Physica C 420 (2005) 1–10

www.elsevier.com/locate/physc

Time evolution of quenched state and correlationto glassy effects

K. Kilic a, A. Kilic a,*, A. Altinkok a, H. Yetis� a, O. Cetin a, Y. Durust b

a Department of Physics, Turgut Gulez Research Laboratory, Abant Izzet Baysal University, 14280 Bolu, Turkeyb Department of Chemistry, Abant Izzet Baysal University, 14280 Bolu, Turkey

Received 25 October 2004; accepted 1 December 2004

Abstract

In this work, dynamic changes generated by the driving current were studied in superconducting bulk polycrystalline

YBCO sample via transport relaxation measurements (V–t curves). The evolution of nonlinear V–t curves was inter-

preted in terms of the formation of resistive and nonresistive flow channels and the spatial reorganization of the trans-

port current in a multiply connected network of weak-link structure. The dynamic re-organization of driving current

could cause an enhancement or suppression in the superconducting order parameter due to the magnitude of the driving

current and coupling strength of weak-link structure along with the chemical and anisotropic states of the sample as the

time proceeds. A nonzero voltage decaying with time, correlated to the quenched state, was recorded when the magni-

tude of initial driving current is reduced to a finite value. It was found that, after sufficiently long waiting time, the evo-

lution of the quenched state could result in a superconducting state, depending on the magnitude of the driving current

and temperature. We showed that the decays in voltage over time are consistent with an exponential time dependence

which is related to the glassy state. Further, the effect of doping of organic material Bis dimethyl-glyoximato Copper

(II) to YBCO could be monitored apparently via the comparison of the V–t curves corresponding to doped and

undoped YBCO samples.

� 2005 Elsevier B.V. All rights reserved.

PACS: 74.72.Bk; 74.25.Qt

0921-4534/$ - see front matter � 2005 Elsevier B.V. All rights reserv

doi:10.1016/j.physc.2004.12.014

* Corresponding author. Fax: +90 374 253 4642.

E-mail address: kilic_a@ibu.edu.tr (A. Kilic).

1. Introduction

The dissipation induced by the motion of the

flux lines in a type-II superconductor depends

strongly on distribution and type of the pinningcenters. The main mechanism which governs the

ed.

2 K. Kilic et al. / Physica C 420 (2005) 1–10

dissipation is attributed to the competition

between pinning and depinning, provided that

thermal fluctuations are negligible compared to

pinning [1–9]. In one hand, depinning which favors

spatially the ordering of the vortices, in the otherhand, pinning which arises from inhomogeneities

and defects inside the sample promotes disorder

by decreasing the vortex–vortex interactions and,

thus, destroy the long-range order of the flux line

lattice [6,7,10]. This competition evolving between

pinning and depinning can be observed in details

by magnetic and transport measurements via the

response of the moving entity to the applied cur-rent and external magnetic field [6,11–15]. Experi-

mental observations show that the competition

between pinning and depinning causes several

unusual and interesting phenomena, such as low-

frequency noise [3,16], slow voltage oscillations

[17], history dependent dynamic response [18],

memory effect etc. [6,19], which deserve further

investigations.It is well known that one of the remarkable

features of high temperature superconductors

(HTSCs) is the presence of large flux creep effect

[20]. Although the phenomenological flux creep

theory could explain many magnetic and transport

properties of HTSCs, there are some difficulties to

describe the reorganization of vortices evolving to

a state with vanishingly small voltage values, sothat this case may sometimes result in a true super-

conducting state [11,18,21]. In the description of

this physical case, the flux creep picture and the

other theories cannot solely explain some magnetic

or transport data without invoking current/field

induced glassy state. Indeed, the experimental

observations on both low Tc superconductors

LTSCs [11,18] and HTSCs [21–25] supportstrongly the presence of a glassy state which

reminds classic spin glasses [26]. After the work

of Muller et al. [22], not only the magnetic data,

but also the transport measurements were inter-

preted in terms of the glassy state effect [21]. For

instance, the exponential time decay of the voltage

in bulk polycrystalline superconducting YBCO

sample was explained by this effect [21]. Recently,the fast transport measurements performed by

Henderson et al. [11] and Xiao et al. [6] have con-

firmed such a glassy relaxation in single crystal

samples of 2H–NbSe2 and Fe-doped 2H–NbSe2,

respectively.

