Displacive-order-disorder crossover at the ferroelectric-paraelectric phase transitions of BaTiO3 and LiTaO3

HAL Id: jpa-00232089

https://hal.archives-ouvertes.fr/jpa-00232089

Submitted on 1 Jan 1982

HAL is a multi-disciplinary open access

archive for the deposit and dissemination of

sci-entific research documents, whether they are

pub-lished or not. The documents may come from

teaching and research institutions in France or

abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est

destinée au dépôt et à la diffusion de documents

scientifiques de niveau recherche, publiés ou non,

émanant des établissements d’enseignement et de

recherche français ou étrangers, des laboratoires

publics ou privés.

Displacive-order-disorder crossover at the

ferroelectric-paraelectric phase transitions of BaTiO3

and LiTaO3

K.A. Müller, Y. Luspin, J.L. Servoin, François Gervais

To cite this version:

K.A. Müller, Y. Luspin, J.L. Servoin, François Gervais. Displacive-order-disorder crossover at the

ferroelectric-paraelectric phase transitions of BaTiO3 and LiTaO3. Journal de Physique Lettres, Edp

sciences, 1982, 43 (15), pp.537-542. �10.1051/jphyslet:019820043015053700�. �jpa-00232089�

Displacive-order-disorder

crossover

at

the

_{ferroelectric-paraelectric}

phase

transitions

of

_BaTiO3

and

_LiTaO3

K. A. Müller

IBM Zurich Research _Laboratory, 8803 Rüschlikon, Switzerland

Y.

_Luspin

_(*),

J. L. Servoin and F. Gervais

Centre de Recherches sur la

_Physique

des Hautes _{Températures,} Centre National de la Recherche

_{Scientifique,}

45045 Orléans, France

(Refu le

_{12 fevrier}

1982, revise le 22 _{avril, accepte} le 4 mai ₁₉₈₂₎

Résumé. 2014 On _{compare les données} reçues de mesures

_précises

de réflectivité

_infrarouge

et de

cons-tantes

_{diélectriques 03B50(T)}

dans certains

_{ferroélectriques ABO3.}

Dans

_BaTiO3,

le mode

_{ferroélectrique}

se sature au-dessus de la transition

_cubique

_tétragonale tandis _que

_03B50(T)

tend à

_diverger.

Ceci

s’inter-prète en terme de

_changement

de

_régime

dominant, passant de

_displacif

à ordre-désordre à

_l’approche

de _Tc, en accord avec la dimensionalité

_critique

dans les

_systèmes

_{cubiques dipolaires}

_{dc = 4}

> d = 3. Dans le

_composé

uniaxe

_LiTaO3

où d

_{= dc}

= _3, le

_phénomène

_est en effet moins

_marqué.

Abstract 2014 A detailed

comparison

between accurate infrared

_reflectivity

data and dielectric constant

03B50(T)

measurements has been carried out in

_ABO3

ferroelectrics. In

_BaTiO3,

the ferroelectric mode saturates above the

_{cubic-tetragonal}

transition, whereas

_03B50(T)

tends to

_diverge.

This _supports an

intrinsic crossover from

_displacive

to order-disorder behaviour on

_{approaching Tc}

because the critical

dimensionality

in these cubic

_dipolar

_systems is

_dc

= 4 > d = 3. In the uniaxial

LiTaO3

with

d

_{= dc}

= 3, the _crossover is less

pronounced.

Classification

Physics

Abstracts

77.80c - 64.70p - 78.30j

From

_computer

simulations

[ 1, 2],

as well as

_{analytic theory [3],}

a new view

_regarding

the beha-viour of

_displacive

continuous structural

_phase

transitions

(SPT)

near

_T~,

has

_{emerged :}

the crossover from a

_regime

in which the collective behaviour has classical

_displacive

soft-mode behaviour to a

_regime

whose features are better described in the

_{language traditionally}

reserved for order-disorder _systems

[4].

The _present work indicates this to occur in the

_important

class of ferroelectric

_perovskite

_systems,

and thus

_points

towards a resolution of the

_{long-standing}

contro-versy between the soft-mode versus order-disorder

_description

in

_BaTi03

and

_KNb03

as well as in

_LiTa03.

The soft-mode behaviour was

_{supported by early}

infrared

_reflectivity

measure-ments

_[5]

and later inelastic

_{neutron-scattering}

data

_[6].

