Influence of the magnetic field sweep rate on flux creep in highly textured thin film of YBa2Cu3O7−δ

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Journal of

ALLOYS

AND CONeOONDS ELSEVIER

Journal of Alloys and Compounds 251 (1997) 150-155

Influence of the magnetic field sweep rate on flux creep in highly textured thin film of YBa 2Cu307_ 8 K. Frikach ~'*, S. Senoussi", A. Taoufik b, M. Boudissa" "Lahorteoire de Physique des Solides (assot'i~;au CNRS. URA 0002). Universit~ Paris Sud. 91405 Orsay Cedex. Frant'e "lbnou-Zohr University. Physics department. Agadir. Moroco

Abstract We investigated the influence of the field sweep rate on the magnetic relaxation and the critical current density of a highly textured thin films of YBa,Cu~OT_ ~ at different temperatures and fields parallel to the c-axis. We find that the actual M versus In t relationship can be deduced experimentally by a translbrmation of the form t-->t + ~'+ ~',, in which r is a transient time proportional to R×(dHI&)-~. r,, the time constant of the magnetometer (~0.25 s) and R the effective radius of the superconducting tilm averaged along the a - b planes. As a result, all the relaxation curves collapse into a single.master one that is independent of the experimental conditions. The parameter r obey:, approximately the relationship r x d H I d t ~ 2 0 e in the range T<30 K and depends on the film thickness. The resulting J versus In t relationship deviates from linearity fiw all the explored temperatures and fields. Key.ords' Flux creep; Thin lihn

!. |mreMuc|ion It is well known thut the critical current don,~ity of hi[~ll tempcratu~ ~uperconductors (HTSC) exhibits very rapid relaxation as compared to conventional materials. It turn,, out that this large ilux creep cannot be accounted tbr correctly in the fi'amework of the conventional Kim= Anderson [2,31 mMel and other generalizations of this n~nlel 14,51. As a consequence, more general collective pinning and collective creep theories have recently been elaborated i 1,6,71 and tnany important properties of HTSC materials have been explained successfully within the framework of such models. Nevertheless, there is still a wide region of the To=Hplane where flux pinning and flux creep effects arc not easy to describe using the collective description. For instance, this is the ca~ for the so-called fishdail hysteresis cycle, both near the central peak [8I and at fields higher than the second maximum of this cycle, This is why more ex~rimental work is needed to define the domain of validity of these models. Very often, the comparison between the experimental data and the theoretical predictions is made difficult by the fact that some startling hypothesis of the theo~tical models can not be fulfilled experimentally. This is especially true for the origin of time (entering into the *C~s~ndinLZ author. rN25,8388t97t$17.~ © 1997 Elsevier Science S.A. All rights reserved Pll S0925-8388{ 90102790.9

theoretical equations), the role of which is very crucial dne to the logarithmic nature of magnetic relaxation. In addition, there are always some inherent uncertainties on the "experimental" origin el' lhll¢ connected with tile experimental procedure. According to the weak collective phmitlg theory (WCP). the J(t) relationship would be of the form J

=

J~ll +

(kTIU,) In((t

+ t,,)h,,)l

~'"

(I)

where U,. is an energy scale, # a critical exponent (that depends on the pinning regime) and .I, the critical current density existing in the critical state (i.e.. before thermal and quantum diffusion of vortices has had time to occur). The parameter t,, can be regarded as the macroscopic life time of this critical state (t.= i0 ~ to 10 ~u s typically) [I.9-13]. What is then important to note is that formula I assumes implicitly that the experiment starts tYom the critical state, the life time of which is of the order of t,,. [Infortunately, because of the smallness o1' t,. it is practically imlmssible to have acces.' - "s experimentally to this state. A natural question is then: how to deline the origin of time in real experiments? Clearly, because of the logarithmic term in Eq. (I), the answer to this question is not trivial. This problem has actually been the object of several studies in the last few years [I,9-16], particularly by Gurevich et al. [91 who calculated the influence of both

