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Dielectric constant and microwave conductivity of the vanadium bronze Na0.33V2O5
S o h d State Communacatlons, Vol. 26, pp. 155-159. ~ P e r g a m o n Press Ltd. 1978. Printed an Great Britain
DIELECTRIC
CONSTANT
AND MICROWAVE
VANADIUM
W.J.
OO38-1098/78/O415-O155 $02.00/0
BRONZE
GUNNING
CONDUCTIVITY
OF THE
Nao.33V205
and A.J.
HEEGER
D e p a r t m e n t of P h y s l c s and L a b o r a t o r y for R e s e a r c h on the S t r u c t u r e of M a t t e r , U n l v e r s l t y of P e n n s y l v a n l a , P h l l a d e l p h t a , P e n n s y l v a n i a 19174, U.S.A.
and R.H.
WALLIS,
Laboratolre
(Received
N.
SOL
and
A.
ZYLBERSZTEJN
C e n t r a l de R e c h e r c h e s , 914010rsay, FRANCE 13 J a n u a r y
1978
by M.
THOMSON-CSF,
Balkanska)
M e a s u r e m e n t s of the d i e l e c t r i c c o n s t a n t and m l c r o w a v e c o n d u c t l v t t y are r e p o r t e d for the v a n a d l u m b r o n z e Na O ~ V 2 0 5 . The d l e l e c t r l c c o n s t a n t is h i g h l y a n i s o t r o p l c and'~ry l a r g e p a r a l l e l to the h i g h l y c o n d u c t l n g d £ r e c t l o n , w h i l e the c o n d u c t i v i t y is s t r o n g l y d l s p e r s l v e . The r e s u l t s can be c o n s a s t e n t l y i n t e r p r e t e d by c o n s l d e r t n g Na n ~ V o O 4 as a q u a s l - o n e - d a m e n s l o n a l c o n d u c t o r in w h i c h , atV~ ~ e ~ p e r a t u r e s , a p s e u d o - g a p o p e n s in the o n e - e l e c t r o n d e n s i t y of s t a t e s due to m n t e r - s l t e c o r r e l a t l o n s .
R e c e n t i n v e s t l g a t a o n s I-5 of the ~-phaee vanadium bronzes MxV205 have s h o w n that t h e i r e l e c t r o n l c p r o p e r t i e s are so h i g h l y a n l s o t r o p i c as to m e r a t the d e s c r i p t i o n s of t h e s e m a t e r i a l s as q u a s l one-dlmenslonal.The a n l s o t r o p y of the d.c. c o n d u c t i v i t y of N a o . 3 3 V 2 0 5 is 130 at r o o m t e m p e r a t u r e and r l s e s as h l g h as 400 at lower t e m p e r a t u r e s 1,2, w h i l e the o p t i c a l r e f l e c t l v l t y s h o w s a p l a s m a edge for l i g h t p o l a r i z e d w a t h its e l e c t r i c f i e l d v e c t o r p a r a l l e l to the h l g h l y c o n d u c t l n g b - a x l s 2 , 3 . In b o t h C u x V 2 0 5 - B 4 and N a x V 2 O s - ~ 2 , 5 the E S R l i n e s h a p e is s y m m e t r i c a l w h e n the e l e c t r i c f i e l d is p e r p e n d i c u l a r to the b - a x l s but a s y m m e t r i c a l and c h a r a c t e r i s t i c of a m a t e r i a l wlth hlgh macrowave conductlvaty when p a r a l l e l to it. In thls p a p e r w e r e p o r t m e a s u r e m e n t s of the d i e l e c t r i c c o n s t a n t of N a o . 3 3 V 2 0 5 b o t h p a r a l l e l to the b-axis and perpendicular to it, and also of the m i c r o w a v e c o n d u c t l v l t y a l o n g the b - a x l e . T h e r e s u l t s s u p p o r t the idea that NaxV205 i s a q u a s i - o n e - d i m e n s i o n a l materlal in which, at low temperatures, tntersite correlations within the conducring c h a i n s p r o d u c e a p s e u d o ~ p in the o n e - e l e c t r o n d e n s i t y of s t a t e s , T h e ~ - p h a s e v a n a d i u m b r o n z e s are a c l a s s of n o n - s t o i c h i o m e t r t c m a t e r l a l s in w h i c h the V 2 0 5 h o s t l a t t i c e is d l s t o r t e d in such a w a y as to a c c o m m o d a t e the r e l a t l v e l y l a r g e a m o u n t of m o n o v a l e n t m e t a l tons M (M - Na, Cu, K, LI, ...) in "tunnels". The resulting crystal structure is m o n o c l l n i c w l t h the t u n n e l s all
r u n n l n g p a r a l l e l to the b - a x l s . The t u n n e l " w a l l s " are f o r m e d f r o m d l s t o r t e d V O 6 o c t a h e d r a s t a c k e d so that the v a n e d l u m ions lle on s y s t e m s of d o u b l e c h a i n s , w h l c h also run p a r a l l e l to the b - a x l s . The outer s - e l e c t r o n of e a c h M a t o m is t r a n s f e r r e d into the u n f a l l e d d - s h e l l of the v a n a d l u m ions, as s h o w n by the lack of a K n l g h ~ s h l f t on the LI n u c l e l in L l x V 2 0 5 v, and r e c e n t l y c o n f l r m e d b y E S R m e a s u r e m e n t s of the a b s o l u t e spin s u s c e p t l b l l i t y of V 4+ ions in N a x V 2 0 5 5 . T h r e e d l s t i n c t c r y s t a l l o g r a p h a c v a n a d i u m sltes can be i d e n t i f i e d , p r e s e n t in e q u a l n u m b e r s . U s a n g the s t r u c t u r a l d a t a of W a d s l e y 7, G o o d e n o u g h 8 has a r g u e d that the v a n a d l u m sites l a b e l l e d V 1 in W a d s l e y ' s c l a s s l f l c a t i o n are e n e r g e t i c a l l y the l o w e s t and h e n c e the e l e c t r o n s w a l l be c o n f i n e d to the V 1 d o u b l e - c h a l n s only. It as the r e l a t i v e l y l a r g e s e p a r a t a o n b e t w e e n V 1 d o u b l e - c h a l n s w h l c h is r e s p o n s l b l e for the e l e c t r l c a l a n i s o t r o p y of t h e s e m a t e r l a l s . The m e a s u r e m e n t s reported here were all performed on s a m p l e s h a v i n g t h e composition, as determined by electron m i c r o p r o b e a n a l y s i s , of N a o . 3 3 V 2 0 5 . T h l s c o m p o s l t l o n c o r r e s p o n d s to f l l l l n g of e x a c t l y h a l f the s o d l u m s i t e s : h o w e v e r , b e c a u s e they o c c u r in p a l r s w h i c h c a n n o t be s i m u l t a n e o u s l y o c c u p i e d , all a v a l l a b l e s i t e s an the t u n n e l s are e f f e c t i v e l y f i l l e d . S i n c e one thlrd of the v a n a d i u m tons are V 1 s i t e s , t h e r e Is one e l e c t r o n a v a i l a b l e for e v e r y two V l ' s and so the
