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Thermoelectric power of Na0.33V2O5
Solid State Communications, Vol.36, p p . l O I 7 - 1 0 1 9 . Pergamon Press L t d . 1980. Printed in Great B r i t a i n .
THERHOELECTRIC POWER OF Nao.33V205 E. P. Chock and G. Gr~ner Department o f P h y s i c s , U n i v e r s i t y of C a l i f o r n i a a t Los A n g e l e s , Los A n g e l e s , C a l i f o r n i a 90024 USA (Received 28 Sept. 1979 by A. A. ~Laradudln) Thermoelectric power (TEl)) and conductivity measurements are reported on t h e h i g h l y a n t s o t r o p i c c o n d u c t o r Nao.33V20s. The h i g h t e m p e r a t u r e TEP i s i n t e r p r e t e d i n t e r m s o f s p i n e n t r o p y , c h a r a c t e r i s t i c o f s y s t e m s w i t h s t r o n g o n - s i t e Coulomb c o r r e l a t i o n s , w i t h n e a r e s t n e i g h b o r c o r r e l a t i o n s i m p o r t a n t a t low t e m p e r a t u r e s (T < 130 K). The c o n d u c t i v i t y i s suggested to r e f l e c t the importance of d i s o r d e r and/or impurity e f f e c t s .
Due ¢o p e c u l i a r i t i e s o f t h e c r y s t a l s t r u c t u r e , B - p h a s e vanadium b r o n z e s have h i g h l y a n l s o t r o p i c e l e c t r o n i c p r o p e r t i e s . I I n t h e most s t u d i e d member o f t h i s c l a s s o f m a t e r i a l s , Nao. 3]VzOs, t h e a n i s o t r o p y o f t h e c o n d u c t i v i t y i s l a r g e , and t h e o p t i c a l z ' ~ and d i e l e c t r i c ~ properties demonstrate highly auisotropic charge p r o p a g a t i o n . R e c e n t ESR e x p e r i m e n t s s ' 6 show t h a t t h e m a g n e t i c s u s c e p t i b i l i t y can be r e p r e s e n t e d by a C u r i e - W e i s s law, X " ~ 2 ~ / 3 k ( T + G ) w i t h O ~ 150 K a t h i g h t e m p e r a t u r e [ ~ Z f o l l o w e d by a f l a t t e n i n g o u t below 150 g . T h i s b e h a v i o r i s representative of a highly correlated electron band w i t h an e f f e c t i v e Fermi t e m p e r a t u r e T F 150 K, o r t o a o n e - d i m e n s i o n a l ltubbard model, where on-slte Coulomb c o r r e l a t i o n s a r e l a r g e compared t o t h e band w i d t h . We have p e r f o r m e d t h e r m o e l e c t r i c power (TEP) and c o n d u c t i v i t y e x p e r i m e n t s on Na0.3sV2Os. Rec e n t TEP e x p e r i m e n t s on h i g h l y a n i s o t r o p i c o r g a n i c c o n d u c t o r s proved t o be e x t r e m e l y u s e f u l i n s t u d y i n g c o r r e l a t i o n e f f e c t s ; I t a l s o gave i n s i g h t t o t h e d e t a i l s o f t h e band s t r u c t u r e . We show t h a t e l e c t r o n - e l e c t r o n c o r r e l a t i o n s a r e imp o r t a n t i n Nao.3~VzO$, and t h e TEP can be w e l l a c c o u n t e d f o r by e n t r o p y c o n s i d e r a t i o n s , a s f i r s t s u g g e s t e d by Chaik£n e t e l . f o r o r g a n i c c o n d u c tors.as5,1o The s a m p l e s were p r e p a r e d by slow c o o l i n g o f Na20 + V2Os m e l t s a c c o r d i n g t o t h e s t o i c h i o m e t r y Nao. 33V205. Upon s o l i d i f y i n g , t h e Na s h e d s i t s oxygen ( b u b b l i n g o f f ) and moves i n t o t h e VzOs lattice, r e s u l t i n g i n n e e d l e shaped c r y s t a l s w i t h the long axis parallel to the conducting axis. The c o n d u c t i v i t y was measured w i t h t h e s t a n d a r d four probe t e c h n i q u e , using s i l v e r p a i n t for electronic contacts. The TEP was measured w i t h equipment d e s c r i b e d by C h a i k i n e t e l . |1 The t y p i c a l c o n d u c t i v i t y , measured b e t w e e n 20 and 500 K, i s shown i n F i g . I . The c o n d u c t i v i t y a g r e e s w i t h t h a t measured by W a l l i s e t e l . , 1 below room t e m p e r a t u r e . The i n s e r t shows the resistivity in the high temperature region. The TEP measured on t h e t~o s a m p l e s i s shown i n F i g . 