Submillimeter spectroscopy of tilted Nd 1.85 Ce 0.15 CuO 4−δ films: Observation of amixed ac -plane excitationA. Pimenov, A. V. Pronin, A. Loidl, A. P. Kampf, S. I. Krasnosvobodtsev, and V. S. Nozdrin Citation: Applied Physics Letters 77, 429 (2000); doi: 10.1063/1.126999 View online: http://dx.doi.org/10.1063/1.126999 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/77/3?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Complex microwave conductivity of Pr 1.85 Ce 0.15 CuO 4 − δ thin films using a cavity perturbation method J. Appl. Phys. 104, 123914 (2008); 10.1063/1.3054293 Doping and Momentum Dependence of Charge Dynamics in Nd2−x Ce x CuO4 (x = 0, 0.075, and 0.15) Studiedby Resonant Inelastic Xray Scattering AIP Conf. Proc. 850, 403 (2006); 10.1063/1.2354756 On the nature of the anisotropy of the resistivity of Nd 2−x Ce x CuO 4+δ with different cerium and oxygenconcentrations Low Temp. Phys. 30, 885 (2004); 10.1063/1.1820018 Superconducting Nd 1.85 Ce 0.15 CuO 4−y bicrystal grain boundary Josephson junctions Appl. Phys. Lett. 72, 2888 (1998); 10.1063/1.121449 Properties of polycrystalline (Nd1−x Gd x )1.85Ce0.15CuO4−y compounds J. Appl. Phys. 81, 4250 (1997); 10.1063/1.365137

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Submillimeter spectroscopy of tilted Nd 1.85Ce0.15CuO4Àd films:Observation of a mixed ac -plane excitation

A. Pimenov,a) A. V. Pronin, and A. LoidlExperimentalphysik V, EKM, Universita¨t Augsburg, 86135 Augsburg, Germany

A. P. KampfTheoretische Physik III, EKM, Universita¨t Augsburg, 86135 Augsburg, Germany

S. I. Krasnosvobodtsev and V. S. NozdrinLebedev Physics Institute, Russian Academy of Sciences, 117942 Moscow, Russia

~Received 21 March 2000; accepted for publication 24 May 2000!

The anisotropic conductivity of a series of tilted Nd1.85Ce0.15CuO42d thin films was measured byquasioptical spectroscopy in the frequency range 6 cm21,n,40 cm21. Two characteristic featureshave been observed in the low-temperature transmission spectra. The first one atn512 cm21 wasshown to reflect thec-axis plasma frequency of Nd1.85Ce0.15CuO42d . The second feature representsa mixed ab-plane/c-axis excitation. The frequency of this resonance may be changed in acontrollable way by rotating the polarization of the incident radiation. ©2000 American Instituteof Physics.@S0003-6951~00!03629-9#

Among the cuprate superconductors, Nd22xCexCuO4

~NCCO! has attracted considerable interest because it can beconsidered as an electron-doped compound,1 which revealsthe (T8) tetragonal structure and is extremely two-dimensional.1,2 Earlier in-plane microwave experiments onNCCO ~Refs. 3–5! appeared to be consistent with the con-ventionals-wave BCS predictions. However, recent data in-cluding flux quantization6 and penetration depth atmicrowave7 and at rf frequencies8 have provided strong ex-perimental evidence ford-wave symmetry of the pairingstate.

In contrast to a number ofab-plane experiments, thereexists minimal information concerning thec-axis propertiesof NCCO, primarily due to the small dimensions of thesamples along thec-axis. Most experiments onc-axisdynamics9,10 were carried out using ceramic NCCO samples.Alternatively, the method of grazing-incidence reflection isknown to be a powerful technique in extractingc-axis prop-erties of strongly anisotropic superconductors.11 The experi-ments using, instead of the grazing reflection, a tiltedsample12 and normal-incidence geometry may be consideredas a modification of this method.

In this letter, we present the results of submillimeter-wave (6 cm21,n,40 cm21! experiments on tiltedNd1.85Ce0.15CuO42d films at low temperatures. The spectrareveal two features below the superconducting transition,which are identified as:~i! plasma resonance along thec-axis, and~ii ! mixed ab-plane/c-axis excitation. Using themeasurements at different polarizations of the incident radia-tion, it was possible to separate the effective conductivity ata tilted angle into components within theab plane and alongthe c axis.

