EFFET RAMAN ET THÉORIERAMAN SCATTERING FROM FERROELECTRIC MODES IN THE KDP ISOMORPHOUS PHOSPHATES AND ARSENATES

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EFFET RAMAN ET THÉORIERAMAN

SCATTERING FROM FERROELECTRIC MODES IN THE KDP ISOMORPHOUS PHOSPHATES AND

ARSENATES

J. Ryan, R. Katiyar, W. Taylor

To cite this version:

J. Ryan, R. Katiyar, W. Taylor. EFFET RAMAN ET THÉORIERAMAN SCATTERING FROM FERROELECTRIC MODES IN THE KDP ISOMORPHOUS PHOSPHATES AND ARSENATES.

Journal de Physique Colloques, 1972, 33 (C2), pp.C2-49-C2-51. �10.1051/jphyscol:1972211�. �jpa-

00214947�

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EFFET RAMAN ET THEORIE

RAMAN SCATTERING FROM FERROELECTRIC

MODES IN THE KDP ISOMORPHOUS PHOSPHATES AND ARSENATES

J. I?. RYAN, R. S. KATIYAR and W. TAYLOR Physics Department, University of Edinburgh, Scotland

RbumB.

- Nous avons etudit les spectres Raman a basse frequence pour un certain nombre d'isomorphes

a

KH2P04 (KDP) dans la phase paraelectrique pour une certaine gamme de tempe- ratures.

Nous avons prolong6 les mesures jusqu'a des frequences de

250

cm-1 et fait coincider avec notre modkle l'interfkrence caracteristique entre les phonons optiques fortement amortis et ceux

a

basse frkquence ayant la meme symetrie.

Nous avons donne la premii.re observation d'un mode amorti de symetrie B2 dans le spectre Raman pour (NH4)H2P04. La variation du temps de relaxation de Debye en fonction de la temp&

rature

a

la fois pour les modes

E

et B2 dans (NH4)H2P04 est comparee aux mesures dielectriques.

Abstract. -

The low frequency Raman spectra of a number of KH2P04 (KDP) isomorphs have been recorded over a range of temperatures in the paraelectric phase. We have extended the measurements to frequencies of

²⁵⁰

cm-1 and have included in our model fitting the characte- ristic interference between the overdamped and the low frequency optical phonon of the same symmetry. We report the first observation of an overdamped mode of BZ symmetry in the Raman spectrum of (NH4)H2P04. The temperature dependence of the Debye relaxation times for both

E

and BZ modes in ( N H ~ ) H z P O ~ are compared with dielectric measurements.

Since the first observation of an overdamped mode in the Raman spectrum of KH2P0, by Kaminow and Damen [I], there have been several reports of similar experiments. The most extensive of these is that of Wilson [2]. In each case, a temperature depen- dent overdamped mode of B2 symmetry, appearing as wings on the Rayleigh line, is observed, and has been fitted with the spectral response function

where

and

,(a)

=

(efiwlkT -

(3)

to give a mode frequency

o,

and damping constant TI.

When the damping is very large most of the scat- tered intensity from this mode occurs a t low frequency, i. e. w < w,, and so

- -

sitive to absolute values of TI and w, and that these

two parameters are highly correlated.

Fw. 1.

-The Raman spectra of ND4D2P04 (DADP), NH4H2P04 (ADP), KDzP04 (DKDP), KHzPO4 (KDP), We have observed these overdamped modes in the phosphates and arsenates isomorphous with KH2As04 (KDA) and C S H ~ A S O ~ orientation

X ( Y X ) Y.

The incident laser intensity 1s different in (CSDA) at

T

-

²⁹⁵

^OK,

each case. The Debye relaxation time for the overdamped and have extended the measurements mode in each spectrum is shown

ⁱⁿ

parenthesis (Units are

1 0 - 1 3

s) 250 cm-l, so as to include the nearest underdamped Slitwidth equals

10

cm-1.

The quantity (~,/co:) is the Debye relaxation time,

z, _I _I _I _I _I _[r-4.5]

for the overdamped mode. This is equivalent to saying

⁰ so 100 150 zoo 250 300

that for large damping, the quality of the fit is insen-

^FREOUENCY(CM-~

-

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1972211

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C2-50 J. F. RYAN, R. S. KATIYAR AND W. TAYLOR

transverse optical mode of B2 symmetry. The spectra are shown in figure 1. The asymmetry in this TO pho- non lineshape suggests that there is strong anhar- monic coupling between it and the overdamped mode.

The spectral response may then be expressed in terms of the Green function Gij(o) and the two mode strengths PI, P,.

where

Simple soft mode theory predicts that o t / ~ ;

=

l/z, varies as (T

- T,)/T where T, is the temperature of

the dielectric anomaly of the free crystal. Kaminow and Damen [ l ] have verified this in KH2P04, but they have not taken into account the coupling between the overdamped mode and the transverse optic mode.

They used the simple damped harmonic oscillator

model of eq. (2) to fit their data at all temperatures whereas Wilson [2] has found that as the crystal temperature is lowered towards the transition, the

-

^COUPLED^MODES

----

^UNCOUPLED^MODE¹

---

UNCOUPLED M O E 2

,,:

..

