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SPECIFIC HEAT AND THERMAL CONDUCTIVITY OF TmVO4 AND DyVO4 WITH AN APPLIED
MAGNETIC FIELD
B. Daudin, B. Salce, S. Smith
To cite this version:
B. Daudin, B. Salce, S. Smith. SPECIFIC HEAT AND THERMAL CONDUCTIVITY OF TmVO4 AND DyVO4 WITH AN APPLIED MAGNETIC FIELD. Journal de Physique Colloques, 1981, 42 (C6), pp.C6-277-C6-279. �10.1051/jphyscol:1981681�. �jpa-00221617�
JOURNAL DE PHYSIQUE
CoZZoque C6, suppZ6ment au n012, Tome 42, d6cembre 1981 page C6-277
SPECIFIC HEAT AND THERMAL CONDUCTIVITY OF TmV04 AND DyV04 WITH AN APPLIED MAGNETIC FIELD
B. Daudin, B. Salce and S.H. smithf
S e m i c e des Basses !L'e'emp6ratures, Laboratoire de Cryophysique, Centre dlEtudes NucZ6aires de GrenobZe, 85 X, 38041 GrenobZe Cedex, Franee
* Czarendon Laboratory, Oxford University, U. K.
A b s t r a c t - S p e c i f i c h e a t and thermal c o n d u c t i v i t y measurements o f TmV04 and DyV04 w i t h a p p l i e d magnetic f i e l d a r e r e p o r t e d . Experimental r e s u l t s f o r TmV04 a r e w e l l d e s c r i b e d b y a m o l e c u l a r f i e l d t h e o r y whereas such a c a l c u l a - t i o n f a i l s t o i n t e r p r e t t h e DyV04 r e s u l t s as s h o r t range o r d e r i n t e r a c t i o n s a r e n o t t a k e n i n t o account.
1. I n t r o d u c t i o n . - TmV04 and DyV04 b e l o n g t o t h e RX04 f a m i l y ( R = r a r e e a r t h and X = V , As o r P ) whose most members undergo a c o o p e r a t i v e J a h n - T e l l e r t r a n s i t i o n a t l o w temperature. A l o t o f e x p e r i m e n t a l and t h e o r e t i c a l work has been done on t h e s e com- pounds (1) b u t h e a t t r a n s p o r t mechanisms a r e n o t w e l l known. We have p r e v i o u s l y r e p o r t e d l o w t e m p e r a t u r e t h e r m a l c o n d u c t i v i t y measurements of TmVO,,, TmAs04, DyV04 and TbV04 samples. I n a d d i t i o n , TmVO,, and TmAs04 were measured w i t h a p p l i e d magnetic f i e l d and s t r o n g e f f e c t s were observed i n b o t h cases (2,3). These measurements were extended t o DyV04 and s p e c i f i c h e a t o f TmV04and DyV04 w i t h a p p l i e d magnetic f i e l d was c o n j u n c t l y measured i n o r d e r t o check t h e v a l i d i t y o f t h e t h e o r e t i c a l e x p r e s s i o n we used t o c a l c u l a t e t h e thermal c o n d u c t i v i t y .
2. Experimental r e s u l t s . - The DyV04 sample was n e e d l e shaped w i t h a square s e c t i o n o f a p p r o x i m a t e l y 1 x 1 mm2 and a l e n g t h o f 6 mm. A l l samples a r e n a t u r a l l y o r i e n t e d a l o n g t h e c - a x i s . The thermal c o n d u c t i v i t y was measured w i t h t h e magnetic f i e l d , H, p a r a l l e l o r p e r p e n d i c u l a r t o t h e c - a x i s and t h e r e s u l t s a r e shown i n Fig.1. The main f e a t u r e i s a decrease o f K ( T ) when H i s p a r a l l e l t o t h e c - a x i s whereas a s t r o n g K(T) i n c r e a s e i s observed when H i s p e r p e n d i c u l a r t o t h e c - a x i s and p a r a l l e l t o t h e a - a x i s o f t h e sample.