In the glassy state relaxation, it is assumed that

there are several energy states for the moving enti-

ties with a hierarchy of barriers. Within thisdescription, it is assumed that the energy difference

between the neighboring barriers is small, while

the difference between the more distant barriers

is higher [21]. It can be assumed that such an en-

ergy landscape (associated with the frustrated

superconducting domains coupled by weak links)

leads to the concept of the superconducting glass

model. Due to the external force or thermal activa-tion, the vortices in an inhomogeneous distribu-

tion of the energy landscape can easily overcome

the neighboring barriers, but may fall in a deeper

barrier. Thus, bundle of vortices remaining at the

bottom of deeper barriers can not overcome the

barriers and give no contribution to the measured

voltage.

Recent studies reveal that the time evolution ofthe sample voltage (i.e., V–t curves) is one of the

best methods to monitor preciously the dynamic

variables which are sensitive to the external forces

[6,8,9,11,16–18]. Both fast and slow transport mea-

surements associated with these studies can pro-

vide an accurate way to determine the metastable

states, motional reorganization, dynamic transi-

tions, and dynamics of driven vortices etc.[6,8,9,11,16–18]. The aim of this study is to inves-

tigate the time effects induced by the transport cur-

rent via the time evolution of the sample voltage

(i.e., V–t curves) measured in an undoped poly-

crystalline bulk superconducting Y1Ba2Cu3O7�d

(YBCO) material and the doped one by organic

material Bis dimethyl-glyoximato Copper (II),

respectively. For this purpose, slow transportrelaxation measurements were performed as a

function of driving current (I), and temperature

(T). It was observed that, when the transport cur-

rent is interrupted, the voltage response becomes

abruptly zero within the time constant of the

experimental set-up. However, it was found that

the reduction of initial current to finite value re-

sults in only smooth exponential voltage decaysor the voltage decays with transitions evolving to

lower voltage values. The transitions result in a

true superconducting state depending on the mag-

K. Kilic et al. / Physica C 420 (2005) 1–10 3

nitude of transport current or the temperature

range considered. Furthermore, the effect of the

organic material introduced to YBCO material

could be observed apparently by means of the

V–t curves. Thus, the difference between dopedand undoped YBCO samples could be distin-

guished separately. The experimental results were

discussed mainly in terms of the suppression or

enhancement of the superconducting order param-

eter in a multiply connected network of the weak

link structure and also by the glassy state relaxa-

tion in an inhomogeneous energy landscape.

2. Experimental

The YBCO sample was prepared from the high

purity powders of Y2O3, BaCO3 and CuO by using

the conventional solid state reaction [8,9]. In order

to eliminate possible heating effect which will oc-

cur at current leads due to the high currents, thesample for the transport measurements was

shaped carefully in the dimensions of length

l � 4 mm, width w � 0.1 mm, and thickness

d � 0.2 mm. The four conductive pads were placed

onto the sample by using silver paint and annealed

�1 to 2 h at 150 �C under O2 atmosphere. The

pure copper wires were attached by silver paint.