2. Due t o t h e h i g h r e s i s t a n c e o f t h e samp l e a , we w e r e n o t a b l e t o e x t e n d t h e TEP m e a s u r e ment8 below 60 K. The h i g h and t e m p e r a t u r e - i n d e p e n d e n t TZP a b o v e 130 K r u l e s o u t any i n t e r p r e t a t i o n i n term8 o f • s i m p l e m e t a l o r s i m p l e s e m i c o n d u c t o r
where k i n e t i c e n e r g y t e r m s d o m i n a t e t h e TEP. I n t h e m e t a l c a s e , t h e TEP would be p r o p o r t i o n a l to the temperature, while for a semiconductor, S ~ 1/T. A t e m p e r a t u r e i n d e p e n d e n t t h e r m o e l e c t r i c power, however, is characteristic of a situation where entropy terms dominate, as has been extensively discussed by Chaikin e t at. In g e n e r a l , f o r s t r o n g c o r r e l a t i o n e f f e c t s , t h e TEP m e a s u r e s t h e e n t r o p y p e r c a r r i e r , i n c l u d i n g b o t h t h e s p i n and o r b i t a l c o n t r i b u t i o n to t h e entropy. I n Na0.33V2Os, t h e o u t e r s - e l e c t r o n o f the Na atoms i s t r a n s f e r r e d t o t h e u n f i l l e d s h e l l o f the V ions. There a r e t h r e e d i s t i n c t c r y s t a l l o g r a p h i c vanadium s i t e s present in equal numbers. One t y p e o f s i t e s tz ( l a b e l e d Vt) has t h e l o w e s t energy in the c r y s t a l . These s i t e s form a d o u b l e c h a i n , w l t h l a r g e s e p a r a t i o n between them. Such l a r g e s e p a r a t i o n i s r e s p o n s l b l e f o r t h e high a n i s o t r o p y of the c o n d u c t i v i t y . As one t h i r d o f t h e V atoms a r e a t VI s i t e s , the s t o i c h l o m e t r y l e a d s t o one t r a n s f e r r e d e l e c t r o n f o r e v e r y two VI a t o m s . Thus t h e band i s 1/4 f i l l e d (0 " N e l / N s i t e " I / 2 ) . E n t r o p y c o n s i d e r a t i o n s l e a d t o a TEP which d e p e n d s b o t h on o n - s i t e and n e a r e s t n e i g h b o r e l e c t r o n - e l e c t r o n i n t e r a c t i o n s and a l s o on t h e band f i l l i n g . Assuming t h a t i n t e r a c t i o n s b e t w e e n n e a r e s t n e i g h b o r V atoms can be n e g l e c t e d , i f t h e o n - s i t e Coulomb i n t e r a c t i o n Uo i s l a r g e , d o u b l e o c c u p a t i o n o f t h e V atoms would be f o r b i d d e n , and t h e t h e r m o e l e c t r i c power would be
w h i l e i f t h e r e i s no o n - s i t e s =
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Coulomb I n t e r a c t i o n , (2)
A l t h o u g h S a s g i v e n by E q s . ( I ) and (2) r e p r e s e n t s i n f i n i t e and z e r o Coulomb l n t e r • c t i o n s r e s p e c t i v e l y , one c a n a r g u s t h a t Eq. (1) h o l d s when J0 >> kT and Eq. (2) when Ue << kT. We • ISo n o t e t h • t b o t h Eqso ( l ) and (2) a r e compat i b l e w l t h a C u r l s - W e i s s s u s c e p t i b i l i t y where e i s d e t e r m i n e d by t h e d e t a i l s of t h e i n t e r a c t i o n ; ~ e f f " however, i s d i f f e r e n t in t ~ c • e e s . 1017
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Temperature dependence of the conductivity parallel to the chain axis of Na0.33V=Os. I n s e r t : High temperature resistivity.