The s p e c i f i c h e a t r e s u l t s f o r TmV04 and DyV04 a r e shown i n Fig.2 and 3. The TmV04 sample was measured w i t h H p a r a l l e l t o t h e c - a x i s . DyV04 was measured w i t h H p a r a l l e l t o t h e a - a x i s . The measure was made d i f f i c u l t by t h e s i z e o f t h e samples whose w e i g h t was 340 mg and 193 mg r e s p e c t i v e l y f o r TmV04 and DyV04 , d e s p i t e t h e f a c t t h a t a dynamical a d i a b a t i c d i f f e r e n t i a l t e c h n i q u e was used. *
* R.LAGNIER, J.PIERRE and M. J.MORTIMER, Cryogenics 17, 349 (1977)
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1981681
JOURNAL DE PHYSIQUE
' 7 - TmV04 H=?T/
....-. experiment 6 - -calculation
5 -
x 2 4 -
0 5 10 15 X ) 25
T ( t o
F i g u r e 1 F i g u r e 2
T ( K )
F i g u r e 3
3. D i s c u s s i o n . - The s p e c i f i c h e a t o f TmVO, was p r e v i o u s l y measured i n zero magnetic f i e l d ( 4 ) and was c o r r e c t l y d e s c r i b e d i n t h e frame o f a m o l e c u l a r f i e l d t h e o r y . If t h e two l o w e s t energy l e v e l s o f t h e ~ m ~ + i o n a r e c o n s i d e r e d as an i s o l a t e d d o u b l e t ( t h e f i r s t e x c i t e d i s a s i n g l e t a t 54 c f l ( 5 ) ) t h e energy s p l i t t i n g 2W i n a p p l i e d ma- g n e t i c f i e l d i s g i v e n by : W/kTc = t a n h (W/kT) ifLg, 6H < W and W ='gc8H o t h e r w i s e
2 2
w i t h T, = 2.15 K, q; = 1 0 and 6 = Bohr magneton.
The s p e c i f i c h e a t was c a l c u l a t e d as C = CS + C,, , where CS i s t h e c o n t l r i b u t i o n o f t h e S c h o t t k y anomaly due t o t h e t h r e e l o w e s t l e v e l s ( t h e s i n g l e t i s t h e n assumed t o be f i e l d independent and have no i n t e r a c t i o n w i t h t h e ground s t a t e d o u b l e t ) . CD i s t h e l a t t i c e c o n t r i b u t i o n c a l c u l a t e d i n t h e Debye model and was a d j u s t e d t o
CD = 1.5 K 10-4T3 J/K mole.
The r e s u l t s o f t h e adjustement a r e shown i n Fig.2. To o b t a i n a s a t i s f a c t o r y agreement i t was necessary t o assume t h a t t h e c r y s t a l was c o n t a i n i n g 13 p e r c e n t o f i m p u r i t i e s , which i s c o h e r e n t w i t h t h e presence o f l a r g e f l u x i n c l u s i o n s .
The two main c o n c l u s i o n s a r e as f o l l o w s : a ) t h e m o l e c u l a r f i e l d t h e o r y accoun- t s w e l l f o r t h e observed s p e c i f i c h e a t .
b ) we observe no enhancement o f spe- c i f i c h e a t a t t h e maximum o f t h e S c h o t t k y anomaly as would be e x p e c t e d f r o m t h e p r e - sence o f t h e c o u p l e d mode (6,7).
So f a r as DyV04 i s concerned, t h e r e s u l t s a r e more c o m p l i c a t e d . A c a l c u l a t i o n o f t h e s p e c i f i c h e a t based on a m o l e c u l a r f i e l d t r e a t m e n t f a i l e d t o e x p l a i n t h e ex-
p e r i m e n t s s i n c e s h o r t range o r d e r i n t e r a c t i o n s w h i c h a r e i m p o r t a n t i n DyV04 a r e n o t t a k e n i n t o a c c o u n t by t h i s approach ( 8 ) . On t h e o t h e r hand, c a l c u l a t i o n s based on
"compressible" I s i n g model f i t c o r r e c t l y l i n e a r b i r e f r i n g e n c e experiments ( 9 ) and i t would be i n t e r e s t i n g t o i n t e r p r e t o u r s p e c i f i c h e a t measurements w i t h i n t h e frame o f t h i s model. Such c a l c u l a t i o n s a r e now i n p r o g r e s s .
As a general c o n c l u s i o n , i t appears t h a t t h e s p e c i f i c h e a t o f TmV04 i s w e l l d e s c r i b e d t a k i n g i n t o account a S c h o t t k y anomaly a s s o c i a t e d w i t h t h e thermal popu- l a t i o n s o f t h e energy l e v e l s . Such a d e s c r i p t i o n i s presumably c o r r e c t f o r DyV04 p r o v i d e d we a r e a b l e t o c a l c u l a t e t h e e n e r g y l e v e l s o f t h e system. T h a t means t h a t t h e huge enhancement o f thermal c o n d u c t i v i t y w i t h a p p l i e d magnetic f i e l d observed i n b o t h cases i s n o t r e l a t e d t o anomalous s p e c i f i c h e a t b e h a v i o u r b u t i s p r o b a b l y due t o a d r a s t i c m o d i f i c a t i o n o f phonon s c a t t e r i n g .
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