The measured contact resistance by using thethree-point method was of order of �10�3 X below

Tc and �10�2 X at room temperature. In this case,

the power dissipated at the current contacts would

be �9 · 10�7 W for a current of I = 30 mA, and,

the power generated at the current leads is negligi-

ble and will not affect the evolution of the V–t

curves. The transport measurements were carried

out using standard four-point method, and per-formed in a closed cycle He-refrigerator (Oxford

Instruments (OI) CCC1104). In the experiments,

Keithley-182 with a resolution 1 nV and Keith-

ley-220 were used in measuring the sample voltage

and supplying the current, respectively. The mea-

sured voltage is the average value of five readings

for each data point. After the current is applied,

just at this time, we start to measure the develop-ing voltage across the sample as a function of time.

Thus, monitoring of all details of the time evolu-

tion including the transient effects becomes avail-

able. In the experiments, to create a glassy state,

the dc current was interrupted or reduced to a

finite value. The temperature was recorded by a

calibrated 27 X Rhodium–Iron thermocouple (OI

Calibration number 31202), and a temperaturestability better than 10 mK was maintained dur-

ing the experiments (OI, ITC-503 temperature

controller).

The undoped YBCO sample used in this study

has zero resistance at �92 K with a transition

width DTc of about 3 K at zero field and zero mag-

netic field critical current density of �25 A/cm2

at T = 88 K determined by using the 1 lV/cmcriterion.

3. Experimental results

One of the best ways to observe the time effects

induced by the transport current is to record the

sample voltage continuously as a function of time,i.e., to measure the V–t curves. Thus, all dynamic

changes including the transient effects can be mon-

itored. During the time evolution of the sample

voltage, the transport current (I1) can be inter-

rupted or reduced to a finite value (I2) so that a

quenched state which is reminiscent of the glassy

state can be obtained. Indeed, to create such a

state, one of the requirements is to interrupt thepower supply which generates the transport cur-

rent (or the external magnetic field) or to reduce

the transport current (or the external magnetic

field) to a lower value. For this purpose, in our

measurements, a dc driving current I1 was applied

to the sample and maintained for sometime (i.e.,

53 s) to achieve a steady state. Then, the current

was reduced from I1 to a lower value I2 duringcourse of the measurement, and this value kept

at rest of the relaxation process, (i.e., up to

120 s). In the mean time, the sample voltage was

recorded continuously.

Fig. 1(a) shows a set of typical V–t curves mea-

sured at T = 87 K for I1 = 30 mA, and I2 = 0, 2, 4,

6, 8, 10, 12, 14, 16, 18, and 20 mA. It is seen, be-

fore reducing the driving current from I1 to I2,that the sample voltage evolves in two stages: In

first stage, a sharp increase in sample voltage is

observed for t 6 10 s, and, then, in second stage,

Fig. 1. (a) Time evolution of the V–t curves of undoped YBCO

sample measured at T = 87 K for I1 = 30 mA, and I2 = 0, 2, 4, 6,

8, 10, 12, 14, 16, 18, and 20 mA. The initial current I1 = 30 mA

was applied for 53 s, it is then reduced to I2 and left on the

sample. The dashed lines through the data points are guides for

the eye and the solid lines are the calculated curves defined by

Eq. (1). (b) Variation of the critical time tc with the current I2.

The dashed line is a guide for eye.

4 K. Kilic et al. / Physica C 420 (2005) 1–10

the current becomes approximately constant,

which implies that a steady state develops in the

sample. After reducing the current from I1 to I2,the sample voltage exhibits several different behav-

iors depending on the magnitude of the current I2together with a sharp drop. When I2 = 0, the sam-

ple voltage becomes zero and no trace of relaxa-

tion effect is observed. This indicates that (i)

there is no residual voltage on the sample to be re-

laxed within the time response of the experimental

set-up; and (ii) the voltage decays observed forI2 > 0 are physical, which are not originated from

the limitations of the experimental set-up.

The V–t curves measured in the current range of

2 mA 6 I2 6 10 mA evolve in the form of voltage

decays with two stages after a sharp drop. A

smooth transition which follows the first voltage

decay develops after a certain critical time (tc) va-lue which depends on the magnitude of I2. Here,

the tc is the elapsed time from the beginning of

the voltage decay to the onset of the transition

time. The variation of tc with I2 is plotted in Fig.