Long r a n g e Coulomb i n t e r a c t i o n s a r e e x p e c t ed t o l e a d t o a ground s t a t e , where c h a r g e s a r e o r d e r e d and t h e c o n f i g u r a t i o n a l e n t r o p y i s s t r o n g l y r e d u c e d . In p a r t i c u l a r , f o r a q u a r t e r f i l l e d band, when n e a r e s t n e i g h b o r i n t e r a c t i o n U1 i s i m p o r t a n t , a n d , f o r r e p u l s i o n i n t e r a c t i o n , e v e r y second s i t e i s o c c u p i e d t h e c o n f i g u r e l i o n e l e n t r o p y would be z e r o . In t h i s l i m i t a gap d e v e l o p s a t t h e Fermi s u r f a c e and t h e TEP l s given by S -~
kB [(~ET)p - (~ET)n 1 , kT J ÷ A
(3)
where E_ i s the w e i g h t e d a v e r a g e o f t h e energy transported per hole or electron. A is indep e n d e n t o f t h e t e m p e r a t u r e and r e f l e c t s t h e c o n t r i b u t i o n o f s c a t t e r i n g p r o c e s s e s and r e s l d u al entropy terms. For N a o . l l V a O s , 0 = 1 / 2 , Eq. (1) leads to S - - 6 0 u V / ' K , i n d e p e n d e n t o f the t e m p e r a t u r e , w h i l e Eq. (2) g i v e s S - -95 uV/'K. Our h i g h t e m p e r a t u r e TEP showing S - 55 uV/'K i n d i c a t e s t h a t t h e U0 << kT limit i s not a p p r o p r i a t e , and correlation effects are important. With d e c r e a s i n g t e m p e r a t u r e , t h e TEP s t a r t s to increase; the onset of the increase coincides w i t h the f l a t t e n i n g o f f o f the s u s c e p t i b i l i t y . A g r a d u a l o p e n i n g o f a gap due to t h e influence o f n e a r e s t n e i g h b o r i n t e r a c t i o n s where UI > kT l e a d s t o a s e r a i c o n d u c t i n g gap, w i t h g r a d u a l a p p e a r a n c e o f t h e k i n e t i c e n e r g y terms as s u g g e s t ed by Eq. ( 3 ) . I n t h e a b s e n c e o f band s t r u c t u r e c a l c u l a t i o n s , we a r e not a b l e to d e c i d e w h e t h e r t h i s would l e a d t o a d e c r e a s i n g or i n c r e a s i n g TEP, a n d , i n d e e d , b o t h o c c u r i n o r g a n i c c o n d u c t o r s w i t h q u a r t e r f i l l e d b a n d s . ~'1~ Our p i c t u r e , t h e n , i s t h a t o n - s i t e c o r r e l a t i o n s are important in Na0.33V20$ at ell temp e r a t u r e s , but nearest neighbor interactions lead to e gradual ordering o f charges and to a
s e m t c o n d u c e i n g gap o n l y below a b o u t 130 K. The s i t u a t i o n i s thus s i m i l a r t o + t h a t suggested f o r the complex TCNQ s a l t s , 1~ D (TCNQ);. The g r a d u a l o r d e r i n g o f charges due to n e a r e s t n e i g h b o r i n t e r a c t i o n s has a l s o been suggested e a r l i e r on t h e b a s i s o f d i e l e c t r i c c o n s t a n t ~ and s u s c e p t i b i l i t y measurements. Is F i n a l l y , we comment on the t e m p e r a t u r e dependence o f t h e c o n d u c t i v i t y . Our i n t e r p r e t a t i o n o f t h e TEP suggests a s e m l c o n d u c t i n g behavi o r o n l y below 130 K, I n c l e a r c o n t r a s t to the b e h a v i o r o f O(T) as suggested by F i g . 