Shielding currents and current-voltage characteristics of Bi2Sr2Ca1Cu2O8+δ single crystal

IWg

Physica C 219 (1994) 99-108 North-Holland

Shielding currents and current-voltage characteristics of Bi2Sr2CalCU208 + single crystal A.A. Zhukov ", H. Kupfer b, V.A. Rybachuk ", L.A. Ponomarenko ", V.A. Murashov c and A.Yu. Martyukiu ¢ • Physics Department, Moscow State University, Moscow 117234, Russian Federation b Kernforschungszentrum Karlsruhe, Institutfur Technische Physik, Postfach 3640, tV-7500 Karlsruhe, FRG c Moscow Institute of Radioengineering, Electronics andAutomation, Moscow II 7454, Russian Federation Received 16 March 1993 Revised manuscript received 28 September 1993

The dependence of the irreversible mAm~etizafion on the external magnetic field sweep rate, dHe/dt, and its time relaxation are studied ill a Bi2+xSr2+j,CAt,+zCu2Os+8 (x--0.11, y=0.12, z = - 0 . 2 5 ) single crystal. Two characteristic regions are found with a transition temperature T" between 15 and 20 K d ~ l ~ d i n ~ on dHe/di and relaxation time. Below T* the magnetic field depend©rice of the shieJdin~ ourrents follows a scaling law./,(He, T)/J,(0, T) ---j~He/J,(0 , T) ] with 8 univ~-sal function findependent of temperature and sweep rate of magnetic field. V o l t a s e - c u ~ n t characteristics are described quite weU by a power-like law E~ Ec-- (J,/J©)" with n~ I/T. Above T* a deviation from the ./.(He) scaling behavior and a transition to much steeper voltagecurrent characteristics are observed. Possible reasons of these different shielding current behaviours are discussed.

1. Introduction Resistivity caused by thermoactivated vortex movement is much more pronounced in high-To than in conventional superconductors. Therefore, the measured transport or shielding currents are lower than the critical value which corresponds to the transition into the flux flow state without activation. This results in shielding currents being dependent on the experimental conditions, in particular on the sweep rate of magnetic field, according to the voltage-current characteristics (I-Vcurves) of a sample [ 1-8 ]. In the case of the B i 2 S r 2 C a l C u 2 0 8 + 6 p h a s e , these effects are well pronounced, which makes this system convenient for their study. On the other hand, this phase is characterized by a weak coupling between the CuO2 planes leading to a very strong anisotropy of superconducting parameters. According to the theoretical analysis [9,10], one expects such interesting phenomena as the Kosterlitz-Thouless transition, the evolution from the vortex lattice to the vortex liquid phase, etc., to be present here. Previous studies of BiaSr2CalCu208 +s single crystals re-

vealed essentially different magnetization behaviors at low and high temperatures [ 11-16]. These results were explained by the melting of the vortex lattice [8], the change of the pinning mechanism [12,13,15], the presence of a surface barrier [16] and the transition into the granular state [ 16 ]. In this work we have undertaken a detailed study of the magnetic properties of a Bi2Sr2CatCu2Os+j single crystal in the field direction parallel to the caxis of the crystal. The main attention was paid to the dependence of the hysteresis width on external magnetic field, temperature and the magnetic field sweep rate dH/dt. The relaxation of the magnetic moment was measured and the current-voltage characteristics were extracted.

2. Sample preparation and experimental procedure The Bi2+~eSr2+yCal+zCu2Os+~single crystal was prepared using the flux growth technique from nonstoichiometric mixtures of the oxides. Details of the preparation are described elsewhere [ 17 ].

0921-4534/94/$07.00 © 1994 Elsevier Science B.V. All rights reserved.

SSDI 0921-4534(93)E0267-5

A.A. Zhukovet al. / ShieldingcurrentsofBiaSr2Ca~CuzOs÷~

100

The sample studied had the dimensions of 2.2 X 2.4 × 0.01 mm 3. The sample composition measured by electron beam microprobe analysis yielded x = 0.11, y = 0.12, z = - 0.25. The transition temperature determined by the appearance of a diamagnetic signal was Tc=93.5 K. Magnetic measurements were made on a vibrating sample magnetometer in the orientation of magnetic field H parallel to the c-axis. The field was cycled with different constant sweep rates. Relaxation measurements were made after the magnetic field was increased to a value several times higher than the penetration field and subsequently reduced to zero.

