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Low temperature specific heat of single-domain and polydomain ferroelectric NaNO2
~
Solid State Communications, Voi.38, pp.807-808. Pergamon Press Ltd. 1981. Printed in Great Britain.
0038-1098/81/210807-02502.00/0
LOW TEMPERATURE SPECIVIC HEAT OF SINGLE-DOMAIN AND POLYDOMAIN FERROELECTRIC NaNO 2 R. Villar +, E. Gmelin Max-Planck-Institut f~r Festk0rperforschung, Heisenbergstr. I, D-7000 Stuttgart 80, Federal Republic of Germany and S. Vieira Dpto. de Fisica Fundamental, Universidad Aut6noma de Madrid, Madrid, Spain Received: February 15, 1981, by M. Cardona The specific heat of a NaNO 2 sample has been measured between 2 K and 40 K in both single-domain and polydomain states. In this regio~ the specific heat of the single domain sample follows exactly the T dependence. A clear excess contribution which in this temperature range has a temperature dependence between T and T 2 has been detected for the polydomain sample. It is attributed to domain walls.
The low temperature specific heat ( C ) of several ferroelectrics m e a s u r e d above 2 KPshows a strong deviation from the Debye T3-term. 1, 2 This anomalous behaviour was described as a T 3/2 excess contribution and was first I postulated to be due to quantized domain wall oscillations and later to surface layers. 2 A model 3 based on the excitation of ferroelectric dipole waves, analogous to the spinwaves in a ferromagnet, was suggested to explain such a temperature dependence. In addition, a m a x i m u m in the curve Cp/T 3 versus T 2 shows up at a relative temperature T/SD, unusually low in comparison with the general temperature dependence of the specific heat of dielectrics. Lawless I has analysed this feature in terms of an Einstein contribution. However, to our knowledge, no measurement has been performed with the same sample in the singledomain and polydomain state to test the influence of domain walls upon the low temperature specific heat. We report here the first results of such measurement of Cp performed for NaNO 2 for T>2 K. NaNO 2 is a simple structured order-disorder ferroelectric with a Curie temperature T c = 163.4°C. Its room temperature structure is orthorhombic with space group Im2m. Most of the spectroscopic data for this material are described in ref. 4. Our sample was the same one used by de las Heras et al. ~ to measure the spontaneous polarization. It was cut from a crystal grown from the melt by the slow cooling method (IK/h). The initial material was a Merck pro analysi product. It was prepoled (i.e. forced into single-domain state) by heating it abo~:e the Curie temperature and cooling under an applied field of -50 V / c m in the direction of the ferroelectric axis. The weight of the sample was 1.892 ~. The measurement of the spontaneous polarization shows that the sample was indeed single-domain. After measuring the C of the single-domain P sample, it was made polydomain by heating it over T c and cooling the sample without applied field. + Alexander von Humboldt Fellow, on leave from Universidad Aut~noma de Madrid, Madrid, Spain.
The initial crystal broke during this procedure. One of the pieces having a weight of 0.624 g was used in one of the polydomain measurements (sample A). Another crystal (sample B) of mass 2.646 g was taken to perform the second polydomain measurement. This was done in order to measure a polydomain sample with a similar contribution from sample holder, heater and thermometer (addenda) as in the monodomain case. This second specimen was grown with the same method and the same products as described above. The crystal was kindly supplied b y de las Heras. The heat capacities were determined in a computer controlled adiabatic calorimeter. 6 The addenda 7, measured in a separate run, contributes about 20% to the total huat capacity for Sample B and the single-domain crystal. For sample A it amounts to 50%. The sample holder was recently tested with a 13 g calorimetry copper standard to an accuracy of 0.2%. This shows that any systematic error is b e l o w this figure and we estimate our overall experimental accuracy in 1.5%. The results are plotted in Fig. I as C/T 3 versus T. A clear contribution in excess to the T 3 term appears for the polydomain sample below 8 K. This contribution is absent in the specific heat of the single-domain NaNO 2 in this temperature range. The Debye term is the same in both cases. The T3-region extends over a wide range of temperature in comparison with other ferroelectrics measured by Lawless 1,2, in which additional low frequency modes contribute significantly in the region 5 K
Vol. 38, No. 9
S I N G L E - D O M A I N AND P O L Y D O M A I N F E R R O E L E C T R I C N a N O 2
808
15
'--' "7"
/
0.8
I
,x,o
~E
I
i
Y
7 -6
10
C~
rO
2
LLI I 0 11 r,j ILl CL u'l
o.
uJ i L.) LL U
5't o°" 0 "' ""YP°lyd°main{ Sa~:~'~:
Fig.
0
20 TEMPERATURE
40
0.4
0.2 0
W
Fig.
