PHYSICAL REVIEW B 67, 035102 ~2003!

Far-infrared phonon-polariton dispersion probed by terahertz time-domain spectroscopy

Seiji Kojima*Institute of Materials Science, University of Tsukuba, Tsukuba, Ibaraki 305-8573, Japan

Naoki Tsumura† and Mitsuo Wada TakedaDepartment of Physics, Faculty of Science, Shinshu University, Matsumoto, Nagano 390-8621, Japan

Seizi NishizawaCooperative Research Center, Faculty of Science, Shinshu University, Nagano, Nagano 380-8553, Japan

~Received 18 June 2002; published 6 January 2003!

We report observations of the intensity and phase transmission spectra related to phonon-polariton propa-gation using coherent far-infrared radiation for a high-quality ferroelectric bismuth titanate crystal plate. Inorder to determine the polariton-dispersion relation, the phase delay was determined minutely as a function ofthe THz radiation frequency in the region between 3 and 100 cm21. The anisotropy of polariton dispersionrelation was also successfully determined on thec plate simply by switching the polarization direction of anincident beam fromEia to Eib. The observed polariton dispersion relations are consistently reproduced by thecalculation using Kurosawa’s formula.

DOI: 10.1103/PhysRevB.67.035102 PACS number~s!: 78.47.1p, 71.36.1c, 77.84.Dy

oet

pise

u-ivnio

orctafretthe-e

arpo

fo00

eprbn

hen-n.o

herro-for

h-orfora-

sityr aialaron-ontion

f

ure-

ticsto-

d aactesthewn

fo-hee isthe

I. INTRODUCTION

Dielectric properties of terahertz~THz! regions are ofgreat importance due to the rich physical and chemical prerties in this range. Very recently the generation of coherTHz radiation by a femtosecond pulse laser has enabledvery promising technique of THz time-domain spectrosco~THz-TDS!.1–4 This technique has a better signal-to-noratio at frequency below 100 cm21 than conventional far-infrared Fourier transform spectroscopy. It is based ontrashort THz electromagnetic~EM! pulses, which are generated and detected by small photoconductive antennas drby femtosecond laser pulses. This time-gaged coherentture makes it possible to determine not only the transmissintensity but also its phase delay accurately. Furthermunique applications for dispersion relations for various extations have become possible. In fact, for a photonic crysby measuring the phase delay as a function of radiationquency, Wada and co-workers recently succeeded in dmining the dispersion curves of EM waves related tophotonic band structure.5,6 However, such a phase delay rlated to other excitations has not yet been reported, forample, for a bulk phonon-polariton. Phonon-polaritonsuniversally known as propagating EM waves coupled tolar optical phonon.

In ferroelectric materials, soft optic modes responsibleferroelectricity appear in the far-infrared region below 1cm21. The measurement of complex dielectric constantsTHz frequency is very useful. Since ferroelectric soft modare infrared active and they propagate as polaritons, thelariton dispersion in the far-infrared region gives very impotant information for both fundamental and technical prolems in ferroelectrics. The ferroelectric materials of curreinterest are mostly perovskite families with oxygen octadra. Their ferroelectricity originates dominantly from the istability of polar soft modes in a ferroelectric transitioTherefore, THz dynamics is very important for the study

0163-1829/2003/67~3!/035102~5!/$20.00 67 0351

p-nthey

l-

ena-ne,i-l,

e-er-e

x-e-

r

atso---t-

r

characterization of ferroelectric properties. As one of tgreat technological achievements in the 1990s, oxide feelectric thin films have attracted a great deal of attentionuse in nonvolatile memories.7,8 However, there are still someproblems to overcome in order to measure very higfrequency dielectric properties accurately for thin films or fvery thin plates. Consequently, an experimental methoddetermining THz dielectric properties is desired for fundmental and practical research.

In this paper, we report on a measurement of the intenand phase of complex transmission using THz-TDS foferroelectric bismuth titanate crystal, which is a key materin ferroelectric memories. We then show that this nonlinedispersion relation, determined from the phase delay, is csistently interpreted by taking account of phonon-polaritpropagation in the crystal. The observed dispersion relais in a good agreement with the calculated one.