1. The t e m p e r a t u r e dependence o f the c o n d u c t i v i t y , when i n t e r p r e t e d i n terms o f a semlconducting gap A and w e a k l y t e m p e r a t u r e dependent m o b i l i t y sugg e s t s t h a t ~ i s o f the o r d e r o f a few hundredths K. Random p o t e n t i a l b a r r i e r s and i m p u r i t y pot e n t i a l s , h o w e v e r , c a n l e a d to e l e c t r o n l o c a l i z a t i o n and s t r o n g l y i n c r e a s i n g c o n d u c t i v i t y w i t h i n c r e a s i n g t e m p e r a t u r e , even a t t e m p e r a t u r e s where t h e i n t r i n s i c p r o p e r t i e s , sampled by the TEP which I s u n a f f e c t e d by p o t e n t i a l b a r r i e r s , Imply a m e t a l l i c s t a t e . The n o n e x p o n e n t l a l temp e r a t u r e d e p e n d e n c e o f o and t h e g r a d u a l f l a t tenlng off at hlgh temperatures is characterl s t L c o f h i g h l y a n i s o t r o p t c m a t e r i a l s where the p r e s e n c e o f random b a r r i e r s I s w e l l documente d . Is We b e l i e v e t h e r e f o r e t h a t o(T) in Na0.33V2Os r e f l e c t s t h e e f f e c t o f random p o t e n tlal barriers. The o r i g i n o f t h e random p o t e n t i a l s I s not c l e a r ; i t may a r i s e from randomly p o s i t i o n e d Ha c o u n t e r i o n s , for small o f f - a t o i c h l o m e t r y or from i m p u r i t i e s and i n t r i n s i c d e f e c t s . Acknowledgments - We wish t o t h a n k P. C h a l k l n , T. H o l s t e i n , and R. Orbach f o r u s e f u l d i s c u s sions. T h i s work was p a r t i a l l y s u p p o r t e d by t h e NFL Grant #DNR 477-23577 (GG) and by NSF Grant #DMR 7827129
(EPC).
1019
THERMOELECTRIC POWER OF Na0.33V205
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Temperature dependence of the TEP p a r a l l e l tO rhe chain a x i s in two samples of Nee. ~V2Os. References
1.
R . H . Wallls, N. Sol, and A. ZylberszceJn, Solid State Comm. 2_~3, 539 (1977).
10.
2.
A. Friederlch, D. Kaplan, N. Sol, R. H. Wallis, end A. Z y l b e r s z t e J n , Pro~. 13th Int. Conf. on Phy~oa of Smnioo~d~tors, Rome (1976), p. 357. O. Kaplen end A. Z y l b e r s z t e J n , J. d~ Phys. 37, L123 (1976). W . J . G u n n i n g , A. J . t l e e g e r , R. H. W a l l t s , N. S o l , and A. Z y l b e r s z t e J n , S o l i d S t a t e Comm. 2_~6, 155 (1978). G. Sperllch, W.D. Let&, and G. Bang, SoZid S t u ~ Co~,. 16, ~89 (1975). A. F r t e d e r i c h , D. Kaplan, and N. Sol, S o l i d Sta2t~ Comm. 25, 633 (1978). P . M . Chatkin, in T-~osZeot~*i~t~j in M e ~ Z I ~ o Con~u,ot, oz,e, ~d. by F. J. Blare and P. A. Schroeder (Plenum P r e s s , 1978), p.359. J . Kwak, G. Beni, and P. M. Cbalkin, Phys. Rev. 8 1...~3, 641 (1976). J . P . Kwak and G. Bent, Phys. Rev. B 13, 652 (1976).
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G. Beni, d. F. Kwak, and P. M. Chaiktn, S o l i d S t a t e C~v~,. 17, 1549 (1975). P. M. Chaikin and J . F. Kwak, Rev. S ~ . I n s t r . 46, 218 (1975). A. D. Wadsley, Asia Cr~dSt. 8, 695 (1955). E. M. Conwell, Phys. Reu. 8 18, 1818 (1978). G. Mih~ly, K. H o l c z e r , K. P i n ' ~ r , A. J~nossy, G. Gr~ner, and M. MilJak, SoZid S t a ~ Comm. 17, 1007 (1975); G. Mlh~ley, K. Ritvay-Emandicy, A. J~nossy, K. Holczer, and G. Grfiner, S o l i d S ~ Comm. 21, 721 (1977). N. F. Molt, He~Z-InsuL2to~ Tvaneit£mu~ (Taylor and Francis, London, 1973). O. Gr~ner, A. J~nossy, K. Holczer, and G. Mih~ly, Le~tu~o Notes in Physioe, VoZ. 96: Quasi One ~mansio,al Co,duotors If, Prooeedingg, Dubrovntk, 1978, p. 246, ed. by S. Barlsi~, A. BJellls, J. R. COoper, and B. Leonti~ ( S p r i n g e r - V e r l a g , 1979).
