Fang, L.

Griessen, R.P.

Hoekstra, A.F.T.

Si, M.S.

Wen, H.H.

Yan, S.L.

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VOLUME 79, NUMBER 8 P HY S I CA L REV I EW LE T T ER S 25 AUGUST 1997Field Induced Vanishing of the Vortex Glass Temperature in Tl2Ba2CaCu2O8 Thin Films
H.H. Wen,1,2 A. F. Th. Hoekstra,1 and R. Griessen1
1Institute COMPAS and Faculty of Physics and Astronomy, Vrije Universiteit, De Boelelaan 1081,
1081 HV, Amsterdam, The Netherlands
2National Laboratory for Superconductivity, Institute of Physics, P.O. Box 603, Beijing 100080, People’s Republic of China
S. L. Yan, L. Fang, and M. S. Si
Department of Electronics, Nankai University, Tianjing 300071, People’s Republic of China
(Received 16 October 1996)
The current density js and relaxation rate Q have been measured on a ring shaped Tl2Ba2CaCu2O8
film between 4.2 K and the irreversibility temperature in magnetic fields up to 7 T. The temperature
and field dependent exponent msT , Bed used to parametrize the activation energy U in the form
Us js , T , Bed ­ sUcymd fs jcyjsdm 2 1g is determined for many different fields. In the Be-T phase
diagram we associate the m ­ 0 line with the glass temperature Tg and find that Tg essentially
drops to 0 K at Be ø 0.7 T, which indicates a dimensional crossover at this field. The m . 0 region
sBe , 0.7 T, T # 55 Kd corresponds to 3D elastic vortex motin while the m , 0 region corresponds to
2D dislocation mediated flux creep. [S0031-9007(97)03832-5]
PACS numbers: 74.60.Ge, 74.60.Jg, 74.72.FqThe small coherence length, the presence of weak and
dense point pinning centers, and the layered structure of
high-Tc superconductors are at the origin of the intricate
nature of the mixed state phase diagram of these super-
conductors [1–4]. A lot of effort has been put into in-
vestigations of various phases and phase transitions [5–8].
It is generally believed that below the irreversibility line
Birr sTd there exists a vortex solid state which is usually
described in terms of collective flux pinning (CFP) [3,4]
or vortex glass (VG) [2,9] models. Both the CFP and VG
models are based on elastic vortex motion. Dissipation due
to the thermally activated motion of vortices is associated
with an electric field E ­ y0Be expf2Us js, T , BedykBT g,
where Us js, T , Bed ­ sUcymd fs jcyjsdm 2 1g is the acti-
vation energy at the external magnetic field Be and tem-
perature T , y0 an attempt hopping velocity, and Uc the
characteristic pinning energy. The superconducting cur-
rent density js is always smaller than the critical current jc
for which U vanishes. Many different values have been
predicted theoretically for the parameter m on the basis of
the CFP and VG models. For all regimes and dimension-
alities [1–4,9], however, it is found that m $ 0. A direct
conclusion then is that the activation energy diverges when
the current js approaches 0. This is reasonable for a 3D
elastic vortex system, but for a 2D vortex system, it may
not be true [9]. For example, for a 2D system, the vor-
tex glass state does not exist at finite temperatures [1,10].
As mentioned by Vinokur et al. [4], in strongly layered
systems such as Bi2Sr2CaCu2O8 and Tl2Ba2CaCu2O8 pin-
ning is too strong at high magnetic fields to allow vor-
tices to creep collectively. Instead, dislocation-mediated
(plastic) creep is expected to be predominant. However,
as far as we know, no direct evidence has been found for
plastic creep except in a small part of the phase diagram
sT . 81 K and Be , 6 Td of a YBa2Cu3O7 single crys-0031-9007y97y79(8)y1559(4)$10.00tal with a fishtail effect [11]. In this Letter, we conclude
from a detailed investigation of the vortex dynamics in
high quality Tl2Ba2CaCu2O8 thin films that the Be-T plane
below the irreversibility line is separated into two regions
by a m ­ 0 line with a remarkable shape. At low fields
where m . 0 vortex motion occurs via elastic creep while
plastic creep [12] is made possible at higher fields by a 3D
to 2D transition around 0.7 T.
The sample considered here is aTl2Ba2CaCu2O8 thin
film deposited on a (100) LaAlO3 substrate by means of
dc magnetron sputtering. Postannealing is done between
720 and 760 –C. Details of the fabrication of the films are
published elsewhere [13]. ac susceptibility measurements
show that Tcszerod ­ 106 K and DTc ø 3 K. The film is
lithographically patterned into a ring of radius r ­ 1.5 mm
