Effect of the electric field on the elastic and dielectric properties of a lithium-potassium tantalate crystal

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Effect of the electric field on the elastic and dielectric properties of a lithium-potassium tantalate crystal

P. Doussineau, C. Frénois, A. Levelut, S. Ziolkiewicz

To cite this version:

P. Doussineau, C. Frénois, A. Levelut, S. Ziolkiewicz. Effect of the electric field on the elastic and

dielectric properties of a lithium-potassium tantalate crystal. Journal de Physique I, EDP Sciences,

1994, 4 (1), pp.147-158. �10.1051/jp1:1994128�. �jpa-00246887�

J. Phys. l France 4 (1994) 147-158 _JANUARY 1994, PAGE 147

Classification Physics Abstracts

62.20D 64.90

Effect of the electric field

_on

the elastic and dielectric properties

of

_a

lithium-potassium tantalate crystal

P. Doussineau, C. Frénois, A. Levelut and S. Ziolkiewicz

Laboratoire

d'Acoustique

_et

Optique

de la Matière Condensée (*) Université P. et M. Curie, Case 78, 75252 Paris Cedex 05, France

(Received

3 June J993, revised J5

July

J993,

accepted

J3

September

J993)

Abstract. We have measured in _a Kj

_~Li~TaO~

crystal with _x

= 1.7 % the elastic _constant with

longitudinal

acoustic _waves of

frequency

between 30 and 330 MHz and the dielectric constant between 10 Hz and MHz in the temperature _range tram 4 to 200 K under _an electric field

applied

upon cooling. ^The main effect of the applied field _on the dielectric _{constant is} attributed to space charges. ^{The real} part ^{of the elastic} constant (the sound velocity) _was round _to increase when the field _was applied

perpendicular

to the acoustic _wave vector and to decrease when it was

applied parallel

to the _{wave vector.} The effect of the cooling rate was aise studied. These results _are

explained

by ^the occurrence of clusters of oriented

dipoles

borne

by

the Li+ ions, favoured by the field.

Introduction.

The

study

^of the disorder

generated

in

KTaO~ crystals by

random substitution of K+ ions

by

smaller Li+ ions _enters the

general

^{framework of the}

study

of

randomly interacting

systems. Indeed, because of the different _sizes of these _ions, the Li+ ions occupy off-centre

positions

thus

generating

electric and elastic

multipoles.

The interaction between the electric

dipoles

is

thought

to

play

a fundamental rote _in the formation of the low temperature

phase,

the

nature of which is still controversial. The double _nature of the

multipoles

allows the

coupling

to different

probes

: the electric

dipole

located _on each substituted site is

coupled

to the electric field while the elastic

quadrupole

interacts with the local elastic _stram.

Moreover,

the Li

concentration _x

changes

the _nature of the low

temperature phase

:

dipolar glass

below 2 fb and disordered ferroelectric above. Ail these

features,

which still need to be

carefully

checked, make the

Ki_~Li~TaO~ (KLT) crystals

_an attractive system ^{for the}

study

^{of random} interactions in condensed matter

[1, 2]. Actually,

_numerous

techniques

have

already

been

applied

to this system

X-ray

diffraction

[3],

Raman scattenng

[4], optical birefringence [5, 6],

nuclear

magnetic

_resonance

[7, 8],

dielectric

study [5, 9, 10],

acoustic

study [11-13]

etc.

However,

due

perhaps

to technical

difficulties,

the _acoustic measurements are rather few.

(*) Associated with the Centre National de la Recherche Scientifique.

In this paper we present ^{the results of}

high frequency

acoustic measurements

perforrned

on a

KLT

crystal

of Li concentration

equal

to 1.7

iii,

_a value close to the border which is

supposed

to separate ^the two kinds of low temperature

phase.

In

fact,

the attention _is focused on the rote of the

applied

electric field.

Subsidiary

dielectric measurements which

help

^{with the}

mterpretation

of the acoustic data _are aise

given. Finally,

_some conclusions

conceming

bath the

high

and the low temperature

phases

_are drawn.

Prehminaries _on

experiments.

All the present measurements on the

complex

elastic constant and the

complex

dielectnc

constant have been achieved _on the _same KLT

sample. They

_are part of _a

systematic study

on a

series of KLT

crystals

of various concentrations. In order to

keep

a coherent

labelling

inside the

series,

_we refer _to this

crystal

_as

sample

V. Acoustic measurements

[12]

and dielectric

measurements

[14] perforrned

_on this

sample

have

already

been

published.