155
156
PROPERTIES OF Na0~
V I double-chalns are on a v e r a g e h a l f occupied. T h e s a m p l e s u s e d in thls i n v e s t l g a t l o n w e r e p r e p a r e d in two w a y s . N e e d l e s h a p e d s a m p l e s w l t h the long axls p a r a llel to the h i g h l y c o n d u c t l n g b - a x l s w e r e p r o d u c e d by the r a p i d c o o l l n g of NaVO3/VO2/V205 m e l t s . S l o w c o o l l n g of the s a m e m e l t s ~n a s t r o n g t e m p e r a t u r e gradlent (Brldgman method) produced Irregular shaped crystals wlth typical dlmens~ons of s e v e r a l m l l l l m e t r e s , f r o m w h l c h o r i e n t e d s e c t i o n s c o u l d be cut and p o l i s h e d as r e q u l r e d . The "needles" wlth typical dimensions 3.5 X 0 . 0 8 X 0 . 0 3 m m 3 , w e r e i d e a l l y s u i t e d to the m e a s u r e m e n t lJ of the b - a x l s d l e l e c t r l c c o n s t a n t c~ and the c o n d u c t i v i t y (E 2 = 0"// /EoC0) u s i n g the mlcrowave cavity perturbation technique previously developed for s t u d i e s on the o r g a n i c c h a r g e t r a n s f e r s a l t s 9-II. M e a s u r e m e n t s of the c a v l t y f r e q u e n c y s h i f t Af and the r e s o n a n c e h a l f w i d t h o 6o/2 w e r e m a d e o v e r the t e m p e r a t u r e r a n g e f r o m 4.2 K to 300 K. T h e r e s u l t s for (~ll c o v e r the completerl t e m p e r a t u r e r a n g e but t h o s e for E 1 w e r e r e s t r i c t e d to b e l o w ~ O O K b e c a u s e at h l g h e r t e m p e ! Jl r a t u r e s g 2 >> g I l e a d i n g to the saturation of Af and the c o n s e q u e n t ~nsensltlvlty o f ° t h e d a t a to the v a l u e of E~i. The cavlty perturbatlon technique c o u l d n o t be u s e d for the m e a s u r e m e n t of ~I, the d i e l e c t r i c constant perpendicular to the b - a x l s , b e c a u s e the n e c e s s a r y n e e d l e - s h a p e d samples c o u l d n o t be g r o w n w l t h o t h e r o r l e n t a tlons. As an a l t e r n a t i v e , a pulse technique previously a p p l i e d to V O 2 1 2 w a s used. In thls m e t h o d , the d l e l e c trlc c o n s t a n t is m e a s u r e d relative to that of a l u m i n a b y m e a s u r i n g the tlme d e l a y of the p e a k of a n a r r o w pulse propagating along a mlcrostrlp c i r c u i t w h e n p a r t of the a l u m i n a dlelectrlc is r e p l a c e d b y the m a t e r i a l under investlgatlon. The d e l a y tlme, measured on a s a m p l l n g o s c i l l o s c o p e , is t h e n u s e d to c a l c u l a t e the g r o u p v e l o c i t y vg of the p u l s e , f r o m w h i c h the d l e l e c t r l c c o n s t a n t can be f o u n d f r o m the a n a l y s i s d u e to W h e e l e r 13. By w o r k i n g w l t h v e r y n a r r o w (~ 50 pS) p u l s e s , the m e a s u r e m e n t is e f f e c t i v e l y m a d e at m i c r o w a v e frequencles since the d o m i n a n t F o u r i e r c o m p o n e n t s ~n the p u l s e are at s e v e r a l g l g a h e r t z . The samples used,were In the f o r m of p l a telets typlcally 6 X 2 X 0.08 mm 3 w l t h the b - a x l s p a r a l l e l to the l o n g e s t dlmenslon. A f t e r a 0.2 m m w l d e g o l d s t r i p e had b e e n e v a p o r a t e d a l o n g the l e n g t h of the u p p e r f a c e , the l o w e r f a c e w a s a t t a c h e d to the s a m p l e h o l d e r ground plane wlth conducting silver p a i n t and the g o l d s t r i p e c o n n e c t e d to the m l c r o s t r l p c i r c u i t on top of the a l u m i n a w l t h g o l d r l b b o n . S i n c e the p u l s e p r o p a g a t e s in the d l r e c t l o n of the b - a x i s and a T E M - m o d e a p p r o x l -
33V205
Vol
26, No
m a t l o n is v a l i d , the e l e c t r l c f l e l d penetratlon into the s a m p l e ~s a l w a y s perpendicular to the b - a x l s so that Vg is d e t e r m i n e d o n l y by ~i Typical pulse propagation times w e r e iO0 pS Measurements w e r e m a d e at 4 2 K and 77 K o n l y at i n t e r m e d i a t e temperatures s t a b i l i t y was a p r o b l e m w h i l e at h i g h e r t e m p e r a t u r e s the i n c r e a s e d conductivity again prevented measurem e n t s , in thls case b y m a k i n g the dlelectrlc relaxation tlme l a r g e r than the p u l s e w i d t h so that the p u l s e becomes heavily distorted and a t t e nuated. At 4.2. K the s a m p l e s w e r e sufficiently resistive to p e r m i t m e a s u r e m e n t s of b o t h Ei~ and E~ at low frequencies, using a capacitance bridge w h i c h c o v e r e d the r a n g e IO0 Hz iO0 KHz. For thls p u r p o s e s i l v e r p a l n t e l e c t r o d e s w e r e a p p l i e d to o p p o s i t e f a c e s of s a m p l e s in the f o r m of p l a t e lets. T h e r e s u l t s o b t a i n e d by the cavity perturbatlon t e c h n i q u e are s h o w n in Fig. I and 2. In Fig. i the b-axls conductivity at l o I O H z , q#s (iO G H z ) , has b e e n p l o t t e d l o g a r l t h m l c a l l y a g a i n s t I/T. A l s o s h o w n for comparlson are the d.c. c o n d u c t i v i t y d a t a of W a l l l s , Sol and Z y l b e r s z t e j n I. At h i g h e r t e m p e r a t u r e s the two sets
./
.-,0~ "3 E o
i# 0
10
E o
.-,-10 GHz d c ( f r o m refl)
