Magnetic field depedennce of pinning mechanisms in Bi2Sr2Ca1Cu2O8+x thin films

PHYSICA ELSEVIER

Physica C 255 (1995) 239-246

Magnetic field dependence of pinning mechanisms in Bi2Sr2CalCU208+ x thin films C. Attanasio

a, C. Coccorese a, V.N. Kushnir b, L. Maritato a,*, S.L. Prischepa a,b, M. Salvato a

a Dipartimento di Fisica, Universit~ degli Studi di Salerno, Baronissi (Sa), 1-84081, Italy b Belorussian University of Informatics and RadioElectronics, P. Brovka str. 6, 220600, Minsk, Belarus

Received 2 June 1995

Abstract We performed investigation of the pinning mechanisms in Bi2Sr2CaCu208+ x (BSCCO) thin films as a function of the temperature, magnetic field and bias current. The specimens were prepared by molecular beam epitaxy deposition technique with a subsequent "ex-situ" annealing in air atmosphere. Transition temperatures Tc exceeded 86 K and critical current densities arc were of the order of 105 A / c m 2 at T = 4.2 K. Analyzing the temperature dependence of the resistivity p ( T ) data we show that they could be well described by an activation process. The absolute value of the activation energy U depends crucially on the elaboration procedure, while the obtained magnetic field dependence U ( H ) does not depend on the selected model. Introducing a pinning strength distribution we were able to describe the U ( H ) dependence taking into account a crossover from an individually pinned vortex regime to a collective behavior. This crossover was also confirmed by the current dependence of U. In fact, below the crossover field H o the curves U ( J ) were well described by a spatial washboard-type variation of the pinning energy, while for H > H o the U ( J ) curves showed a logarithmic behavior.

1. Introduction Large intrinsic anisotropy together with the small coherence lengths and the high values of the critical temperatures lead to the pronounced thermally assisted motion of vortices in high temperature superconductors (HTSC). As a result, the resistive transitions of HTSC broaden in applied magnetic fields and under bias currents [1-3]. Small values of the pinning potential energies U lead to the emergence of a long tail on the resistive transition down to

* Corresponding author. Fax: +39 89 953804; e-mail: [email protected].

small temperatures. In this case the flux creep resistivity can be described in the limit of small imposed stresses (due both to the external magnetic field and to the bias curren0 by [4,5] P = Po exp( - U / k B T ) ,

(1)

where P0 is some coefficient related to the vortex volume, to the average hopping distance of vortices, to the magnetic induction and to the characteristic frequencies with which vortices try to escape from the potential well; k B is the Boltzmann constant. Usually P0 is the order of Pn, the resistivity in the normal state just above the onset of the superconducting transition. Taking into account that U is a function of the temperature T, the bias current I and

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240

C. Attanasio et al. / Physica C 255 (1995) 239-246

the magnetic field H, from Eq. (1) follows that analyzing p(T) data at different values of I or H one can extract information about values of U and its current and magnetic field dependences. This type of information allows the vortex dynamics and the pinning mechanisms in HTSC to be investigated. In particular, the obtained magnetic field dependence U(H) is well described by the law U(H) ~ H -°'5 for BSCCO films of both 2212 and 2223 composition [6,7], while for the less anisotropic YBa2Ca307 (YBCO) superconductor the U ( H ) ~ H - 1 law is usually observed [8,9]. These two dependences for U(H) can be well described by the Tinkham model of flux neighboring shear, in which the expression for U(t) is [10] U(t)

:

U(0)(I

- / 2 ) 2 - n ( 1 -- ta'n/2) ,

(2)

where t = T/T~. The exponent n identifies the temperature scaling behavior of the pinning energy and could be equal to 1, 2, or 3 [10-12]. For the triangular vortex lattice, the experimentally observed law U(H) ~ H -°'5 for BSCCO gives n = 2 [12]. The same U(H) dependence is predicted considering as the mechanism of vortex depinning the plastic deformation of the vortex lattice in an anisotropic superconductor. In this case the energy of plastic deformation is written as [13] UpI(T , H ) = 2Eva 0 = qb~a0 A-2 ~ (Tc -- T ) H -°5,