In _{contrast to} the present

experiments,

the former _were done without

biasing

^electric field while the latter _were

focused _on the distribution of the relaxation times.

The

sample

was grown in _our

laboratory.

It is characterized

by

its transition temperature

T~, defined _as

explained

below and found to be

equal

to 34 K.

Then, using

the relation

T~

(K

₌ 535 x~~~~~

[8],

_we deduce the lithium concentration _x

=

1.7 fG. Another concentration

measurement was

independently performed by Secondary

Ion Mass

Spectroscopy (SIMS)

using

_as reference _a

crystal

with 5.7iiiLi (T~ =

79K)

and

measuring

the ratio of the

?Li+

_-ion

_emissions,

_{the lithium} concentration _is found to be _x

=

1.6 iii in _our

sample

V. The agreement ^is _very

satisfying.

At _room

temperature,

^{the KLT}

crystal

has cubic symmetry. ^{Ail the end-faces of the}

sample

are cut

perpendicular

to one of the three

equivalent

fourfold

crystallographic

_axes. Two

pairs

of opposite ^{faces have received metallic films which} serve as electrodes. On _one of these

electrodes _a

piezoelectric

transducer is

bounded,

which _can generate into the

sample

longitudinal

waves

propagating along

a

[100]

axis ; therefore the measured elastic _constant C coincides above _T~ with the elastic _constant

C)i

of the cubic symmetry ^{class. Between the other} pair of electrodes _an alternative

voltage

is

applied,

for the dielectric measurements ; in this

case the measured dielectnc constant _s is, ^for T

larger

^than _{T~, any ~,,} component ^{of the}

isotropic

dielectric _tensor.

Using

_{one pair} of electrodes or the other, a static

biasing

field may be

applied during coolmg.

Then the

biasing

field may be either

parallel

_or

perpendicular

to the

displacement

vector

(and

the _wave

vector)

for elastic measurements and either

parallel

or

perpendicular

to the

oscillating

electric field _vector for dielectric measurements.

The

explored

temperature range was between 4 K and 200 K. In most of the expenments, the data were recorded when

heating

the

sample,

witho~lt

applied

static electnc field _:

they

are

zero field

heating (ZFH) experiments (if

a field _was

applied,

this _was

dunng

the

coohng

process

only).

It is

implied

that the

symbols

C and _e stand for

C(w,

T, E, _r~,

r~)

and

s(w,

T, E, r~,

r~)

which _mean that these

quantities

are two functions of the

frequency f

(w

=

2

wf)

and

the temperature T, measured upon

heating,

with the

heating

rate r~ and without electric field, after the

sample

has been cooled in the electric field E, with the

coohng

rate r~.

We present ^ail our data _m the forrn of dimensionless

quantities.

For the dielectnc

measurements we use the relative

complex

^dielectric constant _e while for the elastic

measurements we grue the reduced

change

of the

complex

elastic _constant

ôC/Co

^{which is}

related to the

directly

measured

quantities by

Re

(ôC/Co)

=

ôC'/Co

=

2

ôV/Vo

Im

(ôC/Co)

=

ôC

"/Co

=

«Vo

In

(10)/(20 «fi

N° ELECTRIC FIELD EFFECT ON

Kj

~Li~TaO~ 149

where

Vo

and

Co

_are

respectively

the sound

velocity

and the elastic constant measured _{at some} reference temperature ^and _« is the sound attenuation measured in decibels per

length

unit. The choice of

Co

is in fact of

secondary importance

_since its

change

results _{in a}

simple

translation of the

velocity

curve as a whole.

However,

in the theoretical part ^{of this} paper

(see below)

it is

convenient _to choose for

Co

the

extrapolation

^of C at T

=

0.

The acoustic

experiments

_were

performed

for

frequencies f ranging

from 30 MHz to

330 MHz. We used _an automatic method which _was

specially

conceived for

highly

accurate

sound

velocity

measurements

[15].

The characteristic features observed when the temperature is

changed (see Fig,

l, _upper

part)

_{are :}

ii

from about 90 K to at least 220

K,

_a

quasi-linear

and

dispersionless

variation of the sound

velocity,

due _to the lattice

anharmonicity

_;

ii)

_a

dip

in the sound

velocity (a slowing

down of the acoustic

wave),

due _{to a} relaxational process, the

position

and

intensity

of which _are

frequency dependent (in

the upper part ^of

Fig.

l, it appears near 100

K)

iii)

_an increase of the sound

velocity

when the temperature mcreases from the lowest

temperatures to about 70 K _;

iv)

_a shoulder _on this

velocity

increase, located at about 35K

independently

of the

frequency,

attributed _{to a} transitional effect

(see below)

_;

v)

an attenuation

peak,

associated with the sound

dip,

and also

frequency dependent

;

vi)

an attenuation occurring below 70 K.

