Far infrared properties of the incommensurate ferroelectric Rb2ZnCl 4

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Far infrared properties of the incommensurate ferroelectric Rb2ZnCl 4

J. Petzelt, A.A. Volkov, G.V. Kozlov, S.P. Lebedev, J.P. Chapelle

To cite this version:

J. Petzelt, A.A. Volkov, G.V. Kozlov, S.P. Lebedev, J.P. Chapelle. Far infrared properties of the incommensurate ferroelectric Rb2ZnCl 4. Journal de Physique, 1982, 43 (9), pp.1359-1363.

�10.1051/jphys:019820043090135900�. �jpa-00209515�

Far infrared properties ^{of the} incommensurate ferroelectric Rb2ZnCl4

J. Petzelt

Institute of Physics, ^{Czech. Acad.} Sci., ^{Na Slovance} 2,180 ⁴⁰ Prague 8, Czechoslovakia

A. A. Volkov, ^{G. V.} Kozlov, ^{S. P.} Lebedev and

Lebedev Physical Institute, Acad. Sci. U.S.S.R., ^Leninskii Prospekt 53, ^V-312 Moscow, ^U.S.S.R.

J. P. Chapelle

Laboratoire de Physique Cristalline, Université Paris-Sud, ^Centre d’Orsay, ⁹¹⁴⁰⁵ Orsay, ^France

(Reçu ^le 16 février 1982, accepté le 30 avril 1982)

Résumé.

Les constantes diélectriques ^de Rb2ZnCl4 ^{ont été} déterminées dans la région comprise ^{entre 6 et}

400 cm-1 _{pour 300} et 90 K. Dans la région comprise ^{entre 30 et 400 cm-1 elles ont} été évaluées à partir ^{de mesures}

de réflectivité ; ^{entre 6 et 22 cm-1 elles ont} été calculées à partir ^{de mesures} d’indices de réfraction complexes

réalisées sur un spectromètre ^BWO monochromatique ^et accodable. Tous les modes polaires ^{ont été} approxima-

tivement attribués et leurs paramètres ^{ont été} déterminés. Nous n’avons observé ni amplitudon ⁿⁱ phason ^dans

la phase incommensurable en raison d’un fond continu d’absorption intense. Un mode dur de type A1 ^a été observé à 18 cm-1 au-dessous de 130 K, ^{en accord avec les} résultats de l’effet Raman.

Abstract.

Dielectric spectra ^of Rb2ZnCl4 ^were determined in the 6-400 cm-1 region for 300 and 90 K. In the 30-400 cm-1 region they ^{were evaluated from bulk} reflectivity measurements, ⁱⁿ the 6-22 cm-1 region they ^were

calculated from complex transmittance measurements performed ^{on a} tunable monochromatic BWO spectro-

meter. All polar ^{modes were} approximately assigned ^{and their} parameters determined. No amplitudon ^and phason

were observed in the incommensurate phase because of a high background absorption. ^{A hard} A1 ^{mode at 18 cm-1}

was seen below 130 K in agreement with Raman results.

Classification Physics ^Abstracts

63.20

64.70K - 77.40

78.30

1. Introduction.

Rubidium tetrachlorozincate

Rb2ZnCl4 (RZC) ^{is one} of the incommensurate ferro- electrics of the fl-K2SO4 ^structure which have recently

attracted much attention [1, ^2, 3]. ^Its high-temperature phase ^is nonpolar orthorhombic (space ^group D2b-

Pman, Z ⁼ 4, b > a > c). At T; ^{= 302 K it} undergoes

a second-order transition into ^an incommensurate

phase characterized by ^a distorting modulation with the wavevector k ; == (t - b) ^a* [2]. ^{As it is} typical ^for

incommensurate phases, ^{6 is} temperature dependent changing ^from b(Ti) ^{= 0.028 to} ð(Tc) ^{= 0.015. At} Tc - ^{192 K a} lock-in transition into ^a commensurate

improper ferroelectric phase ^with P., // ^{c takes} place

characterized by kc = 3 ^a* (space group Cl,-P2, ^an,

Z ⁼ 12). This transition sequence is identical to that of

K2Se04, ^{the best} investigated incommensurate crystal.