0 Fig.
I
004
008
012 ~T(K-1)
The c o n d u c t i v i t y at I o I O H z p a r a l l e l to the m o n o c l l n l c b-axls, plotted logarlthmlc a l l y a g a i n s t I/T Also shown for c o m p a r i s o n are the d.c. r e s u l t s of Ref I The inset s h o w s the m i c r o w a v e values of @la at low t e m p e r a t u r e s , p l o t t e d a g a l n s t T.
3
Vol. 26, No. 3
PROPERTIES OF Na0.33V205 ! •II
1000
ml•
500
• D
•i
~ •na
I
m
•
o I
-5(x
160
0 Fig.
2
150
T(K
200
The d£electrlc constant p a r a l l e l 11to the m o n o c l z n l c b - a x l s El, m e a s u r e d by the cavity perturbation technique, p l o t t e d a g a i n s t T. The i z m l t e d a c c u r a c y at h i g h e r t e m p e r a t u r e s is i n d i c a t e d by the e r r o r bars.
of r e s u l t s are in good a g r e e m e n t but, as the t e m p e r a t u r e f a l l s , d l s p e r s l o n b e c o m e s s l g n z f l c a n t and by 4.2 K O# (I0 GHz) is m a n y orders of m a g n i t u d e g r e a t e r than G , ( d . c . ) . The t e m p e r a t u r e d e p e n d e n c e of EJ~ m e a s u r e d at I0 GHz is p r e s e n t e d in Fzg. 2. At low t e m p e r a t u r e s g I can be seen to be l a r g e and p o s t t l v e , h a v i n g a v a l u e of 360 at 4.2 K, r i s i n g to 750 by 77 K and p a s s i n g t h r o u g h a m a x i m u m of Ii00 at 120 K. A b o v e 120 K e~ d e c r e a s e s , c r o s s i n g zero to n e g a t l v e v a l u e s a b o v e 150 K. A l t h o u g h the a b s o l u t e a c c u r a c y zs r a p l d l y d e c r e a s i n g a b o v e 150 K, as s h o w n by the e r r o r b a r s in Flg. 2, the trends in the d a t a and the zero c r o s s i n g are g e n u i n e f e a t u r e s (even at 150 K, the c l a s s l c a l s k l n d e p t h zs m o r e than t w i c e the s a m p l e t h l c k n e s s ) . In c o n t r a s t to the l a r g e low t e m p e r a t u r e v a l u e s of EJ~, the v a l u e of ~i o b t a i n e d by the p u l s e t e c h n i q u e w e r e m u c h s m a l l e r , b e i n g 24.5 at 4.2 K and 42 at 77 K, and so g l v l n g v a l u e s for the a n l s o t r o p y E~/E~I of 14.7 at 4.2 K and 17.9 at 77 K. M e a s u r e m e n t s w l t h the low f r e q u e n c y b r i d g e at 4.2 K g a v e c o m p a r a b l e v a l u e s , 460 for E'i and 26.5 for E~, i n d e p e n d e n t of f r e q u e n c y in the r a n g e i00 Hz to I00 KHz, and g i v i n g el/E 1 e q u a l to 17.4. F r o m the a b o v e r e s u l t s it a p p e a r s that the d l e l e c t r l c c o n s t a n t
is a l m o s t i n d e p e n d e n t of f r e q u e n c y f r o m 102 to I0 I0 Hz (the 20% d l f f e r e n c e in the v a l u e s of E~ o b t a l n e d by the b r l d g e and c a v l t y p e r t u r b a t x o n t e c h n l q u e s c o u l d e a s z l y r e s u l t f r o m the l l m l t e d a b s o l u t e a c c u r a c y of the l a t t e r due to n o n - l d e a l s a m p l e g e o m e t r y ) . B e f o r e the h l g h a n l s o t r o p y of the d l e l e c t r l c c o n s t a n t can be a t t r l b u t e d to the q u a s l - o n e - d l m e n s l o n a l e l e c t r o n l c p r o p e r t l e s of N a 0 , 3 3 V 2 0 5 , the p o s s l b 1 1 1 t y that the s o d i u m ions are r e s p o n s z b l e for the v e r y h i g h v a l u e of E~ m u s t be e l i m z n a t e d . The c o m p l e t e lack of f r e q u e n c y d e p e n d e n c e m e n t i o n e d a b o v e , t o g e t h e ~ w l t h the fact that the v a l u e of E 1 r e m a l n s h z g h r l g h t d o w n to h e l i u m t e m p e r a tures, s u g g e s t s that thls is not the case. F u r t h e r m o r e , it £s n o t at all c l e a r that the s o d i u m Ions s h o u l d m a k e thezr m a j o r c o n t r l b u t z o n p a r a l lel to the b - a x l s , b e c a u s e a l t h o u g h the t u n n e l s w h z c h a c c o m m o d a t e t h e m run in thls d i r e c t i o n , e a c h Na Ion o c c u p l e s only one of a pazr of a v a i l a b l e sites is the a-c p l a n e , so that they m ~ g h t be e x p e c t e d to be m o r e w e a k l y b o u n d in th£s d l r e c tlon and so c o n t r l b u t e i n s t e a d to E~. We t h e r e f o r e c o n c l u d e that the h i g h v a l u e of eli at low t e m p e r a t u r e s is £ n d e e d e l e c t r o n i c in orlgin. Such a h l g h v a l u e is s u g g e s tlve of a n a r r o w gap s e m i c o n d u c t o r . The p r o p a b l e o r i g i n of thls gap w i l l be d i s c u s s e d b e l o w . A c c o r d i n g to K h a n n a et al. 9, the d £ e l e c t r l c c o n s t a n t for a o n e - d l m e n s l o n a l s e m l c o n d u c t o r is EJI 1 = I + 0.65 ~ p 2 / ~ g 2 Takznge the low f r e q u e n c y v a l u e of 460 for E 1 at 300 t e m p e r a t u r e and w l t h the p l a s m a f r e q u e n c y ~ as f o u n d f r o m the o p t i ~ l r e f l e c t l v i t y 3 of 3 . 