The

frequency

_range of the dielectric

experiments

extended from

f

=

10 Hz _to

f

=

MHz.

The _main observed features

(see

the lower part ^of

Fig, l)

_{are :}

i)

a

positive frequency dependent

relaxational step in the real part ^{of the}

complex

dielectric

08

1.7 Li

f 273 MHz

ôc'/co

04

ôc"ico

o

1.7 x Li

f 1000 Hz

O £'

O O C4

£

0 TEMPERATURE (K) 200

Fig.

l.

Upper

part : real and

imaginary

_parts of the relative _variation of the elastic _constant measured _at

273 MHz

in a KLT

sample

with 1.7 % Li

plotted

_{as a} function of temperature. Lower part : real and

imaginary

parts ^of the dielectnc _constant measured _ai kHz. The two sets of data, performed in the _same sample, refer to measurements without

applied

electnc field dunng coolmg ^and

heating.

constant

(which

would

correspond

to a

slowing

down of the

electromagnetic

_{wave at} these

frequencies), superimposed

_{on a}

background

which does _not

depend

_on

frequency

ii)

_a relaxational

peak

in the

imaginary

_part of the

complex

dielectric constant,

correspond- ing

to the step.

Indeed the _same process

(w/2 jump

of Li+

ions)

is

responsible

for the _two relaxational attenuations and

dispersions

observed in the elastic and dielectric measurements.

They

_appear

at different temperatures

(100

K and 50 K

respectively)

because the measurement

frequencies

are very different

(five

orders of

magnitude).

The

displacement corresponds

to an Arrhenius relaxation with _a barrier

height equal

to 900 K

[12].

Ail these

features,

in the

complex

elastic _{constant as} well _as in the

complex

dielectric constant, were observed upon

heating

without

biasing

field

(ZFH)

after _{a zero} field

cooling (ZFC).

In the

following

sections the rote of the

cooling

rate and the effects of field

cooling (FC)

are described.

Dielectric

experiments (data

and

analysis).

There is _a great ^difference between the data obtained from experiments ^{with the}

biasing

field E

parallel

_or

perpendicular

to the

oscillating

field. This is shown for E

=

75 kV/m _in

figure

2, where the fuit fines show the data with E

=

0,

for reference.

1.7 Li 1.7 Li

o ~f 68.5 Hz f 68. 5 Hz

o

g

^8'

j

O

" 8"

0 T(K) 80 0 T(K) 80

Fig.

2. Real (left) and

imagmary (right)

_parts of the dielectric constant measured at 68.5 Hz in _a KLT sample ^with 1.7 % Li

plotted

_{as a} function of temperature. ^{All the} measurements were performed without

applied

^electric field, alter coolmg either _m zero field (full hne) _or in _a 75 kV/m _static electric field applied

parallel

(dashed-doubly dotted lme) _or

perpendicular

(dashed-dotted line) _ta the oscillatmg

electnc field.

If the static field

applied during

FC is

parallel

ta the

oscillating

field of ZFH, ii generates contributions _to the real part ^{and the}

imagmary

part ^{of the dielectric} constant which _are both

positive

and vary as w~~ The exponent v and the

amplitude

of the contributions _are temperature

dependent

_: the value of

v varies between 0.3 and 0.7 while the

amplitudes

have

maxima near 22 K

(dashed-doubly

dotted

hnes).

Another contribution of the _same type is

hardly

observed _near 50 K.

If the

crystal

is cooled in _a

biasing

field

perpendicular

to the

oscillating

field, _in addition to the features observed in the previous case, there _{are new} positive contributions. The first _ones

are similar _to those observed in the

parallel

_case

(proportional

to w~ ^~ for both real and

N° ELECTRIC FIELD EFFECT ON

Kj _,Li~TaO~

151

imaginary parts),

but here with their maxima _near 50K. The second ones are

large, independent

of the

frequency

for the real

part

^and

varying

_as

w for the

imaginary

part, over our lowest two decades

(at higher frequencies, they

become

negligible)

_; their maxima are also

near

22K, independently

of the

frequency (dashed-dotted fines).