THERHOELECTRIC POWER OF Nao.33V205 E. P. Chock and G. Gr~ner Department o f P h y s i c s , U n i v e r s i t y of C a l i f o r n i a a t Los A n g e l e s , Los A n g e l e s , C a l i f o r n i a 90024 USA (Received 28 Sept. 1979 by A. A. ~Laradudln) Thermoelectric power (TEl)) and conductivity measurements are reported on t h e h i g h l y a n t s o t r o p i c c o n d u c t o r Nao.33V20s. The h i g h t e m p e r a t u r e TEP i s i n t e r p r e t e d i n t e r m s o f s p i n e n t r o p y , c h a r a c t e r i s t i c o f s y s t e m s w i t h s t r o n g o n - s i t e Coulomb c o r r e l a t i o n s , w i t h n e a r e s t n e i g h b o r c o r r e l a t i o n s i m p o r t a n t a t low t e m p e r a t u r e s (T < 130 K). The c o n d u c t i v i t y i s suggested to r e f l e c t the importance of d i s o r d e r and/or impurity e f f e c t s .
Due ¢o p e c u l i a r i t i e s o f t h e c r y s t a l s t r u c t u r e , B - p h a s e vanadium b r o n z e s have h i g h l y a n l s o t r o p i c e l e c t r o n i c p r o p e r t i e s . I I n t h e most s t u d i e d member o f t h i s c l a s s o f m a t e r i a l s , Nao. 3]VzOs, t h e a n i s o t r o p y o f t h e c o n d u c t i v i t y i s l a r g e , and t h e o p t i c a l z ' ~ and d i e l e c t r i c ~ properties demonstrate highly auisotropic charge p r o p a g a t i o n . R e c e n t ESR e x p e r i m e n t s s ' 6 show t h a t t h e m a g n e t i c s u s c e p t i b i l i t y can be r e p r e s e n t e d by a C u r i e - W e i s s law, X " ~ 2 ~ / 3 k ( T + G ) w i t h O ~ 150 K a t h i g h t e m p e r a t u r e [ ~ Z f o l l o w e d by a f l a t t e n i n g o u t below 150 g . T h i s b e h a v i o r i s representative of a highly correlated electron band w i t h an e f f e c t i v e Fermi t e m p e r a t u r e T F 150 K, o r t o a o n e - d i m e n s i o n a l ltubbard model, where on-slte Coulomb c o r r e l a t i o n s a r e l a r g e compared t o t h e band w i d t h . We have p e r f o r m e d t h e r m o e l e c t r i c power (TEP) and c o n d u c t i v i t y e x p e r i m e n t s on Na0.3sV2Os. Rec e n t TEP e x p e r i m e n t s on h i g h l y a n i s o t r o p i c o r g a n i c c o n d u c t o r s proved t o be e x t r e m e l y u s e f u l i n s t u d y i n g c o r r e l a t i o n e f f e c t s ; I t a l s o gave i n s i g h t t o t h e d e t a i l s o f t h e band s t r u c t u r e . We show t h a t e l e c t r o n - e l e c t r o n c o r r e l a t i o n s a r e imp o r t a n t i n Nao.3~VzO$, and t h e TEP can be w e l l a c c o u n t e d f o r by e n t r o p y c o n s i d e r a t i o n s , a s f i r s t s u g g e s t e d by Chaik£n e t e l . f o r o r g a n i c c o n d u c tors.as5,1o The s a m p l e s were p r e p a r e d by slow c o o l i n g o f Na20 + V2Os m e l t s a c c o r d i n g t o t h e s t o i c h i o m e t r y Nao. 33V205. Upon s o l i d i f y i n g , t h e Na s h e d s i t s oxygen ( b u b b l i n g o f f ) and moves i n t o t h e VzOs lattice, r e s u l t i n g i n n e e d l e shaped c r y s t a l s w i t h the long axis parallel to the conducting axis. The c o n d u c t i v i t y was measured w i t h t h e s t a n d a r d four probe t e c h n i q u e , using s i l v e r p a i n t for electronic contacts. The TEP was measured w i t h equipment d e s c r i b e d by C h a i k i n e t e l . |1 The t y p i c a l c o n d u c t i v i t y , measured b e t w e e n 20 and 500 K, i s shown i n F i g . I . The c o n d u c t i v i t y a g r e e s w i t h t h a t measured by W a l l i s e t e l . , 1 below room t e m p e r a t u r e . The i n s e r t shows the resistivity in the high temperature region. The TEP measured on t h e t~o s a m p l e s i s shown i n F i g . 2. Due t o t h e h i g h r e s i s t a n c e o f t h e samp l e a , we w e r e n o t a b l e t o e x t e n d t h e TEP m e a s u r e ment8 below 60 K. The h i g h and t e m p e r a t u r e - i n d e p e n d e n t TZP a b o v e 130 K r u l e s o u t any i n t e r p r e t a t i o n i n term8 o f • s i m p l e m e t a l o r s i m p l e s e m i c o n d u c t o r