However, ^unlike K2Seo4, ^a further transition into a

monoclinic ^or triclinic phase ^{occurs in RZC at 74 K} [4, 5].

All transitions are displacive. ^{This was shown} by

Raman scattering which revealed an underdamped totally symmetric amplitudon below - 240 K [6] ^and

a locked in phason ^{in the} c(ac)b geometry ^below

’" 90 K [4]. ^{Moreover, another} totally symmetric ^soft

mode was seen below the 74 K transition [4].

No far infrared data have been available _up to now.

In the isomorphic K2SeO4 ^both amplitudon ^and pha-

son were observed in the _very far infrared [7, 8], ⁱⁿ

agreement ^with specific selection rules for incommen- surate phases. ^Similar spectra ^are expected ^for RZC,

as well. Therefore we performed measurements in the 6-400 cm - 1 region ^and report ^on the results in this paper.

2. Experimental.

^A large single crystal ^{of RZC} (~ 5 cm3) grown from water solution was x-ray

oriented, ^{cut and} polished ^{to obtain} (010) ^and (100) platelets. ^Two experimental techniques ^{were used. In}

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:019820043090135900

1360

the 30-400 cm -1 region ^bulk reflectivity ^{was measured} using ^a RIIC FS-620 Fourier interferometer adapted

for reflectivity measurements of small samples [9]

(5-8 ^mm diameter, - ^{1 mm} thickness). ^{In the}

6-22 cm -1 ¹ region ^a complex transmittance of plane- parallel platelets ^was determined using ^{a monochro-}

matic spectrometer ^{with a} tunable electron-beam backward-wave oscillator (BWO) as a source [10]. ^Two independent quantities ^were measured : the intensity ^T

of the transmitted light ^{and its} phase ^shift cp ^{on a} two-beam Rozhdestvensky (Mach-Zehnder) ^inter-

ferometer. Both quantities ^{were measured} for several temperatures between 300 and 80 K. The sample

thickness used were 557 gm’((010) plate) ^{and 753} gm

((100) plate).

3. Results and evaluation.

The results of polarized reflectivity measurements at room and liquid nitrogen temperature ^{are shown in} figure ^1. Within the accuracy of measurements (~ ± 0.03) ^no changes were seen on

heating ^the crystal ^above T;. Orientative ^measure- ments in a higher frequency region performed ^on

Perkin Elmer 577 spectrometer have shown that no

peaks ^{in the} reflectivity ^{are seen above 400 cm -1. From}

the reflectivity spectra ^the complex dielectric function

was evaluated by ^{means of} Kramers-Kronig analysis.

For this purpose the reflectivity ^was extrapolated

below 30 cm -1 using the results calculated from the

low-frequency transmission measurements (dotted part ⁱⁿ Fig. 1). ^{For E I/a and E 1/ b} spectra, ^where only ^room temperature transmittance was measured,

the extrapolation ^for’ both 90 and 300 K reflectivity spectra ^was chosen identical. Above 400 cm -1 the

reflectivity ^was extrapolated by ^a constant, ^{but a} linear correction of the phase ^{0 of the} complex ^reflec- tivity li ^{e - i8 was applied to remove negative values}

Fig. ^1.

Polarized normal reflectivity ^{of RZC at room and} liquid nitrogen temperature. ^{The dotted} low-frequency ^tails

are calculated from transmission measurements.

Fig. ^2.