and width w ­ 25 mm. Its thickness is d ­ 200 nm.
A very sensitive torque magnetometer (sensitivity
10210 10211 Nm [14,15]) is used to measure the torque
due to the magnetic moment of the sample. The field Be,
provided by a 7 T Oxford Instruments cryomagnetic
system, is applied at an angle of 45– with respect to the
c axis of the film. The temperature is stabilized to better
than 60.1 K during field sweeps. For each temperature
and field, the sweeping rate is varied between 1.25
and 40 mTys, corresponding to induced electric fields
E ­ sry2d sdBeydtd between 9.375 3 1027 and 3 3
1025 Vym, respectively.
By sweeping the magnetic field up and down at a given
rate around a certain field, we measure the width DM of the
irreversible magnetic moment curve. For the ring geome-
try of our sample, the current density js can be determined
directly from DM by means of js ­ DMys2pr2wdd.
Since js ~ DM and E ~ dBeydt the measured DM vs
dBeydt curves can be converted into E vs js curves (or I-V
curves). In Fig. 1 we present a selection of the extensive© 1997 The American Physical Society 1559
VOLUME 79, NUMBER 8 P HY S I CA L REV I EW LE T T ER S 25 AUGUST 1997data accumulated during this study. Figure 1(a) shows the
temperature dependence of the current density jssT , Bed
measured at given fields Be with dBeydt ­ 40 mTys. The
slopes of the ln js vs lnE curves are plotted as a function
of T in Fig. 1(b). As has been extensively discussed in
Refs. [16,17], Q ; d ln jsyd lnsdBeydtd ­ d ln jsyd lnE
determined in a magnetic dynamic relaxation experiment
is closely related to the normalized relaxation rate R ;
2d lnMyd ln t measured in a conventional magnetization
relaxation experiment. From Fig. 1(b) one can easily see
that a plateau in the Q vs T curves exists only when the
field is below approximately Bcr ø 1 T. A similar behav-
ior was found in YBa2Cu3O7 films for fields at least up to
7 T and was ascribed to the occurrence of a 3D vortex
glass or collective creep [18,19]. When the field exceeds
Bcr , the plateau disappears completely and the Q value in-
creases monotonously. This indicates that the magnetic
field drives the vortex system from the 3D collective creep
(or vortex glass) regime to another one to be specified in
this Letter.
To proceed with the analysis and discussion of the
measured data in Fig. 1 we parametrize the activation
energy Us js, T , Bed for thermally activated vortex motion
in the form [19]
FIG. 1. Temperature dependence of (a) the superconducting
current density js and (b) the dynamic relaxation rate Q ;
d ln jsyd lnsdBeydtd ­ d ln jsyd lnE for fields ranging from
0.1 to 6 T. A plateau of Q can be observed in the intermediate
temperature region when the field is lower than about 1 T. The
plateau disappears completely at higher fields. The lines are
guides to the eye.1560Us js, T , Bed ­
UcsT , Bed
msT , Bed
•µ
jcsT , Bed
jssT , Bed
¶msT ,Bed
2 1
‚
,
(1)
where m, Uc, and jc are explicitly allowed to vary with
temperature and magnetic field. Only the parameter m
influences the current dependence of U, which for all
values of m is a decreasing function of js. This form
is chosen because it contains the weak collective pinning
models (m ­ 17 , 32 , 79 etc. [1]), the Kim-Anderson model
sm ­ 21d, and the Zeldov logarithmic model sm ­ 0d
as special cases. For m , 0 it also includes expressions
developed for plastic motion of dislocations as discussed
below. Equation (1) is thus physically meaningful for any
value of m, both positive and negative, as well as 0, in
contrast to other forms such as Us jd ­ Ucs jcyjdm [11]
or Us jd ­ Uc sgnsmd fs jcyjdm 2 1g [20] which lead to
unphysical results when j ! jc or m ! 0. Equation (1)
is most suitable for a consistent analysis when a transition
occurs in the type of pinning as reported in this Letter.
From the general creep relation
Us js, T , Bed ­ kBT ln
µ
2n0Be
r dBeydt
¶
(2)
for a thin film ring of radius r , Eq. (1) and the definition
of the dynamic relaxation Q, one finds that
T
QsT , Bed
­
UcsT , Bed
kB
1 msT , BedCT , (3)
where C ­ lnfs2y0Bedysr dBeydtdg. As shown in
Refs. [17,21] the parameter C at a given field Be
can be determined from the low temperature slope of
the ln js vs T curves in Fig. 1(a) by means of C ­
sTyQd s2d ln jsydT d after correction for quantum creep.
Here we find C ­ 22.
In Fig. 2 we show the temperature dependence of TyQ
for various fields. At low fields, TyQ first exhibits a posi-