where k i n e t i c e n e r g y t e r m s d o m i n a t e t h e TEP. I n t h e m e t a l c a s e , t h e TEP would be p r o p o r t i o n a l to the temperature, while for a semiconductor, S ~ 1/T. A t e m p e r a t u r e i n d e p e n d e n t t h e r m o e l e c t r i c power, however, is characteristic of a situation where entropy terms dominate, as has been extensively discussed by Chaikin e t at. In g e n e r a l , f o r s t r o n g c o r r e l a t i o n e f f e c t s , t h e TEP m e a s u r e s t h e e n t r o p y p e r c a r r i e r , i n c l u d i n g b o t h t h e s p i n and o r b i t a l c o n t r i b u t i o n to t h e entropy. I n Na0.33V2Os, t h e o u t e r s - e l e c t r o n o f the Na atoms i s t r a n s f e r r e d t o t h e u n f i l l e d s h e l l o f the V ions. There a r e t h r e e d i s t i n c t c r y s t a l l o g r a p h i c vanadium s i t e s present in equal numbers. One t y p e o f s i t e s tz ( l a b e l e d Vt) has t h e l o w e s t energy in the c r y s t a l . These s i t e s form a d o u b l e c h a i n , w l t h l a r g e s e p a r a t i o n between them. Such l a r g e s e p a r a t i o n i s r e s p o n s l b l e f o r t h e high a n i s o t r o p y of the c o n d u c t i v i t y . As one t h i r d o f t h e V atoms a r e a t VI s i t e s , the s t o i c h l o m e t r y l e a d s t o one t r a n s f e r r e d e l e c t r o n f o r e v e r y two VI a t o m s . Thus t h e band i s 1/4 f i l l e d (0 " N e l / N s i t e " I / 2 ) . E n t r o p y c o n s i d e r a t i o n s l e a d t o a TEP which d e p e n d s b o t h on o n - s i t e and n e a r e s t n e i g h b o r e l e c t r o n - e l e c t r o n i n t e r a c t i o n s and a l s o on t h e band f i l l i n g . Assuming t h a t i n t e r a c t i o n s b e t w e e n n e a r e s t n e i g h b o r V atoms can be n e g l e c t e d , i f t h e o n - s i t e Coulomb i n t e r a c t i o n Uo i s l a r g e , d o u b l e o c c u p a t i o n o f t h e V atoms would be f o r b i d d e n , and t h e t h e r m o e l e c t r i c power would be
w h i l e i f t h e r e i s no o n - s i t e s =
-
- ~ tn
Coulomb I n t e r a c t i o n , (2)
A l t h o u g h S a s g i v e n by E q s . ( I ) and (2) r e p r e s e n t s i n f i n i t e and z e r o Coulomb l n t e r • c t i o n s r e s p e c t i v e l y , one c a n a r g u s t h a t Eq. (1) h o l d s when J0 >> kT and Eq. (2) when Ue << kT. We • ISo n o t e t h • t b o t h Eqso ( l ) and (2) a r e compat i b l e w l t h a C u r l s - W e i s s s u s c e p t i b i l i t y where e i s d e t e r m i n e d by t h e d e t a i l s of t h e i n t e r a c t i o n ; ~ e f f " however, i s d i f f e r e n t in t ~ c • e e s . 1017
1018
~OET-~-~RIC I
I
POWER OF Na0.3~V 2 05 i
I
90
V o l . 36, No. 12 I
*SSomple A Sample B
70
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°I
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200
100
300
T(°K) F i g . 1.
Temperature dependence of the conductivity parallel to the chain axis of Na0.33V=Os. I n s e r t : High temperature resistivity.