II. EXPERIMENT

The sample used was a thinc-plate of a flux-grown bis-muth titanate Bi4Ti3O12 ~BIT! single crystal with the area o15315 mm2 and a thickness ofd50.23 mm. Since thecleavage perpendicular to thec axis is very strong, like micacrystals, very flat cleaved surfaces were used for measments. The THz time domain spectrometer used5 is shown inFig. 1. To reduce the absorption by water vapor, all the opand the sample were placed in a vacuum chamber. Femsecond pump pulses with a wavelength of 780 nm anpower of 20 mW were generated by a mode-locked compfiber laser with a repetition rate of 80 MHz. The pump pulswere focused by an object lens onto the biased gap ofphotoconductive antenna made of low-temperature groGaAs. The emitted THz radiation was collimated andcused by a pair of off-axis paraboloidal mirrors onto tsample. The spot size of the THz beam on the samplabout 2 mm in diameter. The signals transmitted from

©2003 The American Physical Society02-1

KOJIMA et al. PHYSICAL REVIEW B 67, 035102 ~2003!

FIG. 1. Experimental setup of the THz time domain spectrometer.

pive

rrhb

o-it

-igoiisni

rv

s,c

the-

the. 3.fer-pro-

in-0

LO

sample were collimated again, and focused by anotherraboloidal mirror onto a detector of a GaAs photoconductantenna. The received signals were gated using incidpulses. An ammeter was used to measure the dc photocuinduced by the transmitted radiation field from a sample. Twaveform of transmitted EM pulses was determinedchanging the delay time. The total acquisition time is 1 h andthe number of scan is 30.

III. RESULTS

BIT is one of the most important key materials in ferrelectric memories. BIT has a monoclinic-layered perovskstructure with the point groupm at room temperature. It undergoes a ferroelectric phase transition at 675 °C, and a htemperature paraelectric phase is tetragonal with the pgroup 4/mmm.9 The direction of spontaneous polarizationinclined at a small angle of about 4.5° toward the monoclia axis in thea-c plane. Thea- andc-axis components of thespontaneous polarization are 50 and 4mC/cm2, respectively.In the ferroelectric phase, the displacive nature was obsewith the underdamped soft optic mode at 28 cm21 and atroom temperature.10 Regarding optical phonon modeA8(x,z) andA9(y) modes are both infrared and Raman ative where the mirror plane is perpendicular to they axis.The soft optic mode has anA8(x,z) symmetry where thecoordinatez is parallel to thea axis.

Transmission spectra of thec plate of BIT were observed

03510

a-ententey

e

h-nt

c

ed

-

at room temperature by using THz-TDS.A8(x,z) andA9(y)modes are active when the light polarization is parallel toa axis (Eia) andb axis (Eib), respectively. First, the timedomain THz signal for the polarizationEia was recorded asshown in Fig. 2. Second, this signal was converted intofrequency-domain power and phase, as shown in FigThird, the transmission power was normalized by the reence one without the sample to be measured. The samecedure was carried out for the polarizationEib. Figures 4~a!and 4~b! show the frequency dependence of transmissiontensity and phase delay~f/2p! in a range between 3 and 10cm21 for Eia andEib, respectively. It is found thatf vs vshows nonlinear behavior near the gap edges at TO and

FIG. 2. The time-domain THz signals for the polarizationEia.

2-2

aseityon.la-

ed

la

th

s

ines

FAR-INFRARED PHONON-POLARITON DISPERSION . . . PHYSICAL REVIEW B67, 035102 ~2003!

FIG. 3. The frequency-domain power and phase for the poization Eia.

FIG. 4. Transmission intensity and phase shift spectra offerroelectric bismuth titanate crystal on thec plate for the polariza-tion along~a! thea axis and~b! theb axis. Closed and open circledenote the transmission intensity and phase shift, respectively.

03510

mode frequencies. The increase of the gradient in the phdelay at the edges indicate the slowing of group velocwhich is reasonable for the propagation of phonon-polaritIn order to determine the phonon-polariton dispersion retion, we calculated the wave vectork(v) of the phonon-polariton from the phase delay using the equationf5$k(v)2v/c% d, where c is the light velocity. Thus thedispersion relations were obtained as shown in Figs. 5~a! and5~b!. For the polariton dispersion,c2k2/v25«(v).11,12

When the damping of phonon was negligible, a factorizform of «~v! was derived by Kurosawa.13 Consequently, thepolariton-dispersion relation is given by

c2k2

v2 5«~v!5«~`!)i 51

NvLOi

2 2v2

vTOi2 2v2 . ~1!