0 5 x l O l S s -I i g i v e s a v a l u e for ~g of 1 . 1 5 x l O 1 4 s -I and h e n c e an e n e r g y gap E g ( T = O ) = ~ g of 76 meV. The i n i t i a l t e m p e r a t u r e d e p e n d e n c e of E~ seen in Fig. 2 s u g g e s t s that the gap s h r i n k s as the t e m p e r a t u r e rises. The s u b s e q u e n t d e c r e a s e in El~ a b o v e 120 K w o u l d r e s u l t f r o m the i n c r e a s i n g l y important (negatzve) contrlbutlon from carrlers thermally excited a c r o s s the gap. The m i c r o w a v e c o n d u c t i v i t y m e a s u r e m e n t s s h o w n in Fzg. i are c l e a r l y not, h o w e v e r , c o m p a t l b l e w l t h a r e a l gap in the d e n s i t y of s t a t e s , s i n c e t h e r e is no a c t z v a t l o n e n e r g y at low t e m p e r a t u r e s . In f a c t , the d l s p e r s l v e c o n d u c t l v l t y seen in Fig. i s u g g e s t s that the c o n d u c t l v l t y is b y h o p p i n g b e t w e e n l o c a l t s e d s t a t e s at the F e r m i level. In thls case w e s h o u l d e x p e c t 15 the a.c. c o n d u c t i v i t y ori(~) to be p r o p o r t i o n a l to k T { N ( E F ) } 2 . At low t e m p e r a t u r e s oi|(I0 GHz) has the r e q u i r e d p r o p o r -
157
158
PROPERTIES OF Na0.33V205
t z o n a l i t y to T, as s h o w n in the i n s e t to F i g . i. T h u s , t h e r e c a n be no r e a l g a p in t h e d e n s i t y of s t a t e s , but instead a pseudogap with a finite density of l o c a l i z e d states at the F e r m l l e v e l . T h i s is to be expected in a q u a s l - o n e - d l m e n s l o n a l s y s t e m w h e r e a n y k l n d of d i s o r d e r Is k n o w n to p l a y a d o m i n a n t role. These localized states will also contribute to the d i e l e c t r i c constant, although it is d i f f i c u l t to e s t i m a t e their importance with any certainty. The salient features of the above results, t h a t Is, a h i g h l y anzsotropzc dielectric constant wlth a l a r g e v a l u e of EJ~ w h i c h increases with temperature and a conductivity at m i c r o w a v e frequencies much greater t h a n at d . c . , a r e r e m a r k a b l y similar to the p r o p e r t i e s of o t h e r h i g h l y conducting quasi-one-dimensional materials. In p a r t i c u l a r these results bear a strong resemblance to the b e h a v z o u r of t h e s o - c a l l e d complex 1:2 T C N Q 1 6 - 1 9 s a l t s ( s u c h as Ad(TCNQ) 2 and Qn(TCNQ)2) in w h i c h t h e r e is o n e e l e c t r o n f o r e v e r y two s i t e s on t h e T C N Q s t a c k . It h a s b e e n p r o p o s e d 20 t h a t in t h e s e m a t e r i a l s t h e r e m a y be a o n e - d i m e n s i o n a l pseudogap d u e to the t e n d e n c y of the electrons to o c c u p y the a v a i l a b l e s i t e s in s u c h a w a y as to m z n z m z s e their electrostatic energy, a posslbiIzty originally suggested by O v c h z n n z K o v 21. T h a t is, n o t o n l y d o e s the i n t r a - s z t e Coulomb repulsion U split the b a n d i n t o two H u b b a r d bands, but the i n t e r - s i t e Coulomb repulsion produces a f u r t h e r splitting of the l o w e r Hubbard b a n d . We b e l i e v e t h a t the s a m e m o d e l is a p p l i c a b l e to N a O $ 3 V 2 0 5 at low temperatures, as w a s o r i g i n a l l y suggested b y M o r t 22. In N a o . $ 3 V 2 0 5 t h e r e a r e t w i c e as m a n y V I s l t e s as Na a t o m s so t h a t a s i t u a t i o n analogous to t h a t in the c o m p l e x 1 2 TCNQ salts exists. Furthermore the observation of C u r z e - W e l s s paramagnetzsm
