KTN 誘電体温度計

第 3 章量子強誘電体 25

3.4 KTN 誘電体温度計

3.4.1 KTN ^{の量子強誘電性}

一般式ABO3で表されるペロブスカイト構造を図3.6^に示す．

A O B

図3.6 ペロブスカイト構造

前述のようにKTaO3 は量子常誘電体，ニオブ酸タンタル（KNbO3，Tc = 707 K^）は古典的強誘電体であり，これらの混晶体をタンタル酸ニオブ酸カリウム（KTN: KTa₍₁₋_x)Nb_xO₃）とよぶ．KTaO₃ にKNbO₃ を加え双極子相互作用をわずかに強くすることで，量子強誘電性が発現することが報告されている^(17)(18)．KTNのキュリー点Tc は混晶比率xに依存し，

Tc =





676x+ 32 (0.05≤x≤1.00) 276(x−xc) (x≤0.05)

(3.5) と表される．ここで，x_c は強誘電相が発現する x の下限値であり，x_c ≃ 0.008 である．

KNbO3 希薄混晶系におけるxとTc の関係およびxによる誘電率の温度依存性を図3.7および図3.8^に示す．KNbO3 希薄混晶系において起こる相転移はx^によらず2^{次相転移である．}

図3.7，3.8に示すように，混晶比率xによりT_cを制御し，さらに，T_c以下の温度における誘電率の温度依存性を制御可能である．同様の手法により，量子常誘電体であるチタン酸ストロンチウム（SrTiO3）と古典的強誘電体であるチタン酸バリウム（BaTiO3，Tc = 393 K）の混晶体である，Sr₍₁₋_x)Ba_xTiO₃の量子強誘電性も報告されている⁽¹⁹⁾．

QQJ.UME $9,^+UMBER ¹⁸

PHYSICAL REVIEW LETTERS

$1^OGTQBER 1977 the only known

example4 of a cubic solid solution

which

undergoes a second-order transition to a ferroelectric phase

whose

transition temperature can be continuously varied

_by

chemical composi-tion over a

wide

range. Pure KTaO, (i, e.

x =0) does not undergo a ferroelectric phase transition, '

but it does exhibit a dielectric anomaly near 7 ^=0,

The solid solution KTa, »Nb~050„however, be-comes ferroelectric at about 60 K,

^and

starting from this composition, the critical temperature increases almost linearly

with

increasing

con-centration

until

a T, ^of ⁷⁰⁰ ^K is obtained for pure KNb03.

the system KTa, „Nb, O„ ^the

^Nb

concentra-tion x

may

be treated as

interaction parame-ter

^on

the basis of the

following

considerations:

First,

in the

classical limit (i.e.

for x &0.008), the transition temperature is

found

to be a linear function' of x. It appears ^{that the}

^Nb

concentra-tion enhances the dipolar interaction since it is

unlikely to influence the fluctuations of the polar-ization, Second, in the

quantum

limit, the effects

(10

'}

associated

^with

increasing x resemble those

re-sulting f rom external pressure. Ferroelectricity

KTaO, has been induced'

_by

a pressure of 6

x20'

N/m2.

It has also been recognized as being

mainly due

to anisotropic

oxygen

polarizability. '

It is

thus

reasonable to neglect the randomness of

the

dipolar interaction

with

respect to the aver-age enhancement.

In the present work, the spontaneous polariza-tion P, ^has been measured at various tempera-tures from a hysteresis loop at 0. 25

for sam-ples

with

varying

^Nb

concentration. The

low

fre-quency

of 0, 025

was necessary in order to en-sure complete ferroelectric switching. The

curves of P, ^{versus T}

^have

been extrapolated to 0 K,

^and

the resulting values were used to

deter-mine

the

critical index P„. ^The ^curves ^{of e} '

ver-sus T

ⁱⁿ

Fig.

¹ ^show

that there is a

minimum

of

' _for _each _sample

_with

_x &0.008,

^and

that the temperature at

which

this

minimum

occurs (i.e.

the

Curie temperature) increases

with

increasing

x. The peculiar shape of the c ' _{versus T} _curve

close to x„however, ^prevents a reliable

deter-mination of T, .

^An

^accurate determination of T,

^may

^be ^made, ^however,

^by

^measuring ^the elastic compliance s» ^{using the} ^ultrasonic

reso-nance technique. ' _The same samples were

em-ployed in

deter

ming e

' _{as a} function of tempera-ture

and

the results are

shown

in Fig. 1. The val-ues of

' extrapolated to 0 K are

shown in

Fig. 2.

The elastic constant s» ' _is _plotted versus tem-perature

Fig. 1,

^and

it is seen to change dras-tically

ⁱⁿ

^the same temperature range in

which

the dielectric

maximum

occurs. This change of the elastic constant is attributed to symmetry breaking

the paraelectric phase.