In

figure

3, where the

logarithmic

scales show the

frequency behaviour,

the _two contributions

(1.e.

the difference

between the measurements with and without

field)

_at 22.5 K and 50 K _are

sÉetched.

_The

w contribution

corresponds

to fosses

independent

of the

frequency,

that is to say, ^to a

purely

ohmic

phenomenon.

7 Li

4 T m 22. 5

~

~

~0

tù

~~

$ ^{~ ~~ ~ ~}

"fI,

ÎÎ "',

~ _Î

", i(0~

~0

', ~ 0

'

1.7 Li

4 T 50

w

o

m

O

~X~Î',

'x~à~

₀

~,0°

log,~ l (Hzj ⁷

Fig. 3. Log-log plots of the difference between the dielectric constant measured alter field cooling and measured alter _zero field

coolmg

(real part crosses and imagmary part : open circles) _{as a} function of

frequency

for _a KLT

sample

with 1.7 % Li for two temperatures. ^{A 75} kV/m static electric field _was

applied perpendicular

ta the

oscillating

electric field

dunng cooling.

The dashed fines have _a

slope equal

ta -1

(top)

and 0.53 (bottom).

We first remark that the

frequency dependences

^of our data _{are in} agreement ^{with the}

Kramers-Kronig

relations since

they respectively corresponds

to the two

susceptibility

forms _:

s(w)

=

Ajcos (ver/2)

-1sin

(ver/2)1(wr)~ ~, s(w)

=

Ajorô(wr)

i p-p-

(1/wr)i,

where ris _some relaxation time.

Secondly,

_we notice that in the two

quoted experiments

the _same static electric field _was

applied along

two

equivalent perpendicular

axes.

Therefore,

it is

expected

that the _same effect is

produced

in both

geometries.

But in _{one case} the

remaming

^{fourfold axis} is

perpendicular

to the

measuring

electrodes, while in the other _case it is in their

plane.

This

explains

the

difference in _{our two sets} of data.

The

biasing

electric field is known _to generate a space

charge trapped

on the oxygen vacancies

[16].

The

hopping

^of the

trapped

electronic

charges

^leads to a contribution to the

complex

dielectnc constant

proportional

to w ^~

(0

~ v ~ l

).

Such _a behaviour has been

described

by

Jonscher for many materais

[17]

and

Ngai [18]

has

explained why

it is _so

commonly

encountered. We do observe this behaviour in the two

geometries

studied.

If the static field is

supposed

to also generate ^surface

charges

which occupy a thin

layer

at the interface _{near a}

biasing electrode,

then _our result _can be understood _as follows _: if the

oscillating

field is in the

plane

of this

layer (1.e.

is

perpendicular

to the static

field),

_an ohmic electronic conduction _{can occur} inside the

layer

^since the electrons may have _a

long path

_; this

is not

possible

_in the other geometry ^{where the electron}

path

^{is hmited}

by

the

layer

thickness.

Therefore, the main result of _our dielectric measurements after _a FC process is to show the presence of space

charges

which

persist

at temperatures ^much

higher

than _{T~ as} shown

by

the w~~ contribution that extends up to at least 70K.

They strongly perturbed

the dielectric

measurements,

specially

under T~,

possibly hiding

the effect of the field _on the

dipoles. They

also

played

_a fundamental rote in the

interpretation

of the acoustic experiments ^above T~

(see below).

Acoustic experiments

(data).

Our

experiments,

_as

already said,

_were

nearly

ail

perforrned

_upon

heating

the

crystal,

in zero

field. This _was because a

high voltage applied

on the

sample

could be hazardous for _our very sensitive

(10~

^~~ W detection. In order that the temperature ^{of the}

sample

be well

equilibrated,

our

heating

rate was low

(r~

= + 0.25 K per

mn).

~ We have first studied the rote of the

cooling

rate in ZFC expenments. ^This can be _{seen in}

figure

4 where the dashed fines _are relative to a

rapid cooling (RC),

with the

cooling

rate

r~ = -5K per mn while the fuit fines

correspond

to a slow

coohng (SC)

with r~ =

0.25 K per mn, both with E

= 0. After the SC, the sound

velocity

^{has decreased} more

(by

a

factor of

2)

than after the

RC,

but the shoulder observed _on both _near 34 K is much _more

pronounced

in the latter _case

(upper

_part of

Fig. 4). Similarly,

the SC induces _a very strong

08

1.7 Li

f 96 MHz

04 _--'

ôc'/co

1.7 x Là

f 96 MHz

ôC"/Co

04

0 TEMPERATURE (K) 200

Fig.