K. Fri~ach et ai. I Journal of Alloys ¢,nd Compounds 251 (1997) 150-!.$5

151

d H i d t and R on the apparent J versus In t law in various

theoretical models. The aim of this paper is to help clarify this point by investigating very carefully the various transient effects affecting the experimental J(ln(t)) relationship in a thin film sample. For the sake of simplicity we classify these experimental transient times into two main categories: The first one is related to the time constants of the various instruments expressed into a single one denoted I"m=0.25 s in the present VSM. The second and perhaps more fundamental transient time (hereafter referred to as r) affecting Eq. (!) is connected with the field sweep rate (v~=dH/dt) and the sample characteristics through both its microstructure and macroscopic dimensions (including the demagnetizing factor). To help clarify the physical origin of r, we briefly present a very simple experimental argument which makes use of the fields Hp.m..,~ and Hp of complete flux penetration within the material in the critical state and in the experimentally accessible (or relaxed) state, respectively. In addition, we shall make the usual assumption that J is independent of H (Bean model). The penetration fields introduced above arc related to the radius of the sample by the approximate formulas below II71: Hp.,,,,, = L R ( I - N);

H,, = J R ( I - N )

(2)

Here, J is the experimentally accessible critical current while J,, refers to the critical state. Let us now consider the formal experiment schematized in Fig. I and conceived to give the same hysteresis cycle as the actual one we are concerned will): ( I ) First, we consider the "real" lield profile across the sample at a given instant t, produced by the applied lield H , ( t ) ~ ( d H I d t ) t . This profile is represented by tbe heavy line labelled t in the ligure. (2) Second, let us imagine a formal experiment in which the field can be suddenly increased from the value H.(t) to a new value H,(t)= H,(t)+ (H,..,,,,- Hp). in a time interval less than or equal to t.. The corresponding field profile would be given by the dashed curves labelled l + t.. Since in this lbrmal experiment the variation of H was faster than t,, the associated induced field profile H(r) (dashed lines) would represent the critical state. (3) Third, to let this critical current evolve into the experimental one produced by the applied field, we must wait during some transient time ~" defined by: ( d H I d t ) ( t + t, + ¢) = H,(t) + Hp,,.,,~ - tip

(3)

Combining Eqs. (2) and (3) above and neglecting t,, leads to the relationship: r = a(Hp...,~ - H p ) / d H I d t = a ( J c - J)R( I - N ) l d H I d t

(4)

Hz(t)

tl+ x+to

. . -._.

tl+to

Hp,max-Hp .I.

tl

Fig. I. Qualitative determination of the transition time ~" separating the critical state repre~nted by the dashed field profile and the relaxed experimentally accessible states denoted by the solid lines. Here r is the life time of the critical state while H,,...... and H o denote the fields of complete flux penetration in the critical and the relaxed states, respectively. See text for other details.

It is now interesting to recall that in the asual KimAnderson model [2,3] one has kT L - J = L T T In(t/,,,)

(5)

The combination of Eqs. (4) and (5) leads to the following expression:

k?"

J V

(6) It is to be emphasized that, apart from a logarithmic factor (which is ill defined anyway) omitted in Eq. (6) above, this equation is the same as the one obtained theoretically and independently by Gurevich et al. [91 for N~0, and in the case of Kim-Anderson model. Clearly, Eq. (6) allows us to remove most of the ambiguities in the time origin of the logarithmic relaxation, at least in the approximation of Kim-Anderson model. More specifically, it defines the time interval (for given d H / d t and R) that can not be explored by any macroscopic measurements. Then, for comparison with experiment it is useful to replace Eq. (5) by the tbllowing one: J ( t ) = Jc

I-~ln(t+t

o + ¢)lt o

(7)

Note that we have neglected the effective time constant of the magnetometer, ¢,,,. Note also that to is in general much smaller than the other time scales of the experiment and can be omitted.

g. Frikaci~ el al. I Jourmd qt" Alloys mul Compounds 251 t 1997) 150-155

152

2. Experimental details and discussion

Arbitrary unit !