(3) where ev is the vortex energy per unit length along the CuO 2 planes, a 0 is the intervortex spacing, @0 is the flux quantum and a is magnetic field penetration depth. The model successfully explains the U ( H ) ~ H-0.5 law but predicts a linear temperature dependence for the plastic deformation energy. The linear dependence of U(T) for BSCCO films was observed in Refs. [6,7,14], while in Ref. [15] a good agreement with Eq. (2) was observed for n = 1 at B = 6 T both for BSCCO and YBCO films. On the other hand it is known that the shape of the pinning potential and the pinning strength distribution influence the U(H) curve. As was pointed out by Inui et al. [16], a crossover from individually pinned vortices to a regime of elastic vortex interaction is expected in BSCCO at fields of the order of 1 T. At small magnetic fields, the intervortex forces

are negligibly small and one should be concerned about the motion of individual vortices in the field of unperturbed pinning centers. For an exponential type of pinning energy distribution, f ( U ) ~ e x p ( - ( U -Uo)/O-), U(H) is then given by [16]

U( H ) = Uo + ~r ln( H o / H ) ,

(4)

where U0 is some "average" activation energy corresponding to H o, the crossover field between the single vortex and the collective behavior. For large magnetic fields, one has to take into account the motion of the vortex lattice in the field of the pinning centers, which can deform the vortex lattice. The role of the elastic forces is then important and cause the vortices to return to their equilibrium positions with a consequent decreasing of the pinning energy. Using a harmonieal one-dimensional model, the pinning potential is expressed as

U ( x ) = ( 1 / 2 ) U o cos K ( x - x o )

+ 3,x 2,

(5)

where x is the position of the pinning center, K = 27r/ap and y = de~oH/(32xr21~okBh 2) is the elasticity modulus of the vortex lattice [16]; here ap is the spatial period of the potential and d c is the length of deformation of the flux line along the c-direction. In the limit y << U0 K 2 the amplitude of the potential barrier is [16]

U( H ) = Uo - y('rr/K) 2.

(6)

So Eqs. (4) and (6) describe the different behavior of

the U(H) curve: a logarithmic decrease for H < H o and a linear decrease for H > H 0. In this work we show that, in order to clarify the pinning mechanisms, it is necessary to investigate not only the U(T) and U(H) dependences, but also the U(J) dependence at different values of the magnetic field. Such a complex approach allows us to distinguish two different pinning mechanisms at low (isolated vortices in a washboard type potential in the presence of a pinning strength distribution) and high magnetic fields (interaction of vortices).

2. Film properties and experimental procedure The results of this article have been obtained on highly oriented Bi2Sr2CaCu208+ x (BSCCO) films on MgO(100) snbstrates. Films have been prepared

C. Attanasio et al. / Physica C 255 (1995) 239-246 2.5

iii

)lJl,lx~-Jll

,llll~,,

Jl(ll,ltllllkl',l~t

Jl),ll

2.0

u

1.0

D

u

0.5

o u n

O,O

i,iil~t,I

.......

50

iiI))111111~11111)1111[111111)1

100

150

200

250

a'(~) Fig. 1. The R(T) dependence of the MBE141 unpattemed thin film.

