Table Of ContentAmorphization of Vortex Matter and Reentrant Peak Effect in
YBa Cu O
2 3 7 δ
−
0
0
D. Pal1, D. Dasgupta2, B. K. Sarma2, S. Bhattacharya1,3 S. Ramakrishnan1,∗ and A. K.
0
2 Grover1,†
n 1 Department of Condensed Matter Physics and Materials Science, Tata Institute of Fundamental
a
Research, Mumbai-400005, India
J
5 2 Department of Physics, University of Wisconsin, Milwaukee, WI-53201
1 3 NEC Research Institute, 4 Independence Way, Princeton, NJ-08540
]
n
o
c
Abstract
-
r
p
u
s Thepeakeffect(PE)hasbeenobservedinatwinnedcrystalofYBa Cu O
2 3 7−δ
.
t for H c in the low field range, close to the zero field superconducting transi-
a
k
m tion temperature (T (0)) . A sharp depinning transition succeeds the peak
c
- temperature T of the PE. The PE phenomenon broadens and its internal
d p
n structure smoothens out as the field is increased or decreased beyond the in-
o
terval between 250 Oe and 1000 Oe. Moreover, the PE could not be observed
c
[ above 10 kOe and below 20 Oe. The locus of the Tp(H) values shows a reen-
trant characteristic with a nose like feature located at T (H)/T (0) 0.99 and
1 p c
≈
v H 100 Oe (where the FLL constant a penetration depth λ). The upper
0
5 ≈ ≈
partof the PE curve (0.5 kOe<H<10 kOe) can befitted to a melting scenario
1
2 with the Lindemann number c 0.25. The vortex phase diagram near T (0)
L c
1 ≈
determined from the characteristic features of the PE in YBa Cu O (H c)
0 2 3 7−δ k
0 bears close resemblance to that in the 2H-NbSe2 system, in which a reentrant
0
PE had been observed earlier.
/
t
a
m PACS: 74.60 Ge, 64.70 Dy, 74.25 Dw.
-
d
I. INTRODUCTION amongst the elasticity of vortex medium, the
n
o pinning of vortex lines and the fluctuation
c effects of the thermal energy is expected to
: The advent of high T superconductors
v c yield an ordered vortex solid (presumably a
i [HTSC] provided a new impetus [1] to stud-
X dislocation freeBraggglass phase [2]), aplas-
ies on phase transformations in the flux line
r tically deformed vortex solid ( presumably a
a lattices (FLL) of type-II superconductors in
vortex glass phase with proliferation of dislo-
general and they remain a subject of con-
cations) and a pinned as well as an unpinned
siderable current interest. The competition
∗E-mail:[email protected]
†E-mail:[email protected]
1
liquid phases in different parts of the field- ations in J signal a change in the state (i.e.,
c
temperature (H,T) phase space [1–6]. In the interms of spatialandtemporalcorrelations)
HTSC cuprate systems, thermal fluctuations of the vortex matter. In the collective pin-
are large and in the high temperature part ning framework due to Larkin and Ovchin-
of the (H,T) space (i.e., for t = T 0.9, nikov [33], J relates inversely to the corre-
Tc(0) ≥ c
where Tc(0) is the superconducting transi- lation volume Vc of the Larkin [34] domain
tion temperature in zero field), a first order as,
melting transition occurs between an ordered
solid and a nearly pinning free vortex liquid JcH = rnp<Vfcp2>, (1)
state [7–9]. This transition in the most in-
where n is thedensity of pinning centers and
vestigated YBa Cu O (YBCO) system is p
2 3 7−δ
f is the elementary pinning interaction. Fur-
located [10–13] at the upper edge of the peak p
thermore, in the context of LTSC systems, it
effect (PE) phenomenon in the critical cur-
isnowknown[35]thatuponincreasingtheef-
rent density J for fields of the order of a few
c
fectivepinningeitherexternallybyenhancing
tesla. At lower temperatures (i.e., t < 0.9)
the quenched random inhomogeneities in the
and higher fields, where thermal fluctuations
atomic lattice or by changing the magnetic
are weaker, a ‘fishtail’ or ‘second magnetiza-
field in a given sample, the PE often devel-
tion peak’ anomaly occurs [14] presumably
opsinternalstructure. Thishasledtosugges-
across a transformation between a weakly
tions [22,24,35] of a richer and more complex
pinned solid and astronger pinned solid [2,3].