In an

ideal homogeneous sample, coupling of the strain to the order parameter leads to a step discontinuity' of the elastic constants at T, .

^In

^an actual sample

TEMP.

(K)

60—

50—

40—

x10-4

—₁₂

—₁₀

-08-0 20

40 60 80 100 ^'l20

TEMPERATURE (K)

PEG.

1.

^The inverse of the

dielectric

constant and the inverse

elastic

compliance

are

shown

as

functions

of

temperature. The curves

are

labeled according to the Nb percentage

as

determined by

electron

micro-probe analysis. Each curve contains about 50 data points.

30—

20 ^'—

10—

0::

2 3 4

Nb CONCENTRATION (PERCENT)

FIG.

Best fits

of the transition line and the

zero-point susceptibility by power laws.

図3.7 KTNのキュリー点T_c と混晶比率xの関係．U. T. H¨ochli et. al., Phys. Rev.

Lett. 39, 1158, (1977).

6834 D.RYTZ, A. CHATELAIN, AND U.T.HOCHLI

60 70 80

10— KTal-„Nb„03

z 8-

7-O -x=

3—

x=0

2-10 20 30 40 50 60 70

TEMPERATURE (K)

FIG.3. Temperature dependence ofthe static dielectric constant ewith concentration xas a parameter. The data were obtained _by aconventional bridge technique at 1 kHz. The temperature was changed at a rate ofno more than 0.5K/min.

Note the change on the temperature scale for

x=0.

057.

Curie-Weiss anomaly appears to be quenched and the experimental curves suggest a strong steplike discontinuity (with finite width). Close to

T„

^the

i(T

⁾ ^function ^is a superposition of the _{step plus} the Curie-Weiss singularity. This second contribu-tion to the elastic anomaly has not been sufficiently well resolved in previous studies. Figure ³ shows the Curie-Weiss behavior found for the dielectric constant, and establishes the close correspondence of the respective T,^'s ^for ^the ^dielectric ^and ^elastic peaks. Before we analyze these data, we plot in Fig.

s»(T) ands»'(T)

for KTai

„Nb„03

^mixed

crys-tals with larger concentrations (0.18

(x (0.

³⁶⁾ ^and,

for the sake ofcomparison, also for SrTi03.

Common to all curves is the temperature coeffi-cient far above T,^:^{In terms} of the effective elastic rigidity, we observe, for

T —

_T,_&20 _K _and _for _all

x's, a relative variation equal to

ii'(T) s» (o)]/[s ii'(0—

⁾T]

=3.

3&&10

measured in K

'.

_Below

_T„some

acoustic loss is encountered in all the samples. It is attributed to the motion of domain walls under the influence of

the driving field (a phenomenon known as

"hE

ef-fect,

"

_see _Ref. ₂₇ _for an analysis in SrTi03). There-fore no evaluation of the data is attempted for

—

_10&_T_&_T,

_.

peaks are truncated: No transition occurs to the fer-roelectric phase at positive temperatures. This sug-gests a common origin for the leveling off of the dielectric constant and of the elastic compliance.

The quantum-mechanical stabilization of the paraelectric phase analyzed previously for the dielectric properties is thus also observed in elastici-ty, as ^will be discussed in Sec.

III.

For x &0.0075, the elastic anomalies in

KTa~,

^Nb 03 ^and ⁱⁿ SrTi03 ^{look much} alike, except for a broadening of

the response in KTa~ ~Nb

03.

It is tempting to at-tribute this broadening to compositional inhomo-geneities. Improved control ofcrystal growth allows us to check experimentally the role of inhomogenei-ty in the elastic compliance measurements.

To test the influence of concentration _gradients, three probes were measured, all cut from one single crystal. One of them (L) had its length parallel to the growth direction z, the other two (A,B)^were per-pendicular to z [see Fig 5(a)]. Following the re-marks developed in the preceeding section, L is less homogeneous than A or

8

^because ^its ^{length is}

paral-lel to the concentration gradient. Figure 5(b) displays the changes in the inverse elastic compli-ance due to the increase ofthe Nb concentration as a function of position in the as-grown sample. The concentration values that could be deduced from the phase diagram when measuring the T,^'s ^(see ^Refs.

3, 7, and also Sec. III) via the dielectric peak are in 図3.8 KTNの量子強誘電性．D. Rytz et. al.,Phys. Rev. B 27, 6831, (1983).