by the molecular beam epitaxy (MBE) deposition technique [17]. Four elements (Bi, Sr, Ca, Cu) were evaporated by four different shutter controlled sources: bismuth and calcium were evaporated by two Knudsen cells while strontium and copper were evaporated by two 12 keV electron beam guns. The vacuum during the deposition was not higher than 10 - 7 T o r r , the average deposition rate was 0.7-0.8 A / s and the final film thickness d, also checked by an optical interferometer, was about 0.2-0.3 p.m. The molybdenum substrate holder was not specially heated and its temperature did not exceed 90°C during the deposition process. All the obtained samples were annealed in air atmosphere at temperatures 870-880°C during 20-30 min. We reproducibly obtain high-quality films with T ~ ( p = 0 ) _ > 8 5 K and A T < 6 K, where AT = T ( 0 . 9 p n ) - T(0.1pn). The R(T) dependence for the film MBE141 is shown in Fig. 1. The results of the resistive measurements (T~) were confirmed by AC magnetic susceptibility measurements. The samples were patterned in microbridge configuration by the usual photolithography. The ob-

241

tained critical current density values Jc, using a voltage criterion V = 0.1 IzV ( E = 2 × 10 -3 V / m ) , were about 105 A / c m 2 at T = 4.2 K. These slightly low values of Jc could be due to the "ex-situ" annealing procedure. X-ray analyses show the presence of the 2212 phase with the c-axis perpendicular to the MgO(100) substrate surface [17]. Transport properties were measured with a DC current source generator. All the temperature measurements were taken using a sample holder with a copper block in which the sample was held in close thermal contact with a Si doped thermometer suitably designed for magnetic measurements. A superconducting solenoid with a high uniformity of the field in the zone where the samples were situated was used for creating the external magnetic field. The magnetic field was oriented perpendicular to the surface substrate (parallel to the c-axis of the film). The experimental set up allowed measurements in the temperature range 4.2-100 K with the externally applied magnetic field up to 3 T. The characteristics of two MBE BSCCO samples are summarized in Table 1.

3. Results and discussion

Figs. 2(a) and 2(b) show the resistivity p versus temperature T data of the B141 and B212 samples plotted in Arrhenius fashion for different values of the perpendicular applied magnetic field. We assume the slope of the In p versus T curves to be the value of the effective pinning potential U*(T)=-k

d(ln(p)) B d(T-')

U(T)-T

dU(T) d~'

where U is the real pinning potential. To analyze the data of Fig. 2, it is necessary to take into account the temperature dependence of the pinning potential which at temperatures close to T~ is very pro-

Table 1 Characteristics of two MBE prepared BSCCO patterned samples Sample

Thickness d (lxm)

Width w ()~m)

Length 1 (p,m)

Tc (R = 0) (K)

Jc (4.2 K) ( A / c m 2)

R(300 K)/R(100 K)

B141 B212

0.30 0.28

20 25

50 30

88.48 86.08

9.4 × 104 1.2 × 105

2,50 2.43

242

C. Attanasio et a l . / Physica C 255 (1995) 239-246 2000

nounced. Substituting Eq. (2) in the expression for U * , we get * t

[

2t2

i

,

,

,

,

,

,

,

,

i

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]

2t4

U ( ,n)=U(t)tl+(2-n)l_-]--~+nlT-~]

1500

DDDDD n = , 3 n=l

=-- U( t) fl( t, n).

0,)00,'3 n=2

(7)

This means that the slope of the Arrhenius plot gives the value of the effective pinning potential U * (t, n)

~.~ IOOO

50o

1000

i,

,1111,

, , , , r l l ~ , l , , , l l , , i , i i t , , l l

" ~ '

(a'~

0.7 k0e

.....

?-

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~.'%, "l~'%."~Ikk"qll~.

5A ~AAAA 7.3 ~ o ~ o 1 1.7

~'~"k.%"~"~

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/~oH(T)

~6.8

Fig. 3. The U(H) dependences for different values of the exponent n for the sample B212. The U values are calculated in the limit T ~ 0. The solid lines represent the best power fit U(H) ~ H-'* (oe = 0.43). The a value does not depend on the choice of

. . . . .

10

n.

aaaa

*.

°° F,,o

1 i1~

i i i i i I i i t t l l l l l l

0.8

A

illl

1.3

¢ %* ii

.

