Frequency dependence of the surface resistance in high-temperature superconductors

FREQUENCY DEPENDENCE IN HIGH-TEMPERATURE D.W. Cooke,

E.R. Gray,

H.H.S.

Los Alamos

Javadi,

National N. Klein,

Bergische

Universitat,

OF THE SURFACE RESISTANCE SUPERCONDUCTORS

R.J. Houlton,

Laboratory, G. Muller,

Gesamthochschule

B. Rusnak,

Los Alamos, S. Orbach

Wuppertal,

E.A. Meyer and P.N. Arendt

NM 87545, USA

and H. Pie1

D-5600 Wuppertal

L. Drabeck Department

003%1098/90 $3.00 + .OO Pergamon Press plc

Vol. 73, No. 4, pp. 297-300, 1990.

Solid State Communications, Printed in Great Britain.

1, Federal

Republic

of Germany

and G. Gri.iner

of Physics and the Solid State Science Center, University Los Angeles, CA 90024, USA

of California,

Los Angeles,

and J.Y. Josefowicz, Hughes

Research

D.B. Rensch Laboratories,

(Received 11 July 1989; in revisedform

and F. Krajenbrink Malibu,

CA 90265, USA

11 September 1989 by A.A. Maradudin)

We have measured the surface resistance at 22 GHz, 86GHz, and 148 GHz of a YBa,Cu,O, film (5000 A) deposited on a LaGaO, substrate. X-ray diffraction data show the film to be highly c-axis and a-axis oriented, and the low values of measured surface resistance suggest that the film is of high quality. In the measured spectra1 range, the temperature-dependent contribution to the surface resistance is, within experimental error, proportional to the square of the frequency, i.e. R, cc co*. This result is consistent with various models of loss mechanisms in superconductors.

S’CTRFACE resistance (R,) is one of the most important technical parameters which determines the usefulness of the recently discovered high-temperature superconductors in various high-frequency applications [ 11. For high-quality materials, R, may also provide information on the fundamental properties of the superconducting ground state and the low-lying excitations. Several groups have reported results of R, measurements in the microwave and millimeter-wave spectra1 range for ceramics [2,3], films [4-61, and single crystals [7]. In general, it is found that R, exceeds the MattisBardeen limit, i.e. the calculated surface resistance based on the BCS theory, and that most specimens exhibit a substantial “residual” surface resistance, R,,, . The measured R,(T) for a superconductor is expected to be given by [2], R,(T)

=

R,,(T)

+ R,,.

(1)

For a perfect superconductor (one that is defect free) R,(O) = 0 at T = 0; this is not realized in practice even in the best available Nb. Clearly, R,, is related to the surface conditions of the superconductor and not to any intrinsic property. Calculations following BCS

theory lead to the following frequency dependence for the temperature-dependent contribution to R,V(T) in the temperature range T < T,./2 [8], R,,.(T)

=

A$(Trln(&)exp(-

6)

(2)

where A is a numerical constant, A is the singleparticle energy gap, T is the temperature, and o is the measurement frequency. At frequencies ho 4 A, equation (2) predicts a frequency dependence for R,Y that is approximately quadratic, R, CC 02. Detailed experiments [2] on conventional superconductors such as Nb and Nb, Sn indeed give a frequency dependence which can be expressed as R, = Bo” with n close to 2, in good agreement with expectations. The two-fluid mode1 of the superconducting state combined with the frequency independent London penetration depth 2 of the microwave field into the superconductor also leads to a surface resistance proportional to w2. If the residual resistance R,, is caused by large normal conducting areas (lateral dimensions large compared to A) then it is expected to scale like o”‘. If on the other hand the residual losses are pre-

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dominately originating in the intergranular region then the field penetration depth is determined mainly by the superconducting grains and R,,, should be proportional to III*. In the oxide superconductors R,,, B dominates the surface resistance R,(T) for T < T,./2. e 2 Therefore a fit to our experimental data using equation (2) would not give any information on the energy 5 gap A or the amplitude A. However at 70 K, where the !5 approximation of equation (2) is not valid, a strong ii temperature dependence of R, is observed and the ; contribution of R,,(T) is substantiated. In analogy to the conventional superconductors R,, (T) should be very small at 30K and R,,, should dominate. Therefore a measurement at 70 and at 30K should give information on both the frequency dependence of