3. The genendized critical state model and ex/ract/ou of current-voltase ~ from magnetic messm~meut data For a macroscopically homogeneous superconductor of the second type in the case of the intervortex distance ao~ (Oo/B) I/2 significantly less than the characteristic scales which are of interest, it is possible to use the approximation of homogeneous media [ 18 ]. Then, the general equations are

rotHfOD/Ot+j rotE=-aB/0t

divD=0, divB=0;

(1)

j f f ( E, B ), B= lzlzoH, D=~eoE;

(2)

M=½ J [].r] dV.

(3)

This system, eqs. (1-3), needs to be added to by starting and boundary conditions. For an experimentally attainable frequency region the term aD/Ot is negligible and may be omitted. Really, ( 1/j) 019/ 0t~a~Eop~: 1 for t o ~ 10 ~s Hz if ~= 1 and p--- 10 -3 D cm. The well-known Bean model [ 19 ] corresponds to the special case of the steplike current-voltage characteristic f(E----0, B) = ~ ,

f(0, B) = 0 .

The system (1) and (2) may be reduced to the diffusion-like equation (/z= 1 ) 0j 0j 0E AE=-/Zo~-~ =/Zo~-~ at "

(4)

The equations of this type were studied long ago for such problems of diffusion in non-linear media as properties of non-linear magnetic materials, nonstationary gas filtration in porous media, non-linear thermoconductivity [20,21] and pulsed magnetic fields in superconductors [22]. Later, this problem was considered for certain I - V relations in superconductors of different shapes [23-25]. The exact solutions may be obtained for the superconducting thin-wall cylinder and torroid [ 5 ]. However, except for paper [22], the main efforts have been concentrated on the direct problem of the determination of magnetic properties on the basis of a known I - V relation. From the experimental point of view, the procedure of J-E curve extraction using magnetic data (the inverse problem) is much more important. In the general case this is a very complicated task, but it may be simplified by certain approximations. First, it is very often possible to neglect the influence of the self-field. This is valid when the variation of the current within the sample is small. Considering in this case Aj~ (Oj/OB)AB, we may obtain the criterion of such an approximation ( 01nj/0B)AB ~ 1, where the variation of magnetic induction in the sample may be estimated by the value of the penetration field, that is the f e l d needed to create the critical state from the virgin one. This criterion is always fulfilled at high magnetic fields and often for the remanent state too. For our sample the penetration fields are HD~. 3 kOe ( T = 4 . 2 K ) and 0.04 kOe ( T = 2 5 K ) . Supposing that aln J,/~B and aln 1,/OHc values are close and using the maximum slope of the lnJ,(H) curve in small fields, we have found for the remanent state 7~alnJs/OHffIp=0.33 ( T = 4 . 2 K) and 0.4 ( T = 2 5 K). Such a relation allows one, as a first approximation, to neglect the field distribution in the sample. The largest error arises for the remanent state. It is less than 7 and has systematic character if ~ is constant as is approximately valid for our sample. For the experimental y values and the exponential j,(B) dependence our numerical calculations in the case of an inscribed disk show that the standard Bean expression gives an error in j , ( 0 ) determination for the remanent state less than ~ I0%. As another approximation, we suppose the I - V curves to be sharp with alnj/alnE~ 1. Then we may

A.A. Zhukovet al. / ShieldingcurrentsofBi~r ~CajCu2Os+8 neglect the space dispersion o f j completely. Really, for the cylindrical symmetry: R

1

m= -~5

f Y(r)r dr .

2

101

and the point of integration. Using the same approximation of the spatially homogeneous currents, one can obtain A, : (/Zo/4n) [j.(R) ] ~ (dV/p).

0

(8)

R

rdj(r)

This integral may be calculated for an in£mite cylinder and a thin disk with the thickness D ~ R. Then the relation for the electric field acquires the following form:

1 rZdr~r -3ddl.r )

1 {J(R~ " R3 --,/~"

0

:

[j(R)R/3]f 1 .

~

-1

"

1

E= (3/zo/SxR 2) (dM/dt)Io, dkJ(R) X

d(lnr)kj.