,11

1.8

~tr

,Ill

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1 0 0 / T (K - 1 )

ooooo

(b)

lOOO ~

.....

k

* * * * *

..... tO0

"~

0.7 kOe

zo

..... 5.8 0oo*0 14.6 21.9 29.2

I

10

o

0.8

ii

iiiIi

a Itrll}l

1.3

~l

la

I i ,i

1.8

0 ~ ,%ll~llIT

**

2.3

f IPl

,I

8.8

100/T (K -I) Fig. 2. Arrhenius plot of p(T) of the two BSCCO patterned films, B141 (a) and B212 (b) for different values of the perpendicular applied magnetic field.

enhanced by /3(t, n) with respect to the real value

u(t). All the data presented in Fig. 2 have been measured with a bias current density J = 142 A / c m 2. The U(H) dependence obtained according to the Tinkham approach, for the sample B212, is presented in Fig. 3 for different values of n. The U values were calculated in the limit T-+ 0. The character of the U(H) dependences does not depend upon the choice of n and the exponent ot in the law U(H) ~ H -~ is almost equal to 0.5 independently of the value of n ( a = 0.45 for B141 and a = 0.43 for B212). In Fig. 4 we show the Upl(H) dependence. The exponent a in the dependence U(H) ~ H -~ for the two cases and the two samples is presented in Table 2. We point out that, independently of the absolute values of the pinning energy at T = 0 and with the assumed pinning mechanism, the U(H) dependence in BSCCO seems to be well described by the law U(H) ~ H -°'5. In order to go deeper into the problem we investigated the U(J) dependences at different magnetic fields. We measured the U(J) dependence for the sample B212 both in the case of weak ( / , o H = 0.29

C. Attanasioet al./ Physica C 255 (1995)239-246 4 0 0 0

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= 0.29 T

:::::

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.....

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T(K) 300

T) and large magnetic fields ( / z 0 H = 1.83 T). From Eq. ( i ) follows that

~ l l l l l l l l l l l l l

#oH

,*111111:

~ l l t , l , l l l l l l ~ , l l l l l l

I111111111111

t~ ~o %

1.83 T

(8)

Some results o f the U(T) dependences at different values of the bias current for two values of magnetic field, as obtained from p(T) curves according to Eq. (8), are presented in Figs. 5(a) and 5(b). The U(J) dependences for the same sample are presented in Figs. 6(a) and 6(b). The absolute U values were calculated in the Tinkham (squares) and in the plastic deformation models (triangles) in the limit T = 0. The solid line in Fig. 6(a) ( / z 0 H = 0.29 T) corresponds to the best fit obtained using the equation

U ( j ) = U ( O ) [ ( 1 - - j 2 ) l / 2 - - j cOS-1

"'Xk \~A

Fig. 4. The U(H) dependence at T = 0 as obtained from the plastic deformation model, for the sample B212.

p ( T , H, J ) ] .

\

i

,onCT)

U(T, H , J ) = kBT[ln P o - I n

2

j]

~oo

100

0

%:.:o}~

(b)

~k

~

..... 14 A/cm2 ..... 148 ~,~ 426 ooo0o 1850

I I IIII

IIII

20

I I I I p l I I

I I I I I I I I I I I I

40

o

III

60

I t III

~

II111

80

I I1~1~

100

T(K)

= U(0)(1 _j),.5,

(9)

which follows from the assumption of a washboard pinning potential spatial shape [18-20]; j in Eq. (9) is equal to J/Jco, where Jco is the critical current Table 2 The exponent a in the dependence U ~ H -a for two BSCCO samples, as obtained from different experimental data elaboration procedures Sample upl ~T c - T U=U*/~(t, n = l ) B 141 B212