1(b). It is seen from this figure that tc increases

nonlinearly with increasing of I2. For I2 = 2, 4, 6,

and 8 mA, the smooth transition results in a super-

conducting state since the measured voltage iszero. The evolution of the superconducting state

occurs in shorter times for low values of I2 as com-

pared to that of observed for higher I2 values.

Although a transition evolving to the supercon-

ducting state is observed in the V–t curves ob-

tained for I2 = 10 and 12 mA, the zero resistance

state is not yet established for these current values

within the time scale of the experiment (see Fig.1(a)). On the other hand, the behavior of the V–t

curve corresponding to I2 = 12 mA is somewhat

different from the V–t curves for I2 6 10 mA. In

this V–t curve, a transition to superconducting

state is not so prominent as for the curves with

I2 6 10 mA. It can be assumed that the current

I2 = 12 mA separates the low and high current re-

gions. Because, the V–t curves corresponding toI2 > 12 mA decay over time without showing any

transition during the measurement.

In order to assess the effect of temperature on

the evolution of the V–t curves, similar measure-

ments at 86.5 K were carried out by applying the

same experimental procedure described in Fig.

1(a). The reason of choosing a temperature which

is very close to that in Fig. 1(a) is that the evolu-tion of V–t curves is very sensitive to small changes

in temperature. The measurements were repeated

for the same current values of I1 = 30 mA and

I2 = 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, and 20 mA.

The experimental data are plotted in Fig. 2(a).

The inset of Fig. 2(a) shows the V–t curves for

I2 = 18 and 20 mA with I1 = 30 mA. Here, differ-

ently, the initial current I1 is left on the samplefor the first 71 s. It is seen from the main panel

of Fig. 2(a) that, as the magnitude of current is re-

duced from I1 = 30 mA to I2 at t = 53 s, the sample

Fig. 2. (a) Time evolution of the V–t curves of undoped YBCO

sample measured at T = 86.5 K for I1 = 30 mA, and I2 = 0, 2, 4,

6, 8, 10, 12, 14, 16, 18, and 20 mA. The initial current

I1 = 30 mA was applied on the sample for 53 s, it is then

reduced to I2 and left on the sample. The inset shows the V–t

curves measured at the current values I2 = 18 and 20 mA,

respectively. The reduction from I1 to I2 was carried out at

t = 71 s of the time evolution. The dashed lines are a guide for

the eye and the solid lines are the calculated curves defined by

Eq. (1). (b) Variation of the critical time tc with current I2. The

dashed line is a guide for eye.

Fig. 3. Time evolution of the V–t curves of undoped YBCO

sample measured at T = 87 K for I1 = 20 mA, and I2 = 0, 2, 4, 6,

8, and 10 mA. The initial current I1 = 20 mA was applied for

53 s, it is then reduced to I2 and left on the sample. The inset

shows the variation of the critical time tc with the current I2.

The dashed lines through the data points are guides for the eye

and the solid lines are the calculated curves defined by Eq. (1).

K. Kilic et al. / Physica C 420 (2005) 1–10 5

voltage drops abruptly, and, then, decays nonlin-early up to a certain time tc (the critical time)

which depends on the magnitude of I2. The varia-

tion of critical time tc with I2 extracted from Fig.

2(a) is illustrated in Fig. 2(b). For t > tc a transi-

tion follows the initial smooth decay evolving to

lower voltage values. For the current values of

I2 = 2, 4, 6, 8, 10, and 12 mA, the transition results

in a superconducting state, whereas, for I2 = 14and 16 mA, the smooth voltage decays together

with transitions do not result in a superconducting

state in the time scale of the experimental set-up.