(5)

(9)

where 1

Taking into account the relation dj/dlnr= (dj/ dinE) (dinE~din r) and 81nE/Olnr~ 1 [26] in the case of a sharp I - V curve, we may obtain as the approximation the Bean relation [ 19 ] for the magnetization m=j(R)R/3 with the current j(R) corresponding to the circumference of the sample. In fact, this approximation corresponds to the spatially homogeneous current distribution [ 27 ]. To fred the corresponding E-value, let us consider two main measurement regimes: (1) with He variable in the case of the hysteresis curve recording, and (2) with the external magnetic field H e - const, used for the study of relaxation. In the first r e , me the electric field varies linearly with radius and for circumference:

E(R) = (IzoR/2) ( d H J d t )

I o ~ 4 J ( 1 - t 2 ) l n [ l + t ) / ( 1 - t ) ] dt=6.656

In the case of the thin disk, and Io = ~ (R/D) for the infinite cylinder. This analysis is also supported b y the direct comparison with transport measurements [28]. In fact, the approach outlined above consists in the substitution of the real current distribution in the sample with a constant value, as is the case in the Bean model. However, the shielding current density involved is not now equal to the critical value Jc but

J,

10 8

,A/era 2

~5 o~

(6)

Using eq. ( 5 ) this allows one to determine the exact solutions for power-like current-voltage characteristics E ~ j " m = j ( R ) R / ( 3 + l / n ) and for the relation E=Eoexp ( - (Uo-ctj)/kT), m=j(R)R{1 - k T /

0

x

10 5

0

,

o

0

, 0 [30 DO

x

*

[3 @ * o ~®

[3aj(R) ]}/3.

D

For the relaxation, the electric field may be calculated from the relations dt

0 o

oO

+

H8

10 4

+

+

"i-

+

'

T,K

O(R)-- f Bds= f Adl=2~4., A= ~ I ~dV=A,e,,

(10)

0

i03~

(7)

where p is the distance between the observation point

'

'

' 1o ' ~

~

'210'

'

, 3 to

,

,

, 4 '0

Fig. 1. The real and model distributionof shieldingcurrents in the sample for different magnetic fields produced by the flux change.

A.A. Zhukov et al. / Shielding currents o f Bi2Sr2CalCu 2Os +s

102

J, , A / c m = . ln(J//Jo)

o8

lOS

o

:(< 0

dltv/dt=5 0 e / s

,

°Oo, -

10 5

•

OO0 *

.%

-

•

-IOK

•

-15K

o 4.2K i ~ _ n 7K

-

•

"A

zx I O K

+

0* 8

+ +'.

+

<) 1 2 . 5 K

4"~+ +

10 4

-

+

4-

+

15K

+

,

t

I

1o

'

'

'20

'

'

' 30

'

'

•

× 1 7.5K

x

¢

T,K ,

tO

4.2K

' 40

Fig. 2. The temperaturedependenceof the shieldingcurrent density J, determined for H=0 from the hysteresis width at dH/ dtffi120 Oe/s (stars) and I Oe/s (plus signs), from remanent magnetization after 20 s (circles) and 2000s (squares) relaxation, and for H= 3 T from hysteresiswidth, dH/dt--120 Oe/s ( filledcircles). is determined by the voltage at the outer border of the sample (fig. 1 ).

4. Experimental results

4.1. The temperature and magnetic field dependence of the shielding currents. The temperature dependences of J, for different external magnetic fields H= and experimental conditions are given in fig. 2. As in previous studies [ 1217 ] one may distinguish two intervals with different behaviours of shielding currents. In accordance with the papers [12-17], at high temperatures J, decreases much more weakly with T than at low temperatures. The transition point T* is dependent on magnetic field and the sweep rate of magnetic field [ 12,13 ]. For high magnetic fields this transition disappears. In this case J, tends to zero at a temperature much lower than T~. For the low-T interval a scaling behavior of the magnetic field dependences of shielding currents was found. The curves J, ( T, He) can be reduced to a single one if both J, and H• are normalized by the corresponding values J,(T, 0) (see fig. 3). Consequently, a universal behavior J, ( T, H.)=J,( T, O) ~(H•/Ho(T) ) takes place with a temperature-inde-

d//JdT= 120 Oe/s

HJJo, ,

0.05

i

0. I

,

i

i

,

cm i

,

0. f5

Fig. 3. The scaling behaviour o f the shielding current dependence on magnetic field for two magnetic field sweep rotes, d H / d t ffi 120