^Real (a) ^and imaginary (b) part ^{of the dielectric} function evaluated from reflectivity measurements. The dotted low-frequency ^{tails are} calculated ^from transmission

measurements.

of 0 (i.e. negative ^{values of} E"). ^The resulting ^dielectric spectra ^{are shown in} figure 2. From them in a standard way ^we evaluated the mode parameters : ^transverse mode frequencies vT from maxima of s"(v) spectra,

damping YT ^{as a} full width at half height ^of B"(v) peaks, ^{i-th mode} strength (contribution ^{to the static} permittivity) ^{A£I =} B VT ’YT ^{and the} longitudinal

viT

mode frequencies from maxima of Im [1/E*(v)] spectra

see e.g. [11]j. The results are listed in table I.

The low-frequency part ^{of our} spectra (dotted part in figure 2) ^was calculated directly ^from transmission

measurements. Figure ^{3 shows an} example ^{of a} typical

transmittance spectrum T(v) ^{for E II c recorded} by tuning ^{of one} BWO. In the low-frequency part ^{of the} 84 K spectrum, ^{where the} sample ^is relatively transpa- rent, interference oscillations are seen. In addition, ^at

the high-frequency ^{end a} sharp absorption peak

appears. The room-temperature spectrum ^is featureless

and its nonlinear fall down shows an increasing

absorption ^with increasing frequency. ^Such T(v)

spectra in combination with p( v) spectra ^{were eva-}

luated to obtain the optical constants n (refractive

Table I.

Transverse mode frequencies vT, its damping vT and strength ^{As and} corresponding longitudinal ^mode frequencies ^{VL as} evaluated from reflectivity measurements.

index) ^{and k} (absorption index) using ^{the formulae}

for the amplitude ^and phase ^{of a} transmitted mono-

chromatic wave with wavenumber v which incidents

normally ^{onto an} absorbing layer ^{of thickness d} along ^a main axis of the dielectric tensor [10]. ^The resulting dielectric spectra for E Il c (c ^{is the ferro-}

electric axis; ^{for this} polarization ^{the active} amplitudon

and phason ^are expected) ^{at several} temperatures ^are shown in figure ^4.

4. Discussion. - As all polar ^modes lay ^{in our} spectral region it is of interest to compare the static

and optic permittivity ^{with the} strength of all modes.

This is best done by checking ^the generalized Lyd-

dane-Sachs-Teller relations [11]

The results are summarized in table II. In some cases

(especially ^{for E II a} (300 K)) ^the right-hand ^{side of} equation (2) ^is appreciably greater ^{than the left-hand} side, which is measured with much higher accuracy.

This means that in these cases we overestimated the

mode strengths, especially ^{at the low} frequency ^end

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Table II.

Low- and high-frequency permittivity ^and Lyddane-Sachs-Teller relations for ^RZC. s. (90 K) ^{is taken} equal ^to £, (300 K).

Fig. ^3.

Transmittance of the (010) sample ^{for E//c.}

Only ^the spectral region ^{of one BWO is shown. Notice the} log T(v) ^scale.

Fig. ^4.

Low-frequency dielectric spectra ^{of RZC for E //c}

at several temperature. ^The high-frequency part ^{of the} 296 K spectra ^{could not be measured on our} sample ^because

of too high absorption.

(30-100 cm-1 ), ^{where the} experimental errors are the greatest. ^{Therefore our values of} vT ^{are more reliable}

and accurate than values of Ae’and vL.

Let us compare the list of polar ^{modes in table I}

with theoretical expectations. ^The group-theoretical analysis ^{in all} phases ^was performed previously [6, ^7, 12]. According ^to it there should be 7 B1u ^{+ 12} B2u ⁺