The order-disorder

_picture

stemmed from the observation of _strong diffusive

_X-ray

_{scattering [7],}

as well as Raman

_activity

above the

tetra-(*) Permanent address : Laboratoires d’Etudes

_Physiques

des _Matériaux, Université d’Orléans, 45045

Orleans, France.

L-538 JOURNAL DE PHYSIQUE - LETTRES

gonal-cubic

transition

_[8]

and more recent Raman

_{investigations}

in the

_tetragonal

_{phase [9].}

The situation turned out to be

_similarly

controversial in

_{LiTa03 [10].}

The

_displacive

to order-disorder

_regime

is due to intrinsic anharmonic behaviour from

corre-lated fluctuations near wave vector _q = 0

(in

_{space and}

time).

One

_expects

from

renormalization-group

(R.G.)

theory

that correlated fluctuations near

_T~

are more

_pronounced

the

_larger

E =

dc -

d

is,

dc

being

the critical

_{dimensionality}

of a _system

_{[ 11 ].}

The antiferrodistortive SPT in

_{SRT’O 3}

has dc

=

4, d

=

3, i.e., 6=1,

and

experimental

results established

quantitatively

_precursor

order

_[12].

In

_KH2P04,

_dc=2.5

due to

_{soft-mode/acoustic-mode coupling.}

With

_{~=3, e= 20130.5}

one

_expects

Gaussian mean-field behaviour. It has been shown

[13]

that in

_KH2P04,

the statics and

_dynamics

follow

_{quantitatively}

mean-field behaviour. Courtens was the first to

_suggest

_[13a]

the

_{possible importance}

of the critical

_{dimensionality dc}

in the

_question

of the occurrence of intrin-sic central

_peaks.

Uniaxial ferroelectrics like TGS with their

_{long-range dipolar}

interactions have a critical

dimen-sionality dc

= 3. In this _case critical behaviour is

given by logarithmic

corrections _to classical

Landau results

_[14].

_Thus,

fluctuation effects are

_already

_present but not

_{dominating. Isotropic}

dipolar

systems

with

_dipolar

and

_short-range

interactions have been

_{investigated using}

R.G.

theory [ 15].

The static critical behaviour calculated is

_{nearly indistinguishable}

from that in cubic

short-range

systems

[11, 15]

and dc

= 4. In real cubic oxide

ferroelectrics,

cubic

anisotropic

interactions are also

_present

Their

fixed-point

behaviour

_depends

on the cubic

_anisotropy

of the

soft-modes. The

_fixed-point

behaviour is either

_{isotropic dipolar,}

not stable

_{(BaTi03 ?)}

or cubic

dipolar [ 16].

Kind and Muller

_{[ 17]}

measured the

_exponent

of the dielectric

_{susceptibility}

₈₀ above the second-order

_phase

transition in a cubic

KTao.9Nbo.103

crystal

to be _y = 1.7

[17],

well

outside the mean-field behaviour of _y = 1

[ 11 ].

Thus,

_one

might

_expect

that for cubic ferroelectrics

like

_BaTi03

and

_KNb03,

a crossover from

displacive

to _{order-disorder behaviour may exist} on

approaching

T~ .

Infrared

_reflectivity

measurements

_{[ 18]}

show this occurs as described below.

The new soft-mode data have been obtained

_using

a Fourier-transform

_{scanning interferometer,}

Bruker IFS 113. These modern i.r.

_{spectrometers}

are

_extremely

well-suited to measure infrared active modes

_accurately

in the

_frequency

_{range from 10} to 4 000

cm -1

_{and up} to

_high

_temperatures

( 1300

K).

The infrared

_reflectivity

data were

_analysed

on the basis of a factorized form of the

dielectric function

_{[18]. Typical experimental}

data and an

_example

of data fits are shown in

figure

la. Simulations of infrared

_{reflectivity,}

restricted for

_simplicity

to the soft-mode alone and inserted in

_figures

I b and c, show that

changes

of TO soft-mode

_{frequency (Fig. I b)}

and linewidth

(Fig. Ic) typical

of oxidic

_{perovskites give}

rise to

_quite

_significant

_changes

of

_{reflectivity profiles.}

In

_fact,

infrared

_{reflectivity yields}

information on the

_{real part}

of the dielectric function in addition to the

_imaginary

_part.