Oe/s and 5 0 e / s ( J o f J . ( T, O) )

pendent scaling function ~0and scaling field Ho proportional to J,(T, 0). This scaling is found to be independent, within experimental accuracy, of magnetic field sweep rate. After a quite steep J, (H) drop at small fields the scaling function becomes close to an exponential one. It is worth emphasizing that this scaling differs from the case of melt-textured Bi2212 samples [29,30] and Bi2223 tape [31 ]. For those samples the scaling field Ho is not proportional to J, (T, 0). Both parameters demonstrate approximately exponential temperature dependences but with different slopes [ 30,31 ]. For the studied sample disappearance of the proportionality between Ho and J,(T, 0) was observed only at temperatures above 15 K. Another important point is the strong dependence of the shielding currents on the sweep rate of magnetic field which is even more pronounced than in melt-textured samples [ 20 ] or in tapes [ 31 ] and significantly larger than for YBCO single crystals [ 32 ]. As shown in fig. 4, the dI-Ie/dt variation may change J, by more than one order of magnitude at high magnetic fields, the effective resistivity p=E/J,, though, being still much less than the Bardeen-Stephen resistivity for flux flow pr~=p,B/B~2 [33]. Really, considering, for example, B=0.3 T and d//=/dt= 120 Oe/s, it may be found that d,~.700 A/cm 2, E = 9 X 10- s V/cm and p ~. 1.2 X 10-1o ~ cm, whereas

103

A . A . Z h u k o v et al. / S h i e l d i n g c u r r e n t s o f B i z S r z C a l C u ~ O s + 8

-5-

I J.,A/e~na

lgE,

""v/m

•

$

•

•

*

•

•

,,

•

T=25K --7-

•

~"

$

Fo

0

i0

25K

x

n

0

¢

x

o

x

o

0

x x

0 0

!

o

o 5

0

50

H, I

g o v~ o

x

t£O 0 , / ~ i

4

I

-11-

I

Fig. 4. The magnetic field dependence of shielding currents for different magnetic field sweep rates at T= 25 IC

the flux flow resistivity PFF> 10 -7 ~ cm calculated using p , > 10 -5 ~ cm and B=2=30 T [34] is significantly larger. So, in this case, we are far below the critical Jc value which corresponds to the vortex depinning by the Lorentz-force. It is, therefore, meaningless to compare different shielding current measurements without referring to the experimental procedure.

4.2. The experimental current-voltage characteristics

12.5K 10K

g 0 0

o

g 0 O

oo

o

7K 4.2K

15K

o 17.5K

-12-

Q rl

lgJ (A/cm 2 )

20K

-13

:

0

o

o O

, KOe

6

&~

~

o°

.

0 0

0

-10-

x

2

2

o

o

a

a

O"

--

~

o

x 0

& &

0

o

×

0

0 0

~

0

o

o

a

4 5 6 Fig. 5. The currant-voltage characteristicsextracted from the relaxation (open symbols) and from the dependence of the hyster~is width on the swcep rate of the magnetic field (elo~'d symbols) for different temperatures at zero external field.

15' E, V/m 16 16'

10 Using the approach described above, we have extracted the current-voltage characteristics from the relaxation data and the magnetization loops measured at different sweep rates. The results given in figs. 5 and 6 demonstrate two different regimes. For currents higher than ( 3 - 5 ) × 104 A / c m 2 the currentvoltage characteristics are approximately linear in the log-log scale, thus corresponding to the power-like dependence. For lower currents, the E(J) curves become steeper, as can be seen for temperatures above 15 IC The slope dlogE/dlogJ corresponding to the power of the characteristic n becomes dependent on the voltage for the region T > 15 K. In the region of high E ~ 10- s V / m it decreases with increasing temperature from n ~ 2 3 . 4 ( T f 4 . 2 K ) to n ~ 5 . 1 ( T - - 2 0 K ) . This decrease, shown in fig. 7, corresponds to a dependence n - - U o / k T with Uo/k~92 IC The data for the sample of ref. [ 12 ] show very

15 f~ - IJ

!0

:OA~ 9 K

:~x

J, A / c m " -t,~

I

1Oto

to 5

Fig. 6. The cur~nt-voltage characteri~ics extracted from the relaxation in the region of the transition.

similar results. The transition temperature T* determined as the deviation point from the power-like I - V dependence varies with voltage from ~ 15 K ( E ~ 1 0 - g V / m ) to ~ 2 0 K ( E ~ 10 -5 V / m ) . Extrapolated from the power-like parts, the I-V curves intersect approximately in the vicinity of the point J=~,2.8 X 106 A / c m 2 and E c ~ 4 X 10 -2 V/cm. This fact, in combination with the experimental de-

104

A.A. Zhukov et al. ~Shielding currents o f Bi ~,SrzCa lCu zOs +~

I/n

o

0.25 0

0.20 0.20 0

IOK

0 0

,0

0.15

0.10

0

0 0

*0

0. I 0

4.2K [3

0.00

T,K I

I

l

l

l

l

0

l

l

l

I

10

20

Fig. 7. The temperature dependence of the inverse slope l / n of the logE vs. log/curve for the studied sample (circles) and for the sample of ref. [ 12] (stars).