transformations occurring in a stepwise man-
The detailed characteristics of the evolu- ner between an ordered ( quasi-lattice) phase
tion of the anomalous variation in J across and a fully amorphous one. Even more inter-
c
the (H,T) region of the second magnetization estingly, the low field part of the phase dia-
peak and that of the conventional peak effect grams[37,38]intheweakly pinnedsamplesof
are far from being understood in the context anarchetypal LTSCsystem [19,36]2H-NbSe
2
of a variety of HTSC systems [14–18]. In show a variety of novel features, including a
contrast, in the conventional low T super- reentrance into a disordered phase which is
c
conductors(LTSC)withconsiderablysmaller qualitatively similar to a reentrant glass /
(but often not negligible) thermal fluctua- reentrant pinned liquid, postulated theoret-
tions, a PE near the normal state bound- ically [1,3,39].
ary (H line) is a common occurrence over In this paper, we report on the search
c2
the entire field-temperature regime [19–24]. and the identification of the anomalous vari-
Various attempts [25–28] to gain an under- ations in J via the ac magnetization mea-
c
standing of theanomalousvariationsinJ at- surements in a twinned crystal (T (0) 93.3
c c
≈
tribute this phenomenon to a softening of the K) of the YBCO system in the rarely re-
(weakly pinned) ordered lattice and a con- ported low field-high temperature part of
sequent transformation into a more strongly the vortex phase diagram. In the YBCO
pinned amorphous solid or a pinned liquid system, the presence of twin boundaries is
phase [29,30]. Disentangling the effects of considered [10,17,27] to facilitate the occur-
the various possible sources of pinning and rence (anddetection) ofthePEphenomenon.
that of the thermal fluctuations has however The twinned crystal piece (dimensions
∼
remained difficult [19,26–28]. Despite this, 0.5 0.5 0.04 mm3 and mass 700 µg) cho-
× × ∼
there is a widespread acceptance ( supported senforthemeasurements beingreportedhere
by evidence from microscopic µSR studies as is obtained by flux growth technique, along
well[31,32])thattheanomalous(sharp)vari- with detwinned YBCO crystals [40] on which
2
the first order melting transition was ob- FLL a 1.1 104˚A), χ (T) is still feature-
0
≈ × ′
served via differential calorimetry [9]. In this less, though the superconducting transition
twinned crystal, we are able to detect the PE is broader. Figures 1(b) and 1(c) show that
phenomenon over a wide a field range (20 Oe as H increases from 40 Oe ( a 8 103˚A) to
0
≈ ×
to 10 kOe), the lower limit being much lower 170 Oe (a 4 103˚A), a characteristic fea-
0
≈ ×
than any previous study. The evolution in ture reminiscent of the PE develops across
the characteristic of the PE is similar to that the temperature region marked by a pair of
in the weakly pinned samples of a variety of arrows at T and T in the respective pan-
pl p
LTSC systems [22,24,37,38], but some signif- els. The shape of the χ (T) curve at H=250
′
icant differences exist as well. Oe (a 3.3 103˚A) in the inset of Fig.1(f)
0
≈ ×
identifies the PE phenomenon.
II. EXPERIMENTAL DETAILS
Within the Bean’s critical state model
prescription of the magnetization of irre-
The acmagnetization measurements were
versible superconductors [43], the shielding
performed using a well shielded home built
response χ (T) can be approximated as [44]:
ac susceptometer [41]. The dc field (co-axial ′
with ac field) was kept parallel to the c-axis χ′(T) ∼ −1+αhJacc ; for hac << H∗, (2)
of the YBCO crystals. Both twinned and
detwinned samples were investigated but PE χ (T) β Jc ; for h > H∗, (3)
was detected only in the former. Data were ′ ∼ − hac ac
taken in both the field-cooled and the zero where α and β are geometry and size depen-
field-cooled (ZFC) modes. Most of the data dent factors, H∗ is the (threshold) parametric
shown are in the former case, where the PE field at which the magnetic field penetrates
is more conspicuous. the center of the sample. Equations 2 and 3
imply that the temperature variation in χ is
′
governed by the temperature variation of J
c
III. RESULTS AND ANALYSIS in a given H. Thus, the observed minimum in
χ (T) in the inset of Fig.1(f) marks a peak in
′
A. Location of the Peak Effect and J , i.e., the PE, which is characterized by two
c
elucidation of its characteristic features temperatures, the onset T and the peak at
pl
T . The vanishing of J above T , i.e., the
p c p
Figures 1 and 2 present a collation of depinning of the vortex state is characterized
the temperature dependent in-phase ac sus- by thesharp increase in χ to its normalstate
′
ceptibility data recorded with h of 0.5 Oe value. A depinning temperature T (notion-
ac dp
(r.m.s.) and at the frequency 211 Hz in the ally the mid point of collapse in J ) is ob-
c
field ranges where anomalous variations in tainedfromthepeakindχ (T)/dT,examples
′
J could be identified. In zero field, the nor- of which are shown in the insets of Fig.1(b)
c
malized 4πχ has a value -1 (c.g.s. units) and Fig.2(d).