Since the measured frequency is below 100 cm21, we usedthe following approximation to fit the data:

r-

e

FIG. 5. Dispersion relations of phonon-polariton for ac-platebismuth titanate crystal for the polarization along~a! thea axis and~b! theb axis. Closed circles denote observed values, and solid lare calculated curves using Eq.~2!.

2-3

ion

yo

fs

athiulkm

b

Raetr

-ro

-

n.

st-nt

theakorlari-ingtionl foreryun-ci-es torytter-silyers,them-

anoft

e-s ac-thre-on

oncyri-ns.there-n

ionalsoheedc-

er-is

ech-

24ing,

g,

KOJIMA et al. PHYSICAL REVIEW B 67, 035102 ~2003!

k~v!5A«~1!

cv)

i 51

2 H vLOi2 2v2

vTOi2 2v2J 1/2

, ~2!

where we renormalize the contribution of the modesi>3 tothe fitting parameter«~1!, as given by

«~1!5«~`!)i 53

NvLOi

2

vTOi2 . ~3!

In BIT, «~v! is anisotropic and depends on the polarizatdirection. For light polarization parallel to thea axis (Eia)and theb axis (Eib), we studied«a(v) and«b(v), respec-tively. For the two directions, two different low-frequencpolariton branches were separately observed down tcm21. The solid curves in Figs. 5~a! and 5~b! denote thecurves calculated by Eq.~2! using mode frequencies oA8(x,z) and A9(y) symmetries, respectively. There wagood agreement between the observed and calculpolariton-dispersions. Therefore, it is concluded that tnonlinear relation reflects the dispersion relation of bphonon-polariton. Table I, shows the values of fitting paraeters for observed polariton-dispersions.

IV. DISCUSSION

Up to now, phonon-polariton has been studied mainlyforward Raman scattering experiments.14,15The problem wasthe observation of low-frequency polariton below 100 cm21

because the intense elastic scattering causes the strongleigh wings which screen the polariton peak from Ramspectra. Although the lower limit had been markedly reducupon the use of a Raman spectrometer with the highest slight rejection of 10214 at 20 cm21, the observation below 20cm21 was still difficult.16 Since 1992, several different techniques for the observation of phonon-polariton were intduced such as impulsive stimulated Raman scattering~ISRS!with femtosecond laser pulses.17–20However, ISRS measurements on LiTaO3 and LiNbO3 resulted in conflicting resultsconcerning splitting in the low-frequency polaritobranches,20–22 whereas no such splitting is observed here

*Email address: kojima@bk.tsukuba.ac.jp†Present address: Tochigi Nikon Corp., Ohtawara, Tochigi 38625, Japan.1M. van Exter and D. Grischkowsky, Appl. Phys. Lett.56, 1694

~1990!.

TABLE I. Fitting parameters of Eq.~2!.

A8(x,z):Eia A9(y):Eib

vTO1 28.0 cm21 36.0 cm21

vLO1 32.5 cm21 42.0 cm21

vTO2 68.0 cm21 85.0 cm21

vLO2 74.5 cm21 98.5 cm21

« ~`! 6.76 6.76« ~1! 49.0 81.0« ~0! 79.2 149.0

03510

3

eds

-

y

ay-nday

-

Finally we discuss the advantages of THz-TDS for inveing low-frequency polariton. THz-TDS has four importaadvantages compared with previous methods. First, sinceincident beam is not intense visible light but rather weTHz radiation, no optical damage occurs in coloredopaque samples. Second, concerning extraordinary potons of which Raman tensor is off-diagonal, other scattermethods have serious problems. Since the polarizaplanes of incident and scattered beams are orthogonaextraordinary polaritons, these methods cannot cover vlow frequencies due to birefringence which causes theavoidable finite difference of wave vectors between the indent and scattering beams even if the scattering angle gozero. Therefore, in the low-frequency region, only ordinapolariton was studied by other methods, i.e., Raman scaing, ISRS and CARS, whereas, by THz-TDS, we can eameasure polariton frequency down to a few wave numbeven for extraordinary polaritons. Third, we can measurek dependence minutely without changing the optical geoetry, and the uncertainty ofk is very small especially forsmall k. In contrast, with Raman scattering,k is determinedby a scattering angle, and the uncertainty increases ask ap-proaches zero. Fourth, THz-TDS can be applied to Raminactive but IR-active modes, especially to ferroelectric smodes in paraelectric phases.