The experiments were carried out on differentNd1.85Ce0.15CuO42d films yielding similar results. For sim-plicity, the results from only one film are presented. The

films were prepared using a two-beam-laser deposition onyttrium-stabilized ZrO2 substrates.13 X-ray analysis revealedthe c-axis orientation of the films. The substrate of the filmwas tilted from the~001! plane by an anglea50.8°60.4°.Therefore, the film was also tilted by the same angle fromthe idealc-axis orientation. Theac-susceptibility measure-ments revealed a narrow superconducting transition(DT@10%290%#50.9 K) with the onset temperature of20.1 K. The film thickness, estimated from the depositiontime, wasd5170 nm.

The transmission experiments in the frequency range6 cm21,n,40 cm21 were carried out in a quasiopticalarrangement,14 which allows the measurements of both,transmission and phase shift of a film on a substrate. Theproperties of the substrate were determined in a separate ex-periment. Utilizing the Fresnel optical formulas for the com-plex transmission coefficient of the substrate–film system,the absolute values of the complex conductivitys* 5s1

1 is2 were determined directly from the observed spectrawithout any approximations. The radiation in this method iscontinuously tunable in frequency and is linearly polarized.This allows one to perform experiments for different direc-tions of the currents induced in the sample. The geometry ofthe transmission experiment is represented in the inset ofFig. 1.

Figure 1 shows the transmission spectra of aNd1.85Ce0.15CuO42d thin film at T56 K and atT'TC . Anew feature that can be observed in the spectrum of the su-perconducting state is a transmission peak atn512 cm21.This feature may be called ‘‘antiresonance’’ because it cor-responds to anincrease in transmission. In addition tothis antiresonance, a suppression of the low-temperaturetransmission is seen in the frequency range18 cm21 , n , 30 cm21. This suppression corresponds to abroad resonance and is somewhat masked by the interferencepattern caused by the substrate.

Figure 2 shows the effective conductivity of the film asa!Electronic mail: andrei.pimenov@physik.uni-augsburg.de

APPLIED PHYSICS LETTERS VOLUME 77, NUMBER 3 17 JULY 2000

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calculated from transmission and phase-shift spectra forT56 K. Because the exact expressions for the complex trans-mission coefficient were used, the substrate interference pat-terns are absent in this presentation. The effective conductiv-ity is shown for different orientations of incident radiationand is labeled by the anglew ~inset of Fig. 1!.

The comparison of Figs. 1 and 2 clearly shows that azero crossing ofs2 and a peak in the loss function Im(1/«* )correspond to the antiresonance atn512 cm21. The suppres-sion of the transmission atn;23 cm21 yields a peak in thereal part of conductivity. Interestingly, both features exhibita completely different dependence upon the polarizationplane angle~w!. As will be seen below, the antiresonance at12 cm21 corresponds to thec-axis plasma frequency and is,therefore, independent of incident radiation polarization. Incontrast, the peak at 23 cm21 (w560°) represents the mixed

ab-plane/c-axis excitation. The degree of mixing may becontrolled by the geometry of the experiment, which ex-plains thew dependence of the peak position.

The spectra forw50° correspond to currents flowingonly within the ab planes and resemble the spectra of asuperconductor below the gap frequency:s1 has only a weakfrequency dependence and is suppressed by approximately afactor of 3 compared to the normal-state conductivity,whereass2 is strongly enhanced compared to the normalstate and reveals approximately a 1/v frequency dependence.From its slope the low-frequency penetration depthlab(6 K)5230630 nm can be estimated.

In order to calculate the effective conductivity of a tiltedsample, consider a free-standing film of thicknessd in auniform electromagnetic fieldEe2 ivt, as shown in the insetof Fig. 1. For simplicity, the film is assumed to be thin com-pared to the penetration depth,d!l. In this case, the currentand field distribution may be considered to be uniform. Tak-ing into account the charges formed at the surface, the fol-lowing equation for the effective conductivity is obtained:

seff52 i«0v~sa cos2 a1sc sin2 a!1sasc

2 i«0v1sa sin2 a1sc cos2 a. ~1!

Here, «0 is the permittivity of free space,sa (sc) is thecomplex conductivity in theab plane~along thec axis!, andv is the angular frequency.