D

0.05

/LoH,, T 0.00 0

f

,

I

2

i

i

i

I

4

i

I

i

I

6

i

i

,

I

8

I

i

i

I

tO

Fig. 9. The magneticfield dependence of the inverseslope 1/n of the logE vs. log Ycurve for T= 10 K. E,

10

V/1'11,

fields higher than the penetration field HD ~ 1.7 kOe for T = 10 K~ This supports the applicability of our analysis to the case H - - 0 .

-7

1 0 -e

10

5. Discussion

-s

20KOe 11

10

-~¢1 0 "

I

I

lOKOe 5KOe I

I

I

I I~1

2KOe I

10 ~

Fig. 8. The current-voltage charactvristicsextracted from the relaxation for different magneticfields at T= lO K. pendences n ( T ) a n d E ( J ) , leads to the conclusion that for low temperatures the behaviour of a vortex bundle activation energy is described by the relation U=kTln(E/Ec)=nkTfUolnJc/J, [35,36] with temperature-independent U0 and 1c. As one can see from f~gs. 8 and 9, the magnetic field does not change the power-like character of the I - V curves but leads to the decrease of n and, consequently, Uo values. The power n also shows scaling behavior and n-~ has approximately linear dependence on magnetic field at high H. No s i ~ i f i c a n t difference is observed between the remanent state voltage-current characteristics and those in magnetic

In the last part of this paper we shall discuss the reasons for the two main observations - the existence of the power-like voltage-current characteristics with n ~ 1/ T for low temperatures and the drastic change of the shielding current behaviour above T*. Both of them may be related to several origins. As for the dependence E ~ J " , there are the Kosterlitz-Thouless phase of the vortex-antivortex pairs [9,36,37], and the 2D vortex-glass regime [9]. The transition at T* may be related to the change of the pinning mechanism produced by either thermofluotuation depinnlng of low-temperature pinning centres or melting of the vortex lattice [ 38,39 ]. The alternative possibilities are also an induced inhomogeneity or a surface barrier influence [ 16,40,41 ]. Further on we shall discuss these points in more details. As was shown, the E ~ J" dependence may originate if the pinning force changes logarithmically with the distance. This gives rise to the nucleation of barriers with a height growing as a logarithm of current density U ~ l o g J [35,37]. Thus, one should consider mechanisms having the logarithmic dependence of

A.A. Zhukov et al. ~Shieldingcurrents ofBi2SrzCalCuzOs+s

the pinning force on the distance, at limited space interval. Such a behavior may be observed pancake vortex-antivortex excitations 2D vortex lattice [9,36 ]. The energy citation is [35-37]

least within a in the case of (VAV) for the of such an ex-

U= [ 2Edln ( r / ~) +2Ec - JOor ] d ,

( 11 )

where the first term with E d -~ ¢~o2/16x2/ZoA 2 determines the interaction energy between VAV on the distance r, the second one corresponds to the core energy and the last one takes into account the work of the Lorentz force. The maximum barrier corresponding to rc= 2Ed/ JOo gives U ( J) = Uoln ( J¢.J) where J¢----2Edexp[ (E~--Ed)/Ed]/OO~b, Uof2dEd. Using the values for the interlayer spacing d= 1.5 nm, A~b=220um [42] and ~ = 4 n m [43], we found Uo= 97 K and, in the case of E¢ ~ Ed, Jc = 8 × 106 A/ cm 2. This estimation is in rough correspondence with the experiment. Another possibility may be related to the 2D vortex glass phase. In this case the behavior of the system at high currents is determined by the glass correlation length ~ which diverges at zero temperature ~,G~, ( 1/T) - ~ (v2~ 1 ). On scales smaller than ~ the barrier for vortex motion may again grow logarithmically, leading to the power-law, I - V curves with

n,,, (losT)IT

[9].