Long r a n g e Coulomb i n t e r a c t i o n s a r e e x p e c t ed t o l e a d t o a ground s t a t e , where c h a r g e s a r e o r d e r e d and t h e c o n f i g u r a t i o n a l e n t r o p y i s s t r o n g l y r e d u c e d . In p a r t i c u l a r , f o r a q u a r t e r f i l l e d band, when n e a r e s t n e i g h b o r i n t e r a c t i o n U1 i s i m p o r t a n t , a n d , f o r r e p u l s i o n i n t e r a c t i o n , e v e r y second s i t e i s o c c u p i e d t h e c o n f i g u r e l i o n e l e n t r o p y would be z e r o . In t h i s l i m i t a gap d e v e l o p s a t t h e Fermi s u r f a c e and t h e TEP l s given by S -~
kB [(~ET)p - (~ET)n 1 , kT J ÷ A
(3)
where E_ i s the w e i g h t e d a v e r a g e o f t h e energy transported per hole or electron. A is indep e n d e n t o f t h e t e m p e r a t u r e and r e f l e c t s t h e c o n t r i b u t i o n o f s c a t t e r i n g p r o c e s s e s and r e s l d u al entropy terms. For N a o . l l V a O s , 0 = 1 / 2 , Eq. (1) leads to S - - 6 0 u V / ' K , i n d e p e n d e n t o f the t e m p e r a t u r e , w h i l e Eq. (2) g i v e s S - -95 uV/'K. Our h i g h t e m p e r a t u r e TEP showing S - 55 uV/'K i n d i c a t e s t h a t t h e U0 << kT limit i s not a p p r o p r i a t e , and correlation effects are important. With d e c r e a s i n g t e m p e r a t u r e , t h e TEP s t a r t s to increase; the onset of the increase coincides w i t h the f l a t t e n i n g o f f o f the s u s c e p t i b i l i t y . A g r a d u a l o p e n i n g o f a gap due to t h e influence o f n e a r e s t n e i g h b o r i n t e r a c t i o n s where UI > kT l e a d s t o a s e r a i c o n d u c t i n g gap, w i t h g r a d u a l a p p e a r a n c e o f t h e k i n e t i c e n e r g y terms as s u g g e s t ed by Eq. ( 3 ) . I n t h e a b s e n c e o f band s t r u c t u r e c a l c u l a t i o n s , we a r e not a b l e to d e c i d e w h e t h e r t h i s would l e a d t o a d e c r e a s i n g or i n c r e a s i n g TEP, a n d , i n d e e d , b o t h o c c u r i n o r g a n i c c o n d u c t o r s w i t h q u a r t e r f i l l e d b a n d s . ~'1~ Our p i c t u r e , t h e n , i s t h a t o n - s i t e c o r r e l a t i o n s are important in Na0.33V20$ at ell temp e r a t u r e s , but nearest neighbor interactions lead to e gradual ordering o f charges and to a
s e m t c o n d u c e i n g gap o n l y below a b o u t 130 K. The s i t u a t i o n i s thus s i m i l a r t o + t h a t suggested f o r the complex TCNQ s a l t s , 1~ D (TCNQ);. The g r a d u a l o r d e r i n g o f charges due to n e a r e s t n e i g h b o r i n t e r a c t i o n s has a l s o been suggested e a r l i e r on t h e b a s i s o f d i e l e c t r i c c o n s t a n t ~ and s u s c e p t i b i l i t y measurements. Is F i n a l l y , we comment on the t e m p e r a t u r e dependence o f t h e c o n d u c t i v i t y . Our i n t e r p r e t a t i o n o f t h e TEP suggests a s e m l c o n d u c t i n g behavi o r o n l y below 130 K, I n c l e a r c o n t r a s t to the b e h a v i o r o f O(T) as suggested by F i g . 1. The t e m p e r a t u r e dependence o f the c o n d u c t i v i t y , when i n t e r p r e t e d i n terms o f a semlconducting gap A and w e a k l y t e m p e r a t u r e dependent m o b i l i t y sugg e s t s t h a t ~ i s o f the o r d e r o f a few hundredths K. Random p o t e n t i a l b a r r i e r s and i m p u r i t y pot e n t i a l s , h o w e v e r , c a n l e a d to e l e c t r o n l o c a l i z a t i o n and s t r o n g l y i n c r e a s i n g c o n d u c t i v i t y w i t h i n c r e a s i n g t e m p e r a t u r e , even a t t e m p e r a t u r e s where t h e i n t r i n s i c p r o p e r t i e s , sampled by the TEP which I s u n a f f e c t e d by p o t e n t i a l b a r r i e r s , Imply a m e t a l l i c s t a t e . The n o n e x p o n e n t l a l temp e r a t u r e d e p e n d e n c e o f o and t h e g r a d u a l f l a t tenlng off at hlgh temperatures is characterl s t L c o f h i g h l y a n i s o t r o p t c m a t e r i a l s where the p r e s e n c e o f random b a r r i e r s I s w e l l documente d . Is We b e l i e v e t h e r e f o r e t h a t o(T) in Na0.33V2Os r e f l e c t s t h e e f f e c t o f random p o t e n tlal barriers. The o r i g i n o f t h e random p o t e n t i a l s I s not c l e a r ; i t may a r i s e from randomly p o s i t i o n e d Ha c o u n t e r i o n s , for small o f f - a t o i c h l o m e t r y or from i m p u r i t i e s and i n t r i n s i c d e f e c t s . Acknowledgments - We wish t o t h a n k P. C h a l k l n , T. H o l s t e i n , and R. Orbach f o r u s e f u l d i s c u s sions. T h i s work was p a r t i a l l y s u p p o r t e d by t h e NFL Grant #DNR 477-23577 (GG) and by NSF Grant #DMR 7827129
(EPC).