^4. Relative change of the elastic constant measured at 96 MHz, _upon

heating

in _zero field alter zero field

coobng,

_in a KLT

sample

with 7 % Li _{as a} function of temperature.

Top

real part ^bottom

imaginary part. ^{Full line slow} cooling (- 0.25 K/mn), dashed hne rapid cooling (- 5 K/mn).

N° I ELECTRIC FIELD EFFECT ON Kj ~Li~TaO~ 153

attenuation at low temperatures

(lower

part ^of

Fig. 4).

It is very cleai _on the

velocity

measurements that the two curves coincide

only

^{above 70 K} and the

quality

of the coincidence

shows that the

discrepancy

between them is much

larger

than _our accuracy.

Our

heating

rate and _our SC _{rate were} similar

(except

^{for the}

sign)

and, in that _case, the

velocity

and attenuation _{curves were}

quasi-identical

_upon

heating

and upon

cooling, mdicating

that _some

thermodynamical equilibrium

is

practically

obtained in these _two processes, at any temperature.

The FC processes were achieved with both SC and RC and the

biasing

field _was

E

=

75 kV/m.

Figure

5 shows the rote of the electric field and the rote of the

cooling

rate

(fuit

hne for SC and dashed fines for

RC). Obviously,

the direction of the field has _a strong

influence : if the field is

applied parallel

to the _{wave vector} and the

displacement

vector

(left part),

^{it induces} a

large

decrease of the sound

velocity

on the contrary, ^{if it is}

applied perpendicular

to these vectors

(right part),

the result is _an increase. However, the influence _on the sound attenuation is rather

weak,

smaller than _m the _case E

= 0

(compare Figs.

4 and

5).

When the

biasing

field _was E

= 150

kV/m,

the effect _was

larger

but _not twice

larger

: there _{is a} saturation.

08

1.7 Li 1.7 Li

f 96 MHz f 96 MHz

ôc'ico ôc'ico

ôc../co ôc../co

0 T(K) 80 0 T(K) ⁸⁰

Fig.

5. Real and

imaginary

_parts of the elastic constant measured _ai 96 MHz, _upon

heating

in _zero field after field

coolmg,

in _a KLT sample with 1.7 % Li as a function of temperature. ^Static electnc field

applied parallel

(left) or

perpendicular

(right) to the acoustic wavevector. Full [me slow

coolmg

(- 0.25 K/mn), dashed line rapid coolmg (- 5 K/mn).

Indeed,

the most

important result,

shown

by figure

5, is that the _two sound

velocity

curves

relative _to the two different

coohng

rates but the _same field E _are different at low temperatures and merge into _a

unique

_curve at 34 K. This remarkable temperature is the _same for the _two field orientations. Therefore, _we attnbute _to this temperature ^the meaning of _{a transition}

temperature T~.

The left part ^of

figure

6 presents a sound

velocity

curve obtained after _a ZFC and _{two curves} relative _to the two different field orientations. Ail _were recorded after _a slow

cooling.

However,

they

do not merge ^at T~. Indeed,

they

coincide

only

at

higher

temperatures, near

70 K. This _is also _true for the sound attenuation, shown _in the

nght

part ^{of the} same

figure.

All these effects do not

depend

on the

frequency

_m the studied range.

.08

~,

_{i.7 Li 1.7 Li}

'~

f 96 MHz f 96 HHz

~04

ôC'/Co

ôC"/Co

0 T(K) 80 0 T(K) 80

Fig.

6, -Reai (left) and

imaginary

(right) _parts of the eiastic _constant measured ai 96 MHz, _upon

heating

_{m zero} field, in _a KLT sampie with 1.7 % Li _{as a} function of temperature. ^{For the three} sets of

data the sample was cooled

slowly,

either in _zero field (fuit fine) or in a 75 kV/m field

apphed parallel (dashed-doubly

dotted bne) _or

perpendicular

(dashed-dotted line) to the acoustic wavevector.

Acoustic

experiments (analysis).

Our

experiments

show that the FC process has _no effect _on the relaxation of the Li+ ions since the sound

velocity

and attenuation _curves relative to FC and ZFC _are identical in the temperature range of the relaxation step ^{and relaxation}

peak (around

100K for _our

frequency range).

^{This is} not

surpiising

since the

change

of the electrostatic energy of _an isolated

dipole

E _p~~~ is of the order of K

only,

while _a

typical

_energy of the

problem

is the barrier

height, equal

to 000 K.