′
in the superconducting state and it crashes The other noteworthy features contained
sharply towards the zero value (the transi- in Fig.1 and Fig. 2 could be summarized as
tion width (10-90%), ∆T (0) 0.8 K [42]) in follows.
c
≈
a featureless manner (see inset of Fig.1(a)). (1) The PE is sharpest around an interme-
We now focus on the χ (T) responses shown diate field of 1000 Oe, it becomes a broad
′ ∼
in the Figs.1(a) through 1(f) as H increases anomaly for both higher and lower fields, and
from 20 Oe to 250 Oe. In H=20 Oe (where cannot be detected above 10 kOe and below 40
3
Oe. fied with the differential paramagnetic effect
(2) Characteristic structure (e.g., two well (DPE) [47]. Between T (H) and T (H), the
irr c
resolved minima instead of a single compos- vortex state is reversible, for which dM/dH
ite minimum in χ ), very similar to what is positive, i.e., diamagnetic dc magnetiza-
′
has been seen in LTSC systems, appears in tion decreases as H increases, implying, a
the intermediate field regime as evident in DPE. The paramagnetic peaks in the χ (T)
′
Figs.1(f), 2(a) and 2(b). Such a structure data in single crystals of YBCO and BSCCO
has been reported in an other study [12], but had been reported in other studies as well
in higher fields than is shown here. [48–50]. Morozov et al [48] had reported a
(3) Depinning phenomenon across T is a sharp paramagnetic peak in a single crystal
dp
sharp anomaly. A simple fit of the form: of Bi Sr CaCu O (BSCCO) via local micro-
2 2 2 8
4πχ = a + T/∆T , yields a character- Hall sensors at temperatures where a step
dp
′
istic width ∆T , whose field dependence is change in equilibrium magnetization (M )
dp eq
shown in the inset of Fig.2(b). Interest- due to FLL melting is expected. However, no
ingly, ∆T (H) is smallest for H 1000 Oe peakeffecthasbeenreportedinthesestudies.
dp
≈
and increases for both increasing and decreas- The question, as to whether the sharp onset
ing fields, as shown in the inset of Fig.2(b). of the DPE peak marks the step change in
The ∆T (H) at 1 kOe is smaller than its M attheFLLmeltingtransition[48]and/or
dp eq
value even at zero field (see the encircled data it reflects the depinning transition located at
point), the latter is very close to the ∆T (0), the upper edge of the PE phenomenon, re-
c
which is shown in the inset of Fig.1(a). quires more detailed investigations. We note,
however, that Ishida et al [12] and Raviku-
mar et al [51] have presented evidence of a
B. Observation of the Differential
step change in M across the PE region in
eq
Paramagnetic Effect
the low field-high temperature part of the
(H,T) phase space insingle crystals of YBCO
Figures 3(a) and 3(b) show the χ (T)
and 2H-NbSe , respectively. Thus, the sharp
′ 2
values measured with a higher h of 2 Oe
ac transitionfromthePEpeaktoaDPEpeakin
(r.m.s.) at a frequency of 211Hz for the vor-
weakly pinned systems (as in Fig.3(a)) may
tex states obtained in 320 Oe and 20 Oe,
indeed mark the transition from a pinned to
respectively. The PE in the main panel of
an unpinned state of the vortex matter.
