The microwave response of a thin film of high temperature superconductor YBa2Cu3O7 - δ was measured for a wide region of temperatures and magnetic fields. From the measured complex frequency shift, the complex conductivity was calculated. The model for effective conductivity in the mixed state was fitted to the complex conductivity data and the values of upper critical fields Bc2(T) and depinning frequencies ω0 (T) have been obtained as fitted parameters.Mjerili smo mikrovalni odziv tankog filma visokotemperaturnog supravodiča YBa2Cu3O7−δ u širokom području temperatura i magnetskih polja. Iz izmjerenog kompleksnog frekventnog pomaka izračunali smo kompleksnu vodljivost. Numeričkom prilagodbom modela efektivne vodljivosti u miješanom stanju odredili smo vrijednosti gornjeg kritičnog polja Bc2 (T) i frekvencije opuštanja ω0(T)

Barišić, N.

Dulčić, A.

Paar, D.

Požek, M.

English

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ISSN1330–0008CODENFIZAE4MICROWAVE CONDUCTIVITY OF THIN YBCO FILM IN MAGNETICFIELDN. BARIŠIĆ, A. DULČIĆ, M. POŽEK and D. PAARDepartment of Physics, Faculty of Science, Bijenička 32, HR-10000 Zagreb, CroatiaDedicated to Professor Boran Leontić on the occasion of his 70th birthdayReceived 12 November 1999; Accepted 10 April 2000The microwave response of a thin film of high temperature superconductorYBa2Cu3O7−δ was measured for a wide region of temperatures and magnetic fields.From the measured complex frequency shift, the complex conductivity was calcu-lated. The model for effective conductivity in the mixed state was fitted to thecomplex conductivity data and the values of upper critical fields Bc2(T ) and de-pinning frequencies ω0(T ) have been obtained as fitted parameters.PACS numbers: 74.25.Nf, 74.60.Ec, 74.60.Ge, 74.76.Bz UDC 538.915Keywords: YBa2Cu3O7−δ, high temperature superconductor, thin film, complex fre-quency shift, complex conductivity, upper critical fields, depinning frequencies1. IntroductionMeasurements of the microwave response can be very important in the studyof superconductors. From this type of measurements one can extract the complexconductivity which is an intrinsic property of superconductors. In the Meissnerstate of classical superconductors, for microwave frequencies lower than the super-conducting gap (h̄ω < 2∆), the only contribution to the real part σ1 of the complexconductivity σ̃ arises from thermally activated quasipartical excitations, while theimaginary part σ2 determines the superconducting penetration depth. In the caseof high temperature superconductors (HTSC), microwave measurements gave thefirst evidence of the existence of nodes in the pairing states [1], thus indicating thatthe superconducting gap has no longer the symmetry of an isotropic s-wave.FIZIKA A (Zagreb) 8 (1999) 4, 245–252 245barǐsić et al.: microwave conductivity of thin ybco film in magnetic fieldWhen a DC magnetic field is applied, driving a type-II superconductor into themixed state, unpaired electron states are excited in the vortex cores in addition tothose thermally excited in the bulk. These unpaired states give a remarkable rise tothe real part of the microwave conductivity. The contribution of the vortices to thecomplex conductivity depends on whether they are pinned or not. There is a char-acteristic frequency, the so called depinning frequency ω0, above which the vorticesare practically in the flux flow regime, i.e. for such high microwave frequencies theviscous drag force exceeds the pinning force. For classical type-II superconductors,the depinning frequency is lower than 100 MHz [2], and one can consider the vor-tices at all microwave frequencies to be in the flux-flow regime. On the contrary,HTSC have been reported to have depinning frequency in the microwave region [3]and it