The YBa~Cu.~OT_~ sample investigated here was made by Laser ablation in a SrTiO~ substrate (Siemens) with the dimensions ,rx2 mm ~×0.45 p,m. The transition temperature as deduced from susceptibility measurements in 4 0 e , was about 91 K while its width was of the order of 0.3 K. The experimental procedure used here is illustrated in Fig. 2 which was recorded as follows: after the sample had been cooled in zero field down to the measurement temperature (30 K in this example), the first hysteresis cycle was recorded at the fastest sweep rate dHIdt = v, = 1 kOe s- ~ in field H,,,,, = 35 kOe. The field is then increased to H a = 10 kOe (in this example). This cycling procedure allows the preparing of the sample into a well-defined reference state that is completely penetrated by the field. The first relaxation experiment was subsequently recorded during 2400 s. After that, the hysteresis cycle was retraced again at the same standard sweep rate (v,). following the sequence H,--cHIn, ~--->-H,.,,~--cH,, with H~ < H , (see figure). Then. dHIdt was reduced automatically to a new value v,=v,
unit~ arbitrair¢)

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~

I0

~

L _ _

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I

H(kG)

Fig, 2, An example illustrating the experimental prt~edure Ibllowed here, To ~eobutld up the ~ta0dard ~tate of the sample heft}re each relaxation ~x~rin~nt, the cycle was recorded at~mt twenty times ~parated by al~mt 90 am each, Tire field sweep rate was the same everywhere W, ~- 10' G s ~) except in the Iteld interval (HI, H2) whe~ dHldt was varied hetween V~ {~ 100 G s '} and ~ (see on~t and text) at H~H~,The relaxation experiment is performed at H v It is to be noted that all of the 20 hysteresis cycles coincide with a very high precision, except in the ~gion H, ~ H, where dHIdt varies tram cycle to cycle, This shows that the ex~ri~ntal data arc perfectly ~:p~ucible during the 16 hours ~lmrating the first and the last M(t) measurement.

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t(s) Fig. 3. This example shows how we determine the experimental origin of time (see dashed vertical line) from the registered H(In t) and M(In t) functions, in this example, the collection of the data starts about i.5 ,~conds before the command stop the field variation is ,,cent by the Turbo.Pascal program to the current power supply. Note that the experimental origin of time is obscured not only by the various time constants described in the text but also by the delays in the program itself.

Indeed. the influence of the noise from the current power supply on the measured magnetization ceases to be negligible when its amplitude (AH) becomes comparable to the penetration field H o = J R ( i - N ) . The latter can be very small for thin films. For instance, in the present case Ht, was as low as 10 Oe at T~70 K and H ~ 2 0 kG. This shows that the condition AH depends considerably on dHIdt and exhibits the following properties as a function of this variable: ( I ) For the lowest lield sweep rates ( <400 Oels at 18 K and < ~ ~ s ~' at 30 K. respectively) the variation of M with In t exhibits a positive curvature at relatively short time scales then becomes independent of dHIdt and quite linear at the largest time scales. (2) On the contrary, for the curves associated with the fastest sweep rate dHIdt= I kOe s ~ . we observe a negative curvature with no plateau, except during a short transient period of about 0.2 s at T = 30 K. However, this negative curvature has no physical meaning as the corresponding time interval is smaller than the time constant of the VSM. We arc now in a position to try to deduce the actual M(In t) relationship from the experimental data. For this purpose we simply re-plot the ensemble of the curves of Fig. 4 and Fig. 5 after replacing the "experimental time t" defined above by the new variable t+¢. Here, ¢ is determined independently for each curve by the condition that all the M(In t) isotherms must collapse into a single one after performing the above transformation. Obviously, the resulting master curve should correspond to the true M(ln t) relationship. The master curves determined in this

K. Frikach et ai. I Journal of Alloys and Compounds 251 (1997) 150-155

153

-0.4

-0.5

150. /

T=18K

H=12kG

T=18K

-0.6

kG/s

•

I0"~-10r' l0t' 10' 10z l(Pt(s)

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•

~''"'J

"

" ' ' " J

°

° °'"*J

. . . .

|l~

•

"'"

10-2 10-1 100 10 ] lo2 ]03

Fig. 4, This ligure illustrates the inlluence of the lield sweep rate on the apparent M versus In t relationship at T= 18 K and H = 12 kG.