Therefoie, only

three features observed in _our acoustic

experiments

have to be

explained.

a)

The elastic _constant of cubic pure

KTaO~ crystals

is known _to

steadily

_increase when the temperature ^{is decreased down} to 4 K

[19]. Here,

this behaviour is observed _on the sound

velocity

^down to

70K,

but below, an

unexpected

decrease _{occurs even} upon ZFC. This

variation between _T~ and 70 K is the first

point

to elucidate.

b)

There is _an effect of the electric field _on the elastic

properties

of the KLT

crystal, specially

_on the sound

velocity,

^below _T~. The effect is _net weak _: for comparison, with E

=

75

kV/m

the relative

velocity change

_is of the _same order _as the

change

induced

by

the lattice

anharrnonicity

_over 200 K.

Moreover,

it

depends

_on the

biasing

field orientation. This _is the second point to interpretate.

c)

^Between _T~ ^and 70

K,

the sound

velocity

is _not the _same after different FC processes.

This _iemanence in the

high

tempeiatuie

phase

_is the thiid

point

to

explain.

We discuss _our

experimental

results

successively according

to the

following

^hnes :

i)

the _occurrence of

packets

^{of oriented}

dipoles (clusters)

which exist _even in ZF and

high

temperature ^and favorized

by

the field (this

explains

the first _two

points)

ii)

the presence of space

charges,

still present ^above _T~, ^which generate a residual field

(this explains

the last

point).

However, before _a

semi-microscopic analysis,

we recall the main results of the Devonshire

theory [20],

which is _a macroscopic and

phenomenological description

of

ferroelectrics,

because its

piedictions

_{piesent some}

analogy

with the obseived featuies

(ii

is

expected

to

apply

N° ELECTRIC FIELD EFFECT ON

Kj _~Li~TaO~

155

here if the clusters _or domains _aie

large enough).

In this

theory,

the four temperatures To ~ T~ _~

Tj

_~ T~

play

remarkable rotes.

They

separate ^{the different} states listed below _:

ii

if T _~

To, only

_a ferroelectric

phase

can exist ;

ii)

if

TO~T~T~,

_a stable ferroelectric

phase

and a metastable

non-polar phase

_are

possible

iii)

if

T~~T~TI,

_a metastable ferroelectric

phase

and _a stable

non-polar phase

are

possible

_;

iv)

if

Ti

~ T~

T~,

the

only

stable

phase

^is

non-polar

but _an

applied

field _can induce _a

ferroelectric

phase

_;

v)

if T~ ~

T,

the

only

stable

phase

is

non-polar

and _{even an}

apphed

field _cannot induce _a fetToelectric

phase.

Such _a system possesses the

following properties

_:

a)

in absence of

field,

it

reversibly

follows _a

cycle starting

from _a temperature

higher

than

Ti, going

down _{to a} temperature

higher

than T~ ^{and then}

coming

back _to the initial temperature,

always

_{staying in a}

non-polar phase

b)

if it follows the

previous cycle

with _an

applied

field

during

the

cooling

_process, it is driven into _a ferroelectnc

phase

which

persists

_upon

heating,

if the field is switched

off,

_up to the temperature

Ti.

Now,

if _{we assume} that

Tj

=

34 K and T~ ~ 4 K

(the

lowest temperature ⁱⁿ our

experiments),

our observations _are well descnbed. In ZFC down to 4

K,

_no transition

happens

: the

crystal

stays ⁱⁿ a

non-polar phase.

In FC down _to 4

K,

_a stable ferroelectric

phase

is

mduced,

which

becomes metastable when the field is switched off _; then upon

heating

this

phase persists

_up to

34K where it transforrns into _a

non-polar phase.

In this scheme the

limit-temperature

Tj

must be

independent

of E, as we observe in first

approximation

and must be identified with

(.

Indeed _some

rounding

exists, below

Ti

because of the relaxation of the metastable _state towards the stable

non-polar

state and above

Tj,

due to the residual field associated with the space

charges.

In this forrn, the Devonshire

theory

is, in

principle,

^valid

only

for

homogeneous

media since it

neglects

fluctuations and disorder. In

fact,

the KLT system is disordered. This leads _to

specific properties

due, in

particular,

to static random fields

(SRF).

