Raman scattering by polaritons in tetragonal BaTiO3

Solid State Communications,

Vol. 7, Pp. 139—142, 1969.

Pergarnon Press.

Printed in Great Britain

RAMAN SCATTERING BY POLARITONS IN TETRAGONAL BaTiO3* A. Pinczuk, E. Burstein and S. Ushioda Physics Department and Laboratory for Research on the Structure of Matter University of Pennsylvania, Philadelphia, Pennsylvania (Received 6 September 1968)

Raman scattering spectra by polaritons of A1 symmetry in tetragonal BaTiO3 at room temperature are used to establish the q ~ 0 TO phonon frequencies and to estimate the dielectric constant along the ferroelectric axis e,,~. Values of ~ = 37 ±5 and ~ = 38 ±6 are found from the LST relation and the polariton dispersion curves respectively. It is also found that the two broad bands centered at 270 cm’ and 520 cm’ correspond to TO phonons. Their widths are explained by large anharmonic couplings and a frequency dependent damping constant.

IN THIS letter, we present data on the Raman scattering by polaritons (coupled photon—phonon modes) of A1 symmetry in tetragonal BaTiO3 at room temperature. These data establish the frequencies of the TO phonons of A1 symmetry at q ~ 14 0 over whichthe there hasq been some controFurther, c&. vs. curves derived versy. from the data yield a value of 38 ±6 for the low frequency dielectric constant along the

grating spectrometer designed and built by Dr. A. Filler at the University of Pennsylvania. The detector was a S20 photomultiplier tube and the spectrum was recorded on a digital output. The results discussed here correspond to the zz of the Raman thecomponent incident radiation along scattering the x axis,tensor so thatwith on the basis of the polarization selection rules7 only the A 1 modes will contribute to the spectra. The forward scattering geometry was chosen in a way that the scattering wave vector, qsuch = k 0 k8, was along the y or z axis. The scattered light that reached the spectrometer was within a cone of 0.25°aperture inside the sample.

c-(ferroelectric-) axis. Essentially the same value (~~= 37 ±5) is obtained by means of the the 5 and Lyddane, Sachs, Teller (LST) relation LO and TO phonon frequencies obtained in our experiments,

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The forward scattering experiments were 6 which carried using aextinctions single domain crystal showed out complete between crossed polarizers. A 50 mW Spe,rry-Gyroscope He—Ne laser operating at 6328 A was used to excite the spectra which were analyzed with a double *

bands of A The results indicate that the1 three , 270cm’ and 1 symmetry centered at 170cm 520 cm’ in the spectra for scattering wave vectors outside the polariton region, shown in Fig. 1(a), display a dependence of frequency on the magnitude of the scattering wave vector as expected for polaritons. We may therefore condude that these bands correspond to the TO

Supported in part by the U.S. Army Research Office, Durham. 139

140

RAMAN SCATTERING BY POLARITONS IN TETRAGONAL BaTiO3

Vol.7, No.1

270

q1!Y

I85 (b) 9#Z

475

FIG. 1. (a) Raman spectrum for TO phonons of A1 symmetry. (b) Raman spectrum for LO phonons

of A1 symmetry. The incident and scattered light are polarized along the z-axis. phonons at the Brillouin zone center. The assignment of the two broad bands at 270 cm~ and 520 cm~in the large angle scattering spectra

with the value, ~ the LST relation;

have been the subject of some discussion. Pinczuk et al.’ have, on the basis of the observed shifts in the frequency of the bands with direction of the scattering wave vector relative to the c-axis,8 concluded thathand, the bands were first On the other Di Domenico et al.3 order. and Rousseau and Porto4 consider the bands to originate in higher order scattering processes. The polariton data clearly confirm the assignments of Pinczuk et al.’ The frequencies of the LO phonons were obtained from the spectrum shown in Fig. 1(b) (the bands labeled a. and ~ are in part due to backscattering from the TO phonons at 270 cm’ and 520 cm and in part to higher order processes). The results of our experiments are summarized in Table 1.

1~~ co~

~~

1w

~

‘2

/

tn

in which and wT,l are the LO and TO phonon frequencies in are Table 1 and ~ 5.07.~Thosegiven values considerably lower than the value of 80 ~ obtained by direct electrical measurements. The estimates obtained from the LST relation and the polariton dispersion curves are more reliable, since they are not sensitive to the spurious effects present in ferroelectric materials to which the capacitance measurements are sensitive.

Table 1. Optical phonons of A BaTiO3. w~and

In Fig. 2 we show the experimentally determined w vs. q curves for the polaritons corresponding to phonons of A1 symmetry propagating along the y-axis. On extrapolating the low frequency polariton branch to the origin, we obtain from the slope at w ~ 0 a value, = 38 ± 6, for the static dielectric constant along the c-axis. This value is in agreement

37 ±5, calculated from

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1 symmetry in are TO and LU phonon frequencies

WL1

S~ (cm~) 170 270 520

1.52 4.24 0.20

(cm 185 475 725

1)

Vol.7, No.1

RAMAN SCATTERING BY POLARITONS IN TETRAGONAL BaTiO3

t1

(cm-’)

141

a

5’

SOC

400

-

300

20 S~OPe’E

>,

~.

