Millimeter-wave surface impedance measurements of YBa2Cu3O7−δ ceramic superconductors

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Solid State Communications, Vol. 67, No. 4, pp. 373-377, 1988. Printed in Great Britain.

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MILLIMETER-WAVE SURFACE IMPEDANCE MEASUREMENTS OF YBa2Cu307-8 CERAMIC SUPERCONDUCTORS Anand M. Awasthi, John P. Carini, Barakat Alavi and George Grfiner Department of Physics and the Solid State Science Center University of California, Los Angeles CA 90024-1547 Received April 29, 1988 by A. Zawadowski

We have measured the temperature dependence of the surface impedance, Zs(T), at 102 GHz of several YBa2Cu307-~5 ceramic superconductors. We compare our results for the magnitude of the surface resistance, Rs, with values from microwave measurements, with millimeterwave measurements conducted on oriented films, and with a calculation using the Mattis-Bardeen theory.

Several studies 1-7 of high transition temperature superconductors have focused on measurements of the temperature dependence of the absorption of low frequency, hcm(kBTc, electromagnetic waves, where co is the measurement frequency and Tc is the transition temperature. For ceramic samples, the results of these measurements typically show a microwave absorption that drops rapidly below the normal state value as the temperature is decreased below Tc, but at low temperatures there remains a significant residual loss which seems to be somewhat sample dependent. In this report, we present measurements on the temperature dependence of the 102 GHz surface impedance of YBa2Cu307-5 ceramic superconductors. These experiments were made at frequencies about an order of magnitude higher than the results at microwave frequencies mentioned above. Our results are qualitatively similar to those, and therefore, by comparing these measurements, the frequency dependence of the loss over a moderate spectral range can be determined. We find that the measured losses are several orders of magnitude greater than the estimated losses in a homogeneous and isotropic superconductor. The frequency dependence of Rs/Rn(Tc)), where Rs is the surface resistance and Rn is the normal state surface resistance, can be described by a power law dependence from 3 GHz to 100 GHz: Rs/Rn(Tc)o~ o~(T). The value of the exponent, a(T), may differ from 1.5, which is expected for a superconductor, for example,

a(T/Tc=0.77)= 0.5. We have also measured the surface reactance, Xs=Im(Zs), as a function of temperature. When the complex surface impedance at 102 GHz is analyzed as a whole, it is obvious that the overall electrodynamic response may be qualitatively different from that of a bulk superconductor. This situation makes it difficult to obtain important quantities from our surface impedance data, such as the temperature dependence of the superconducting penetration depth, or to draw simple conclusions about the source of the absorption for temperatures well below Tc. Our ceramic samples were prepared from an oxide powder resulting from a citric acid precipitation from a solution of nitrates of Y, Ba, and Cu in stoichiometric proportions of the metallic ions (1:2:3). The powder was sintered at 900" C in air and the pellet was cooled slowly (4-6 hours) below 700* C. The powder X-ray pattern showed only the 1:2:3 phase. The transition temperature occured at 92 K for our samples, as determined by both the zero dc resistance and the onset of the Meissner effect as measured by the dc magnetization in a 25 Gauss applied field. For measurement of the surface impedance, the surface was smoothed using fine (600 grit) abrasive paper. Further polishing or oxygen annealing of the exposed surface did not reduce the magnitude of the absorption at 102 GHz. The samples were mounted as the end plate of a cylindrical copper cavity operated in the TE011 mode. 8 We measure the change in the mode's bandwidth and frequency as a function of temperature with the sample 373

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mounted compared with the using a polished copper end plate. This change directly measures the real and imaginary surface impedance of the sample, the surface resistance and surface reactance, respectively. In Figure 1 we show the surface resistance Rs(T)and reactance Xs(T) as a function of temperature of a ceramic superconductor at 102 GHz. The rapid drop that we measure in Rs qualitatively agrees with what is observed at microwave frequencies. There is a substantial residual loss at low temperatures: Rs(1.5 K)---0.65 ~. We also observe a corresponding drop in the surface reactance at temperatures below Tc, which indicates that the electromagnetic fields are being screened more efficiently as the temperature is decreased. The residual value of Xs at low temperatures cannot be accurately determined in this experiment due to mechanical imprecision in repeatably disassembling and assembling the cavity. The measured residual value (3.2 f2) is equivalent to a change in the penetration depth of about 4 pan, which is of the same order as the surface roughness and grain size of the ceramic. For temperatures up to about 50 K the loss increases with a power law temperature dependence that is somewhat faster than linear in the temperature. This behavior is reminiscent of the temperature dependence of the loss measured in oriented films 9 below 50 K, except that the residual loss in the ceramics is more than an order of magnitude larger than in the fills.