Within the approximationa'sina!1 and usau@uscu,Eq. ~1! can be written as

seff5sa~sc2 i«0v!

saa21~sc2 i«0v!. ~2!

Two simple conclusions can be immediately drawn fromthis expression. If the real parts of the conductivities(s1a ,s1c) are only weakly frequency dependent, then~i! theeffective conductivity should reveal a peak if Im@saa

21(sc

2i«0v1)#50, and~ii ! the inverse conductivity should show apeak ~i.e., longitudinal resonance! if Im @sc2i«0v0#50. As-suming that only the high-frequency dielectric constant(2 i«0«c,`v) and the superconducting condensate( inse

2/mcv) contribute to the low-temperaturec-axis con-ductivity, the critical frequency in case~ii ! can be estimatedv0

25nse2/@mc(e`11)#, which closely resembles the ex-

pression for the screened plasma frequency. Evidently, theexpression forv0

2 does not depend upon the tilt angle. On thecontrary, a substantial angular dependence is expected forthe resonance atv1 . The change of the tilt angle may beeasily achieved experimentally by rotating the polarization ofthe incident radiation. In this case, the effective tilt anglemay be obtained asaeff5a0 sinw, wherew50° correspondsto the polarization within theab plane.

Using Eq.~1!, it is possible to calculate thec-axis prop-erties of the Nd1.85Ce0.15CuO42d film. The dielectric functionalong thec axis, «c* 5 isc /v«0 , is presented in Fig. 3. Thedata for all polarizationsw collapse into a single curve,thereby supporting the applied concept. It should be notedthat the uncertainty in determination ofa0 represents themost relevant source of errors in the determination of«c* .However, the variation of this angle influences only the ab-solute values of the conductivity and leaves the overall fre-quency dependence unchanged.

FIG. 1. Submillimeter-wave transmission spectra of a Nd1.85Ce0.15CuO42d

film at T5TC ~20 K! and atT56 K. Lines are drawn to guide the eye.Arrows indicate the position of thec-axis plasma frequency and of a mixedac-plane excitation. The inset shows the geometry of the transmission ex-periment.

FIG. 2. Low-temperature conductivity spectra of a Nd1.85Ce0.15CuO42d filmfor different orientations of the incident radiation. Lines are drawn to guidethe eye. Upper panel:s1 . Middle panel:s2 . Lower panel: imaginary part ofthe loss function Im(1/«* ). Arrows indicate the position of thec-axisplasma frequency and of the mixedac-plane excitation.

430 Appl. Phys. Lett., Vol. 77, No. 3, 17 July 2000 Pimenov et al.

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As demonstrated in Fig. 3, the high-frequency(n.20 cm21) c-axis dielectric constant ofNd1.85Ce0.15CuO42d is positive, which can be ascribed to thephonon contribution. A superconducting response becomesdominant for n,15 cm21, from which the low-frequencypenetration depth may be estimated aslc(6 K)52468m.From the zero crossing of the dielectric constant, thescreened plasma frequency can be extracted (np

512 cm21). This value is in excellent agreement with thepowder data of Shibata and Yamada9 and with the recentresults of Singleyet al.15

In conclusion, the anisotropic properties of a series ofslightly tilted Nd1.85Ce0.15CuO42d thin films were measuredin the submillimeter frequency range. Two new featureswere observed in the low-temperature transmission spectra

which showed different polarization dependencies. The anti-resonance atn512 cm21 corresponds to thec-axis plasmafrequency of Nd1.85Ce0.15CuO42d . The second resonancerepresents a mixedab-plane/c-axis excitation. The fre-quency of this resonance can be changed in a controllableway by rotating the polarization of the incident radiation.

The authors acknowledge stimulating discussions withR. Hackl, W. N. Hardy, and T. Timusk. This work was sup-ported by BMBF~Contract No. 13N6917/0-EKM!.

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FIG. 3. Dielectric function of a Nd1.85Ce0.15CuO42d film along thec-axis.Upper panel: «1 . Lower panel: Imaginary part of the loss functionIm(1/«* ). Lines are calculated within the following assumptions:~i! s1c isfrequency independent and~ii ! only high-frequency dielectric constant«`

and superonducting condensate2(lcc/v)2 contribute to«1 .

431Appl. Phys. Lett., Vol. 77, No. 3, 17 July 2000 Pimenov et al.

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