Published by Elsevier Science B.V.
doi:10.1016/S0921-4534(02)02225-6
Physica C 386 (2003) 89–92
www.elsevier.com/locate/physc
1:53 � 1:28 � 0:065 mm3, and the c-axis along the
shortest dimension. The bulk of the crystal is twin-
free except a single twin boundary cutting the very
tip of one of the four corners, forming a triangle,
which has an area less than 0.12% of the total
sample area.Our experiment technique is the acs. Both dc
and ac magnetic fields are along the c-axis of the
crystal. The superimposed ac field has amplitude
hac ¼ 25 G, and frequency f ¼ 1 MHz. The acs
data were extracted from the impedance data of
the coil, measured by a two-phase lock-in ampli-
fier.
3. Results and discussion
Fig. 1 shows the experimental v0 as function of
temperature in various applied fields, where one
can see clearly that in regime from 1 to 70 kG, a
dip (a sharp minimum of v0) effect. Here we define
a ‘‘dip depth’’ of acs in superconducting state asv0
dd ¼ v0max � v0
min at a characteristic field Hdc, v0max
and v0min are maximum and minimum of acs re-
spectively, and Td is the dip bottom temperature atwhich v0 ¼ v0
min. To show the field difference at
which maximum of v0dd and v0
min occur, we re-plot
the v0dd as function of field Hdc in Fig. 2. From
the figures, we can see that the v0 dip and thus Td
moves toward high temperatures with decreasing
dc field. Interestingly, that the behavior of v0dd in
the high field regime (10–70 kG) is quite different
from that in the low field regime (1–10 kG). In theformal regime, with the decreasing Hdc, the dip
depth v0dd gradually increases from point a (Hdc ¼
70 kG) to point d (Hdc ¼ 10 kG). However, when
dc field further decreases the dip depth v0dd turns to
decreasing in spite of the magnitude of the whole
v0ðT Þ is still increasing. This decreasing tendency of
depth of v0dd is continuous as long as the applied dc
field decreases. In fact the dip v0dd at Hdc ¼ 1 kG
has already been too small to probe, becoming a
small kink at point c and one can hardly find the
v0ðT Þ dip below about 1 kG. When Hdc ¼ 0 a usual
sharp transition acs curve as a function of tem-
perature without dip is clearly seen, showing our
high quality single crystal sample. It is worthy
to point out that the v0dd manifests its maximum
at point d (Hdc ¼ 10 kG) while v0min minimums at a
lower field point b (Hdc ¼ 5 kG). Therefore, one
Fig. 1. Experimental v0ðT Þ curves under different dc fields
(Hdckhackc), showing the giant DE. Point a: the highest dc field
in which v0 has DE at v0 ¼ v0min; point b: the dc field in which
v0min turn up; point c: the dc field in which DE is too small to
probe.
Fig. 2. Re-plotting Fig. 1, we construct the v0ddðHdcÞ curves,
v0dd ¼ v0
max � v0min, showing the transition of dip depth. Point d:
the dc field Hdip in which v0dd maximums.
90 J.W. Lin et al. / Physica C 386 (2003) 89–92
can deduce that something happens and the dip is
governed by physics different from that of ac sus-
ceptibility itself.
Meanwhile the v0ðT Þ curve clearly demonstrates
the DE in different Hdc, it seems to us an open
question that whether there is a DE in v0ðHdcÞcurves in different temperature for the same sam-
ple? Up to our best knowledge, there is no refer-
ence reporting the simultaneous observation of
the two DEs in both v0ðT Þ and v0ðHdcÞ curves, al-
though it is well known that the second PE ap-
pears in both jcðT Þ and jcðHdcÞ relationships where
jc is critical current density. Fortunately, it is pos-
sible to testify the issue based on the data points inFig. 1. Re-plotting the field dependent v0 under
different temperatures and re-displaying them in
Fig. 3, we see clearly the DE in v0ðHdcÞ curves in
temperature regime accessed by our experiment.