0.41 5-0.03 0.50 5-0.03

0.45 + 0.03 0.43 + 0.03

Fig. 5. The U(T) dependences as obtained from the p(T) experimental data according to Eq. (8) for different values of the bias current at different magnetic fields for the sample B212: (a) /zoH = 0.29 T and (b) /xoH = 1.83 T. density in the limit of U = 0. As was pointed out by W e l c h [21] and also shown in Ref. [22], the law U(j) ~ (1 _ j ) l . 5 is valid for any smooth, periodic pinning potential form in the limit j ~ 1, if the quantity d 3 U / d x 3 is determined. The U(J) dependence given by E q . (9) was already observed for B S C C O thin films in the case of weak magnetic

244

C. Attanasio et al. / Physica C 255 (1995) 239-246

fields ( H ~ Hc]) [23,24]. The fit parameters for the curve in Fig. 6(a) are the following: Jco(0 K, 0.29 T) = 6 × 10 4 A / c m 2, U(0 K, 0.29 T) = 660 K in the Tinkham approach; Jc0(0 K, 0.29 T ) = 6 × 104 A / c m 2, U(0 K, 0.29 T ) = 1350 K in the plastic deformation model. On the other hand the data in Fig. 6(b) ( / x o H = 1.83 T) are well described by using a a logarithmic relation for U(J) [3,15,25-27]. As was pointed out by Beasley et al. [18] from the U(x) dependence it is possible to derive the U(J) curve. They have done it for a simple washboard type potential. If we reverse the Beasley approach

2000

.........

j .........

~ .........

1,500 I

1000

[3 500

1.0 O

I

0

P

I

I

I

I

I

I

I

I

f

I

i

I

I

I

1

I

I

I

2

I

I

I

I

¢

I

J

i

i I

5

UoH(T)

0.8

Fig. 7. The U(H) dependences as obtained in Tinkham model with n = 1. Triangles correspond to the sample B141, squares to the sample B212. The solid lines represent the best fits as obtained from Eq. (4) (low field part) and Eq. (6) (high field part). The crossover field are p,0H0=0.55 T for the sample B141 and /~oHo = 0.70 T for the sample B212.

0.6

o.4 0.:~

0.0

~

0.0

I p I I I f i I , I I I I I I I ~ I ~

0.2

0.4

0.6

0.8

1.0

J 1.0

, ,,,,,',

i,,,,,,,

,,i,,,,,,,

i ,

(b) 0.9

v 0.8

0.7

0.6 0

500

1000

500

J(A/em 2) Fig. 5. The U(J) dependences, for the sample B212, for/z0H = 0.29 T (a) and /Loll = 1.83 T (b). The solid lines correspond to the Eq. (9) (a) and to the law U(J)~-In(J) law (b). Squares corrcspond to the Tinkham model with n = I, triangles to the plastic deformation model.

and derive the spatial dependence U(x) from the U(J) curves, the result would be an " a v e r a g e " of the actually random flux line energy. Zeldov et al. [3,15] for an experimentally obtained logarithmic U(J) dependence derived the logarithmic U(x) function which was then modified by Welch [21]. Such analyses do not consider the effects of a distribution of the activation energies [28]. Assuming two different kinds of U(H) dependences in the case of small and large magnetic fields, we analyzed the U(H) curves in the framework of the Inui et al. model [16]. In Fig. 7 we show the experimental data of the U(H) dependence for B 141 and B212 samples, obtained from the Tinkham model with n = 1, together with the best fits, calculated according to Eq. (4) (low field part, exponential distribution) and Eq. (6) (high field part). We again point out that, for our data, the U(H) dependence does not depend on the choice of the exponent n. The crossover field /z o H 0 is of the order of 0.7 T, and the other fit parameters are: - for B 1 4 1 : y ( ~ r / K ) 2 = 7 5 K / T , U o = 4 0 0 K, tr = 230 K; - for B212: y(zr/K) 2= 80 K / T , U 0 = 530 K, o-= 370 K.