at h i g h t e m p e r a t u r e 23 i m p l i e s that the s t r o n g C o u l o m b l i m i t is a p p r o priate. One difference is t h a t the V 1 s i t e s do n o t o c c u r in s i n g l e linear chains but are arranged in z l g - z a g f o r m in d o u b l e - c h a l n s . T h e i d e a t h a t in N a x V 2 0 5 the electrons condense at l o w t e m p e r a tures has already been Invoked to explain recent ESR measurements 2,24, w h i c h s h o w t h a t b e l o w 150 K the electrons appear to u n d e r g o a second order phase transition, w i t h the spln susceptibility suggesting that at l o w t e m p e r a t u r e s one side only of e a c h V 1 d o u b l e - c h a l n is o c c u p i e d . We n o t e t h a t the t e m p e r a t u r e depend e n c e of the g a p i m p l i e d b y the variation of Ell, i n c l u d i n g the initial increase of ~ as the g a p shrinks followed b y its z e r o c r o s s i n g w h e n the f r e e c a r r i e r contrlbutlon becomes dominant, Is consistent wlth thls model on the contrary it is n o t c o n s i s t e n t wlth the a l t e r n a t i v e picture in w h i c h s t a t e s at the F e r m i l e v e l a r e localized simply by disorder without the i n t r o d u c t i o n of s t r u c t u r e In the density of s t a t e s . In c o n c l u s i o n , we belleve that the r e s u l t s reported here provide strong support for a m o d e l of N a o . 3 3 V 2 0 5 In w h i c h the l o w e r H u b b a r d band progressively undergoes a further splitting below 150 K d u e to i n t e r - s i t e Coulomb repulsion within the o n e dimensional V I double-chains. The small gap which results gives rise to the h i g h v a l u e of t h e r e a l p a r t of the d i e l e c t r i c constant E 1 in the c h a i n d i r e c t i o n , b u t E 2 is dominated by states wxthln the g a p ~knowledgments We w o u l d l i k e to thank Professor N . F . M o r t , Dr. D. K a p l a n a n d Dr. A. F r l e d e r z c h for numerous helpful discussions and J.L. P z n s a r d and D. S a u x f o r h e l p in p r e p a r i n g the s a m p l e s u s e d zn thls investigation
REFERENCES i. 2.
3. 4. 5. 6. 7. 8 9.
Vol. 26, No. 3
W A L L I S R.H. , SOL N. , a n d Z Y L B E R S Z T E J N A. , S o l i d S t a t e Comm., 23, 5 3 9 ( 1 9 7 7 ) . FRIEDERICH A. , K A P L A N D. , S O L N. , W A L L I S R . H . , a n d ZYLBERSZTEJN A. , P r o c . 1 3 t h Int. C o n f . on P h y s i c s of Semiconductors, R o m e , 1 9 7 6 , p. 357. K A P L A N D. , a n d Z Y L B E R S Z T E J N A. , J. de P h y s . , 3 7 , L 1 2 3 (1976). SPERLICH G. , L A Z E W . D . , a n d B A N G G. , S o l i d S t ~ e Comm., 16, 4 8 9 ( 1 9 7 5 ) . FRIEDERICH A. , K A P L A N D. , and SOL N , S o l i d S t a t e C o m m . , 2 5 , 633 ( 1 9 7 S ) . GENDELL J. , C O T T S R. , a n d S I E N K O M . J . , J. C h e m . P h y s . , 37, 2 2 0 ( 1 9 6 2 ) . WADSLEY A . D . , A c t a C r y s t . , 8, 695 ( 1 9 5 5 ) . GOODENOUGH J . B . , J. S o l i d S t a t e C h e m . , I, 3 4 9 ( 1 9 7 0 ) . KHANNA S.K. , E H R E N F R E U N D E. , G A R I T O A . F ~ , and H E E G E R A . J . , P h y s . Rev. B, I O , 2 2 0 5 ( 1 9 7 4 )
Vol. 26, No. 3 i0. ii. 12. 13. 14. 15.
16. 17. 18. 19. 20. 21. 22. 23.
24.
PROPERTIES OF Na 0. 33V205
COHEN M., K H A N N A S.K., GUNNING W.J., GARITO A.F., and H E E G E R A.J., Solld State Comm., 17, 367 (1975). KHANNA S.K., CHIANG C.K., GARITO A.F., and HEEGER A.J., Solld State Comm., 18, 1405 (1976). Z Y L B E R S Z T E J N A., P A N N E T I E R B., and M E R E N D A P., Phys. Letters, 54A, 145 (1975). W H E E L E R H.A., IEEE Trans. M i c r o w a v e Theory and Technlques, 13, 172 (1965). ~-hls value of ~p £s (Ecore) I/2 greater than that given £n ref. 3 because of the d e f i n l t l o n of ~p used there. AUSTIN I.G. , and MOTT N.F. , Advances in Physics, 18, 41 (1969). SHCHEGOLEV I . F . , Phys. Star. Solid1 (a), 12, 9 (1972). GOGOLIN A . A . , ZOLOTUKHIN S . P . , MEL'NIKOV V.I., RASHBA E . I . , a n d SHCHEGOLEV I . F . , JETP Letters, 22, 278 (1975). MIHALY G . , ROLCZER K . , PINTER K . , JANOSSY A . , GRUNER G. , a n d MILJAK M . , S o l i d S t a t e C o m m . , 1 7 , 1OO7, ( 1 9 7 5 ) . MIHALY G . , RITVAY-EMANDITY K . , JANOSSY A . , HOLCZER K . , a n d GRUNER G . , S o l i d S t a t e C o m m . , 2 1 , 721 ( 1 9 7 7 ) . MICHALY G . , RITVAY-EMANDITY K . , a n d GRUNER G . , J . P h y s . C8, L361 (1975). OVCHINNIKOV A . A . , S o v i e t Physics J E T P , 3 7 , 176 ( 1 9 7 3 ) . MOTT N.F., " M e t a l - I n s u l a t o r Transltlonslr-(Taylor and Francls, London, 1973), pp.160-63. See ref. 5.Detalled calculatlons show that the a l t e r n a t l v e suggestlon made in ref. 5, that the C u r l e - W e i s s llke suscept£b11£ty could arlse from a very n a r r o w o n e - d £ m e n s l o n a l band wlthout correlatlon, cannot correctly d e s c r l b e the data. F R I E D E R I C H A., and KAPLAN D., to be publlshed.