Fig.3(a)ispronounced[45]. Asignificantnew
Furthermore, the Fig.3(b) shows yet an-
feature to note, however, is that χ makes
′ other effect of a larger ac amplitude: a resid-
a sharp transition from diamagnetic values
ual PE now visible in contrast with the low
to paramagnetic values across the depinning
amplitudedatainFig.1(a). Itispossible that
temperature T . The inset in Fig.3(a) re-
dp a larger ac signal anneals [52] the dilute lat-
veals a small paramagnetic peak above the
tice thereby making the amorphization more
temperature T (only slightly greater than
irr easily detectable. The possible annealing ef-
the so designated T ), the ubiquitous irre-
dp fect of a larger ac field needs further inves-
versibility temperature. The paramagnetic
tigations. Studies on samples of LTSC had
χ response returns to the background level
′ earlier revealed [45] that specific details of
oncrossing over tothenormalstateatT (H).
c the structure in the χ (T) curve across the
An identical paramagnetic peak located at ′
PE depend on the amplitude of the ac field.
the edge of the depinning transition has ear-
lier been reported in LTSC systems, such as,
CeRu [45] and 2H-NbSe [46] and identi-
2 2
4
C. History effects in χ (T) behavior (i.e., supercool) the amorphous correlations
′
present at (and above) the peak position of
The history effects pertain to the depen- thePE. AFCstateis thereforemorestrongly
dence of χ (H,T) on the path followed in pinned than the corresponding ZFC state.
′
reaching a given H and T. A simple way to The ZFC phase, in contrast, is considered to
explore them is to examine the difference in be prepared by exposing the weakly pinned
χ (T)betweenZFCandFCmodes. Fig.4dis- superconducting sample to an applied field
′
plays the χ (T) data in h of 2 Oe (r.m.s.) which generates vortices that enter the sam-
ac
′
at H = 500 Oe ( c) (i.e., when the PE peak pleathighvelocities[59]andareabletoover-
k
is well recognizable) for both ZFC and FC come the effects of pinning centers to even-
modes. The inset in Fig.4 shows the data tually explore the well ordered stable state
across the PE region on an expanded scale. of the system. It may be speculated here
Note first that above T , χ (T) behavior is thatwhilefieldcoolingintheYBCOcase,the
p
′
the same for both ZFC and FC modes. How- temperatureintervalbetween theirreversibil-
ever, prior to the entry into the PE region ity temperature T and the peak temper-
irr
(i.e., for T < T ), χ > χ . As ature T is so narrow (cf. Fig.3(a)) that
pl | ′FC| | ′ZFC| p
per eqn.(2) andeqn.(3), thisinequality would the sample fails to explore the (equilibrium)
translateasJFC JZFC forT < T . Interms amorphous phase during a very fast cool
c ≤ c p
of Larkin-Ovchinnikov scenario (cf. eqn.(1)), down. The vortex density in the sample is
this implies that the correlation volume V uniform in the FC state, whereas in the ZFC
c
in the FC state in larger than that in the case, in particular at low fields, the strong
ZFC state. This inference agrees with the di- pinning effects near the edges in the platlet
rect observationof better order for thevortex shaped samples of YBCO result in the vortex
states (mostly at low fields) prepared in the density being non-uniform across the cross-
FC manner as compared to those prepared in section of the sample. Large thermal energy
the ZFC manner in crystals of YBCO [53] as would help overcome the effects of pinning
well as in other high T cuprates [54]. How- centers in both cases, however, the FC state
c
ever, the above inequality is in complete con- being more (macroscopically) uniform even-
trast to the situation in weakly pinned sam- tually produces a better ordered FLL with a
ples of LTSC systems on which history de- largercorrelationvolumeV oftheLarkindo-
c
pendent J data have been reported for long main (than that in the ZFC case). We note
c
[55–58,22,24]. that Kokkaliaris et al [18] have recently re-
In transport studies of single crystals of ported that in an untwinned YBCO crystal,
niobium, Steingart, Putz and Kramer [55] which displays the phenomenon of a broad
had noted the inequality, second magnetization peak (to be designated
JFC(H) > Jrev(H) > JZFC(H), (4) as Hsp) at high fields and lower temperatures,
c c c JZFC(H) < Jrev(H) for H < Hs. Such an
where Jrev(H)isthecurrent density whilere- c c p
c inequality is indeed consistent with the be-
versing the field from above H to a given H
c2 havior in LTSC systems (cf. eqn.(4)). The
in an isothermal scan. In recent years, the
role that the width of the PE region could
history effects and metastability (supercool-
play in deciding the nature of the inequality
ing, etc.) has received new impetus [57]. The between JFC and JZFC in LTSC/HTSC sys-
observations that (i)JFC(H) > JZFC(H) for c c
c c tems remains to be further investigated.