tive slope, which is followed by a sharp drop at higher
temperatures. With increasing field the initial slope gradu-
ally changes from positive to negative. At Be ­ 0.7 T
the slope is 0 over essentially the whole temperature range
(from 4.2 to 50 K). The temperature dependence of TyQ
gives directly information about the variation of m with T
since UcsT d is essentially constant below the irreversibility
line in highly anisotropic superconductors. For such super-
conductors TirrsBed in the field range considered here
is so low that the temperature dependence of the char-
acteristic superconducting parameters can be neglected
[1]. Even for the moderately anisotropic YBa2Cu3O7 [17]
and sY, PrdYBa2Cu3O7 [22] one finds experimentally that
UcsTirrd ø UcsT ­ 0d. This is confirmed by theoretical
models, independent of the type of pinning centers [23].
The values of msT , Bed in Fig. 3 derived from the TyQ
vs T data in Fig. 2 show clearly that at a given tempera-
ture m changes from positive to negative with increasing
VOLUME 79, NUMBER 8 P HY S I CA L REV I EW LE T T ER S 25 AUGUST 1997FIG. 2. Temperature dependence of TyQ for fields of 0.3,
0.4, 0.7, 1, 2, 3, 4, 5, and 6 T. At low fields, the slope of
TyQ vs T in the intermediate temperature region is positive.
With increasing magnetic field the slope gradually changes
from positive to negative. Near the crossover field Be ­ 0.7 T,
the slope remains zero up to 50 K. The UcsT ­ 0d line in
the sTyQ, Bed plane, obtained by taking the extrapolation of
TyQ to 0 K, indicates the field dependence of the characteristic
pinning energy. In the sT , Bed plane the Q ­ 1 line indicates
the lowest temperature at which Q ­ 1 is reached at a given
field Be. For higher temperatures the current-voltage curves
exhibit Ohmic behavior.
magnetic field. At low temperatures the extrapolated val-
ues of m are essentially zero for fields above 0.7 T. The
m ­ 0 line exhibits a remarkable plateau at Be ­ 0.7 T
for T , 55 K and an asymptote at low temperatures.
It cuts the Be-T plane into two regions: one where
m , 0 for all T , TirrsBed and one with m . 0 for all
T , TpsBed, where T psBed is a temperature very close to
the irreversibility line Birr sTd corresponding to a current
density of 107Aym2 at dBeydt ­ 10 mTysec. This irre-
versibility line in turn is close to the Q ­ 1 line which
defines the lowest temperature at which Q ­ 1 is reached
for a given field Be. The fact that the m ­ 0 line merges
with the field axis at T ­ 0 K indicates that the glass tem-
perature for Be . 0.7 T is essentially zero.
The occurrence of a m ­ 0 line and of a large region
of the Be-T diagram with m , 0 can be understood as the
combined action of a 3D to 2D transition opening the way
to plastic vortex creep. We discuss these two effects
below.
(i) Dimensional crossover.—Within a vortex glass
model the line in the Be-T plane on which m ­ 0
separates the vortex glass phase from the vortex liquid
phase and is associated with the vortex glass tempera-
ture Tg. This is evident since m ­ 0 implies that
Us jsd ­ Uc lns jcyjsd and consequently, from Eq. (2),
that the js vs dBeydt or js vs E curves exhibit power-
law behavior, which typically occurs at Tg. For fields
B . 0.7 T we find m ø 0 at T ø 0 K and thus Tg ø 0 K.FIG. 3. Temperature and magnetic field dependence of the
exponent m appearing in Eq. (1) for the activation energy
Us js, T , Bed. The corresponding fields are 0.3, 0.4, 0.7, 1.0,
2.0, 3.0, 4.0, 5.0, and 6.0 T, respectively. m is determined
from the data shown in Fig. 2 by using Eq. (1) with the
assumption UcsT d ø Ucs0d. On the sT , Bed plane are shown
(i) the irreversibility line determined with the criterion js ­
107 Aym2 from current measurements with field sweeping rate
10 mTys (open squares), (ii) the Q ­ 1 line defined in Fig. 2
(filled circles), and (iii) the m ­ 0 line. For fields above 0.7 T
there is a large region where m is negative.
According to vortex glass theories a zero glass tempera-
ture is characteristic for 2D systems and we conclude
that around 0.7 T a transition takes place from a 3D
vortex glass to a 2D vortex glass with a vanishing glass
temperature. From 0 to 50 K the 3D to 2D transition
occurs at Be ­ 0.7 T. We note that this crossover field
is much higher than B3D-2D ­ f0yg2s2 > 0.05 T [24]
obtained from the anisotropy parameter g ­ 135 [25] and