A comparison between Fig. 1(a) and Fig. 2(a)

shows that, in addition to similarities, there are

also some differences. For instance, the transition

at I2 = 12 mA in Fig. 2(a) results in a supercon-

ducting state, whereas, for the same current valuein Fig. 1(a), such a behavior evolving to zero resis-

tance state is not seen. This behavior is due to the

change of temperature. On the other hand, the

dependence of tc on the current I2 (Fig. 1(b) and

Fig. 2(b)) demonstrates these differences well and

reveals the effect of the temperature on the evolu-

tion of the V–t curves. The comparison of tc values

obtained at different temperatures shows that boththe evolution of voltage decays and the width of

the transitions depend strongly on the tempera-

ture, which implies the lower the temperature the

lower the critical time. As can be seen from the in-

set of Fig. 2(a), at the higher current values of 18

and 20 mA, only voltage decays without a transi-

tion to superconducting state are observed.

To investigate the influence of the magnitude ofdriving current I1 on the evolution of the V–t

curves, the current I1 was reduced from 30 to

20 mA and the V–t curve measurements were re-

peated for I2 = 0, 2, 4, 6, 8, and 10 mA at

T = 87 K. The data are represented in Fig. 3. A

comparison of Fig. 1(a) and Fig. 3 shows that

there is a similarity between the corresponding

V–t curves. The response of the sample to the

6 K. Kilic et al. / Physica C 420 (2005) 1–10

reduction of I1 = 20 mA to I2 shows nearly the

same behavior as compared to that of observed

in Fig. 1(a), i.e., the time evolution of the sample

voltage occurs in two stages. However, a careful

examination reveals that there are remarkable dif-ferences between the V–t curves presented in Fig.

1(a) and Fig. 3. First of all, just after the current

I1 is reduced to I2, the sample voltage decays and

evolves to superconducting state within shorter

times. This can be easily understood from the inset

of Fig. 3 which shows shorter critical time values

as compared to those Fig. 1(b). For instance, the

tc values corresponding to I2 = 8 mA in Fig. 1(a)and Fig. 3 are 15 and 9 s, respectively. This empha-

sizes that, at low values of the initial current I1, the

smooth transitions are observed within shorter

times.

4. Discussion

We now discuss on the V–t data presented in

Fig. 1(a), Fig. 2(a) and Fig. 3, which evolve in

two stages over time for a current value of I1.

We suggest that, in such V–t curves with two

stages, at the beginning, the transport current tries

to distribute itself and meanders along the nonre-

sistive flow channels for a while. As the time pro-

ceeds, the internal energy of the superconductingmaterial may increase due to the presence of the

transport current so that the effective supercon-

ducting order parameter cannot keep its previous

spatial configuration and can decrease in time.

Thus, an increase in sample voltage may be ob-

served. This means that the transport current pen-

etrates the weak-link network where the weak

superconducting regions exist and disrupt themgradually [27]. As a result, an enhancement in dis-

sipation together with a dynamic process triggered

by the current can appear. The nonlinear increase

in sample voltage observed in this stage can be

evaluated as an indication of the coexistence of

the disruption and reconstruction of the weak-link

structure by the transport current. However, the

voltage response shows that the competition be-tween these two physical mechanisms develops

mostly in favor of disruption in time. Finally, at

second stage, the transport current nearly com-

pletes the redistribution process depending on its

magnitude and a steady process is established

within the time scale of the experiment.

On the other hand, as shown in Fig. 1(a), Fig.

2(a), and Fig. 3, when the transport current isinterrupted, the sample voltage becomes immedi-

ately zero. It can be suggested that the weak links

form a coherent state and the resistive flow chan-

nels disappear within a very short time, at least,

within the time constant of our experimental

set-up. Thus, the effective order parameter should

increase after the interruption of the transport cur-

rent. We note that these experiments can also beconsidered as a test of whether the thermal relaxa-

tion due to the Joule heating at current contacts

[28,29] or hot spot effect [28,30–32] exists or not.