NAN02
0.6
60
T 2 [ K 2]
1 S p e c i f i c h e a t o f NaNO,, s i n g l e - d o m a i n and p o l y d o m a i n r e p r e s e n t e ~ as C p / T 3 vs. T. B e l o w 8 K the e x c e s s s p e c i f l c h e a t in the p o l y d o m a i n sample s h o w s up as a d e v i a t i o n f r o m the h o r i z o n t a l .
We note f r o m this p l o t t h a t in the low t e m p e r a ture r e g i o n (2 K < T < 8 K) b o t h fits are e q u a l l y g o o d for the data. It is a l s o w o r t h o f e m p h a s i zing the c o i n c i d e n c e b e t w e e n b o t h p o l y d o m a i n samples. The r e s u l t s s u g g e s t that the e x c e s s contrib u t i o n in f e r r o e l e c t r i c N a N O o in a d d i t i o n to the T 3 t e r m is due to a d o m a i n w ~ l l contribution. The m e c h a n i s m t h a t g i v e s rise to s u c h a b e h a v i o u r , however, is n o t y e t clear. T h e r e are t h e o r e t i c a l c a l c u l a t i o n s 8,9 w h i c h p r o p o s e a T 2 t e m p e r a t u r e dep e n d e n c e o r e x p l a i n a T 3 / 2 term. Thus, the accurate d e t e r m i n a t i o n of the t e m p e r a t u r e d e p e n d e n c e at s t i l l lower t e m p e r a t u r e s is necessary. F i n a l l y , we p o i n t o u t that r e c e n t m e a s u r e m e n t s 5 o f the t e m p e r a t u r e v a r i a t i o n of s p o n t a n e ous p o l a r i z a t i o n Ps s h o w t h a t the ~ y r o e l e c t r i c c o e f f i c i e n t ~ = d P s / d T follows a T ~ b e h a v i o u r in
÷ ÷ ÷ ÷ ÷÷÷÷÷+_
I
0
I
I
I
I
I
40 I0 20 30 TEMPERATURE T [K]
2 The same d a t a in the region T<8 K repres e n t e d as vs. T 2. The s i n g l e - d o m a i n p o i n t s fall in a line t h r o u g h the o r i g i n (Debye term), b u t the p o l y d o m a i n d a t a f o l l o w a n e a r l y p a r a l l e l line w i t h interc e p t for T = O at 0.22 x 10 -2 J m o l -I K -2. F o r c o m p a r i s o n the d o t t e d line r e p r e s e n t s the fit C = 1.27 x 10 - 3 T 3 / 2 P + 1.95 x IO- 4 T 3 Jmol - I K- I .
Cp/T
the same range of t e m p e r a t u r e s , as found in our s p e c i f i c h e a t m e a s u r e m e n t s . T h i s feature s u g g e s t s t h a t in N a N O 2, in c o n t r a s t to m o s t f e r r o e l e c t r i c s , n o a d d i t i o n a l low f r e q u e n c y o p t i c modes contrib u t e to the low t e m p e r a t u r e s p e c i f i c heat. In c o n c l u s i o n , we h a v e s h o w n that the p r e s e n c e of d o m a i n w a l l s in a f e r r o e l e c t r i c leads to an a d d i t i o n a l c o n t r i b u t i o n to the s p e c i f i c heat. F r o m the p r e s e n t results, it is o b v i o u s that the e x a c t t e m p e r a t u r e d e p e n d e n c e o f such an excess s p e c i f i c h e a t can o n l y be d e t e r m i n e d by m e a s u r e m e n t s b e l o w 2 K. A c k n o w l e d g e m e n t s - We w i s h to thank C. de las H e r a s for the c a r e f u l c r y s t a l p o l i n g and preparation, H. W i t s c h e l for aid in h a n d l i n g the comp u t e r s y s t e m and K. R i p k a for t e c h n i c a l assistance.
References I. W.N. LAWLESS, Phys. Rev. Lett. 36, 478 (1976). 2. W.N. L A W L E S S a n d A.J. MORROW, F e r r o e l e c t r i c s 15, 167 (1977). 3. J.A. GONZALO, F e r r o e l e c t r i c s 2__O, 159 (1978). 4. C.M. HARTWIG, E. W I E N E R - A V N E A R and S.P.S. PORTO, Phys. Rev. B5, 79 (1972). 5. C. DE LAS HERAS, J. G O N Z A L O and S. VIEIRA, F e r r o e l e c t r i c s (in press).
6. E. G M E L I N , T h e r m o c h i m i c a A c t a 29, 1 (1979). 7. E. G M E L I N and K. RIPKA, C r y o g e n i c s 20, 117 ( 1980). 8. S. KIR/K2ATRICK and C.M. VARMA, S o l i d S t a t e Comm. 25, 821 (1978). 9. I.A. PRI---VOROTSKII, Phys. Lett. 62_AA, 173 (1977).