s ­ 1.5 nm appropriate for our sample. At Be ­ 0.4 T,
m ­ 0 is reached around 58 K. At that temperature
Q ø 0.38 which implies that E ~ j2.63s . As theoretically
E ~ js
sz11dysD21d
, where D is the dimensionality of the
vortex system [1], we find z ­ 4.26. Interestingly this
value of z is similar to that determined by Wöltgens
et al. [10] for the 3D superconductor YBa2Cu3O7. We
note, furthermore, that at low fields Be , 0.1 T, m
assumes a value close to 17 as expected for the 3D-single
vortex regime.
(ii) Plastic creep.—UcsT ­ 0d > 150 K (see Fig. 2)
and of the critical currents jcsT ­ 0d > 1012 Aym2 in
the present system are an indication of strong pinning.
It is therefore reasonable to assume that dislocation
mediated plastic vortex creep occurs with increasing field
[26]. This idea is strongly supported by the following
analogy. Above 0.7 T the negative values of m imply
that the activation energy in Eq. (1) can be written in
the form Us jsd ­ U0f1 2 s jsyjcdag with a ; 2m . 0.
This dependence is of the same form as that predicted by
the theory of thermally activated motion of dislocations in1561
VOLUME 79, NUMBER 8 P HY S I CA L REV I EW LE T T ER S 25 AUGUST 1997crystalline solids for which the activation energy Udis
changes with the applied strain f as f1 2 s fyfcdagb
and the exponents a and b satisfy 0 , a # 1 and 1 #
b # 2, respectively. The driving force for dislocation
motion is the applied strain while it is the Lorentz
force (proportional to the current js) for vortices in a
superconductor. The m value found in our experiment
s20.2d at high fields near the irreversibility line implies
a ­
1
5 and b ­ 1. For dislocations in a crystalline solid
this would correspond to the case of pinning sites with a
homogeneous core and long-range interaction [27].
The characteristic activation energy Uc for the mo-
tion of a dislocation in the vortex lattice is of the order
of sf20a0dys4pm0l2gd with f0 the flux quantum, a0 >p
sf0yBed,l London’s penetration depth, and g the anisot-
ropy factor. One thus expects a Be21y2 dependence of the
activation energy for fields Be above a matching field Bp at
which all the strong pinning centers present in the sample
are occupied by a vortex. When Be . Bp the Lorentz
force acting on the weakly pinned additional vortices is
transmitted via shear interactions to the strongly pinned
vortices. Consequently, the pinning energy per vortex de-
creases when Be increases. Although UcsT ­ 0d is found
to decrease slightly for fields above 2 T it does not exhibit
a Be
21y2 behavior between 2 and 6 T yet. The magnitude
of Uc is, however, consistent with the prediction Uc ,
sf20a0dys4pm0l2gd with l ­ 200 nm and g ­ 135 [25]
which lead to Uc , 150 K.
In conclusion from the vanishing of Tg and the negative
values of m we conclude that around Be ­ 0.7 T a 3D to
2D transition occurs, at a much higher field than expected
from B3D-2D ­ f0yg2s2. At Be , 0.7 T there are 3D
vortex bundles in Tl2Ba2CaCu2O8 which move from one
pinned configuration to another. With increasing field
vortex motion at Be . 0.7 T is dominated more and more
by dislocation mediated plastic creep in a 2D pancake
vortex system. Our 3D to 2D transition is thus of a
completely different nature than that reported by Kopylov
et al. [28] which corresponds to a 2D to 3D crossover in
weak magnetic fields when the coherence length jc along
the c axis becomes larger than the interlayer spacing when
T approaches Tc.
In Tl2Ba2CaCu2O8 films plastic creep appears to be
operative in a very large region of the Be-T plane. This is
a rather general property of strongly layered systems with
large critical currents, since we obtained recently similar
results for single crystals of Bi2Sr2CaCu2O8 and electron
doped Pr1.85Ce0.15CuO41d [29].
This work is part of the research program of the
Dutch Stichting voor Fundamenteel Onderzoek der Ma-1562terie (FOM) which is financially supported by NWO. One
of us (H.H.W.) gratefully acknowledges a FOM visi-
tor grant. Furthermore we acknowledge illuminating dis-
cussions with V. B. Geshkenbein, G. Blatter, and V.M.
Vinokur.
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Field induced vanishing of the vortex glass temperature in Tl2Ba2CaCu2O8 thin films.

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Field induced vanishing of the vortex glass temperature in Tl2Ba2CaCu2O8 thin films.

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