159
DIELECTRIC
CONSTANT
AND MICROWAVE
VANADIUM
W.J.
OO38-1098/78/O415-O155 $02.00/0
BRONZE
GUNNING
CONDUCTIVITY
OF THE
Nao.33V205
and A.J.
HEEGER
D e p a r t m e n t of P h y s l c s and L a b o r a t o r y for R e s e a r c h on the S t r u c t u r e of M a t t e r , U n l v e r s l t y of P e n n s y l v a n l a , P h l l a d e l p h t a , P e n n s y l v a n i a 19174, U.S.A.
and R.H.
WALLIS,
Laboratolre
(Received
N.
SOL
and
A.
ZYLBERSZTEJN
C e n t r a l de R e c h e r c h e s , 914010rsay, FRANCE 13 J a n u a r y
1978
by M.
THOMSON-CSF,
Balkanska)
M e a s u r e m e n t s of the d i e l e c t r i c c o n s t a n t and m l c r o w a v e c o n d u c t l v t t y are r e p o r t e d for the v a n a d l u m b r o n z e Na O ~ V 2 0 5 . The d l e l e c t r l c c o n s t a n t is h i g h l y a n i s o t r o p l c and'~ry l a r g e p a r a l l e l to the h i g h l y c o n d u c t l n g d £ r e c t l o n , w h i l e the c o n d u c t i v i t y is s t r o n g l y d l s p e r s l v e . The r e s u l t s can be c o n s a s t e n t l y i n t e r p r e t e d by c o n s l d e r t n g Na n ~ V o O 4 as a q u a s l - o n e - d a m e n s l o n a l c o n d u c t o r in w h i c h , atV~ ~ e ~ p e r a t u r e s , a p s e u d o - g a p o p e n s in the o n e - e l e c t r o n d e n s i t y of s t a t e s due to m n t e r - s l t e c o r r e l a t l o n s .
R e c e n t i n v e s t l g a t a o n s I-5 of the ~-phaee vanadium bronzes MxV205 have s h o w n that t h e i r e l e c t r o n l c p r o p e r t i e s are so h i g h l y a n l s o t r o p i c as to m e r a t the d e s c r i p t i o n s of t h e s e m a t e r i a l s as q u a s l one-dlmenslonal.The a n l s o t r o p y of the d.c. c o n d u c t i v i t y of N a o . 3 3 V 2 0 5 is 130 at r o o m t e m p e r a t u r e and r l s e s as h l g h as 400 at lower t e m p e r a t u r e s 1,2, w h i l e the o p t i c a l r e f l e c t l v l t y s h o w s a p l a s m a edge for l i g h t p o l a r i z e d w a t h its e l e c t r i c f i e l d v e c t o r p a r a l l e l to the h l g h l y c o n d u c t l n g b - a x l s 2 , 3 . In b o t h C u x V 2 0 5 - B 4 and N a x V 2 O s - ~ 2 , 5 the E S R l i n e s h a p e is s y m m e t r i c a l w h e n the e l e c t r i c f i e l d is p e r p e n d i c u l a r to the b - a x l s but a s y m m e t r i c a l and c h a r a c t e r i s t i c of a m a t e r i a l wlth hlgh macrowave conductlvaty when p a r a l l e l to it. In thls p a p e r w e r e p o r t m e a s u r e m e n t s of the d i e l e c t r i c c o n s t a n t of N a o . 3 3 V 2 0 5 b o t h p a r a l l e l to the b-axis and perpendicular to it, and also of the m i c r o w a v e c o n d u c t l v l t y a l o n g the b - a x l e . T h e r e s u l t s s u p p o r t the idea that NaxV205 i s a q u a s i - o n e - d i m e n s i o n a l materlal in which, at low temperatures, tntersite correlations within the conducring c h a i n s p r o d u c e a p s e u d o ~ p in the o n e - e l e c t r o n d e n s i t y of s t a t e s , T h e ~ - p h a s e v a n a d i u m b r o n z e s are a c l a s s of n o n - s t o i c h i o m e t r t c m a t e r l a l s in w h i c h the V 2 0 5 h o s t l a t t i c e is d l s t o r t e d in such a w a y as to a c c o m m o d a t e the r e l a t l v e l y l a r g e a m o u n t of m o n o v a l e n t m e t a l tons M (M - Na, Cu, K, LI, ...) in "tunnels". The resulting crystal structure is m o n o c l l n i c w l t h the t u n n e l s all
r u n n l n g p a r a l l e l to the b - a x l s . The t u n n e l " w a l l s " are f o r m e d f r o m d l s t o r t e d V O 6 o c t a h e d r a s t a c k e d so that the v a n e d l u m ions lle on s y s t e m s of d o u b l e c h a i n s , w h l c h also run p a r a l l e l to the b - a x l s . The outer s - e l e c t r o n of e a c h M a t o m is t r a n s f e r r e d into the u n f a l l e d d - s h e l l of the v a n a d l u m ions, as s h o w n by the lack of a K n l g h ~ s h l f t on the LI n u c l e l in L l x V 2 0 5 v, and r e c e n t l y c o n f l r m e d b y E S R m e a s u r e m e n t s of the a b s o l u t e spin s u s c e p t l b l l i t y of V 4+ ions in N a x V 2 0 5 5 . T h r e e d l s t i n c t c r y s t a l l o g r a p h a c v a n a d i u m sltes can be i d e n t i f i e d , p r e s e n t in e q u a l n u m b e r s . U s a n g the s t r u c t u r a l d a t a of W a d s l e y 7, G o o d e n o u g h 8 has a r g u e d that the v a n a d l u m sites l a b e l l e d V 1 in W a d s l e y ' s c l a s s l f l c a t i o n are e n e r g e t i c a l l y the l o w e s t and h e n c e the e l e c t r o n s w a l l be c o n f i n e d to the V 1 d o u b l e - c h a l n s only. It as the r e l a t i v e l y l a r g e s e p a r a t a o n b e t w e e n V 1 d o u b l e - c h a l n s w h l c h is r e s p o n s l b l e for the e l e c t r l c a l a n i s o t r o p y of t h e s e m a t e r l a l s . The m e a s u r e m e n t s reported here were all performed on s a m p l e s h a v i n g t h e composition, as determined by electron m i c r o p r o b e a n a l y s i s , of N a o . 