is, therefore, very important to investigate the microwave response of HTSCin the mixed state, giving valuable information about the vortex dynamics.In this paper we present temperature and magnetic field dependent microwaveresponse measurements on a thin YBCO film, giving the upper critical fields anddepinning frequencies of the sample.2. ExperimentalThe investigated sample was an epitaxially grown, c-axis oriented, YBa2Cu3O7−δfilm on MgO substrate. The film thickness was 200 nm, grown on the substratewhose thickness was 0.5 mm [4]. For the purpose of measurements, we have cut apiece of the film of area 1 mm ×3 mm.The sample was placed on a sapphire rod in the centre of a cylindrical microwavecavity operating in the TE111 mode at 9.28 GHz. The longest side of the sample(ab-plane) was oriented along the microwave electric field at the position of itsmaximal strength. The c-axis of the sample was parallel to external DC magneticfield.Microwave response was measured in terms of the complex frequency shift∆ω̃pω=∆fpf+ i∆(12Qp), (1)where fp = ωp/2π and Qp are the frequency and Q-factor, respectively, of thecavity loaded with a perfect conductor of the same geometry [5].The Q-factor was measured by using frequency modulation of the microwavesabout resonant frequency. The modulation was in the audiofrequency range so thatthe signal could be detected first in the microwave detector, and the output thenanalysed by a lock-in detector at the modulation frequency and its second andfourth harmonics [4]. The value of the modulation depth was adjusted to be lessthan the half width of the Lorentzian line. The output of the lock-in detector atthe modulation frequency was minimized by automatic adjustment of the klystronfrequency to the centre of the Lorentzian line. This provided the means of measuringthe frequency shift by a microwave counter.246 FIZIKA A (Zagreb) 8 (1999) 4, 245–252barǐsić et al.: microwave conductivity of thin ybco film in magnetic field3. Results and discussionThe temperature dependence of the complex frequency shift in the absence ofDC magnetic field is shown in Fig. 1. The sharp minimum in ∆f/f just belowTc is characteristic for samples thinner than normal-state skin depth, placed in amicrowave electric field [5].      DDIISSP7.>4@SSPFig. 1. Zero field temperature dependence of the imaginary and real parts of thecomplex frequency shift ∆ω̃ω =∆ff +i∆(12Q)for a thin film YBa2Cu3O7−δ onMgOsubstrate.The extraction of complex conductivity from thin film data should be care-fully conducted. The complex frequency shift for a superconductor of an arbitrarythickness is given by(∆fpf)= −2µ0H2‖eVsWcpλ1dsinh(λ1|λ̃|2d)− λ2dsin(λ2|λ̃|2d)cosh(λ1|λ̃|2d)− cos(λ2|λ̃|2d) , (2)FIZIKA A (Zagreb) 8 (1999) 4, 245–252 247barǐsić et al.: microwave conductivity of thin ybco film in magnetic field∆(12Qp)= 2µ0H2‖ eVsWcpλ2dsinh(λ1|λ̃|2d)+λ1dsin(λ2|λ|2d)cosh(λ1|λ̃|2d)− cos(λ2|λ̃|2d) , (3)where d is the sample thickness, and λ̃ = λ1− iλ2 is the complex penetration depth[5]. These relations are approximations which neglect minor effects of the substrateon the field solutions in the superconductor. The relation between the complexpenetration depth λ̃ and the complex conductivity σ̃ = σ1 − iσ2 is given byλ1,2 =√|σ̃| ± σ22µ0ω|σ̃|2 , (4)thus giving, together with (2) and (3), the relation between ∆ω̃p/ω and σ̃. If thesample were thick, the expressions in brackets of relations (2) and (3) would reduceto λ1/d and λ2/d, respectively, and the values of σ1 and σ2 could be analyticallyextracted. In the case of a thin film, however, the extraction should be done nu-merically. The curves in Fig. 1 were given offsets so that the extrapolations to zerotemperature are consistent with zero absorption and London penetration depths of140 nm. The Newton-Raphson method [6] was used for the extraction of σ1 andσ2. The results are shown in Fig. 2. One can note the strong growth of σ1 belowTc which could not be ascribed to the BCS coherence peak. Similar data have beenobserved in good single crystals [7]. The growth in σ1 was ascribed to the growthof scattering time for the quasiparticle excitations, probably due to the opening of      [[[[[[[sssWP7.Fig. 2. The real (σ1) and imaginary (σ2) parts of the complex conductivity extractedfrom the data in Fig. 1.248 FIZIKA A (Zagreb) 8 (1999) 4, 245–252barǐsić et al.: microwave conductivity of thin ybco film in magnetic fielda spin gap, which is still a question of debate. Just above Tc, the real part of theconductivity was close to 1× 106 Ω−1m−1, which appears negligible on the scale ofFig. 2.Much more interesting experimental data have been obtained by imposing aDC magnetic field on the sample. For a given temperature, the magnetic field wasswept and the complex frequency shift was measured. The curves for some of thetemperatures are shown in Fig. 3. There was no hysteresis in sweeping the magneticfield up and down. This is consistent with the demagnetizing effect in the geometryof a magnetic field which is perpendicular to a thin film.D>4@SSP7 .7 .7 7 .    D7 .7 .7 .7 .7 .IISSP%7Fig. 3. Magnetic field dependence of the imaginary and real parts of the complexfrequency shift at various temperatures.From the data on the complex frequency shift, the complex conductivity can benumerically obtained for every point in the field-temperature space. The obtainedfield dependence of the complex conductivity can be successfully modelled usingthe effective conductivity approach for the mixed state, as described by Dulčić andPožek [8]. According to the model, the effective complex conductivity σ̃eff in theFIZIKA A (Zagreb) 8 (1999) 4, 245–252 249barǐsić et al.: microwave conductivity of thin ybco film in magnetic fieldmixed state is given by1σ̃eff=1− b(vvf)(1− b)(σ1 − iσ2) + bσn +bσn(vvf), (5)where b(T ) = Bdc/Bc2(T ) is the reduced field, Bc2 (T ) is the upper critical field,σ1(T )− iσ2(T ) is the complex conductivity of the Meissner state, and σn(T ) is thenormal state conductivity in the vortex core. The ratio of the actual vortex velocityv to the maximum velocity vf in the flux flow regime is given by [2]vvf=1 + i(ω0/ω)1 + (ω0/ω)2, (6)where ω0 is the depinning frequency.         w0 / w7.%&7Fig. 4. The upper critical field Bc2 (T ) and the ratio of the depinning frequencyω0(T ) to the measurement frequency ω = 2π × 9.28 GHz, obtained as the best fitparameters for the curves in Fig. 3.250 FIZIKA A (Zagreb) 8 (1999) 4, 245–252barǐsić et al.: microwave conductivity of thin ybco film in magnetic fieldFor each measured temperature, we have fitted the field dependence of σ̃eff fromEq. (5) to the measured conductivity. The parameters σ1(T ) and σ2(T ) have beentaken from the zero-field measurements (Fig. 2), and σn(T ) is the extrapolatedvalue of the normal state conductivity above Tc. The parameters Bc2 and ω0 havebeen left as fit parameters. The real and imaginary parts of σ̃eff have been fittedsimultaneously, i.e., the two experimental curves have been fitted by only two freefit parameters. The best fit parameters Bc2 (T ) and ω0(T ) are plotted in Fig. 4.One can notice that we have extended the determination of the upper criticalfield to considerably lower temperatures in comparison to the previous measure-ments on a single crystal [9]. The upper critical fields up to 70 T have been deter-mined, although the field range used in the measurements was only up to 8 T. Fortemperatures above 80 K, the fitting procedure could not give satisfactory results.This is an indication of the fluctuation regime for which our mean-field model forthe mixed state does not apply. One