V. CONCLUSIONS

We studied phonon-polariton by using THz-TDS. The frquency dependence of the transmission phase delay wacurately measured for a high-quality ferroelectric bismutitanate crystal. The obtained phonon-polariton dispersionlation was well reproduced using the calculation basedKurosawa’s formula. The lowest branch of phonon-polaritdispersion was determined down to the very low frequenof 3 cm21, which cannot be attained by other optical expemental methods, especially for extraordinary polaritoTherefore, we believe that this is the first observation ofdispersion relation of phonon-polariton in the far-infraredgion by THz-TDS. The anisotropy of polariton dispersiowas also clearly observed simply by rotating the polarizatplane of the incident beam. The present measurementindicates the possibility of accurate determination of tdamping factor of the phonon-polariton in the far-infrarregion by using thek dependence of transmission and refletion amplitude.

ACKNOWLEDGMENTS

We thank Professor K. Sakata of Tokyo Science Univsity for providing the bismuth titanate single crystal. Thwork was supported in part by the Japan Science and Tnology Corporation.

-

2L. Thrane, R. H. Jacobsen, P. U. Jepsen, and S. R. KeidChem. Phys. Lett.240, 330 ~1995!.

3J. T. Kindt and C. A. Schmuttenmaer, J. Phys. Chem.100, 10 373~1996!.

4R. Harel, I. Brener, L. N. Pfeiffer, K. W. West, J. M. Vandenber

2-4

s

.

,

,

a-

n,

im-

FAR-INFRARED PHONON-POLARITON DISPERSION . . . PHYSICAL REVIEW B67, 035102 ~2003!

S. G. Chu, and J. D. Wynn, Phys. Status Solidi A178, 365~2000!.

5M. Wada, Y. Doi, K. Inoue, J. W. Haus, and Z. Yuan, Appl. PhyLett. 70, 2966~1997!.

6T. Aoki, M. Wada, J. W. Haus, Z. Yuan, M. Tani, K. Sakai, NKawai, and K. Inoue, Phys. Rev. B64, 045 106~2001!.

7C. A. Arajo, J. D. Cuchiaro, M. C. Scott, and L. D. MacMillanNature~London! 374, 627 ~1995!.

8J. F. Scott, Phys. Today51 ~7!, 22 ~1998!.9E. C. Subarao, J. Phys. Chem. Solids23, 665 ~1962!.

10S. Kojima and S. Shimada, Physica B219&220, 617 ~1996!.11K. Huang, Proc. R. Soc. London, Ser. A208, 352 ~1951!.12Max Born and Kun Huang,Dynamical Theory of Crystal Lattice

~Oxford University Press, Oxford, 1954!, Chap. II.8.13T. Kurosawa, J. Phys. Soc. Jpn.16, 1298~1961!.14C. H. Henry and J. J. Henry, Phys. Rev. Lett.15, 964 ~1965!.

03510

.

15R. Claus, L. Merten, and J. Brandmuller,Light Scattering byPhonon-Polaritons, Springer Tracts in Modern Phys. Vol. 75~Springer-Verlag, Berlin, 1975!.

16S. Kojima and T. Nakamura, Jpn. J. Appl. Phys.19, L609 ~1980!.17P. C. M. Planken, L. D. Noordam, J. T. M. Kennis, and A. L

gendijk, Phys. Rev. B45, 7106~1992!.18H. J. Bakker, S. Hunsche, and H. Kurtz, Phys. Rev. B48, 13 524

~1993!.19H. J. Bakker, S. Hunsche, and H. Kurtz, Phys. Rev. B50, 914

~1994!.20G. P. Wiederrecht, T. P. Dougherty, L. Dhar, and K. A. Nelso

Phys. Rev. B51, 916 ~1995!.21T. Watanabe, S. Yoshioka, M. Kasahara, K. A. Nelson, T. F. Gr

mins, and T. Yagi, J. Korean Phys. Soc.35, S1400~1999!.22S. Kojima, Ferroelectrics223, 63 ~1999!.

2-5