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In Figure 2 we compare the temperature dependent part of the surface resistance of YBa2Cu307-8 ceramics and oriented fills, that is, with the low temperature residual loss subtracted: [Rs(T)-Rs(T=OK)]/Rn(IO0 K). We also show the results of a calculation of Rs(T)/Rn(IO0 K), which uses the Mattis-Bardeen theory lo to obtain the temperature dependence of the complex

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T (K) Figure 1: The temperature dependence of the surface resistance, Rs(T), and the surface reactance, Xs(T), of a YBa2Cu307-6 ceramic superconductor measured at 102 GHz.

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Figure 2: Top: The temperature dependence of the reduced surface resistance, [Rs(T)-Rs(T=O K)]/Rn(IO0 K) of a YBa2Cu307-8 ceramic and oriented film superconductor. The solid line represents a calculation using the Mattis-Bardeen theory that is described in the text. Bottom: The temperature dependence of the reactive skin depth, 8r(T)=Xs(T)/(I.toO)), compared with the MattisBardeen theory (upper curve) and the empirical dependence for the penetration depth: X(T)/X(T=0 K)=[1-(T/Tc)4]-I/2 (lower curve).

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conductivity, oT), at 102 GHz. The surface impedance is relatedto the complex conductivity by:

Zs [j ~o~ c(T)] 1/2. =

The calculation assumes the existence of an isotropic energy gap, A(T), with A(T=O K)= 1.77kBTc, and a temperature independent normal conductivity. This is probably an unrealistic model for the surface resistance of YBa2Cu307-8, especially since the model does not take into account the anisotropy of the electronic properties. However, for temperatures not too far below Tc (T>Tc/2) the rapid decrease in the low frequency absorption in any superconductor results from a rapid decrease in the superconducting penetration depth. This behavior also dominates in the MattisBardeen calculation in this regime, and therefore the results of the calculation may be regarded as qualitatively typical of a homogeneous superconductor for these temperatures.. The magnitude of the measured losses and their temperature dependence exceed the calculated losses by orders of magnitude for temperatures more than a few degrees below Tc. Although the overall magnitude of the losses in the oriented film are lower than in the ceramics, and the residual losses in the films are much lower, the temperature dependences with the residual loss value subtracted are quantitatively similar. The fact that samples of different forms follow such a similar temperature dependence suggests that the dependence may be a fundamental property, either of the material or of the polycrystalline microstructure of the samples. In the second half of Figure 2 we compare our measurement of the temperature dependence of the reactance with a Mattis-Bardeen calculation for Xs(T)/Xn(Tc) (using the same assumptions and parameters as above for the calculation of the resistance), and also with the empirical T dependence: 11%(T)/%.(T=0 K)=[1-(T/Tc)4]-I/2. The reactance is represented as the reactive skin depth: 8r(T)=Xs(T)/(~toO3)(for o~/(2~)=102 GHz, 1/(I.to03)=1.24 gm/f~). As already discussed, the origin for the reactance axis is not well determined by the experiment. The origin in the figure was chosen to be appropriate for the theoretical formulas. Surprisingly, the Mattis-Bardeen calculation, which assumes weak coupling, describes the reactive skin depth data quite well for temperatures close to Tc. The low temperature limit of the reactive skin depth in the calculation is approximately 0.9 pan. The empirical formula,

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which approximates the temperature dependence of the penetration depth in strong-coupling superconductors,12 does not match the data very well. There are two fitting parameters for the empirical formula: E(T=0 K)--0.8 lxm and the residual reactive skin depth (2.4 grn here), which represents the uncertainty in the change in the geometry of the cavity between the sample run and the copper reference run. As discussed later, an interpretation of the electrodynamic response at 102 GHz may be quite complicated, and the reactive skin depth as shown in Figure 2 may not be directly equated with the penetration depth. It is still interesting to compare the order of magnitude of the fitting parameters with other measurements of the penetration depth. The value of ~,(T=0 K) used here is about a factor of 6 larger than the value found in muon spin relaxation measurements,la but is close to what is measured in dc magnetization measurementsTM on single phase powder samples, ~(T=0 K)---0.6 ~tm. With our measurements at 102 GHz, along with plevious microwave measurements at 3 GHz (on GdBa2Cu307-~5)7 and at 8 GHz3 and 10 GI-Iz2 (on YBa2Cu307-8), the frequency dependence of the surface resistance in the ceramic superconductors may be obtained over more than a decade in frequency, as shown in Figure 3. For the purposes of intercomparison between different experiments performed on different samples, we have plotted the measured values of the reduced surface resistance, Rs(T)/Rn(IO0 K) for several values of the reduced temperature,T/Tc=0.5 and 0.77. We also have plotted the results for the frequency dependence using the Mattis-Bardeen theory. Again, the calculation should be viewed as representative of the standard frequency depen_dence expected for bulk superconductors with local electrodynamic response: Rs/Rn~cO2/~ol/2~o33/2. The apparent frequency dependence for Rs/Rn in the ceramic samples is closer to being o~0.5 for the reduced temperature value 0.77. For the lower reduced temperature value, T/Tc=0.50, the trends in the frequency dependence are not as clear. This is probably due to the different residual values of the reduced surface resistance in the different experiments, which significantly perturbs the temperature dependence. When these residual values are subtracted from the raw data measured at T/Tc=0.50 (the open symbols in Figure 3), the frequency dependence approximately parallels the results of the calculation, although the magnitude of the measured losses remain orders of magnitude greater than the calculation. We note that recent

