Surface resistance and penetration depth anomalies near the superconducting transition in YBCO thick films at low frequencies

PHYSICAG PhysicaC253 (1995) 115-120

ELSEVIER

Surface resistance and penetration depth anomalies near the superconducting transition in YBCO thick films at low frequencies A.C. B6di a,*, T. Kokkomiiki b, S. Leppiivuori b, j. Viiyrynen b a Institute of Experimental Physics, Kossuth University, P.O. Box 105 H-4001 Debrecen, Hungary b Microelectronics and Material Physics Laboratories, University of Oulu, FIN-90570 Oulu, Finland

Received 31 March 1995;revised manuscript received 18 July 1995

Abstract During the normal-superconductor transition, surface resistance and penetration depth peak anomalies have been observed in YBCO thick films on Z r ( Y ) O 2 substrates, between 1 kHz and 1 MHz frequencies. The resonance curve-like anomaly's amplitude depends linearly upon the frequency and not on the thickness of the film. It is not connected directly to the film's intrinsic superconductivity properties, such as Tc and Je, and is not sensitive to the direction of the temperature sweep. The penetration depth presents a A c t f - l frequency dependence. The frequency dependence of the AC flux penetration's onset temperature is in agreement with that predicted by the vortex-glass model. We believe the anomaly could arise from the competition between the temperature dependence of the critical current density and that of the mixed state's volume.

1. Introduction Superconducting thick films can be used successfully as substitutes for electronic circuit components having large surfaces, e.g., inductors for power electronics. In the last few years much work has been focused on the detailed n - s transition of various superconducting materials. Resistivity-peak anomalies close to Tc have been observed for a variety of superconducting systems, such as for different high-Tc thin films [1,10], granular and bulk materials [2,8], crystals [4-7], and even for A1 films or thin A1 wires [3,9]. As a consequence, very different explanations * Corresponding author.

for the origin of the resistivity-peak anomaly were proposed, including: quasi re-entrant-like behavior [2,4], competition between the temperature dependence of the free vortex density and that of the Josephson coupling energy [5], interactions between superconducting fluctuations and conducting electrons [3,9], non-uniform spatial distribution of Tc inhomogeneities [6], or interplay between intragranular and intergranular properties [11]. No definite interpretation has yet been accepted. Because resistivity anomalies have to date been reported on thick films mainly at microwave frequencies [12,13], in this paper we report measurements of low, and low-radio-frequency surface resistance and reactance performed on Y B C O thick films. Particular attention has been devoted to the shape o f

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A.C. Brdi et aL / Physica C 253 (1995) 115-120 70

the surface resistance versus temperature curve close to the superconducting onset temperature.

60

YBCO films

5o

j,,.a

2. E x p e r i m e n t a l

Three 15 × 2 0 m m 2 rectangular YBCO films (having thickness 8.78, 22.2 and 27.7 I~m and critical temperatures 87.48, 85.25 and 86.2 K, respectively) were deposited on polycrystalline substrates of Zr(Y)O 2 (thickness about 0.95 mm) by the screen printing technique. The reverse of the substrate was coated with a conducting material (Cu). The critical temperature was determined via the temperature dependence of a DC voltage produced by a DC driving current, using the conventional four-point probe method with metallic electrodes. The low frequency (1 kHz-1 MHz) resistance and reactance measurements were made using a commercial LCR meter (Hewlett-Packard type 4284A), in " s e l f inductance geometry" in which a single coil (R] = 1.2 1"~, L~ = 10.5 p~H at 1 kHz, diameter 10 mm) is placed on the film. It is important that the coupling between the film and the coil be maximal. To minimize the distance of the outer windings that do not contribute significantly to the measurements, a pancake spiral coil [14] was used, pressed to the film surface, We noted the changes in the coil resistance and reactance as a function of frequency and temperature between 1 kHz and 1MHz, and 14 and 300 K, respectively. The cooling (or heating) time was about two hours. First we determined the variations of the free-standing coil's parameters as a function of the temperature, at different frequencies (base lines). For verification of the experimental setup, we repeated the measurements with the coil pressed to a gold thick film (d = 8 I~m), also on a Zr(Y)O 2 substrate. In both cases, monotonic, anomaly-free variations were observed. During the cooling (or heating) process, the variation of the coil's total resistance (R s, related to global power losses) and total reactance ( X s, related to the global stored energy) were measured as a function of decreasing (or increasing) temperature, at different frequencies, for all three films. Both R s and X s exhibit similar monotonic frequency dependence (Fig. 1). In contrast to these, the temperature dependence of R s (near the transition temperature) is