H < H and(ii)JFC(H) JZFC(H)forH >
p c ≈ c
H in LTSC systems have led to the sugges- It is to be noted that regardless of the
p
tion [22] that FC states attempt to freeze in signofthehistorydependence, inallcases re-
5
ported so far, the T provides an upper limit broken line satisfying the T (H) data points
p dp
of the history dependence. Thus, in analogy for H > 0.25 kOe in Fig.5 attests to the effi-
with disordered magnets such as spin glasses, cacyofthepower lawbehavior. We, however,
T marks a characteristic “transition” tem- find that in the low field region (H<0.5 kOe),
p
perature above which the system is disor- the deviations from the power law relation-
dered in “equilibrium”. ship (H (1-t)n) set in a significant manner
∼
for both the curves T (H) and T (H).
pl p
D. Construction of the vortex phase We recall that a sudden collapse of the ir-
diagram and its comparison with earlier reversibility line between 1 kOe and 0.2 kOe
reports in the twinned and the untwinned crystals
of YBCO was reported by Krusin-Elbaum et
Figure 5 shows a collation of the data
al [60] from high frequency ac susceptibility
corresponding to the PE region marked by
measurements. However, in their data, there
the onset (T ) and the peak (T ) positions
pl p is no evidence of the occurrence of a PE. Be-
alongwiththedepinning(T )andthesuper-
dp low 200 Oe, the irreversibility line of Krusin-
conducting transition (T ) temperatures over
c Elbaum et al [60] can be seen to proceed to-
the (H,T) region, where the PE phenomenon
wards the T (0) value in a power-law manner
c
could be identified. In view of the observa-
once again, but with a different value of the
tion that the sharp depinning transition (i.e.,
exponent n. Following Ref.60, we show in
the irreversibility temperature) immediately
Fig.6, the plot of log H versus log (1-t) for
succeeds the peak of the PE, the T (H) line
p the T line in our sample of YBCO. Note
dp
inFig.5runsparalleltotheT (H)line. Sev-
dp that the data for 6000 Oe H 250 Oe and
eralreports[10–13,17]inthetwinnedandun- ≤ ≤
for70Oe H 20Oecouldbeconsidered to
twinned crystals of YBCO provide evidence ≤ ≤
conform to the power law relationship albeit
that the T (H) values are located either in
p with different values of the exponent n in the
close proximity to the melting temperatures
two intervals [60]. In the high field region ( H
(as determined from the transport studies
> 0.25 kOe), both the exponent n 2 and the
[10,11,17]) of the underlying pristine FLL prefactor H 7.9 106 Oe are c≈omparable
0
or they coincide with the temperatures of a to similar valu≈es (n×2 and H 6 106 Oe)
0
step change in the equilibrium magnetization ≈ ≈ ×
found by Nishizaki et al [17] in a high qual-
[12,13,17]. One could draw the loci of differ-
ity twinned crystal of YBCO. In between the
ent features of the PE phenomenon seen in
high field and low field regions, i.e., between
transport [11,17] and ac susceptibility mea-
250Oeand70Oe,T curveshowsanoselike
dp
surements [12,13,17], however, they all seem
turnaround feature. Such a feature appears
to indicate that H-T lines so drawn would
accentuated in T (H) and T (H) curves, as
p pl
conform to the power-law FLL melting rela-
can be clearly viewed via a replot of the vor-
tionship [1]:
tex phase diagram in a semi-log manner as
H = H (1 T )n, (5) shown in the Fig.7. In order to comprehend
m 0 − Tc(0) the genesis of the turnaround in T (H) curve
p
wheretheprefactorH 106 Oeandn 1to around 100 Oe, we refer to the χ (T) curves
0
∼ ≈ ′
2 [9,11,13,17,18]. Most of the data on the PE displayed in Figs.1(b) to 1(f). These figures
curve or the melting line or the irreversibility show that the PE develops gradually, fol-
line (in YBCO ) intheliterature, which have lowed by a progressively rapid depinning im-
been found to conform to the power law re- mediately thereafter (cf. data in the inset of
lationship, are at fields larger than 1 kOe. A Fig.2(b)). Acarefulexaminationoftheχ (T)
′
6
curves in Figs.1(b), 1(c) and 1(d) at H = 40 is still lacking. The vortex phase diagram in
Oe, 70 Oe and 120 Oe shows how the sharp- YBCO (in Fig.5/Fig.7) thus shows a close
ening ofthePEfeaturesresults inanincrease resemblance with the generic phase diagram
in T (H) ( and T (H)) values with increas- for a weakly pinned superconductor drawn
p dp
ing H. Above about 150 Oe, T (H) values by Banerjee et al [38,46] on the basis of char-
p
starttoshow theusualdecrease withincrease acteristics of the peak effect in the NbSe
2
in H. The shape of the T (H) curve in Fig.7 system.