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Figure 3: The frequency dependence of the reduced surface resistance, Rs(to,T)/Rn(o~,lO0 K), of YBa2Cu307-5 ceramic superconductors for two values of the reduced temperature: T=0.77 Tc and T=0.50 To The microwave data at 3, 8, and 10 GHz are from earlier measurements by other groups. The closed symbols represent the raw data, while the open circles represent the same data with the residual resistance, Rs(T=O K)/Rn(IO0 K), subtracted.The solid line represents a calculation using the Mattis-Bardeen theory that is described in the text.

microwave experiments 4 on single crystals give Rs values forT/Tc>0.5 that are larger than those obtained on the films or ceramics, but with reasonably small residual losses at liquid helium temperature. This result may not be surprising in view of the importance of both the metal and oxygen stoichiometries for the superconducting properties.15 Such concentrational fluctuations may be expected to greatly increase the loss, particularly for temperatures close to Tc, due to spatial fluctuations in the transition temperature. To give further insight into the electrodynamic response, the temperature dependence of the real and imaginary surface impedance at 102 GHz may be analyzed together,16 as shown in Figure 4. In a normal metal (O1>>O2) with local response the magnitudes of the reactance and resistance are equal, and so the impedance will fall on a line drawn through the origin with a slope of one in the complex Z-plane as the normal conductivity is varied. Note that the origin for the reactance scale is not determined by the experiment, and so it is the slopes of the curves in the complex Z-plane should be compared rather than their absolute positions. For a bulk, homogeneous superconductor, the resistance should drop rapidly from the normal

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Rs(~) Figure 4: The surface reactance, Xs(T), as a function of the surface resistance, Rs(T), of a YBa2Cu307-6 ceramic superconductor at 102 GHz, with the temperature, T, as the implicit parameter. The line in the complex Z-plane represents the impedance behavior of a homogeneous, normal metal with local electrodynamic response as the normal conductivity is varied. As described in the text, the choice of the origin for the reactance is not determined by the experiment.

state value, Rn=poO~Sn/2, where Po is the permiability of free space and 8n is the classical skin depth, for temperatures immediately below the transition temperature. At lower temperatures the response is predominantly reactive and is approximately equal to Zs=Xs =j poto~(T), where ~, is the superconducting penetration depth. The response of the ceramics differs from the expected behavior for a homogeneous superconductor. As the temperature is decreased below Tc the changes in the reactance and resistance are approximately the same, as demonstrated by the path on the complex Z-plane that has a slope close to one that would expected for a normal metal. This behavior makes it difficult to perform any additional analysis of the electrodynamic response to obtain, for example, the temperature dependence of the superconducting penetration depth. In addition, a full analysis would require the inclusion of the effects on the electrodynamic response of both electonic anisotropy or of structural inhomogeneity. The

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magnetic field dependence of the microwave absorption has been used as a probe of these structural effects.S In conclusion, we have found substantial qualitative deviations in the elecla'odynamic response at 102 GHz of ceramic YBa2Cu307_8 superconductors from the behavior expected in a bulk, homogeneous, and isotropic superconductor. These deviations may be seen mainly in the magnitude of the low frequency absorption as measured by the surface resistance and the

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associated temperature dependence of the surface reactance. The frequency dependence of the absorption is also not fully consistent with that of a bulk superconductor, while the results at lower temperatures (T/Tc=0.50) do not rule out a bulk behavior. The reactive skin depth that we observe is in broad agreement with what is observed in magnetization measurements. Acknowledgements--This work was supported by the Office of Naval Research.

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