3.4.2 KTN 誘電体温度計

以上の先行研究の結果より，KTN誘電体ではxの値を調整することで相転移温度を制御することができ，それに伴い極低温領域での誘電率の温度依存性も制御可能であると予想した．

そこで，本研究では誘電体マイクロカロリーメータの温度計に利用する誘電体材料の候補としてKTN誘電体を採用し，KTN（x= 0.0065）およびKTN（x= 0.01）誘電体温度計を試作した．

試作した KTN 誘電体温度計の模式図および写真を図3.9に示す．マイクロカロリーメータにおいて検出器の熱容量は小さいことが望ましいが，KTN 誘電体結晶を幾何学的に小さくしすぎると，焼結過程において結晶が破損するなどの技術的な課題から，KTN結晶は製作可能な最小の大きさである1×2×0.2 mm³ とした．KTN 結晶の上下面に厚さ100 nmの金電極を蒸着し，静電容量温度計を構成した．KTN（x = 0.0065）誘電体温度計および KTN

（x= 0.01）誘電体温度計の室温における静電容量，tanδは，振幅100 mV，周波数100 kHz の正弦波測定信号に対して，それぞれ37 pFおよび353 pF，0.09および0.05であった．量子強誘電相転移温度は多くの物質で数10 K程度である．相転移温度付近である数10 Kの温度領域における誘電率の温度依存性は詳細に測定した結果が報告されている．しかしながら，

DMCの動作温度である数100 mKの温度領域における詳細な物性の報告はないため，実測する必要がある．

0.2 mm

100 nm

2 mm

1 mm KTN

金電極

図3.9 KTN誘電体温度計．（左）KTN（x= 0.01）誘電体温度計の写真（右）構造模式図．

ドキュメント内量子強誘電体を温度計とするマイクロカロリーメータに関する研究 (ページ 36-39)

第 3 章 量子強誘電体 25

3.4 KTN 誘電体温度計

3.4.1 KTN の量子強誘電性

PHYSICAL REVIEW LETTERS

example4 of a cubic solid solution

undergoes a second-order transition to a ferroelectric phase

transition temperature can be continuously varied

chemical composi-tion over a

range. Pure KTaO, (i, e.

x =0) does not undergo a ferroelectric phase transition, '

but it does exhibit a dielectric anomaly near 7 =0,

The solid solution KTa, »Nb~050„however, be-comes ferroelectric at about 60 K,

starting from this composition, the critical temperature increases almost linearly

increasing

con-centration

a T, of 700 K is obtained for pure KNb03.

the system KTa, „Nb, O„ the

concentra-tion x

be treated as

interaction parame-ter

the basis of the

considerations:

First,

classical limit (i.e.

for x &0.008), the transition temperature is

to be a linear function' of x. It appears that the

concentra-tion enhances the dipolar interaction since it is

unlikely to influence the fluctuations of the polar-ization, Second, in the

limit, the effects

'}

associated

increasing x resemble those

re-sulting f rom external pressure. Ferroelectricity

KTaO, has been induced'

a pressure of 6

x20'

It has also been recognized as being

to anisotropic

polarizability. '

It is

reasonable to neglect the randomness of

dipolar interaction

respect to the aver-age enhancement.

In the present work, the spontaneous polariza-tion P, has been measured at various tempera-tures from a hysteresis loop at 0. 25

for sam-ples

varying

concentration. The

of 0, 025

was necessary in order to en-sure complete ferroelectric switching. The

curves of P, versus T

been extrapolated to 0 K,

the resulting values were used to

deter-mine

critical index P„. The curves of e '

ver-sus T

Fig.

that there is a

of

' for each sample

x &0.008,

that the temperature at

this

occurs (i.e.

Curie temperature) increases

increasing

x. The peculiar shape of the c ' versus T curve

close to x„however, prevents a reliable

deter-mination of T, .

accurate determination of T,

be made, however,

measuring the elastic compliance s» using the ultrasonic

reso-nance technique. ' The same samples were

deter

' as a function of tempera-ture

the results are

in Fig. 1. The val-ues of

' extrapolated to 0 K are

Fig. 2.

The elastic constant s» ' is plotted versus tem-perature

第 3 章量子強誘電体 25

3.4.1 KTN ^{の量子強誘電性}

but it does exhibit a dielectric anomaly near 7 ^=0,

a T, ^of ⁷⁰⁰ ^K is obtained for pure KNb03.

the system KTa, „Nb, O„ ^the

to be a linear function' of x. It appears ^{that the}

In the present work, the spontaneous polariza-tion P, ^has been measured at various tempera-tures from a hysteresis loop at 0. 25

curves of P, ^{versus T}

critical index P„. ^The ^curves ^{of e} '

' _for _each _sample

_x &0.008,

x. The peculiar shape of the c ' _{versus T} _curve

close to x„however, ^prevents a reliable

^accurate determination of T,

^be ^made, ^however,

^measuring ^the elastic compliance s» ^{using the} ^ultrasonic

reso-nance technique. ' _The same samples were

' _{as a} function of tempera-ture

The elastic constant s» ' _is _plotted versus tem-perature

^the same temperature range in

^an actual sample

_T„some

_.