1019
THERMOELECTRIC POWER OF Na0.33V205
Vol. 36, No. 12 t
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400 T('K) o
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I/T(°K) Fig. 2.
Temperature dependence of the TEP p a r a l l e l tO rhe chain a x i s in two samples of Nee. ~V2Os. References
1.
R . H . Wallls, N. Sol, and A. ZylberszceJn, Solid State Comm. 2_~3, 539 (1977).
10.
2.
A. Friederlch, D. Kaplan, N. Sol, R. H. Wallis, end A. Z y l b e r s z t e J n , Pro~. 13th Int. Conf. on Phy~oa of Smnioo~d~tors, Rome (1976), p. 357. O. Kaplen end A. Z y l b e r s z t e J n , J. d~ Phys. 37, L123 (1976). W . J . G u n n i n g , A. J . t l e e g e r , R. H. W a l l t s , N. S o l , and A. Z y l b e r s z t e J n , S o l i d S t a t e Comm. 2_~6, 155 (1978). G. Sperllch, W.D. Let&, and G. Bang, SoZid S t u ~ Co~,. 16, ~89 (1975). A. F r t e d e r i c h , D. Kaplan, and N. Sol, S o l i d Sta2t~ Comm. 25, 633 (1978). P . M . Chatkin, in T-~osZeot~*i~t~j in M e ~ Z I ~ o Con~u,ot, oz,e, ~d. by F. J. Blare and P. A. Schroeder (Plenum P r e s s , 1978), p.359. J . Kwak, G. Beni, and P. M. Cbalkin, Phys. Rev. 8 1...~3, 641 (1976). J . P . Kwak and G. Bent, Phys. Rev. B 13, 652 (1976).
11.
3. 4.
5. 6. 7. 8. 9.
12. 13. 14.
15. 16.
G. Beni, d. F. Kwak, and P. M. Chaiktn, S o l i d S t a t e C~v~,. 17, 1549 (1975). P. M. Chaikin and J . F. Kwak, Rev. S ~ . I n s t r . 46, 218 (1975). A. D. Wadsley, Asia Cr~dSt. 8, 695 (1955). E. M. Conwell, Phys. Reu. 8 18, 1818 (1978). G. Mih~ly, K. H o l c z e r , K. P i n ' ~ r , A. J~nossy, G. Gr~ner, and M. MilJak, SoZid S t a ~ Comm. 17, 1007 (1975); G. Mlh~ley, K. Ritvay-Emandicy, A. J~nossy, K. Holczer, and G. Grfiner, S o l i d S ~ Comm. 21, 721 (1977). N. F. Molt, He~Z-InsuL2to~ Tvaneit£mu~ (Taylor and Francis, London, 1973). O. Gr~ner, A. J~nossy, K. Holczer, and G. Mih~ly, Le~tu~o Notes in Physioe, VoZ. 96: Quasi One ~mansio,al Co,duotors If, Prooeedingg, Dubrovntk, 1978, p. 246, ed. by S. Barlsi~, A. BJellls, J. R. COoper, and B. Leonti~ ( S p r i n g e r - V e r l a g , 1979).