Then _{we tum to a more}

microscopic description

of the KLT

crystal,

assuming the presence of dusters which takes into _account the fluctuations of

polarization

and _we calculate the effect

on the elastic constant. We

emphasize

^that we use the word _« duster» with the

simple

meaning

of

packet

_or small

region

_; in

particular,

_no idea of

segregation

of lithium atoms is

implied.

The off-centre Li+ ions _are

displaced

in _one of six

equivalent positions along

the three local fourfold _axes. This fact, associated with the

dipolar

interactions,

gives

a trend towards

lowenng,

from cubic _to

tetragonal,

of the symmetry ^{of the}

crystal

and cluster

growth.

^In what follows the superscnpts ^{C and T stand for cubic and}

tetragonal.

In _zero field there _{are as} many dusters oriented in _one direction _{as in} each other. On the contrary, ^if a field is

applied,

there

are more dusters

elongated

in the direction of the field than _in the

perpendicular

directions.

The elastic _constants

C)~

and

C)j,

which govem the propagation ^{of the}

longitudinal

waves

along

the fourfold _axis and the relevant twofold _axes

respectively,

_{are not}

equal

in _a

crystal

with

tetragonal

symmetry. ^{If the acoustic}

wavelength

A (A ₌ ⁸⁰ ~Lm at 100

MHz)

is

large

in

comparison

with the cluster size, the elastic constant C is

approximately

the _mean value calculated from

C)j, C)i, _C)~

_{and the volume fraction}

_{occupied by}

_{each type of dusters.}

Let be p~ = p~

(T, E,

_;~,

r~)

the volume fraction

occupied,

at temperature T,

by

dusters with their

tetragonal

_axis

along

the _{i axis} of the

laboratory

frame (1 = x, y or

z),

after _a

coohng

process m field E, with a

cooling

rate r~ and a

heating

rate i~. The values that the fraction may

take _are limited

by

the conditions 0 _w p, w and 0 _w p~ +

p~

⁺ pz w 1. If E

=

0,

then

p_~ = p~, ⁼ p=. The z-axis is chosen

parallei

_to the acoustic wavevector and therefore the

propagation

is

govemed by

^the mean elastic constant C defined _{as :}

~

~ Î _Ù~x + P>. ⁺ Pr

)1

~

Îl

+

Ù'x

+

Pi )

^~

Îi

+ Pz

~13

Due to the lattice

anharmonicity,

the elastic _constant

C)j

of cubic pure

KTaO~ crystals linearily

increases when the temperature ^{is decreased down} to 4 K

[19].

We _assume the _same

behaviour for the other two elastic _constants and _{moreover we} take the _same

anharmonicity

coefficient b for the three _cases and _we write

down,

with

= or 3 and X

=

C _or T _:

C)(T)

=

C((0)

-bT.

The contribution due to the relaxation of the Li~ ions _{is not} written since it is noticeable

oniy

near 100 K, weii above the range of interest for the present discussion.

Henceforth,

_{we use} reduced

quantities, taking

_as reference

Co

= C

fi (0)

and

putting Kil

"

CII(°)/Co, _K33

"

CÎ3(0)/Co

_{and B}

=

b/Co,

we get :

lC iTl Col/Co

+ BT

~ ~P< ⁺

P»1(Kii

' +

Pz(K33

^'

The temperature ^variation is the _sum of the linear effect due _to

anharmonicity

and the

change

due to the three fractions p,.

From _our

expenments performed

in _zero field and from others,

perforrned

in _a fieid strong

enough

to exhibit saturation, _we put forward _a very crude estimate for the reduced elastic

constants

K,~. They

_are obtained from the difference between the

experimental

data and the

variation,

assumed linear in temperature, ^due to

anharmonicity.

In the upper

part

^of

figure 4,

this variation would be

represented by

a

straight

fine

(not

drawn but

easily imagined)

tangent to

the _{curve m} the 100-200 K range and

cutting

the vertical axis _near 0.07. This value is valid for

ail _our

figures showing ôC'/Co

_smce the _same reference _was chosen.

Consequently,

the left part ^of

figure

6 shows that the effect of the clusters is

slightly positive

in _{one case} (dashed-

dotted

fine, corresponding

to

cooling

in _a field

parallel

to the _acoustic

wavevector)

and

clearly negative

in the other _{two cases}

(fuit

fine and

dashed-doubly

dotted

lme, corresponding

to

cooling

in _zero field and in a field

perpendicular

to the acoustic wavevector,

respectively).

