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doi:10.1016/j.ph

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Physica B 359–361 (2005) 1150–1152

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Direct observation of Drude behavior in the heavy-fermionUPd2Al3 by broadband microwave spectroscopy

Marc Schefflera,, Martin Dressela, Martin Jourdanb, Hermann Adrianb

a1. Physikalisches Institut, Universitat Stuttgart, Pfaffenwaldring 57, 70550 Stuttgart, GermanybInstitut fur Physik, Johannes Gutenberg Universitat, 55099 Mainz, Germany

Abstract

Previous optical studies on the heavy-fermion system UPd2Al3 down to frequencies of about 1 cm1ð¼ 30GHzÞ

revealed a well-pronounced pseudogap at low frequencies (below 3 cm1) that was attributed to magnetic correlations.

Thus, the optical conductivity at even lower frequencies is of notable interest because the Drude roll-off (the high-

frequency characteristic of a metal which will give information on the quasiparticle dynamics) remained hidden at

extremely low frequencies.

Using a novel cryogenic broadband microwave spectrometer employing the Corbino geometry we have studied the

complex optical conductivity of UPd2Al3 thin films in the frequency range from 45MHz to 20GHz at temperatures

from 1.65 to 300K: Our spectra reveal the emergence of a strong Drude-like conductivity roll-off at frequencies of onlya few GHz as the temperature is decreased (in agreement with the increase of the DC conductivity).

r 2005 Elsevier B.V. All rights reserved.

PACS: 71.27.þa; 72.15.Lh; 78.20.e

Keywords: Drude response; Heavy quasiparticles; Microwave conductivity

Heavy fermions owe their name to the very largeeffective mass (compared to the free electron mass)that is used to quantitatively describe experimentalfindings, with the huge specific heat being the bestreputed. This large effective mass is a way toexpress the rather reluctant reaction of the chargecarriers to external excitations, a behavior that can

e front matter r 2005 Elsevier B.V. All rights reserve

ysb.2005.01.308

ng author. Tel.: +49711 685 4893;

5 4886.

ss: scheffl@pi1.physik.uni-stuttgart.de

be probed most directly by studying the character-istic time scales, in particular the relaxation time ofelectronic transport. Following the Drude modelof metallic conduction [1], the relaxation time tcan directly be obtained from the frequency-dependent ðo ¼ 2pf Þ conductivity

sðoÞ ¼ s1ðoÞ þ is2ðoÞ ¼s0

1 iot

¼ s01þ iot1þ o2t2

, ð1Þ

d.

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T (K)

108

109

1010f (HZ)

102

101

10000

100000

σ 1(Ω

–1cm

–1)

Fig. 1. Real part s1 of the conductivity of a UPd2Al3 thin film,obtained as a function of frequency as well as temperature.

M. Scheffler et al. / Physica B 359– 361 (2005) 1150–1152 1151

since t defines the scattering rate G ¼ 1=t; where astrong decrease in s1ðoÞ (‘Drude roll-off’) and apeak in s2ðoÞ occur. At low frequencies sðoÞapproaches the DC conductivity

s0 ¼ne2t

m, (2)

which depends on the charge carrier density n

and their effective mass m as well as the relaxationtime t: For heavy fermions a joint increase ofeffective mass and relaxation time is expected [2].Thus, the scattering rate G of a heavy-fermionsystem is strongly reduced compared to normalmetals.For a normal metal this characteristic fre-

quency range of the Drude roll-off is in the farinfrared, whereas for heavy fermions it is redu-ced to the submillimeter or even microwavefrequency ranges. There were extensive experi-mental studies on the optical properties of heavyfermions in the far-infrared frequency range [3,4]which showed that the Drude roll-off in s1ðoÞindeed has to occur at very low frequencies butdue to fundamental experimental difficulties theactual scattering rate could only be reachedexperimentally by the use of microwave reso-nant cavities which by definition are restric-ted to discrete frequencies. Thus, there havebeen only very few studies that unambiguouslycover the scattering rate and these stem from thecombination of several setups and even severalsamples [5].For UPd2Al3 recent submillimeter spectroscopy