can notice that the mean-field Bc2 vanishesat T ≈ 84 K. It was shown earlier that the mean-field Tc can be equally well de-termined by the temperature dependence of Bc2 and/or by the critical scaling ofthe data in the fluctuation regime [9, 10]. By comparison of Figs. 1 and 4, one canconclude that the mean field Tc corresponds to the minimum in the real frequencyshift and to the Tc defined as the half absorption in the plot of ∆(1/2Q).The lower part of Fig. 4 shows that depinning frequency for the measured thinfilm actually lies in the region 10 – 30 GHz, thus confirming the initial assump-tion that microwave frequencies are characteristic for vortex dynamics in HTSC.Although the depinning frequency decreases slightly above 60 K, it does not vanishup to 80 K, showing that the vortex lattice remains rigid and strongly pinned inpractically the whole of the superconducting region.4. ConclusionsWe have examined the microwave response of a superconducting YBCO thinfilm in magnetic fields up to 8 T and at temperatures down to 20 K. Both the realand imaginary parts of the complex frequency shift were measured, enabling thedetermination of both the real and imaginary parts of the complex conductivityin the field-temperature space. The zero-field complex conductivity shows the be-haviour characteristic of good single crystals, indicating that our thin film sampleis suitable for determination of intrinsic properties.From the measured field dependences, the upper critical fields up to 70 T havebeen determined, extending the Bc2(T ) curve down to 20 K. The values of Bc2 areslightly lower than those usually reported in the literature, but still reasonable fora thin-film sample. From the Bc2(T ) curve, the mean-field Tc is estimated to be 84K although the onset of superconductivity occurs above 88 K, indicating the widetemperature region of fluctuations.The depinning frequencies were also determined for the measured temperatures.They are larger than 10 GHz in the whole temperature region, in agreement withthe observations of Golosowsky et al. [3].FIZIKA A (Zagreb) 8 (1999) 4, 245–252 251barǐsić et al.: microwave conductivity of thin ybco film in magnetic fieldReferences1) W. N. Hardy, D. A. Bonn, D. C. Morgan, R. Liang and K. Zhang, Phys. Rev. Lett. 70(1993) 3999;2) J. I. Gittleman and B. Rosenblum, Phys. Rev. Lett. 16 (1966) 734;3) M. Golosowsky, M. Tsindlekht and D. Davidov, Supercond. Sci. Technol. 9 (1996) 1;4) B. Nebendahl, Ph. D. thesis, University of Stuttgart (2000);5) D.-N. Peligrad, B. Nebendahl, C. Kessler, M. Mehring, A. Dulčić, M. Požek andD. Paar, Phys. Rev. B 58 (1998) 11632;6) W. H. Press, B. P. Flannery, S. A. Teukolsky and W. T. Vetterling, Numerical Recipesin C, Cambridge University Press, New York (1990);7) H. Srikanth, B. A. Willemsen, T. Jacobs, S. Sridhar, A. Erb, E. Walker and R. Flükiger,Phys. Rev. B 55 (1997) R14733; H. Srikanth, Z. Zhai, S. Sridhar, A. Erb and E. Walker,Phys. Rev. B 57 (1998) 7986;8) A. Dulčić and M. Požek, Fizika (Zagreb) A 2 (1993) 43; A. Dulčić and M. Požek,Physica C 218 (1993) 449;9) I. Ukrainczyk and A. Dulčić, Europhys. Lett. 28 (1994) 199;10) I. Ukrainczyk and A. Dulčić, Phys. Rev. B51 (1995) 6788.MIKROVALNA VODLJIVOST TANKIH LISTOVA YBCO U MAGNETSKOMPOLJUMjerili smo mikrovalni odziv tankog filma visokotemperaturnog supravodičaYBa2Cu3O7−δ u širokom području temperatura i magnetskih polja. Iz izm-jerenog kompleksnog frekventnog pomaka izračunali smo kompleksnu vodljivost.Numeričkom prilagodbom modela efektivne vodljivosti u miješanom stanju odredilismo vrijednosti gornjeg kritičnog polja Bc2 (T ) i frekvencije opuštanja ω0(T ).252 FIZIKA A (Zagreb) 8 (1999) 4, 245–252

Mikrovalna vodljivost tankih listova YBCO u magnetskom polju

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