Critical current density and ac harmonic voltage generation in YB a 2 C u 3 O 7−δ thin films by the screening technique
CCritical current density and ac harmonic voltage generation in YBa Cu O − δ thinfilms by the screening technique. Israel O. P´erez-L´opez, Fidel Gamboa, V´ıctor Sosa
Applied Physics Deparment, Cinvestav M´erida, M´exico, Km 6 Ant., Carretera a Progreso, A.P. 73, C.P. 97310
Abstract
The temperature and field dependence of harmonics in voltage V n = V (cid:48) n − iV (cid:48)(cid:48) n using the screening technique havebeen measured for YBa Cu O − δ superconducting thin films. Using the Sun model we obtained the curves for thetemperature-dependent critical current density J c ( T ). In addition, we applied the criterion proposed by Acosta et al. tocompute J c ( T ). Also, we made used of the empirical law J c ∝ (1 − T /T c ) n as an input in our calculations to reproduceexperimental harmonic generation up to the fifth harmonic. We found that most models fit well the fundamental voltagebut higher harmonics are poorly reproduced. Such behavior suggests the idea that higher harmonics contain informationconcerning complex processes like flux creep or thermally assisted flux flow. Key words:
Critical current; Screening technique; flux pinning; thin films
PACS:
1. Introduction
In this contribution we shall determine the tempera-ture dependence of the critical current density J c ( T ) forYBa Cu O − δ thin films by measuring the harmonics ofvoltage V n = V (cid:48) n − iV (cid:48)(cid:48) n ( n = 1 , , ... ) with the screeningtechnique [1]. The calculation is based on the Sun model[2] and the definition of the full penetration field H p fromthe critical-state model [3] . Also an extension to higherharmonics of the this model shall be worked out and com-pared with experimental curves.
2. The Sun Model and Experimental
We have determined the harmonics of voltage V n basedon the theoretical approach developed by Sun et al. [2].He proposed a model to compute the ac susceptibility re-sponse of thin-film superconductors under the influence ofa transversal ac magnetic field H a = H ac sin( ωt ). In re-sponse to H a shielding currents J c induce a diamagneticmoment which Sun et al. found to be m ± ( H a ) = ± H p a (cid:20) exp (cid:18) − H ac ± H a H p (cid:19) − (cid:18)
12 + η (cid:19)(cid:21) (1)where η = 1 / H ac /H p ) and a is the radius of thefilm. The full penetration field stems from the Beanresult, namely H p = J c d/
3, where d is the film thick-ness. Actually the quantity to be measured is the volt- Email address: [email protected] (Israel O.P´erez-L´opez) age V ( t ) induced in the pick-up coil, which is conven-tionally measured with a lock-in amplifier and is pro-portional to dm/dt . The voltage can be expanded as aFourier series: V ( t ) = (cid:80) ∞ n =1 [ V (cid:48) n cos( nωt ) + V (cid:48)(cid:48) n sin( nωt )],where V (cid:48) n = π (cid:82) π V ( t ) cos( nωt ) d ( ωt ) ∝ H ac ωχ (cid:48) n , and V (cid:48)(cid:48) n = π (cid:82) π V ( t ) sin( nωt ) d ( ωt ) ∝ H ac ωχ (cid:48)(cid:48) n stands for thereal and imaginary components of voltage, respectively, χ n is the magnetic susceptibility. Here we shall deal with har-monics with n = 3 ,
5. The fundamental harmonic can befound elsewhere [2]. The solutions for the real part read: V (cid:48) = − m e − h h (cid:20) I ( h ) − hI ( h ) (cid:21) , (2) V (cid:48) = − m e − h h (cid:20) I ( h ) − I ( h ) + h I ( h ) (cid:21) , where m = 2 πJ c da / h = H a /H p is the reducedfield, the functions I ν ( h ) (with ν = 1 , ,
3) are the modifiedBessel functions. The imaginary components are V (cid:48)(cid:48) = f ( h )(3 S − S ) ,V (cid:48)(cid:48) = f ( h )(5 S − S + 16 S ) , (3)where f ( h ) = − m he − h /π and the functions S n are givenby S = − h (cid:26) h cosh( h ) − sinh( h ) (cid:27) , (4) S = − h (cid:26) h cosh( h ) − (cid:104) S + sinh( h ) (cid:105)(cid:27) ,S = − h (cid:26) h cosh( h ) − h ) − S (cid:27) . Preprint submitted to Physica C October 24, 2018 a r X i v : . [ c ond - m a t . s up r- c on ] D ec igure 1: Temperature-dependence of real and imaginary part of thethird harmonic. Inset shows theoretical curves. To determine the critical current density J c ( T ) we havetaken into account the criterion proposed by Acosta et al.[4]. He proposed that H p is the value associated with thehighest peak in the ratio χ ( H ac ) /χ ( H ac ) max . We alsoadd the criterion of Xing et al. [5], based on the measure-ment of the maximum of χ (cid:48)(cid:48) ( T ). Under this method thecritical current density is found to be J c ( T p ) = 3 . H a /d ,where T p is the temperature at the peak. These quanti-ties are reported in SI units. Measurements of harmonicsin voltage using the screening [1] technique were carriedout on superconducting thin films of YB C O − δ with a T c = 86 . H ac field whoseamplitude could vary from 0 to 5000 A/m with a fixedfrequency of 1 KHz. For the ratio χ /χ we have realized11 different plots each corresponding to the temperatures:20, 35, 45, 55, 65, 70, 75, 78, 80, 82 and 83 K. On theother hand, the temperature-dependence of the imaginarycomponent of the fundamental harmonic was realized for8 different field amplitudes i.e., H a =77, 118, 277, 690,1161, 1836, 2315, 2665 A/m rms.
3. Results and Discussion
The upper inset in Fig. 2 shows the curves for the J c ( T )with a systematic uncertanity of 20%. Within the esti-mated uncertainties both the χ /χ and the χ (cid:48)(cid:48) approacheslay in the same order of magnitude. Therefore we concludethat in fact both approaches are equivalent.Taking as an input, in Eqs. 2 and 3, the empirical law J c ( T ) = k (1 − t ) n where t = T /T c is the reduced tem-perature, and k and n are experimental parameters wehave plotted the harmonics of voltaje. We found that inthe high temperature region curves are well fitted with n = 3 . k = 6 . × and for lower temperatures thevalues n = 2 . k = 3 . × fit well. In Figs. 1 and2 we plot both the measured and computed curves for thethird and fifth harmonics, respectively. In the real partof the third harmonic the theory can not account for the Figure 2: Temperature-dependence of real and imaginary part of thefifth harmonic. Bottom inset shows theoretical curves. Top insetshows the curves for the J c ( T ). positive peak. On the other hand, the imaginary part isqualitatively well described. The computed values for thefifth harmonic does not account for the oscillatory behav-ior on the left of the main peaks. As temperature goesdown from above T c the main peaks agree with the theorybut as the system further cools, some new features appearthat suggest the presence of other mechanisms than pin-ning. The overall behavior for harmonics higher than thefirst proposes not only that pinning is the only mechanismimplied in the dynamics of fluxons but also that thermallyassisted flux flow (TAFF) and flux creep are present. Alsoa field-dependence of J c ( B ) is not accounted for in themodel and it may be found in harmonics higher than thefundamental. However, S. Shatz et al. [6] have shownthat the Kim-Anderson model with J c = J c ( B ) also yieldsa universal behavior in the curves which in consequencedoes not produce the additional peaks. This fact has theimportance conclusion: that the observed peaks must becaused only by thermal effects as the transition occurs. Acknowledgements
We acknowledge the support from CONACYT.
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