This is a strong conformation that both the DEs in
v0ðHdcÞ and v0ðT Þ curves take place simultaneously.
This acs result can be considered as an indication
that the PE in JcðHdcÞ is just the one observedin JcðT Þ according to the relationship v0 þ 1 /hac=Jc.
From the behavior of DE in v0 depicted above,
v0dd decreases from Hdc ¼ 10 kG and v0
min turns up
as Hdc 6 5 kG, and finally disappear in smaller
fields. This behavior is consistent with the PE ob-
served in hysteric magnetization loop that the low
field peak (Hdc 0) pronounced and the high field
peak (second peak) weakens and finally disappears
when temperature gradually ascends, see, forexample, [10]. This characteristic is explained in
terms of the competition between the geometric
barriers and bulk pinning. In the elevated tem-
peratures the SB are dominated which causes a
sharp low field magnetic hysteric peak. Whereas at
low temperatures the bulk pinning whose maxi-
mum takes place at high fields governs the hysteric
magnetization loop and results in the second PE[5,11]. According to this scenario, the sharp steps
in low field (Hdc 0) in v0ðT Þ curve corresponds to
the low field peak and the dips in elevated applied
fields manifest the second peaks in JcðT Þ curves as
DE in v0ðT Þ curve. Because it has been numerically
shown that the DE is behavior caused by bulk
pinning, the above explanation is a reasonable
one. This explanation naturally results in that thev0
dd in our experiments is caused by transformation
from the case governed by bulk pinning which is
more important in low temperatures into the state
dominated by SB which is stronger in high tem-
peratures.
It has been pointed out that the PE occurs just
below the vortex liquid to solid phase transition
in a narrow region [3], which is of course a bulkphenomenon. Based on this ideal the DE is used to
construct phase diagram of vortex matter. If the
SB are more and more important as temperature is
elevated the dip is affected more and more by the
SB, which implies that the phase transition line
HdcðT Þ at Hdc > Hdip is no longer the same as that
at Hdc < Hdip because of SB, here Hdip is the
strengths of applied field at which maximum of v0dd
occurs. We therefore construct a phase transition
line based on the v0ðT Þ dip temperature Td. Fig. 4
shows the Hdc–Td curve. In the figure two differ-
ent slopes are visible as the fitting lines. The dot-
ted line in the higher field regime with Hdc ¼H0ð1 � T=TcÞn kG, where H0 ¼ 133 kG, Tc ¼ 88:90
K and n ¼ 1:33, which is consistent with those
determined by using torque magnetometer andcalorimetric measurement for YBCO crystal, in-
dicting a first-order melting transition in the dip in
Fig. 3. Re-plotting Fig. 1, we construct the experimental
v0ðHdcÞ curves under different temperatures (80.25–88.80 K),
showing the same giant DEs in v0ðHdcÞ as in v0ðT Þ.
J.W. Lin et al. / Physica C 386 (2003) 89–92 91
v0ðT Þ on the higher fields. The crossover at
Hdc ¼ 10 kG therefore implies the effect of the SB.
In summary, we have prepared YBa2Cu3O7�d
sample. By means of measurements of ac suscep-
tibility, the DE was observed. It is shown that the
DE is observed in both v0ðT Þ and v0ðHdcÞ curves in
the same time for the sample. We explain the dips
in the experimental v0ðT ;HdcÞ curves as bulk pin-
ning effect in higher fields and lower temperatures.
However, the dips were weakened and finally re-
placed by SB. Our experimental data support theexplanation.
Acknowledgements
One of the authors S.Y. Ding acknowledges the
supports of the Ministry of Science and Technol-
ogy of China (G1999064602) and NNSFC undercontract no. 19994016.
References
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Fig. 4. Dip bottom temperature Td in v0ðT Þ vs. dc magnetic
field. Two different slopes of the fitting lines are clear, showing
the effect of the SB.
92 J.W. Lin et al. / Physica C 386 (2003) 89–92