Our data demonstrate that the observation of zero

voltage for I = 0 (just after the dc current was

turned off) rules out the thermal relaxation associ-

ated with such mechanisms.

The decrease of transport current from I1 to asmaller value of I2, however, causes the appear-

ance of a different voltage response. Following this

procedure, the effective superconducting order

parameter suppressed by I1 is enhanced rapidly,

and a quenched state associated with the distribu-

tion of the transport current is developed. Depend-

ing on the magnitude of the currents I1 and I2, and

the temperature range of measurements, thequenched state reorganizes itself over time and

evolves to low dissipation levels. The decay in sam-

ple voltage can be considered as a measure of this

reorganization process in which the structural dis-

order, chemical and anisotropic states of the sam-

ple play a central role. At relatively low currents,

the effective size of dissipative nonsuperconducting

flow channels begins to decrease gradually withtime and this process leads to an enhancement in

the effective order parameter. At low enough cur-

rents, these channels are closed completely within

a very short time, so that the response is voltage

decay with transition to superconducting state. It

can be suggested that the phase of the order

parameter in a multiply connected superconduct-

ing disordered grains network becomes locked.We also correlate the voltage decays without

transition and the smooth transitions appearing

in V–t curves to the glassy state relaxation

Fig. 4. Variation of the characteristic time s0 with current I2:

(a) extracted from Fig. 3; (b) extracted from Fig. 1(a); (c)

extracted from Fig. 2(a) and its inset. The dashed lines are a

guide for eye.

K. Kilic et al. / Physica C 420 (2005) 1–10 7

(GSR), as in the case of spin glasses [21,22]. It

should be noted that the physical case appearing

in V–t curve cannot be explained alone by the

usual phenomenological theories such as flux creep

theory [33], collective creep model [34] etc., sincethese theories do not explain sufficiently the transi-

tion process evolving from resistive state to true

superconducting state. It has already been shown

[21,22] that such type of relaxation can be ex-

plained by glassy state relaxation (GSR). One of

the requirements of GSR is that the sample voltage

must decrease exponentially in time [21,22]:

V ðtÞ � V ðt ¼ 0Þ ¼ expð�t=s0Þ: ð1ÞHere, V is the sample voltage, s0 is a characteristic

time and depends on the external magnetic field,transport current, and temperature. Eq. (1) estab-

lishes that the sample voltage evolves to lower val-

ues for any time of the relaxation process.

Physically, the decrease in sample voltage can be

considered as a measure of degree of disordered

of the moving entity. For instance, as the time pro-

gresses, some of the vortices can pass locally into a

state of minimum energy within the correspondingenergy landscape and such a physical process can

evolve in the other regions of the sample in time

by enhancing gradually the superconducting order

parameter over the whole sample, which leads to a

decrease in the sample voltage. Therefore, Eq. (1)

gives quite reasonable insight on about the decay

of sample voltage below Tc [21,22]. In addition,

we emphasize that another important requirementto get a glassy state is to switch off the power sup-

ply which generates the transport current (or mag-

netic field), or reduce it to a given finite value.

Thus, it becomes possible to create a quenched

state which is unstable in time, and the measurable

time independent parameters of the system become

remarkably time dependent.

The solid lines through experimental datapoints in Fig. 1(a), Fig. 2(a) and Fig. 3 are calcu-

lated by using Eq. (1). The reasonable agreement

between the calculated curves and the experimen-

tal data suggests that the time evolution of the

quenched state is closely related to GSR relaxa-

tion. The characteristic time s0 values found from

the fitting of Eq. (1) to the experimental V–t curves

given in Fig. 1(a), Fig. 2(a) and Fig. 3 are plotted

as a function of the driving current I2 in Fig. 4.

The characteristic time s0 tends to increase with

current, because the transitions at low currents

are more faster than that at higher currents. In

addition, we note that there is no marked changein values of s0 as the temperature is reduced or

the current I1 is increased (see Fig. 4).