c

R,, and R,,,. The frequency dependence of the surface resistance of high temperature superconductors has not been determined unambiguously, mainly because of the absence of experiments over a broad frequency domain on the same specimen. In general R, increases with increasing frequency [9], but large differences between different specimens for the same preparation procedures have not allowed a clear evaluation of the frequency-dependent electrodynamical response. The only experiment where the same sample was measured at different frequencies (100 and 148 GHz) did not include a large enough frequency range [5]; nevertheless, a value of n = 2.2 was extracted. The issue of the frequency dependence of R,, is important; due to the small sample size, experiments are usually conducted at frequencies higher than anticipated in most applications, and extrapolation procedures rely heavily on the value of n, which is usually assumed to be 2. In this paper we report the first systematic study of the surface resistance over a wide (order of magnitude) frequency domain for a high-quality film of YBa,Cu,O, deposited onto LaGaO,. Our results show that R,y cc o”, where n = 2.06 f 0.14 at T = 70 K, and n = 2.02 + 0.47 at T = 30K, in good agreement with theoretical predictions. Using targets composed of Y, BaF,, and Cu, thin films of YBa2CujF,0, were deposited onto a singlecrystal (00 1) LaGaO, substrate (l-inch diameter) by magnetron co-sputtering. A detailed description of this simultaneous sputtering approach as well as the physical, chemical and structural analysis of the deposited films will be reported elsewhere [lo]. The films were deposited at ambient substrate temperature and were amorphous as deposited. To oxidize and convert the films to the crystalline superconducting phase, they were annealed in wet 0, at 850” C for 1 h followed by cooling in pure O2 at 1.5”Cmin’. 0 - 20 X-ray diffraction data (see Fig. 1) showed that the annealed

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Fig. 1. X-ray diffraction pattern for the YBa,Cu,O, film deposited onto LaGaO,. The a- and c-axis peaks are labeled. Peaks labeled 1, 2, and 3 are identified with BaCuO, phases. superconducting film was highly c-axis and u-axis oriented with only trace amounts of impurity phases, BaCuO,x and CuO,. Additional characterization consisted of measuring the magnetic susceptibility (diamagnetic shielding) of the film. As shown in Fig. 2, the transition to the superconducting state is characterized by a sharp drop in the susceptibility (onset of diamagnetism) at 90 K, which indicates that the film is of high quality. This is confirmed by the low value of R, measured for this film; for example, at 15 K and 22 GHz we find that R, is 3 mR, which is more than a factor of two lower than Cu. The composition of this film, as determined by Rutherford backscattering analysis, is YBa,Cu,,,O,. The surface resistance of this film was measured at three different frequencies (22, 86, and 148 GHz) as a function of temperature using the same experimental technique. The l-inch round sample was first measured in the 22-GHz cavity and then cut into smaller I-cm’ pieces for measurements at 86 and 148 GHz. In each case the end wall of a cylindrical copper cavity (TE,,, mode family) was replaced by the superconducting sample, which consisted of a YBazCu,O, film on a LaGaO, substrate, and the Q-value was measured. The surface resistance is computed from the difference in Q values of the bare cavity and the cavity with the superconducting end wall. Figure 3 shows R, vs T data for the 500OA-film of YBa,Cu,O, on LaGaO,, measured at 22, 86, and 148 GHz. The precipitous drop in R, below T,. (- 90 K) for all three measurement frequencies indicates that the film is high quality, consistent with the X-ray and susceptibility data. The frequency dependence of these data is given in Fig. 4 for T = 70 and

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Fig. 2. Diamagnetic shielding curve for the LaGaO,based film. The sharp transition into the superconducting state occurs near T = 90K. 30 K; the best fit gives R, x o"with n = 2.06 + 0.14 and 2.02 f 0.47, respectively. The absolute errors for R, measured at 148, 86, and 22GHz are 10, 8, and 2 mR. respectively. Thus, at 30 K the relative errors on R,, are quite large, especially for measurements taken at 22 GHz. Nevertheless, the quadratic dependence of R, is observed even at the lower temperatures indicating a quadratic frequency dependence of the R,,, The frequency dependence of R, obtained at higher temperatures. 70 K for example. may be more representative of the intrinsic HTS behavior because the data at that temperature should not be greatly influenced by extrinsic materials properties such as metallic or insulating impurities. We also note that the data should not be affected by the increased penetration depth at 70 K. Assuming that the penetration depth

-0 TEMPERATURE(K)

Fig. 3. Surface resistance of the LaGaO,-based measured at 148, 86, and 22GHz.