The power-like I - V curve (3) with n inversely proportional to temperature may be the reason of the exponential Jl(T) =Jl(0)exp( - T/To) dependence if the critical current J¢ is temperature independent. The measurements made with a fixed d H d d t correspond to a constant electric field Eo determined by eq. (6). Thus, the shielding currents are given by J , = J ~ ( - ~ ) k T / U o =J~exp [ - l n ( E J E o ) k T / U o ]

(12) and, consequently, To= Uo/kln ( E J E o ) . Using the experimental parameters we obtained To= 7.1 K, in rough correspondence with the observed To=4.7 K. Expression (12) also explains the observed dependence of To on the magnetic field sweep rate and the time of waiting (cf. fig. 1 ). Bi-2212 melt-textured samples and tapes show a weaker dependence of To on dI-Ic/dt [20,21 ] which points to a higher E~ value.

105

Further study of this difference is needed. Observed at high magnetic fields, the proportionality behavior n - ~~ kT/Uo", H provides an exponential dependence of the shielding currents on magnetic field, A(H)~e-H/H°, as follows from eq. (12) with n - 1= k T / Uo" H / Ho. This is in correspondence with the observed behaviour (see fi~ 3 and refs. [2931 ] ). The scaling parameter Ho depends on the sweep rate of magnetic field. The existence of the two different regimes for I - V curves easily explains the decrease of the normalized relaxation rate S = d l n M / d l n t with temperature after a maximum observed at an intermediate temperature [12-15]. The analysis shows that [5]

S___pe _ p

1

dln E / d l n j '

(13)

where p and Pd are the resistivity and the differential resistivity, respectively. Thus, as temperature rises, the slope d l n E / d l n j decreases, leading to the increase of S. For higher temperatures, however, another regime dominates and the In E versus l n j slope grows, resulting in lower S values. The transition to the steeper I- V curves above T* may be related to changing of the dominant pinning mechanism. Pinning centres with a small potential depth become less effective with increasing temperature (for example, because of vortex transformation or depinning of vortices by thermal fluctuations [38,39] ) and vortices are pinned only by deep pins. When the concentration of shallow centres is high they determine the critical current at low temperatures but after thermal depinning other defects become dominant. Another possibility might be the phase transition of the vortex lattice (e.g., melting) leading to the change of elastic properties and, consequently, of the pinning force for the same centres. On the other hand, it was found in ref. [ 16 ] that the magnetization becomes independent of the sample size above T*. This may be due to at least two different reasons: ( 1 ) the.granular structure of the sample for this temperature range, and (2) the influence of a surface barrier [ 30,31 ], leading to the appearance of additional irreversible magnetization produced by the surface currents. In the last case, the magnetization is independent of

A.A. Zhukovet al. / ShieldingcurrentsofBia.qrzCatCu2Os+6

106

the sample size and, depending on the surface homogeneity, it varies from He to He~. We have checked the possible presence of granularity for our sample comparing shielding currents determined from the hysteresis width and from the remagnetization field. (This field is needed to invert the shielding currents in the whole sample [44 ].) Figure 10 shows that these currents are very close at zero external field. Another check has been done using the initial slope of the remagnetization curve [45 ]. It is determined by the large demagnetization factor of the sample. Arising inhomogeneity would decrease the initial susceptibility X~due to diminishing of the transverse size of grains leading to lower demagnetization. As can be seen from fig. 10, no significant change of the Xi value is observed for zero magnetic field. Thus, granularity may be excluded at low fields. Only at higher magnetic fields is a change of the ratio .Is (AH)/Js(Am) value observed (fig. 10), in correspondence with the ref. [ 16 ]. On the other hand, the magnetic relaxation shows a distinct asymmetry between increasing and decreasing magnetic field for the temperature region above T* (fig. 11 ). Taking into account also the asymmetry of the magnetic hysteresis curves themselves in this temperature region [ 40,41 ], one may conclude that a surface barrier above T* is involved [40,41,46]. This asymmetry does not appear from the influence of a self-field. The asymmetry of relaxation increases for higher magnetic fields, whereas Jct~ 60

7 6

•

• •

•

50

•

5 4o

4 30

3 20

2 1

t3

0

0

0

0

0

lO

0

o o

0 0

10

20

30

40

5o

T,K Fig. 10. The temperature dependence of the homogeneity criteria J, (AH)/J,(Am) (open squares), initial susceptibility (closed squares) for H = 0 and relation J, (AH)/J,(Am) for H = 1 kOe

(triangles).