More

precisely,

we find _:

(2/3 (Kij 1)

₊

(1/3 )(K~~

m 0.05

,

(Kj

i

1)

_m + 0.01 and (K~~

1)

_m 0.15

Brillouin scattenng measurements have been

performed [21]

on a KLT

crystal

which exhibits _a first order transition _at T~ = 60 K. With _our convention this

corresponds

to the concentration

x = 3.8 fG. From their values _{we can} deduce

(Kjj-1)m+0.04

and

(K~~-1)m-0.33.

Considering

the difference of

concentration,

the agreement ^with our estimate is quite

good

for the order of

magnitude

and

especially

the signs.

In order to

complete

the model, _a caicuiation of _p,

(T,

E, _i~,

r~)

is needed. It must take mto

account both the features descnbed

by

^{the Devonshire}

theory

^and the

quadrupoiar (probably,

dipoiar too)

fluctuations. This is

beyond

the scope of the

essentiaiiy experimental

_present

paper.

N° ELECTRIC FIELD EFFECT ON

Kj _~Li~TaO~

157

However,

the modei deserves severai _comments.

i)

The observed increase

(when

T

increases)

of the elastic constant above _{T~ was} also present

in other KLT

samples [13]

with lithium concentrations

equal

to 1.5

fG,

3.5 fG

(samples

I and II of _our

systematic study)

but _not

clearly

for 5 fG

(sample III), perhaps

because in the last _case the transition occurs at too

high

_a temperature

(75 K).

ii)

These _acoustic expenments on

sample

^III support our scenario _: upon

cooling nothing

happens

at 75 K whilst upon

heating

_a

quasi-discontinuity

is observed at this temperature,

giving

it the meaning of the limit of

metastability Tj.

In this _case,

things

_are clearer since,

because of the

higher

concentration, _a

biasing

field is not needed _to induce the ferroelectnc

phase.

iii)

In ZFC

experiments,

it is _{not true} that

nothing happens

at T~. Indeed there is _a

slight

shoulder _in the sound

velocity

_curve. This may be due to SRF which _can

locally

induce

ferroelectric

microregions.

iv)

In this

schema,

the weakness of the effect of the electric field _on the dielectric

properties

is attributed _to the low

anisotropy

of the dielectric

properties.

Indeed, the

biasing

field in the

present experiments

is

notably

smaller than _was

applied by

^other authors

[22, 23].

v)

The rote of dusters, with symmetry ^{lower than} cubic, present even above _T~ is reminiscent of the

interpretation given by

Di Antonio _et ai. of their Raman

scattering

data

[4]

obtained on

samples

I and II. Because of the symmetry ^{of their}

probe, they

can attribute _a

polarization

to the clusters. In _{our case, since we use} another

probe,

we

only

show the

quadrupolar

_nature of the

clusters,

which is not

incompatible

with the

dipolar

nature. We think that

they

are the _same entities _in both _cases.

vi) Preliminary

Raman

scattering experiments perforrned

in _our

sample

V

by

Toulouse

[24]

show the presence of

polarized

dusters _at temperatures up ^to 105 K. This

clearly

confinas _our

interpretation.

Our dielectric measurements show that _a static electric field generates _space

charges

_in KLT

crystal,

^still present up ^to 80 K

(see Fig. 5).

These

charges

induce _an internai electric field

[16]

which

produces

on the elastic constant an effect similar

(in

the _same

way)

to that

given by

the extemal field which has

generated

the space

charges.

This

explain why

the

splitting

due to FC

persists

at

high

temperatures, ^much above T~.

Conclusion.

The acoustic

experiments

in _a KLT

crystal

with 1.7 fG Li under _an

applied

electric field

reported

here show the existence of _a transition temperature at 34

K, hardly

to be _{seen in zero} field. The

metastability

^of the low temperature

phase

obtained

dunng

field

cooling

is also

shown.

The expenments ^{without electric field} are in agreement ^{with the} occurrence of ordered

microregions (clusters)

_even above the transition which appears very

fuzzy (neither

first order

nor second

order).

These ordered

microregions

_are

obviously _present,

and

probably

_more

developed,

below the transition. This result _seems to rule out the

hypothesis, generally accepted

for Li concentrations lower than 2

fb,

of _a

dipolar glass phase.

Acknowledgements.

The authors _are

grateful

to U. T. Hôchli

(Zurich)

for interestmg comments concermng space

charges,

to J. Toulouse

(Lehigh University, Penn.)

for valuable discussions _on

polanzation

clusters and _to M. Gauneau

(Centre

National d'Etudes des Télécommunications,

Lannion)

^for

the SIMS measurements.

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