3 3 V 2 0 5 . T h l s c o m p o s l t l o n c o r r e s p o n d s to f l l l l n g of e x a c t l y h a l f the s o d l u m s i t e s : h o w e v e r , b e c a u s e they o c c u r in p a l r s w h i c h c a n n o t be s i m u l t a n e o u s l y o c c u p i e d , all a v a l l a b l e s i t e s an the t u n n e l s are e f f e c t i v e l y f i l l e d . S i n c e one thlrd of the v a n a d i u m tons are V 1 s i t e s , t h e r e Is one e l e c t r o n a v a i l a b l e for e v e r y two V l ' s and so the
155
156
PROPERTIES OF Na0~
V I double-chalns are on a v e r a g e h a l f occupied. T h e s a m p l e s u s e d in thls i n v e s t l g a t l o n w e r e p r e p a r e d in two w a y s . N e e d l e s h a p e d s a m p l e s w l t h the long axls p a r a llel to the h i g h l y c o n d u c t l n g b - a x l s w e r e p r o d u c e d by the r a p i d c o o l l n g of NaVO3/VO2/V205 m e l t s . S l o w c o o l l n g of the s a m e m e l t s ~n a s t r o n g t e m p e r a t u r e gradlent (Brldgman method) produced Irregular shaped crystals wlth typical dlmens~ons of s e v e r a l m l l l l m e t r e s , f r o m w h l c h o r i e n t e d s e c t i o n s c o u l d be cut and p o l i s h e d as r e q u l r e d . The "needles" wlth typical dimensions 3.5 X 0 . 0 8 X 0 . 0 3 m m 3 , w e r e i d e a l l y s u i t e d to the m e a s u r e m e n t lJ of the b - a x l s d l e l e c t r l c c o n s t a n t c~ and the c o n d u c t i v i t y (E 2 = 0"// /EoC0) u s i n g the mlcrowave cavity perturbation technique previously developed for s t u d i e s on the o r g a n i c c h a r g e t r a n s f e r s a l t s 9-II. M e a s u r e m e n t s of the c a v l t y f r e q u e n c y s h i f t Af and the r e s o n a n c e h a l f w i d t h o 6o/2 w e r e m a d e o v e r the t e m p e r a t u r e r a n g e f r o m 4.2 K to 300 K. T h e r e s u l t s for (~ll c o v e r the completerl t e m p e r a t u r e r a n g e but t h o s e for E 1 w e r e r e s t r i c t e d to b e l o w ~ O O K b e c a u s e at h l g h e r t e m p e ! Jl r a t u r e s g 2 >> g I l e a d i n g to the saturation of Af and the c o n s e q u e n t ~nsensltlvlty o f ° t h e d a t a to the v a l u e of E~i. The cavlty perturbatlon technique c o u l d n o t be u s e d for the m e a s u r e m e n t of ~I, the d i e l e c t r i c constant perpendicular to the b - a x l s , b e c a u s e the n e c e s s a r y n e e d l e - s h a p e d samples c o u l d n o t be g r o w n w l t h o t h e r o r l e n t a tlons. As an a l t e r n a t i v e , a pulse technique previously a p p l i e d to V O 2 1 2 w a s used. In thls m e t h o d , the d l e l e c trlc c o n s t a n t is m e a s u r e d relative to that of a l u m i n a b y m e a s u r i n g the tlme d e l a y of the p e a k of a n a r r o w pulse propagating along a mlcrostrlp c i r c u i t w h e n p a r t of the a l u m i n a dlelectrlc is r e p l a c e d b y the m a t e r i a l under investlgatlon. The d e l a y tlme, measured on a s a m p l l n g o s c i l l o s c o p e , is t h e n u s e d to c a l c u l a t e the g r o u p v e l o c i t y vg of the p u l s e , f r o m w h i c h the d l e l e c t r l c c o n s t a n t can be f o u n d f r o m the a n a l y s i s d u e to W h e e l e r 13. By w o r k i n g w l t h v e r y n a r r o w (~ 50 pS) p u l s e s , the m e a s u r e m e n t is e f f e c t i v e l y m a d e at m i c r o w a v e frequencles since the d o m i n a n t F o u r i e r c o m p o n e n t s ~n the p u l s e are at s e v e r a l g l g a h e r t z . The samples used,were In the f o r m of p l a telets typlcally 6 X 2 X 0.08 mm 3 w l t h the b - a x l s p a r a l l e l to the l o n g e s t dlmenslon. A f t e r a 0.2 m m w l d e g o l d s t r i p e had b e e n e v a p o r a t e d a l o n g the l e n g t h of the u p p e r f a c e , the l o w e r f a c e w a s a t t a c h e d to the s a m p l e h o l d e r ground plane wlth conducting silver p a i n t and the g o l d s t r i p e c o n n e c t e d to the m l c r o s t r l p c i r c u i t on top of the a l u m i n a w l t h g o l d r l b b o n . S i n c e the p u l s e p r o p a g a t e s in the d l r e c t l o n of the b - a x i s and a T E M - m o d e a p p r o x l -
33V205
Vol
26, No