12 B3. active modes in the high temperature phase ^and

62 Ai ^{+ 62} B2 ^{+ 62} B 1 active modes in the commen- surate phase ^below Te. ^As usually, they ^{can be divided.}

into the higher-frequency internal vibrations of the

ZnCl4 tetrahedra (3 Blu ^{+ 6} B2u ^{+ 6} B3u ^{or 27} Al ⁺

27 B2 ^{+ 27} B 1 ^{in the} D2h ^and C2, phase, respectively)

and lower-frequency external modes (4 B1u ^{+ 6} B2u ⁺

6 B3u ^{or 35} Al ^{+ 35} B2 ^{+ 35} B1). The external modes in the D2h phase ^consist of translational (2 Blu ⁺

5 B2u ^{+ 5} C3u) and librational modes (2 B1u ^{+ 1} B2u ⁺

1 B3u) probably ^mixed together. Concerning ^the ZnCl4

internal modes, V3 ^and v4 ^are strongly IR active in each spectrum, V2 weakly ^active and vl is activated

only ^below Tc’ ^The assignment in table I is based on

known molecular frequencies ^{of the} ZnCl4 - ^group [ 13],

but it should be taken in mind that the assignment especially ^{in the} low-frequency region ^is approximate

and the coupling with external modes can play a ^role.

Comparing the theoretical results with the experiment

in table I, ^{we see} that several modes are missing ^because

of mode overlapping ^or their weakness. This is a common situation with complex crystals ^{like RZC.}

Comparing the dielectric spectra with those of K2Se04

one can see that in RZC the mode frequencies ^are strongly ^shifted downwards. This is caused partially by

heavier atomic masses and probably ^also by ^some

relaxation of the interatomic bonding. ^{The low-} temperature ^modes (A,, B2 ^and Bl) ^{can be also Raman}

active. A comparison with Raman data [6] ^shows, however, ^{that in fact} many modes ^seen in Raman spectra ^{are not seen in IR} spectra ^{and vice versa.}

The most important from the theoretical point ^of

view are the lowest-frequency modes, especially ampli-

tudon and phason. ^{In the} commensurate ferroelectric

phase only ^the q ⁼ 0 amplitudon ^{should be active in}

the A 1 spectrum [14]. ^{As seen from} figure 3, ^below

130 K a sharp distinct mode at - 18 cm-1 arose from the absorption background. The two-oscillator fit

(background plus ^{the 18 cm -1} mode) has revealed that its frequency ^and strength remain ^constant (see

Table I), ^{but its} damping decreases from - 2 cm - I at 130 K to 0.8 cm -1 at 84 K. This mode corresponds ^to

the hard Raman mode rather than to amplitudon [6].

The behaviour of its damping ^can be understood as

caused by ^the coupling with the q ^{= 0} amplitudon

which according ^to Raman data [6] ^{softens from}

~ 25 cm - 1 at 80 K and crosses the 18 cm - 1 mode at about 230 K. The amplitudon ^{itself was not seen in}

our spectra which in fact could be expected ^{if its} strength ^{would be as small as in the case of} K2SeO4.

We note that in the latter case the background absorp-

tion is nearly ^{one order of} magnitude smaller than in RZC. Such a high absorption in RZC is caused by ^the strong polar mode in the 40 cm -1 region. ^{This back-} ground absorption prevents ^{us also to} observe the active q ⁼ 3 ba* phason ^and amplitudon ^{in the}

incommensurate phase ^{which were} observed in

K2Seo4 [7, 8] ^{in agreement with} theoretical expecta- tions [14].

Finally, ^{let us} mention the strong increase ^{of the}

low-frequency ^{E II c} absorption tail with increasing temperature. ^{It seems not to be caused} only by partial softening ^{of the mode} in the 40-30 cm - 1 region ^because

the 8’(v) spectrum ^{is not an} increasing function of

frequency ^{above 223 K, as} it should be for an oscillator model. The additional absorption resembles’ that in

(NH4)2BeF4 [15] ^{where we} interpreted ^{it as a disorder-}

induced one-phonon absorption. ^’In RZC it could be rather a soft-mode enhanced two-phonon absorption.

Acknowledgments.

We would like to thank Dr. V. Dvorak for organizing ^the cooperation ^and standing ^{interest to the} work, Ing. ^V. Subrtova for x-ray orientation of the crystal, ^{Dr. A.} Graja ^and

R. Swietlik for performing ^{the near IR} measurements and J. Kroupa for critical reading ^{of the} manuscript.

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