Solid State Communications, Voi.38, pp.807-808. Pergamon Press Ltd. 1981. Printed in Great Britain.
0038-1098/81/210807-02502.00/0
LOW TEMPERATURE SPECIVIC HEAT OF SINGLE-DOMAIN AND POLYDOMAIN FERROELECTRIC NaNO 2 R. Villar +, E. Gmelin Max-Planck-Institut f~r Festk0rperforschung, Heisenbergstr. I, D-7000 Stuttgart 80, Federal Republic of Germany and S. Vieira Dpto. de Fisica Fundamental, Universidad Aut6noma de Madrid, Madrid, Spain Received: February 15, 1981, by M. Cardona The specific heat of a NaNO 2 sample has been measured between 2 K and 40 K in both single-domain and polydomain states. In this regio~ the specific heat of the single domain sample follows exactly the T dependence. A clear excess contribution which in this temperature range has a temperature dependence between T and T 2 has been detected for the polydomain sample. It is attributed to domain walls.
The low temperature specific heat ( C ) of several ferroelectrics m e a s u r e d above 2 KPshows a strong deviation from the Debye T3-term. 1, 2 This anomalous behaviour was described as a T 3/2 excess contribution and was first I postulated to be due to quantized domain wall oscillations and later to surface layers. 2 A model 3 based on the excitation of ferroelectric dipole waves, analogous to the spinwaves in a ferromagnet, was suggested to explain such a temperature dependence. In addition, a m a x i m u m in the curve Cp/T 3 versus T 2 shows up at a relative temperature T/SD, unusually low in comparison with the general temperature dependence of the specific heat of dielectrics. Lawless I has analysed this feature in terms of an Einstein contribution. However, to our knowledge, no measurement has been performed with the same sample in the singledomain and polydomain state to test the influence of domain walls upon the low temperature specific heat. We report here the first results of such measurement of Cp performed for NaNO 2 for T>2 K. NaNO 2 is a simple structured order-disorder ferroelectric with a Curie temperature T c = 163.4°C. Its room temperature structure is orthorhombic with space group Im2m. Most of the spectroscopic data for this material are described in ref. 4. Our sample was the same one used by de las Heras et al. ~ to measure the spontaneous polarization. It was cut from a crystal grown from the melt by the slow cooling method (IK/h). The initial material was a Merck pro analysi product. It was prepoled (i.e. forced into single-domain state) by heating it abo~:e the Curie temperature and cooling under an applied field of -50 V / c m in the direction of the ferroelectric axis. The weight of the sample was 1.892 ~. The measurement of the spontaneous polarization shows that the sample was indeed single-domain. After measuring the C of the single-domain P sample, it was made polydomain by heating it over T c and cooling the sample without applied field. + Alexander von Humboldt Fellow, on leave from Universidad Aut~noma de Madrid, Madrid, Spain.
The initial crystal broke during this procedure. One of the pieces having a weight of 0.624 g was used in one of the polydomain measurements (sample A). Another crystal (sample B) of mass 2.646 g was taken to perform the second polydomain measurement. This was done in order to measure a polydomain sample with a similar contribution from sample holder, heater and thermometer (addenda) as in the monodomain case. This second specimen was grown with the same method and the same products as described above. The crystal was kindly supplied b y de las Heras. The heat capacities were determined in a computer controlled adiabatic calorimeter. 6 The addenda 7, measured in a separate run, contributes about 20% to the total huat capacity for Sample B and the single-domain crystal. For sample A it amounts to 50%. The sample holder was recently tested with a 13 g calorimetry copper standard to an accuracy of 0.2%. This shows that any systematic error is b e l o w this figure and we estimate our overall experimental accuracy in 1.5%. The results are plotted in Fig. I as C/T 3 versus T. A clear contribution in excess to the T 3 term appears for the polydomain sample below 8 K. This contribution is absent in the specific heat of the single-domain NaNO 2 in this temperature range. The Debye term is the same in both cases. The T3-region extends over a wide range of temperature in comparison with other ferroelectrics measured by Lawless 1,2, in which additional low frequency modes contribute significantly in the region 5 K
Vol. 38, No. 9
S I N G L E - D O M A I N AND P O L Y D O M A I N F E R R O E L E C T R I C N a N O 2
808
15
'--' "7"
/
0.8
I
,x,o
~E
I
i
Y
7 -6
10
C~
rO
2
LLI I 0 11 r,j ILl CL u'l
o.
uJ i L.) LL U
5't o°" 0 "' ""YP°lyd°main{ Sa~:~'~:
Fig.
0
20 TEMPERATURE
40
0.4
0.2 0
W
Fig.