film

Fig. 4. Frequency dependence of R, at 22, 86, and 148GHz. Data are taken from Fig. 3 at T = 70 and 30K.

can be described

by the phenomenological

relation (3)

where & is the penetration depth at T = 0 K (A 0.15 pm) [l 11,and Tc is 90 K, we calculate that i, is 0.19 pm at T = 70 K. A similar estimate follows from the BCS expression for i(T). This value is much less than the film thickness of 0.5pm. Therefore, if the substrate is uniformly covered by the superconducting film, there should be no interaction with the magnetic field, and, consequently, no effect on R,. Alternatively, if the superconducting film is non-uniform and/or has holes, the magnetic field could interact with the substrate to modify R,. Such effects have been observed in thin films deposited on SrTiO, substrates [4, 51. The strongly temperature-dependent permittivity of this material leads to temperature-dependent standingwave patterns which are manifested as oscillations in R, vs T. Because LaGaO, has only a weakly temperature-dependent permittivity [ 121 no independent confirmation of leakage effects can be obtained in the present work. Experiments on specimens with the same quality but different thicknesses are needed to clarify this point. In summary, we have measured the surface resistance as a function of temperature of a high-quality YBa,Cu,O, film (5000 A) deposited on single-crystal LaGaO, at three frequencies, 22,86, and 148 GHz. We find that close to T, (70 K) R, cc tu’, which is consistent with BCS theory and a two-fluid model, and with

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experimental measurements on conventional superconductors such as Nb and Nb,Sn. R,, also scales like o2 at low temperatures indicating that the observed residual losses may originate from the normal or weakly superconducting intergranular regions. Acknowledgements - The work at Los Alamos was supported by the U.S. Army/Strategic Defense Cornmand and the U.S.D.O.E., including lSRD projects X84T and X897. Work at UCLA was supported by the UCLA Consortium on High-Frequency Superconductivity. Stimulating discussions with I.D. Raistrick, J.G. Beery, T.P. Starke and H. Frost are gratefully acknowledged. REFERENCES H. Padamsee, Cornell Laboratory of Nuclear Studies Report 88/864, Presented to the 1988 LTNAC Conference, Williamsburg, Va., October, 1988. H. Piel, M. Hein, N. Klein, U. Klein, A. Michalke, G. Miiller & L. Ponto, Ph,r~sics C 153-155, 1604 (1988). A.M. Awasthi, J.P. Carini, B. Alavi & G. Griiner, Solid State Commun. 67, 373 (1988). N. Klein, G. Miiller, H. Piel, B. Roas, L. Schultz, U. Klein & M. Peiniger, Appl. Phys. Lett. 54, 757 (1989).

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J.P. Carini, A.M. Awasthi, W. Beyermann, G. Griiner, T. Hylton, K. Char, M.R. Beasley & A. Kapiltunik, Phy.r. Rev. B37, 9726 (1988). D.W. Cooke, E.R. Gray, R.J. Houlton, B. Rusnak, E.A. Meyer, J.G. Beery, D.R. Brown, F.H. Garzon, I.D. Raistrick, A.D. Rollett & R. Bolmaro. Submitted to .4pp/. Phys. Lett. 55, 914 (1989). D.L. Rubin, K. Green, J. Gruschus, J. Kirchgessner, D. Mofhdt, H. Padamsee. J. Scars, Q.S. Shu, L.F. Schneemeyer & J.V. Waszczak, Plz~>s. Rev. B38, 6538 (1988). D.C. Mattis & J. Bardeen, Phys. Rev. 111, 412 (1958). J. Carini, L. Drabeck & G. Griiner, Mod. P/IJ’.F. Lett. B3, 5 (1989). J.Y. Josefowicz, D.B. Rensch, A.T. Hunter, F. Krajenbrink & R. Miles, to be published. D.R. Harshmann, G. Aeppli, E.J. Ansaldo, B. Batlogg, J.H. Brewer, J.F. Carolan, R.J. Cava, M. Celio, A.C.D. Chaklader. W.N. Hardy, S.R. Kreitzman, G.M. Luke, D.R. Noakes & M. Senba, Pllys. Rev. B36, 2386 (1987). R.L. Sandstrom, E.A. Giess, W.J. Gallagher, A. Segmiiller, E.I. Cooper, M.F. Chisholm, A. Gupta, S. Shinde & R.B. Laibowitz, Appl. Phys. Left. 53, 1874 (1988).