p
is reminiscent of the reentrant characteristic
in the PE curve noted first by Ghosh et al It is instructive to dwell a little more on
[37] in NbSe . the similarities in the present YBCO crystal
2
and the 2H-NbSe sample studied by Ghosh
2
We further note that the broadening
et al [37]. We note that the nose feature in
and eventual disappearance of the PE phe- t (=Tp(H)) curve occurs at nearly the same
nomenon at fields less than 30 Oe is also sim- p Tc(0)
(H,t) value of ( 100 Oe, 0.99) and the
ilar to the behavior in NbSe . If we assume ∼ ∼
2 PE also disappears in both the samples at
that the PE curve(s) separates the ordered
H<30 Oe. Further, the FLL spacing a near
and disordered phases of vortex matter then 0
the nose feature in NbSe was comparable to
the absence of the PE at low fields (<30 Oe, 2
its in-plane penetration depth λ [46]. We
where a > 1µ) amounts to the absence of an ab
0 find the similar correspondence in YBCO; a
ordered phase, when the dilute vortices are 0
at 100 Oe is 5.0 103˚A and the measured
individually pinned by the quenched random ≈ ×
valueof λis 5.5 103˚A[61]att 0.99 inan-
disorder in the atomic lattice. In analogy ≈ × ≈
other crystal of YBCO grown by flux growth
withtheresultsinNbSe [37]andotherLTSC
2 technique. The upper portion of the t curve
systems [22,24], we have chosen to label the p
in 2H-NbSe was fitted (see inset in Fig.2 of
vortex phase between the higher field upper 2
Ghosh et al [37]) to the FLL melting rela-
portion of the T (H) curve and the T line
p dp
tion with the exponent n=2 and the prefac-
as the pinned amorphous (analogous to the
tor H = β (c4/G )H (0), where the vari-
pinnedliquid)phase. The(H,T)regionbelow 0 m l i c2
ous symbols have their usual meaning [1]. It
the reentrant leg of the T (H) curve at low
p
yielded the Lindemann number c in NbSe
fields has been termed as the ‘reentrant dis- L 2
as 0.17. Following Ghoshet al [37], we plot H
ordered’ ( and filled with dotted lines) in the
versus (1-t )2 in YBCO in the inset of Fig.6.