Fig. 6. The master cmwe associated with Fig. 4 determined by the scaling procedure explained in the text.

way are displayed in Fig. 6 and Fig. 7. In fact, for the present sample we found that these master curves are practically indistinguishable from the initial ones obtained at dHIdt = I kOe s ~ (except for t<0.2 s).

Fig. 8 gives the experimental correlation time ¢ (deduced following the procedure outlined above for T=

~'I

T=30K H=I2kG

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-0.30

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[IIAIIII&|~&

Fig, 5. The same as Fig. 4 except that T= 30 K.

AI~LI~

Fig. 7. The master curve associated with Fig. 5 determined by the scaling procedure explained in the text.

K. Frikach ,,I ,d. I J,mrn,d ,Jl" AIh~ys ,rod Coml,tmn,Lv 251 (1007) 150-155

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apply close to the critical state when J is not very small compared to J~.: a situation more easily approached at low temperatures. However, it is not clear whether this condition holds at high temperature. In fact the situation is quite complicated because S~ decreases slightly with T and can counterbalance partially the effect of J in the RHS of Eq. (8).

"

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3. Conclusion

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(#oe) FiB. 8. The experimentalInUl~ienllime T as a t'UllClionof (dHIdt) K oblaincd from Ih¢ preceding tigurcs,

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In conclusion, we have shown that the first stage of the measured flux creep is generally dominated by two kinds of transient effects: One of these is related to the electronics of the various apparatus composing the magnetometer as well as the details of the measurement technique itself. The present magnetometer together with the experimental procedure outlined in Fig. 2 allowed us to reduce this time window to about O. I-0.2s. The other one (-r) depends on the microstructure of the sample as well as its macroscopic size and the field sweep rate. However, after the correcting of these transient times it was possible to obtain a universal behavior which reflects only the microscopic properties of the material. Finally, it is interesting to remark that for the present sample, 1"depends primarily on the film thickness through H~,.

18 K) as a function of {dHIdt)=, it is now el' interest to compare these curves with Eq, (4) (valid fiw the Kim~ Anderson model) which we rewrite in the t'orm AeknowledRments

kT ~ldH/dt) ~ J, ~ R ( I := N) ~ ,IS, R( I = N)

(8)

In Eq. (X), we have made use of the t'acl thai in the approximatkln ot' Eq. (~). the t'aclor J,(k*I')I(U~ ) is equal to JS, wher~ 5 , ~ = J t(dJIdln l ) o ~ - M , ~ ° ( d M , , I d l n t), is the "inilial" relaxation rate calculated at short tirne scale t < I s, For the ~,,akeof clarity, we recall that J refers to the relaxed current deduced from the irreversible magnetization through the Bean m~el. We can add. that from relaxation data we tbund strong deviation from the linear logarithmic relaxation so that S, is a filctor of 2 to 5 higher than S measured at large time scales such that t > I ~ s, Therefore. in this approximation one has ~'×(dHIdt)= JS, R ( I ~ N ) and fiw thin films, the factor I - N = e l R . where e is the thickness, The same measurements carried out in monocrystal and granular samples [181 show that ~" is higher than the actual one while the current density is lower. This result proves that the transient time ~- depends strongly on the field of complete flux ~nelration. In view of the various approximations involved in the above calculations, we consider this result as quite satisfying and suggest that Eq, iS) is approximately valid at sufficiently low temperature. Such a result is also roughly consistent with the fact that the Kim-Anderson model is expected to

The authors would like, to thank Dr, M,F, Mosbah for vahlable discus,~ion~,

References

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155

[16] L. Pust, Supercond. Sci. Technol., 5 (1992) 497. [17] S. Senoussi, S. Hammond and F. Mosbah, in A. Narlikar (ed.), Studies of HTS, 14, Nova Sciences Publishers. Commack, New York, 1995, p. 107. [18] K. Frikach, S. Senoussi, et al., to be published in J. Appl. Phys.