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T (K) Fig. 1. The variationof Rs and Xs as a function of temperature, for all three films, at different frequencies.

portrayed by a very large resonance-curve-like anomaly. Beginning from the Ton onset temperature, this anomaly is associated (by the flux-expulsion produced) with a sharp decrease of X s in all three films. The anomaly is independent of the direction of the temperature variation. Fig. 2 shows the frequency dependence of the onset temperature of the X s response. The points are experimental data, showing Ton increasing with f. The line is a fit of the form To, = C w l/((z-])~) + Tg with z = 5.29, Tg = 88, and v = 1.3. The vortex-glass model predicts this dependence and these critical exponent values for AC flux penetration at low frequencies [15,16]. The amplitude of the R s anomaly depends linearly upon the frequency (Fig. 3). The very small difference between the high- and low-temperature values of R s indicates that the films are only partly ordered, and of low quality. The sharp decrease of X s and of the DC resistivity data (determined by the usual fourpoint probe method) prove the existence of at least

117

A. C. B6di et al. / Physica C 253 (1995) 115-120 93

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(K)

Fig. 4. The dependence of the Q quality factor and Jc critical current density on the T¢ critical temperature, for all three films.

Fig. 2. The frequency dependence of the To, onset temperature determined from the X s response. The points are experimental data, the line is the fitting curve.

one superconducting percolative component in the films. In order to characterize the R s anomaly, a quality factor has been introduced: Q = max Rs/AT, where max R s is the anomaly's amplitude and AT is the peak's width (at half-height). Comparing Q with the main intrinsic quality parameters of the

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films, i.e. the critical temperature and the critical current density (Fig. 4), two important features have been found. Firstly, the anomaly's quality factor does not depend upon the critical current density. Secondly, Q is not even proportional to T~. The phenomenon appears in a short temperature range of the transition, but is directly connected neither to the intrinsic superconductivity quality parameters nor even to the thickness of the films. At our frequencies the value of the wavelength in the dielectric substrate is always greater than 3 m and resonance conditions for the experimental setup do not appear. Consequently, the reflected wave's influence from the reverse surface of the substrate can be neglected.

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3. The penetration depth and intrinsic surface impedance 4

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200

400

600

800

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Fig. 3. The frequency dependence of the anomaly's amplitude, for all three films.

In order to determine the low-frequency penetration depth in YBCO thick films on dielectric substrates from our data, an equivalent circuit model for the coil-film interaction has been used (Fig. 5). The interpretation of the measurements depends on the calculation of the shielding current induced in the film by the current of the driving coil. Employing the complex amplitude method for the coupled system of

118

A.C. Bddi et al. / Physica C 253 (1995) 115-120

R1 I Ro

RSF

M 1

11

]2

L1

E

LSF

Fig. 5. The equivalent circuit model used for the experimental setup. The coupling between the coil and its image in the superconducting film is modeled as an ideal transformer. R1 and Ll are the resistance and the inductance of the free-standing spiral coil, RSF and LSF are the film's surface resistance and inductance, respectively. I l and 12 are the complex amplitude of the currents, and M is the mutual inductance between the two inductances.

coil L 1 and its induced image LSF (in the film), the following equations can be written [17]:

(R1 +jtoLl)I, +jooMI2= Vl, j t o M l I + ( RSF + j toLsF) I 2 = 0,

where 11 and 12 are the complex amplitudes of the currents flowing in the coil and in the film, respectively. H e r e j 2 = _ l, to = 2"rrf, f is the frequency, and M = k ( L I L s F ) °'5 is the mutual inductance between the coil and its image, and k is the coupling coefficient, depending on the coil-film geometry. For a given coil, the induced (image) current in the film is proportional to the current in the coil: M 12 = --jto

RSF + j toLsF

11.