studies [6,7] showed that the Drude roll-off of thiscompound has to occur below 30GHz; at ex-tremely low frequencies even for heavy-fermionstandards. Thus, we have studied the high-frequency conductivity of UPd2Al3 using a re-cently developed cryogenic broadband microwavespectrometer that covers the frequency range from45MHz to 20GHz and temperatures down to1:65K [8]. The spectrometer employs the Corbinogeometry, i.e. the sample terminates a coaxialtransmission line, thus reflecting the microwavesignal travelling on the line. The complex reflectioncoefficient then directly yields the complex con-ductivity of the sample.

The UPd2Al3 samples for this study are epitaxialthin films grown by MBE [9]. Their high quality isevident from X-ray diffraction and DC resistivity,in particular from large residual resistivity ratiosof up to 30.The frequency and temperature dependence of

s1 as obtained on one of the samples is shown inFig. 1. Here the low-frequency conductivitydirectly corresponds to the DC conductivity foundin independent measurements on the same sampleand exhibits the well-known characteristics [10](upon cooling from 300K: Kondo-like conductiv-ity decrease, increase in the coherent state below80K; kink at the Neel temperature of 14Kfollowed by a strong increase up to the super-conducting transition at 2K which is omitted fromthe figure). At high temperatures the conductivityis frequency-independent in the accessible fre-quency range but at the lowest temperatures astrong decrease in s1ðoÞ is evident above approxi-mately 1GHz: Close inspection of these low-temperature spectra shows that the conductivity(real as well as imaginary parts) is well describedby Eq. (1). Thus, the heavy fermions in UPd2Al3act like a Drude metal with an extremely lowscattering rate.Below 6K; where the full Drude roll-off can be

observed, the temperature dependence of thescattering rate corresponds to that of the DCresistivity r0 ¼ 1=s0: Following Eq. (2) this

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M. Scheffler et al. / Physica B 359– 361 (2005) 1150–11521152

directly shows that the ratio n=m of charge carrierdensity and effective mass is temperature-indepen-dent. From this ratio, using Eq. (2) and literaturedata for the effective mass [10], it can be deducedthat the density of charge carriers participating inthe transport processes that dominate the con-ductivity spectrum is much less than one electronper uranium atom.This finding is backed by an analysis of the

microwave data in terms of the extended Drudemodel [1] which allows for a frequency-dependentscattering rate. As evident from the close resem-blance of the conductivity spectra to the Drudeformula, the experimentally determined scatteringrate is frequency-independent for most of theaccessible frequency range and deviations onlyoccur at its high-frequency limit. But these devia-tions are stronger than expected from Fermi-liquidtheory [11] and can be interpreted as the result of a

combined response of independent conductingsubsystems.

References

[1] M. Dressel, G. Gruner, Electrodynamics of Solids: Optical

Properties of Electrons in Matter, Cambridge University

Press, Cambridge, 2002.

[2] A.J. Millis, P.A. Lee, Phys. Rev. B 35 (1987) 3394.

[3] L. Degiorgi, et al., Z. Phys. B 102 (1997) 367.

[4] L. Degiorgi, Rev. Mod. Phys. 71 (1999) 687.

[5] P. Tran, et al., Phys. Rev. B 65 (2002) 205102.

[6] M. Dressel, et al., Phys. Rev. Lett. 88 (2002) 186404.

[7] M. Dressel, et al., Phys. Rev. B 66 (2002) 035110.

[8] M. Scheffler, M. Dressel, unpublished. For a comparable

instrument see: J.C. Booth, et al., Rev. Sci. Instrum. 65

(1994) 2082.

[9] M. Huth, et al., Physica B 199–200 (1994) 116.

[10] C. Geibel, et al., Z. Phys. B 84 (1991) 1.

[11] D. Pines, P. Nozieres, The Theory of Quantum Liquids,

vol. I: Normal Fermi Liquids, Benjamin, New York, 1966.