_Only

the latter is accessible

_{by scattering (Raman}

or

_neutrons).

Soft-mode

frequency

parameters,

in

_particular,

_{may be}

_accurately

deduced from

_{low-frequency reflectivity}

which appears

slightly dependent

on

_damping

as shown in the left-hand insert of

_figure

la

even

when the

_soft

mode is

_overdamped.

Results at room

_temperature

_agree with those of

_[5].

Both data sets

_disagree

with

_{Ballantyne’s}

_spectrum

_{[ 19]}

at room

_temperature.

Results at other

_temperatures

were

_previously

_{compared [ 18]}

to other

_spectral

data in detail and found to be in

agreement

with

most of the data. In

_{particular, extrapolating}

neutron data of

_[6]

to _q = 0 appears

compatible

with

present

soft-mode

_frequencies.

Results for the soft-mode in

_BaTi03

in the cubic

_paraelectric

and

_tetragonal

ferroelectric

_phases

are

given

in

figure

2~ The curves show a clear-cut soft-mode behaviour over a wide range of

tempe-ratures, whose

extrapolation

intersects the

_temperature

axis near

_T~.

_However,

on

_approaching

_Tc,

OTO

starts to level some 120 K above the

phase

transition to a value of 60

em -1.

Recent

hyper-Raman measurements also confirm the saturation over that

_temperature

_range

[20].

At

_T~,

an

Ai-type

component

is

_abruptly

shifted to : 280

_{cm -1,}

consistent with the first-order

transition,

while an

_E-component

continues to soften to the next

_{tetragonal-to-orthorhombic}

transition.

Fig.

1. -

(a)

Typical reflectivity profiles

in

_BaTi03

at several _{temperatures.} Best fit

_(heavy

full _curve) to

experimental

data ₍₀₎ at 1350 K, for

_example.

See text for inserts

_(b)

and _(c).

Fig.

2. -

Temperature

dependence

of the three ferroelectric soft-mode _components

_{of BaTi03}

(a), and the ratio of the « static » over the dielectric constant calculated from lattice modes _(b) via yat =

£00 n

~2~ o/~l; a

j

Note that the

_Sh’s

are moduli of _complex

_poles

_{(or zeroes).} Insert _{shows passage from}

_underdamped

to

L-540 JOURNAL DE PHYSIQUE - LETTRES

isomorphous phase

of

_{KNb03 [21].}

Furthermore,

in both

_crystals

the soft-mode

_damping

is

heavy,

over ten times that of the next

_modes,

and

_persists

into the lower

_{tetragonal phase (see}

figure

2

_insert).

The ratio of the dielectric constants

_{Scap/’Clat9}

with _{Bcap measured} in the MHz range, above

piezo-electric resonances, and ~~ calculated from the lattice modes shows the

following (Fig. 2b) :

the

soft-mode

_{roughly explains}

_6cap at

_{sufficiently high}

_temperatures

(Fig.

la)

but this becomes less and less true on

_{approaching Tc}

from above

[22].

Thus,

a

dynamical

disorder affects the

displa-cive behaviour and an additional relaxation can be related to disorder

_{[7]. Therefore,}

we arrive at

the conclusion that a

_{displacive-to-order-disorder}

crossover occurs as has been shown to be

present

in the antiferrodistortive SPT of

_SrTi03

[12].

The latter transition is

_{second-order,}

and deviations from mean-field behaviour appear 10

% in

t = (T -

Tc)/ Tc

below

_{T ~ = T o}

for the

rota-tional order

_parameter,

and above

_Tc

for the soft-mode as measured

by

inelastic neutrons

_[23].

In the

_present

case of

_BaTi03,

the deviation in the soft-mode

_DTO

_{appears 25}

%

above the

_To,

where the mean-field

_{extrapolated DTo}

vanishes. This is thus

_comparable

to the

_magnitude

found for the

_{short-range SrTi03}

_system.

In our

_opinion,

these new

_findings

settle the controversy whether the

_{cubic-to-tetragonal}

transitions in

_BaTi03

and

_KNb03

are

_displacive

or order-disorder.

It should be noted that in

figure

2,

the

_{high-temperature}

ratio

_Bcap/Btat

has its

_{low-temperature}

counterpart

reflected

about

_{T ~,}

as is

_expected

from

_scaling

for a continuous

transition,

figure

2a,

but the

_soft

mode has none,

_figure

2b, i.e.,

the

_A1

_component

has

_jumped

to 280

cm-1

and therefore

cannot be

_responsible

for the

_Bcap

enhancement towards

_{T ~}

in any way

[22] !