We obtain the complex impedance of the coil-plusfilm system (indistinguishable from the coil-plusimage coil system), introducing I z into the first equation:

v, __ = Zs = R s +jXs 11 toaM2 = R 1 + RSF R2F q- to2L2sF (

to2M2

+ j co L 1 - LSF R2 F + to2L2F

) ,

where Z s is the total complex impedance, R s and X s are the measured resistance and reactance of the system, respectively, and Rsr and XsF are the film's intrinsic surface resistance and reactance, respectively. From this equation only the ratio RSF

Rs -- R 1

XSF

Xl -- X s

can be directly determined. For superconducting films, this ratio can be defined as [18]: xsFRS---~-=F 0.5/.LtoAZo~-1 1 + s i n h ( d / A ) c o s h ( d / A ) where ix is the magnetic permeability, A is the penetration depth and p. is the normal resistivity extrapolated to the operating temperature. For thicknesses d ~< A, in practice we can write: A -~" 1 / - - p n R s F ~ f - l .

V

Ixto XsF

Taking the superconductor as a network of superconducting grains coupled via Josephson junctions: A2 2 2 = /~j + /~g, where Aj and Ag are the penetration depth of the junctions and of the grains, respectively.

4. Discussion From the measured R s F / X s F data, calculated h values show that even in the superconducting state, and at the highest frequency used, the electromagnetic field penetrates our low-quality films completely (Fig. 6). According to the curve fittings, the penetration depth decreases almost linearly with the increase of the frequency. This is in agreement with the theory presented above. The linear RSF(f) and h ( f ) dependences are between the well-known limiting cases o f f 2 and f0.5 for high-quality and highly granular samples, respectively [19]. During the normal-superconductor transition, over the almost linear decrease, A(T) also presents a hill anomaly (Fig. 7). Its peak's temperature corresponds to the temperature where the slope of the R s and RSF anomalies is the maximum. The observed A(T) dependence can be evaluated using neither the mean-field BCS expression, nor the Gorter-Casimir two-fluid model.

119

A.C. B6di et a l . / Physica C 253 (1995) 115-120 ''I

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Fig. 8. T h e variation o f the surface resistance and reactance as a function o f the decreasing temperature, at different frequencies. Here, a is a constant.

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(K)

and the measured b parameter permits the direct calculation of the surface impedance's components: ZsF = (b 2 + 1)[(R s - R 1) + j ( X 1 - Xs)]. At the normal-superconductor transition, aRs~ presents, over a slow decrease, a resonance-like anomaly, while aXsF presents an exponential increase (Fig. 8). This increase is in accordance with the decrease in penetration depth. The particularities of the inductive (electrodeless) methods used exclude in our case the electrode configuration and also the presence of non-uniformly distributed Tc inhomogeneities as possible causes of the anomaly. It is accepted that, at temperature To,, begin the nucleations of small superconducting regions dispersed throughout the non-superconducting sample. In the mixed state, at low magnetic field intensities, there is always fluctuation of the superconducting islands (instability in the vortex lattice), producing additional dissipation. The presence of

120

A.C. B6di et al. / Physica C 253 (1995) 115-120

fluctuations significantly affects the electronic inelastic scattering rate. But the identical shape and intensity of the anomaly's curve during heating and cooling exclude inelastic electron scattering on superconducting fluctuations as a possible cause of the anomaly. The lack of the Q
5. Conclusion

In summary, we have determined the A(T, f ) and ZsF(T, f ) dependences for printed YBaCuO super-

conducting thick films using contactless lowfrequency measurements and an equivalent circuit model. The observed A(T) penetration depth and RsF(T) surface resistance anomaly do not depend upon the film's intrinsic superconductivity parameters. The A(T) dependence cannot be evaluated using either the mean-field BCS expression or the GorterCasimir two-fluid model. Curve fittings give the

A c~f -1 and the Ton ~ f l / ( ( z - l ) v ) frequency dependences. The z = 5.29 and v = 1.3 values derived from this study are in agreement with the prediction of the vortex-glass theory. The competition between Jc(T) and VM (the mixed-state part of the film's volume which was under the area of the measuring coil) has been proposed as the most simple interpretation of the anomaly.

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