M, em.tt

O.005

0.000

i

"o~

I

~..~O~o~

~

~...

L i

l . l . = 5 k O e ~

~ -0.005

0

~-

i-'~1

~ i~

iI

I0

~'°~) i

i

i iiiill

i

100 ~,

i

i illll~

8

i

i

I000

Fig. 11. The relaxation of the magnetization M f o r the input and output magnetic fields at T= 15 IC

the field induced by the shielding currents must decrease. The self-field values needed for the asymmetry explanation are much higher than the penetration field /-/9=0.7 kOe, which experimentally determines the self-field maximum for this temperature. This is clearly seen after comparing the curves for 5 kOe (up) and 2 kOe (down). They are nearly symmetric, thus leading to the wrong conclusion that the self-field exceeds 1.5 kOe. It is worth mentioning that extraction of the I - F curves from the magnetization becomes uncertain at high magnetic fields and temperatures due to the problem of the relaxation equilibrium point, M~,, determination. The data in fig. 11 demonstrate the strong difference between Mr~v and the mean value of the magnetization for input and output of magnetic field. The only possible point for application of this analysis is H = 0 with M~ev=0. Recently, the relaxation over the surface barrier has been considered by Burlachkov [47]. According to his calculations, for the same magnetic field, the magnetization relaxation rate for the flux entry R~ exceeds the Rex value for the exit of vortices by the factor (m/m,~)3/2:~ 1, where m is the magnetization for flux entry and m,, the equilibrium magnetization. This factor may be decreased by the presence of pinning leading to the symmetrization of relaxations. The same happens for long times when rn~meq. All these predicted features are in qualita-

A.A. Zhukovet al. ~ShieldingcurrentsofBi~SrzCalCu2Os+s rive correspondence with the e x p e r i m e n t a l data. According to the theoretical analysis [47 ], the physical reason o f large a s y m m e t r y is the change o f the barrier w i d t h x. F o r the flux entry it increases f r o m zero to xf, whereas for the exit it r e m a i n s constant a n d equal to xf. Summarizing, magnetic properties of a Bi2 +~Sr2 +j,Ca~ + zCu2Ox (x=0.11, y=0.12, z = - 0 . 2 5 ) single crystal, such as the hysteresis width, its d e p e n d e n c e o n the sweep rate o f external magnetic field a n d the m a g n e t i z a t i o n relaxation, were studied. U s i n g the d e p e n d e n c e o f the shielding current on the sweep rate o f magnetic field a n d the relaxation data, the current-voltage characteristics were extracted. The analysis o f the o b t a i n e d results showed the existence o f the two characteristic t e m p e r a t u r e regions with a c u r r e n t - d e p e n d e n t t r a n s i t i o n p o i n t between 15 a n d 20 K. Being d e p e n d e n t on dHe/dt a n d relaxation t i m e b e l o w T*, the m a g n e t i c field dependences o f the shielding current fit the scaling law J,(He, T)/J,(O, T) = f [ H d J . ( O , T) ], with the universal f u n c t i o n f i n d e p e n d e n t o f t e m p e r a t u r e a n d the sweep rate o f m a g n e t i c field. The v o l t a g e - c u r r e n t characteristics are d e s c r i b e d quite well b y the powerlike law E/Ec=(J/Jc)" with n,,,1/T. F o r higher t e m p e r a t u r e s the d e p e n d e n c e s J , ( T ) b e c o m e m u c h weaker. T h e d e v i a t i o n from the Js(H) scaling is observed. T h e v o l t a g e - c u r r e n t characteristics deviate from the power-like d e p e n d e n c e b e c o m i n g steeper. The change o f p i n n i n g m e c h a n i s m , a surface b a r r i e r a n d a K o s t e r l i t z - T h o u l e s s - v o r t e x fluid t r a n s i t i o n are discussed as the possible reasons for these two types o f shielding current behaviour. Acknowledgements T h e authors w o u l d like to express their appreciation for the useful discussions with A. Gurevich. O n e o f the authors ( A A Z ) is grateful to D A A D for financial s u p p o r t during his stay at K F K , where the m e a s u r e m e n t s have been done. P a r t o f this w o r k was s u p p o r t e d b y the R u s s i a n Council on H T S C in the f r a m e w o r k o f Project 90061. References

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