Thus close to

_Tc

an

additional

_{time-dependent dynamic}

motion distinct from the soft-mode behaviour has to be

present

In

_fact,

a relaxation of the dielectric constant,

along

the FE axis has been observed

recently

near 3-4 GHz at room

_temperature

[24],

the

high-frequency

value

being

in _agreement with

Fig.

3. -

Temperature dependence

of the soft-mode

_frequency

of

_LiTa03

_(lower

_part),

and

_comparison

of

~~t, while no marked relaxation of _6~ was found

_{perpendicular}

to the FE axis above

_{piezoelectric}

resonances, consistent with the results of

figure

2.

Thus,

the vibrational motion of the mobile ion

with

_respect

to its

_neighbours

is very anharmonic and should exhibit a

central-peak

_response near

7~,

in addition to the

_saturating

soft-mode at ~ 60

cm -1.

It has to be

a

relaxational

motion,

which

might

be slowed-down further

_by

_coupling

to

_{slowly relaxing}

_impurities.

The

_computer

simula-tions of Schneider and Stoll

_[25]

show that the

_dynamics

are slowed-down

_by

a constant factor but

are otherwise unaltered in their critical behaviour. Most recent index of refraction measurements for T >

_Tc

in flux and

_{melt-grown BaTi03 crystals}

have been

_interpreted

in terms of intrinsic

dynamic

islands of

_{polarization [26].}

The uniaxial ferroelectric

_LiTa03

has also been

_investigated

with the same method.

_{Dsoft again}

does not

freeze-out,

and

_Bcap/81at

increases on

approaching T~

but the range in

_temperature

is more

restricted to the immediate

_vicinity

of the transition

(Fig. 3).

Thus,

the behaviour is all in all more

« _classical ». This

_is,

_{however, expected}

in view of the fact that for this uniaxial

_crystal

d =

d~

=

3,

i.e.,

the

_{dimensionality}

is

_marginal

and correlated fluctuations for q = 0 _are

_present

but dominate

over a narrower

_T/T~

_temperature

_{range than in}

BaTio3’

In summary, the soft-mode behaviour in

_{AB03 ferroelectrics, especially}

the cubic ones,

satu-rates well above the ferroelectric transition. A

_comparison

with the measured dielectric constants

indicates a crossover from

displacive

to order-disorder behaviour on

_{approaching T~.}

This is in

agreement

with

expectations

of _{precursor order from the}

_{renormalization-group point}

of view. The

_present

_{findings give}

indirect evidence that cubic ferroelectrics do not behave

_classically

as

has

always

been assumed

_except

for one

_{experiment [17]}

on a second-order

_{cubic-to-tetragonal}

ferroelectric transition.

We have benefited from

_{correspondence}

with H.D. Bruce and G. Bums.

References

[1]

SCHNEIDER, T. and STOLL, E.,

Phys.

Rev. Lett. 31 _{(1973) 1254 ;}

_Phys.

Rev. B 13 ₍₁₉₇₆₎ 1216.

[2]

AUBRY, S., J. Chem.

_Phys.

62 _{(1975) 3217 ;} 64 ₍₁₉₇₆₎ 3392 and

KOEHLER, T. R., BISHOP, A. _{R., KRUMHANSL,} J. A. and SCHRIEFFER, J. R., Solid State Commun. 17

(1975) 1515.

[3]

KRUMHANSL, J. A. and SCHRIEFFER, J. R.,

Phys.

Rev. B 11 ₍₁₉₇₅₎ 3535.

[4]

BRUCE, A. D., in Solitons and Condensed-Matter

Physics,

editors A. R.

_Bishop

and T. Schneider

(Springer-Verlag, Heidelberg)

1978, p. 116.

[5]

SPITZER, W. G., MILLER, R. C., KLEINMAN, D. A. and HOWARTH, L. E.,

Phys.

Rev. 126 _{(1962) 1710 ;}

BARKER, A. S.,

Phys.

Rev. 145 ₍₁₉₆₆₎ 391.

[6]

HARADA, J., AxE, J. D. and SHIRANE, G.,

Phys.

Rev. B 4 ₍₁₉₇₁₎ 155.