Fig.7. The reentrant disordered and pinned p
A linear fit to the data above 500 Oe in this
amorphous regions would overlap near the
inset yields c 0.25 (where H (0) 150T,
turnaround in the T (H) curve. At tem- L ≈ c2 ≈
p β = 5.6, G = 10−2 [1]) The disappearance
peratures above the turnaround feature (t m i
of the PE at low fields is rationalized [37] by
> 0.99), the vortex state remains disordered
invoking the notion that the pinning length
at all fields. However, below this tempera-
L and the entanglement length L become
ture (i.e., t<0.98) an ordered vortex phase c E
comparable (cf. eqn.(6.47) of [1]) at H 30
(presumably akin to an elastic/Bragg glass) ≈
Oe. Recalling once again the same relation,
exists between the high field upper portion
the L /L is given as,
of T (H) curve and the ‘reentrant disor- c E
pl
4
dered’ phase [46]. The vortex phase between Lc πκ2lnκ( a0 )2( jc )21(1−t)3,
Tpl(H) and Tp(H) curves is expected to be LE ≃ √2 2πλ(0) Gij0 t
plastically deformed [11,19] and has there- (7)
fore been termed as plastic glass [22,38,46], where the various symbols have their
detailed theoretical understanding of which usual meaning [1]. Note, how the L /L
c E
7
scales with the crucial parameters, like, the trantmelting/reentrant disordered phasewas
Ginzburg number G (= (1/2)(k T /H2ξ3ǫ)2) proposed for 2H-NbSe . Both ideas imply a
i B c c 2
and the ratio j /j , where j and j represent transformation/crossover from an interaction
c 0 c 0
the critical current density and the depair- dominated collective pinning behavior to a
ing current density, respectively. The G in different regime, where pinning/depinning of
i
YBCO ( 10−2) is expected to be two to vortex lines have to be considered in isola-
≈
three orders larger than that in 2H-NbSe tion. The observation of the complexity in
2
[19,37], but it is compensated by the extreme the PE regime (at intermediate fields), which
smallness of j /j value ( 10−5 to 10−6) in comprises the onset of a sudden shrinkage
c 0
∼
typically clean crystals of 2H-NbSe as com- in the correlation volume [22,24] and the in-
2
pared to that ( 10−2 - 10−3) in a clean ternal structure, reinforces the notion of a
∼
YBCO sample [19]. At fields below 30 Oe, stepwise loss of vortex correlations. Car-
where L /L <1, the dilute vortex array is ruzzo and Yu [65] have recently theoretically
c E
expected to be so disordered that it does not proposed a two step softening process of the
display any anomalousvariationinJ (T) cor- FLL, in which a first order transition ini-
c
responding to an order-disorder transforma- tially transforms an ordered vortex solid to a
tion in an isofield scan. This order of magni- (defective) soft vortex solid that has smaller,
tude estimate for the field value of disorder- but, still finite shear modulus. The latter
order transition in FLL correlations appears solid in turn could undergo another first or-
consistent with isothermal Bitter decoration der transition to the vortex liquid state. Our
data in samples of YBCO [62] and BSSCO present results call for more detailed study
[63]. on the PE in different systems to explore
the loss in order of the FLL. The presence of
twin boundaries in YBCO [10]is usually con-
IV. CONCLUSION
sidered to be detrimental to the observation
of a first order melting transition. However,
In summary, we have reported the oc-
in our case, the presence of twin boundaries
currence of the peak effect phenomenon for
has facilitated the observation of the peak
sparse vortex arrays at very low fields as well
effect at low fields. Further, a recent study of
as for the dense vortex arrays at moderately
the first order FLL melting transition on the
highfieldsinatwinnedcrystalofYBCO.The
twinned crystals of NdBa Cu O [66] also
2 3 7
data delineate the order-disorder transforma-
shows the usefulness of the twinned crys-
tion regions at low fields, where the interac-
tals to explore basic issues in vortex state
tion is weaker and the disorder effects of the
physics. As a final remark, we recall that
thermal fluctuations and/or small bundle (or
Grier et al [63] and Horiuchi et al [67] have
individual) pinning dominate. The new ob-
directly demonstrated how the disordered di-
servations at low fields agree with an earlier
lute vortex arrays undergo transformation
report [60] of a collapse of the irreversibility
to an ordered phase as the interaction effect
line in the (H,T) region close to T (0) in the
c increasesduetoanincreaseinthevortexden-
context of the YBCO system. But, in ad-
sity either by an increase in the applied field
dition, it shows a close connection with the
[63,67]or, moreinterestingly, by thecollation
“nose” like turnaround feature in the locus of
ofthevortices aroundastrong pinning center
the peak effect in a LTSC 2H-NbSe system
2 [67]. Such studies in samples of YBCO and
[37]. The notion of the thermal softening of
NbSe , which show reentrant characteristic
2
the vortex cores [64]has been invoked [60] for
in the peak effect curve are highly desirable.
YBCO, whereas a connection with the reen-
8
discussions with Satyajit Banerjee, Shampa
Acknowledgements Sarkar, Mahesh Chandran, Nandini Trivedi,
G. Ravi Kumar, Prasant Mishra, Vinod
It is a pleasure to acknowledge numerous Sahni and Gautam Menon.
9
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