__I-

_ _ - - +

---.

oo

-.-.;;

.--.----.---.-.-r-- , , , ,

-._ --.-.-____

, ,

50 75 100 125 150 175 200 225 250 275

FREQUENCY (cm-' )

-

FIG. 2. - The Raman spectrum of NH4HzP04 at T = 295 OK orientation X ( Y X ) Y. Open circles are experimental data. The solid line is the lineshape obtained when the two uncoupled

modes (dotted lines) interact as described in the text.

b : : ! I : : . : : I : ! : : - l

-2 1) 18 28 78 48 58 60 78 98 '39 108 118 $711 $38 148 I58 I68 178 (08 198 208 218 228 238

FREOUENC1E5 IN WAVE NUHBER

FIG. 3. -The Raman spectrum of NH4H2P04 at various temperatures orientation Z ( X Z ) X. Slitwidth equals 10 cm-1.

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RAMAN SCATTERING FROM FERROELECTRIC MODES C2-51

shape of the spectrum becomes more like the Debye

oscillator of eq. (4). This suggests that there is an additional temperature dependent factor present which is not included in the simple model. When the coupled mode eq. (6) is used to fit the room temperature spec- trum of KH2P04 we find that the Debye model is the most suitable with a relaxation time

e

=

5.7 x 10-l3 s .

We are proceeding with this type of analysis at various temperatures for KH2P04 and KD2P04 and our results will be published elsewhere.

This analysis has already been carried out for KH,AsO, and CsH,AsO, [3] where it was found that 112 varied as ( T - To)/T, with To considerably diffe- rent from Tc. Cowley

et al. [4] have proposed that

this difference is due to an anomaly in the response of the soft mode at low frequencies. This' will be explained in detail by Coombs and Cowley later in this session.

(NH,)H,PO, is isomorphous with KH,PO, but undergoes an antiferroelectric transition at 148

OK

with a large dielectric anomaly occuring in the a-direc- tion and a small anomaly in the c-direction. We report here the first observation by Raman spectro- scopy, of the overdamped mode of B, symmetry.

Earlier infra-red experiments have already indicated its presence

[ 5 ] .

The results of the coupled mode analysis are shown in figure 2. A value for the relaxa- tion time, e,, is found and its temperature depen- dence studied. In figure

3

we show the Raman spectrum of the E symmetry modes in (NH,)H,PO,. Since there are three optical modes in the spectrum any model taking account of coupling between the modes would contain a prohibitive number of parameters.

We have fitted this spectrum with four uncoupled oscillators and studied the temperature dependence

---- ^KAMINOW

MASON

0 0 ' I I I I I I I 0

0 100 200 300 400

TEMPERATURE [OK)

FIG. 4. - Solid line is 117 = l/r,(T- To)/T as obtained from Raman data.The dotted lines correspond to the inverse dielectric

1 4 n

susceptibility - = of NH4H2P04.

II 40, T ) - 1

The static dielectric constant has a Curie-Weiss temperature dependence

of e, for the overdamped mode.

but because in this case the antiferroelectric transition In figure 4 we compare our results for (NH,)H,PO,

with the earlier dielectric data of Mason [6] and occurs at a temperature much higher than the projected ferroelectric transition, it is difficult to extrapolate microwave data of Kaminow

[7].

We have found

accurately and extract a value for T,. It is therefore,

1

T - 29

-

= 3.1

(T) ^{l0l3 s-I} not possible to compare the Raman and dielectric

ZB

measurements in (NH,)H,PO, in the manner in

1 T - 54 which it was done for KH,ASO, and CsH,AsO,.

-

=

1 . 6 ( ~ ) x 1013 s-I

TE

Acknowledgment. -

The authors wish to thank where the extrapolated transition temperatures are

J. F. Scott, R. A. Cowley and W. Cochran. We are To,

⁼29

+ 3 OK also grateful to the Science Research Council for To,

=

54 + ^{5 OK} . financial support.

References

[I]

KAMINOW

(I. P.)

and DAMEN

(T.

C.),

Phys. Rev. [4]

COWLEY

(R. A.),

COOMBS

(G.

J.), KATIYAR

(R.

S.),

Letters, 1968, 20, 1105.

RYAN

(J. F.),

SCOTT

(J. F.), J. Phys. C.

Solid

[2]

WILSON (C.

M.),

Thesis, Johns Hopkins University,

1 a7n State Physics, 1971, 4, L 203.

I I I U .

[3] KATIYAR (R.

S.), RYAN

(J. F.),

SCOTT (J.

F.), Phys. [5] KAWAMURA (T.),

MITSUISHI

(A.),

YASHINAGA

(H.), Rev. B., 1971,

October.

J. Phys. SOC. Japan, 1970, 28,

supplement,

227.

KAT1yAR (R.

S.),

^RYAN(J. F.), SCOTT (J. F.), PrOcee- [6] MA^^^ (W. P.), phys. Rev., 1946, 69, 173.