It is also observed that the reduction in the ini-

tial transport current I1 (see Fig. 1(a) and also Fig.

3) or the decrease in sample temperature (see Fig.

1(a) and Fig. 2(a)) do the same physical impact. It

can be suggested that there should be a correlation

between the transport current and the temperature[13]. Such a correlation has been treated theoreti-

cally and numerically by Koshelev and Vinokur

Fig. 5. (a)–(d) Time evolution of the V–t curves of YBCO

sample doped with an organic material Bis dimethyl-glyoxi-

mato Copper (II) measured at T = 87 K for I1 = 30 mA, and

I2 = 0, 15, 20, and 25 mA, respectively. The solid lines are the

calculated curves defined by Eq. (1).

8 K. Kilic et al. / Physica C 420 (2005) 1–10

[35]. These authors have shown that the random

pinning potential can induce measurable addi-

tional fluctuations on the moving vortices which

resemble the fluctuations associated with the ther-

mal Langevin force. In addition, we note that thiscorrelation can be naturally expected since the

superconducting order parameter strongly de-

pends on both the temperature and transport cur-

rent. The transport current serves here as an

‘‘effective temperature’’ in the sense defined in

the statistical mechanics, and anneals dynamically

the corresponding states during the relaxation pro-

cess [8,9,13,36]. Further, the magnitude of thetransport current determines mainly the annealing

kinetics.

In what follows, it is shown that the V–t curves

can be used to observe any microscopic structural

variation, i.e., deviation from the nominal compo-

sition, doping of any organic or inorganic material

into the superconducting matrix etc. We now

investigate this effect on the evolution of the V–tcurves and also on the evolution of the quenched

state. For this purpose, an organic material Bis di-

methyl-glyoximato Copper (II) was mixed with

sintered YBCO powder in the amount of 0.01%

of the weight of nominal composition of YBCO.

A similar sample preparation route such as mixing,

pelletization and sintering, was applied as like in

undoped YBCO sample whose the experimentalresults are presented above. In addition, in order

to remove the size effects and to make a correct

comparison between doped and undoped YBCO

samples, the doped-YBCO was shaped in the same

dimensions, i.e., length l � 4 mm, width w � 0.1

mm, and thickness d � 0.2 mm, as in the case of

undoped YBCO. The resistivity vs temperature

measurement showed that the addition of Bisdimethyl-glyoximato Copper (II) does not change

of the critical temperature of YBCO. However,

we obtained a small variation in the critical current

density Jc of doped YBCO, i.e., Jc = �30 A/cm2 at

T = 88 K. The higher Jc than that of undoped

YBCO can be attributed to the introducing of

the new pinning centers by addition of the organic

material.The effect of the addition of the organic mate-

rial into YBCO can be observed directly by means

of the V–t curves. Fig. 5 shows the V–t curves mea-

sured for such a YBCO sample at T = 87 K for

I1 = 30 mA, and I2 = 0, 10, 20 and 25 mA. The

evolution of the V–t curves for I1 in Fig. 5 repre-

sents three distinct stages: At first stage, it is seen

that there is no measurable voltage response upto the time value of �5 s. After t > �5 s, several

current carrying regions which connecting the

sample edges from one to another form: The dissi-

pation grows up nonlinearly and levels off at a cer-

tain voltage value at second and third stages,

respectively. As is also seen from Fig. 5(a), on

the other hand, interruption of the current gives

no measurable voltage and also no relaxationeffects to be recorded, as in the other V–t curves