c. Attanasioet al./ PhysicaC 255 (1995)239-246 From the obtained ~/ values follows the typical volume dca ~ = 35 × 10 3 nm 3. We cannot determine accurately the value of d c but, with the assumption do = ap, we get d c --- 33 nm. As is shown in Fig. 7, the experimental data for the U(H) dependence are well described by the model of Inui, Littlewood and Coppersmith. In our case the crossover occurs at /x0H 0 = 0.7 T, which corresponds to a 0 = 0.06 txm. This value is approximately 3 times smaller than A~b(0) = 0.21 txm in BSCCO [29] and the collective pinning seems to be valid in this range of magnetic fields (both below and above H 0) [30]. On the other hand, the single vortex regime in the theory of collective pinning is valid for fields H < Hsb, with Hsb = 5(Jco/J~L)Hc2, where J~L is the GinzburgLandau depairing current [31,32]. Taking into account that Jco/JGL=(~ab/d~) 2, for ~ab=2.5 nm and Hc2 = 20-40 T [33] we obtain H~b = 0.6-1.1 T, which is in reasonable agreement with the crossover field H 0 in spite of the large uncertainty in the values of d~ and Hc2. The crossover in the U(H) dependence (i.e. the crossover in the pinning mechanism) is confirmed by the different U ( J ) behavior at fields less than and above H 0. The open question, which still remains, is whether the logarithmic U ( J ) law is determined by the pinning potential with a long range tail or by disorder [30]. More work is needed to investigate the influence of the pinning strength distribution on the elastic properties of the vortex lattice in different quality samples.

245

are well explained by Eq. (9), while at 1.83 T the U(J) dependences is logarithmic, indicating the possibility of a change of the pinning mechanisms via the magnetic field. Moreover, a more precise analysis shows that the curve U(H) can be divided into two parts: low field (below some crossover field H 0) and high field (above H 0) part. For our samples we found/x 0 H 0 --- 0,7 T. For H < H 0 the pinning mechanisms can be described as pinning of individual vortices in the presence of a pinning strength distribution. The spatial shape of the pinning potential corresponds to a smooth periodic washboard-type, which is in agreement with the U(J) experimental data. Vortices occupy the deepest potential wells. Increasing the density of vortices (that is the external magnetic field H ) we create the situation in which the density of deep pinning centers is smaller than that of vortices and they start to occupy the "norm a l " or not extremely deep pinning centers. It is not clear at present the precise influence of different kinds of activation energies distribution on the U(H) dependences at H > H 0, but the fact that Eq. (6), obtained in the suggestion of washboard potential, describes well the U(H) data indicates that the experimentally observed logarithmic U(J) dependences in the region H > H 0 might be related to a distribution of activation energies. Further investigation related to the influence of different type of pinning strength distributions on the pinning mechanisms in different quality BSCCO samples is in progress.

4. Conclusions Acknowledgements In summary, we have investigated the pinning mechanisms in BSCCO MBE prepared thin films. We find that the understanding of the processes crucially depends on the elaboration procedure of the p(T) experimental data. We conclude that the U(T) dependence is not informative and cannot be used to draw a definite conclusion about the pinning mechanisms. On the other hand the U(H) dependence is more useful. In the range 0.1-3 T the experimental data are well described by the law U ~ H -°5, which seems to be in good agreement with the model of plastic deformation. The U(J) data, obtained on the same sample at 0.29 T and 1.83 T, reveal different types of U(J) dependences. At 0.29 T the U(J) data

S.L.P. was partially supported by INTAS project No94-1783. V.N.K. and S.L.P. acknowledge the support of the Belarus Basic Research Foundation under the grant No. F14-258. The technical assistance during measurements of L. Falco is gratefully acknowledged,

References [1] K.A. Miiller, M. Takashige and J.G. Bednorz, Phys. Rev. Lett. 58 (1987) 1143. [2] T.T.M. Palstra, B. Batlogg, L.F. Schneemeyer and J.V. Waszczak, Phys. Rev. Lett. 61 (1988) 1662.

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