0.65’ I

0

I

2000

I

3000

4000

I

5000

6000

q(cm’)

FIG. 2. Frequency versus scattering wave vector curves for polaritons of A1 symmetry. The various points correspond to scattering angles varying from 0.65° to 8.5°. The contribution of each mode to the static dielectric constant can be evaluated by assuming a simplified dielectric constant of the form: Re

E~(~~) = ~

I

~

~‘

mnl

S~o4~(~_ci.2)’I 2 2)2÷~y2Ct)2)’(1) (wT~ — w

for a given optical phonon are determined by the strengths of the anharmonic coupling parameter and by the combined density of states of the phonons coupled by anharmonicity. The neutron scattering data density for BaTiO3 ‘° indicate that a large combined of two phonon states occurs at the Brillouin zone boundary in the

where S 1 is the parameter which measures the contribution of the ith mode to 08 and )~is theScorresponding damping constant. The values of 1 were calculated by assuming that Re e~(w) goes to zero at the LO phonon frequencies. This is a reasonable assumption since, as shown by Fig. 1(b), the LO phonons exhibit well defined bands with relatively small damping. The results for S, insensitive to the values of 1. Itmakes is interesting to note thatare thegiven modeinat Table 270 cnr’ the largest contribution to c8.

region between 230 cm’ and 280 cm~ due to acoustical phonons. A large combined density1 of states also occurs in the region of 520 cm~ due to processes which involve two TO phonons. This can readily account for the large width of the first order bands. Finally, our data also exhibit the interference effect on the 170 cm~mode previously identified 4 This was assigned to by andbetween Porto. first and second order an Rousseau interference bands. In view of our results concerning the mode at 270 cm~ the possibility has to be considered that the interference occurs between (bands corresponding to) two q ~ 0 TO phonons. Such an interference can occur when the two TO phonons are anharmonically coupled to the same (two or more) acoustical phonons. This coupling mechanism between TO phonons has been used by Barker and Hopfield” to interpret the reflectivity spectra of SrTiO 3 and RaTiO3 ,

A satisfactory fit of the experimental w vs. q curves cannot be obtained using an expression for the dispersion relation involving frequency independent damping factors. Efforts to fit the data using frequency dependent damping factors and frequency dependent TO phonon frequencies are now under w~py.As shown by Maradudin and Fein,9 the frequency dependent damping factors

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RAMAN SCATTERING BY POLARITONS IN TETRAGONAL BaTiO3

Acknowledgement

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Vol.7, No.1

We would like to acknowledge helpful discussions with A.A. Maradudin. REFERENCES

1.

PINCZUKA.,TAYLORW., BURSTEIN E. and LEFKOWITZ L, Solid State Commun. 5, 429 (1967).

2.

PARSONS J.L. and RIMAI L., Solid State Commun. 5, 423 (1967) and RIMAI L., PARSONS J.L., HICKMOTT J.T. and NAKAMURA T., Phys. Rev. 168, 623 (1968).

3. 4.

DIDOMENICO M.,Jr., WEMPLES.H.,PORTO S.P.S. and BAUMAN R.P., Phys. Rev, in press. ROUSSEAU D.L. and PORTO S.P.S., Phys. Rev. Lett. 20, 1354 (1968).

5.

COCHRAN W., Z. Krist. 112, 465 (1959).

6.

Flux grown by Dr. I. Lefkowitz.

7.

LOUDON R., Adv. Phys. 13, 423 (1964).

8.

It should be noted that the frequency shifts with direction of the scattering vector, and the dependence of the polariton frequency on the magnitude of the scattering wave vector, both arise from the associated macroscopic electric fields. ‘~‘

9. 10. 11.

MARADUDIN A.A. and FEIN A.E., Phys. Rev. 128, 2589 (1962). SHIRANE G., FRAZER B.C., MINKIEWICZ V.J., LEAKE J.A. and LINZ A., Phys. Rev. Lett. 19, 234 (1967). BARKER A.S. and HOPFIELD J.J., Phys. Rev. 135, 1732 (1964).

Des spectres de diffussion Raman des polaritons avec symétrie A1 du Ti03 Ba tetragonal obtenus a temperature ambiente donnent les fréquences des phonons TO a q ~ 0 et une estimation de Ia constante diélectrique dans la direction ferroélectrique Nous avons obtenue = 37 ± 5 et C08 = 38 ±6 de la relation LST et des courbes de dispersion des polaritons. Nous avons aussi verifié que deux bandes avec des fréquences de 270 cm et 520 cm I correspondent aux modes TO. Les largeurs de ces bandes sont expliquées par des couplages anharmoniques des phonons. ~

,~