K. Kilic et al. / Physica C 420 (2005) 1–10 9

given in Fig. 1(a), Fig. 2(a) and Fig. 3 for undoped

sample. However, when the current I1 is reduced to

I2, more smooth decrease rather than a sharp drop

in sample voltage is observed. The solid lines be-

long to this part of the measurement in Fig. 5 rep-resent the best fits of Eq. (1) to the data points. It is

seen that there is a reasonable agreement between

the calculated curves and experimental data. We

found from the fitting procedure that the charac-

teristic time, s0 values are 1.6, 4.3, and 6.3 s for

the current values of 15, 20, and 25 mA, respec-

tively. Consequently, we conclude that, for

I2 5 0, the voltage response is in the shape of anexponential decay without exhibiting any interme-

diate transition, which results in a superconducting

state up to the current values of 20 mA. For

I2 P 20 mA, it is observed that the exponential

decay does not result in superconducting state

within the time scale of the experiment. However,

we note that the V–t curves taken for undoped

YBCO in Fig. 1(a) reveal a voltage decay for awhile after a sharp drop, and, for the current (I2)

values low enough, evolve with a smooth exponen-

tial transition following the voltage decrease,

which may result in a superconducting state

depending on the magnitude of the current I2. At

higher currents (I2 P 12 mA) only the exponential

decays which do not show any trace of entering

into the superconducting state are observed withinthe time scale of the experiment. We would like to

note that, in doped YBCO, the superconducting

state still can be observed at the higher values of

I2 as compared to that of the undoped YBCO.

These differences between the V–t curves for doped

(Fig. 5) and undoped YBCO sample (Fig. 1(a)) can

be attributed to the effect caused by the organic

material in the superconducting matrix. Further-more, it can be suggested that the V–t curves intro-

duce a way to observe such a structural change

done with respect to a reference material which is

chosen.

Finally, one of the important points what we

wish to emphasize here is that the time evolution

of the V–t curves given in Fig. 1(a), Fig. 2(a),

Fig. 3 and Fig. 5 also should depict the timedependence of the order parameter, that is, the

relaxation of the order parameter over time.

According to the Ginzburg–Landau (GL) theory

[37] and time-dependent GL theory [38,39], the

superconducting order parameter depends explic-

itly on time, temperature, current density, and

external magnetic field. We suggest that the exper-

imental procedure used in the acquisition of V–tcurves presented in Fig. 1(a), Fig. 2(a), Fig. 3

and Fig. 5 provides a useful way to monitor the

time variation of order parameter, in details. All

these facts underline the importance of the V–t

curve and show that, in addition to the usual

transport measurements, this experimental method

introduced here is a candidate to be one of the

powerful tools to characterize the superconductingmaterials.

5. Conclusion

In this paper, nonlinear transport phenomena

was investigated in bulk polycrystalline supercon-

ducting Y1Ba2Cu3O7�d sample via slow transportrelaxation measurements [i.e., voltage–time, (V–t)

curves] as a function of driving current and tem-

perature. A quenched state was created by inter-

rupting the initial driving current or reducing to

a finite value. As the time progresses, it was found

that the time evolution of the quenched state rep-

resents several interesting properties. The voltage

response results in decay or decay with smoothtransitions evolving to lower voltage levels. In

addition, when the driving current was inter-

rupted, it was observed that the measured voltage

becomes zero. This finding indicated that there is

no residual voltage in the sample to be relaxed.

It was shown that the voltage response decays

exponentially in time and this interesting behavior

was interpreted in terms of glassy state relaxationin an inhomogeneous energy landscape. Further,

the effect of doping of an organic material Bis

dimethyl-glyoximato Copper (II) to YBCO could

be monitored apparently via the comparison of

the V–t curves corresponding to doped and

undoped YBCO samples. The experimental results

were discussed mainly by considering the spatial

reorganization of the driving current and suppres-sion or enhancement of the superconducting order

parameter in a multiply connected network of the

weak link structure.

10 K. Kilic et al. / Physica C 420 (2005) 1–10

Acknowledgments

This work was supported by TUBITAK/TBAG

2037. The authors would like to thank Prof. Dr.

M. Cankurtaran at Hacettepe University for valu-able discussions.

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