[7]

COMES, R., LAMBERT, M. and GUINIER, A., Solid State Commun. 6 _{(1968) 715 ;}

LAMBERT, M. and COMES, R., Solid State Commun. 7 (1969) 305.

[8]

QUITTET, A. M. and LAMBERT, M., Solid State Commun. 12 ₍₁₉₇₃₎ 1053.

[9]

HEIMAN, D. and USHIODA, S., Phys. Rev. B 9

₍₁₉₇₄₎

2122; BURNS, G. and _DACOT, F. H.,

Phys.

Rev. B 18 ₍₁₉₇₈₎ 5750.

[10]

ABRAHAMS, S. C., BUEHLER, E., HAMILTON, W. C. and _LAPLACA, S. J., J.

_Phys.

Chem. Solids 34 ₍₁₉₇₃₎

521 ;

PENNA, A. F., PORTO, S. P. S. and CHAVES, A. _S., in

_Light

_Scattering in _Solids, editors M. Balkanski,

R. C. C. Leite and S. P. S. Porto

(Flammarion, Paris)

1976, p. 890.

[11]

FISCHER, M. E., Rev. Mod.

_Phys.

46 ₍₁₉₇₄₎ 597.

[12]

BRUCE, A. D., MUELLER, K. A. and BERLINGER, W.,

Phys.

Rev. Lett. 42 ₍₁₉₇₉₎ 185.

[13]

a) COURTENS, E.,

Phys.

Rev. Lett. 41 (1978) 1171 ;

b) COURTENS, E., GAMMON, R. and ALEXANDER, S.,

Phys.

Rev. Lett. 43 _{(1979) 1026;} and

c) to be

_published.

[14]

LARKIN, A. I. and KHMEL’NITSKII, D. _E., Sov.

_Phys.-JETP

29 _{(1969) 1123 ;}

STRUKOV, B. A., Ferroelectrics 12

₍₁₉₇₆₎

_{97 ;}

L-542 JOURNAL DE PHYSIQUE - LETTRES

[15]

AHARONY, A. and FISHER, M. E., Phys. Rev. B 8 ₍₁₉₇₃₎ 3323 ; BRUCE, A. D. and _{AHARONY, A., Phys.} Rev. B 10 (1974) 2078.

[16] VERSTRAETEN, G., Z. _Phys. B-Condensed Matter 43 (1981) 149.

[17] KIND, R. and _MUELLER, K. A., Commun. _Phys. 1 (1976) 223 ;

BILZ, H., MIGONI, R., MEISSNER, G. and _MUELLER, K. A., EMF-4, Portoroz,

Yugoslavia,

1979.

[18] LUSPIN, Y., SERVOIN, J. L. and GERVAIS, F., J.

_Phys.

C 13 ₍₁₉₈₀₎ 3761.

[19]

BALLANTYNE, J. M.,

Phys.

Rev. 136 ₍₁₉₆₄₎ 429.

[20]

INOUE, K. and ASAT, N., to appear in J.

Physique.

[21]

QUITTET, A. M., SERVOIN, J. L. and _{GERVAIS, F.,} J.

_Physique

42 ₍₁₉₈₁₎ 493 ; FONTANA, M., METRAT, G., SERVOIN, J. L. and _{GERVAIS, F.,} to be

_published.

[22]

BURNS, G. and BURSTEIN, E., Ferroelectrics 7 ₍₁₉₇₄₎ 297 ;

HALPERIN, B. I. and VARMA, C. M.,

Phys.

Rev. B 14 ₍₁₉₇₆₎ 4030. The

_theory

of «

_{dirty » displacive}

ferroelectrics, i.e.,

containing impurities

which

_couple

to the ferroelectric mode, cannot account

for this behaviour : while the dielectric-constant ratio

_clearly

has

_divergent

character towards

Tc,

the

_{soft-mode frequency}

is _nearly constant.

[23] CURRAT, R., MUELLER, K. A., BERLINGER, W. and _{DENOYER, F.,}

_Phys.

Rev. B 17 ₍₁₉₇₈₎ 2937.

[24]

TURIK, A. V. and _SHEVCHENKO, N. _B.,

_Phys.

Status Solidi B 95 ₍₁₉₇₉₎ 585.

[25]

SCHNEIDER, T. and _{STOLL, E.,}

_Phys.

Rev. B 16 ₍₁₉₇₇₎ 2220.