NAN02
0.6
60
T 2 [ K 2]
1 S p e c i f i c h e a t o f NaNO,, s i n g l e - d o m a i n and p o l y d o m a i n r e p r e s e n t e ~ as C p / T 3 vs. T. B e l o w 8 K the e x c e s s s p e c i f l c h e a t in the p o l y d o m a i n sample s h o w s up as a d e v i a t i o n f r o m the h o r i z o n t a l .
We note f r o m this p l o t t h a t in the low t e m p e r a ture r e g i o n (2 K < T < 8 K) b o t h fits are e q u a l l y g o o d for the data. It is a l s o w o r t h o f e m p h a s i zing the c o i n c i d e n c e b e t w e e n b o t h p o l y d o m a i n samples. The r e s u l t s s u g g e s t that the e x c e s s contrib u t i o n in f e r r o e l e c t r i c N a N O o in a d d i t i o n to the T 3 t e r m is due to a d o m a i n w ~ l l contribution. The m e c h a n i s m t h a t g i v e s rise to s u c h a b e h a v i o u r , however, is n o t y e t clear. T h e r e are t h e o r e t i c a l c a l c u l a t i o n s 8,9 w h i c h p r o p o s e a T 2 t e m p e r a t u r e dep e n d e n c e o r e x p l a i n a T 3 / 2 term. Thus, the accurate d e t e r m i n a t i o n of the t e m p e r a t u r e d e p e n d e n c e at s t i l l lower t e m p e r a t u r e s is necessary. F i n a l l y , we p o i n t o u t that r e c e n t m e a s u r e m e n t s 5 o f the t e m p e r a t u r e v a r i a t i o n of s p o n t a n e ous p o l a r i z a t i o n Ps s h o w t h a t the ~ y r o e l e c t r i c c o e f f i c i e n t ~ = d P s / d T follows a T ~ b e h a v i o u r in
÷ ÷ ÷ ÷ ÷÷÷÷÷+_
I
0
I
I
I
I
I
40 I0 20 30 TEMPERATURE T [K]
2 The same d a t a in the region T<8 K repres e n t e d as vs. T 2. The s i n g l e - d o m a i n p o i n t s fall in a line t h r o u g h the o r i g i n (Debye term), b u t the p o l y d o m a i n d a t a f o l l o w a n e a r l y p a r a l l e l line w i t h interc e p t for T = O at 0.22 x 10 -2 J m o l -I K -2. F o r c o m p a r i s o n the d o t t e d line r e p r e s e n t s the fit C = 1.27 x 10 - 3 T 3 / 2 P + 1.95 x IO- 4 T 3 Jmol - I K- I .
Cp/T
the same range of t e m p e r a t u r e s , as found in our s p e c i f i c h e a t m e a s u r e m e n t s . T h i s feature s u g g e s t s t h a t in N a N O 2, in c o n t r a s t to m o s t f e r r o e l e c t r i c s , n o a d d i t i o n a l low f r e q u e n c y o p t i c modes contrib u t e to the low t e m p e r a t u r e s p e c i f i c heat. In c o n c l u s i o n , we h a v e s h o w n that the p r e s e n c e of d o m a i n w a l l s in a f e r r o e l e c t r i c leads to an a d d i t i o n a l c o n t r i b u t i o n to the s p e c i f i c heat. F r o m the p r e s e n t results, it is o b v i o u s that the e x a c t t e m p e r a t u r e d e p e n d e n c e o f such an excess s p e c i f i c h e a t can o n l y be d e t e r m i n e d by m e a s u r e m e n t s b e l o w 2 K. A c k n o w l e d g e m e n t s - We w i s h to thank C. de las H e r a s for the c a r e f u l c r y s t a l p o l i n g and preparation, H. W i t s c h e l for aid in h a n d l i n g the comp u t e r s y s t e m and K. R i p k a for t e c h n i c a l assistance.
References I. W.N. LAWLESS, Phys. Rev. Lett. 36, 478 (1976). 2. W.N. L A W L E S S a n d A.J. MORROW, F e r r o e l e c t r i c s 15, 167 (1977). 3. J.A. GONZALO, F e r r o e l e c t r i c s 2__O, 159 (1978). 4. C.M. HARTWIG, E. W I E N E R - A V N E A R and S.P.S. PORTO, Phys. Rev. B5, 79 (1972). 5. C. DE LAS HERAS, J. G O N Z A L O and S. VIEIRA, F e r r o e l e c t r i c s (in press).
6. E. G M E L I N , T h e r m o c h i m i c a A c t a 29, 1 (1979). 7. E. G M E L I N and K. RIPKA, C r y o g e n i c s 20, 117 ( 1980). 8. S. KIR/K2ATRICK and C.M. VARMA, S o l i d S t a t e Comm. 25, 821 (1978). 9. I.A. PRI---VOROTSKII, Phys. Lett. 62_AA, 173 (1977).