m a t l o n is v a l i d , the e l e c t r l c f l e l d penetratlon into the s a m p l e ~s a l w a y s perpendicular to the b - a x l s so that Vg is d e t e r m i n e d o n l y by ~i Typical pulse propagation times w e r e iO0 pS Measurements w e r e m a d e at 4 2 K and 77 K o n l y at i n t e r m e d i a t e temperatures s t a b i l i t y was a p r o b l e m w h i l e at h i g h e r t e m p e r a t u r e s the i n c r e a s e d conductivity again prevented measurem e n t s , in thls case b y m a k i n g the dlelectrlc relaxation tlme l a r g e r than the p u l s e w i d t h so that the p u l s e becomes heavily distorted and a t t e nuated. At 4.2. K the s a m p l e s w e r e sufficiently resistive to p e r m i t m e a s u r e m e n t s of b o t h Ei~ and E~ at low frequencies, using a capacitance bridge w h i c h c o v e r e d the r a n g e IO0 Hz iO0 KHz. For thls p u r p o s e s i l v e r p a l n t e l e c t r o d e s w e r e a p p l i e d to o p p o s i t e f a c e s of s a m p l e s in the f o r m of p l a t e lets. T h e r e s u l t s o b t a i n e d by the cavity perturbatlon t e c h n i q u e are s h o w n in Fig. I and 2. In Fig. i the b-axls conductivity at l o I O H z , q#s (iO G H z ) , has b e e n p l o t t e d l o g a r l t h m l c a l l y a g a i n s t I/T. A l s o s h o w n for comparlson are the d.c. c o n d u c t i v i t y d a t a of W a l l l s , Sol and Z y l b e r s z t e j n I. At h i g h e r t e m p e r a t u r e s the two sets
./
.-,0~ "3 E o
i# 0
10
E o
.-,-10 GHz d c ( f r o m refl)
0 Fig.
I
004
008
012 ~T(K-1)
The c o n d u c t i v i t y at I o I O H z p a r a l l e l to the m o n o c l l n l c b-axls, plotted logarlthmlc a l l y a g a i n s t I/T Also shown for c o m p a r i s o n are the d.c. r e s u l t s of Ref I The inset s h o w s the m i c r o w a v e values of @la at low t e m p e r a t u r e s , p l o t t e d a g a l n s t T.
3
Vol. 26, No. 3
PROPERTIES OF Na0.33V205 ! •II
1000
ml•
500
• D
•i
~ •na
I
m
•
o I
-5(x
160
0 Fig.
2
150
T(K
200
The d£electrlc constant p a r a l l e l 11to the m o n o c l z n l c b - a x l s El, m e a s u r e d by the cavity perturbation technique, p l o t t e d a g a i n s t T. The i z m l t e d a c c u r a c y at h i g h e r t e m p e r a t u r e s is i n d i c a t e d by the e r r o r bars.
of r e s u l t s are in good a g r e e m e n t but, as the t e m p e r a t u r e f a l l s , d l s p e r s l o n b e c o m e s s l g n z f l c a n t and by 4.2 K O# (I0 GHz) is m a n y orders of m a g n i t u d e g r e a t e r than G , ( d . c . ) . The t e m p e r a t u r e d e p e n d e n c e of EJ~ m e a s u r e d at I0 GHz is p r e s e n t e d in Fzg. 2. At low t e m p e r a t u r e s g I can be seen to be l a r g e and p o s t t l v e , h a v i n g a v a l u e of 360 at 4.2 K, r i s i n g to 750 by 77 K and p a s s i n g t h r o u g h a m a x i m u m of Ii00 at 120 K. A b o v e 120 K e~ d e c r e a s e s , c r o s s i n g zero to n e g a t l v e v a l u e s a b o v e 150 K. A l t h o u g h the a b s o l u t e a c c u r a c y zs r a p l d l y d e c r e a s i n g a b o v e 150 K, as s h o w n by the e r r o r b a r s in Flg. 2, the trends in the d a t a and the zero c r o s s i n g are g e n u i n e f e a t u r e s (even at 150 K, the c l a s s l c a l s k l n d e p t h zs m o r e than t w i c e the s a m p l e t h l c k n e s s ) . In c o n t r a s t to the l a r g e low t e m p e r a t u r e v a l u e s of EJ~, the v a l u e of ~i o b t a i n e d by the p u l s e t e c h n i q u e w e r e m u c h s m a l l e r , b e i n g 24.5 at 4.2 K and 42 at 77 K, and so g l v l n g v a l u e s for the a n l s o t r o p y E~/E~I of 14.7 at 4.2 K and 17.9 at 77 K. M e a s u r e m e n t s w l t h the low f r e q u e n c y b r i d g e at 4.2 K g a v e c o m p a r a b l e v a l u e s , 460 for E'i and 26.5 for E~, i n d e p e n d e n t of f r e q u e n c y in the r a n g e i00 Hz to I00 KHz, and g i v i n g el/E 1 e q u a l to 17.4. F r o m the a b o v e r e s u l t s it a p p e a r s that the d l e l e c t r l c c o n s t a n t
is a l m o s t i n d e p e n d e n t of f r e q u e n c y f r o m 102 to I0 I0 Hz (the 20% d l f f e r e n c e in the v a l u e s of E~ o b t a l n e d by the b r l d g e and c a v l t y p e r t u r b a t x o n t e c h n l q u e s c o u l d e a s z l y r e s u l t f r o m the l l m l t e d a b s o l u t e a c c u r a c y of the l a t t e r due to n o n - l d e a l s a m p l e g e o m e t r y ) . B e f o r e the h l g h a n l s o t r o p y of the d l e l e c t r l c c o n s t a n t can be a t t r l b u t e d to the q u a s l - o n e - d l m e n s l o n a l e l e c t r o n l c p r o p e r t l e s of N a 0 , 3 3 V 2 0 5 , the p o s s l b 1 1 1 t y that the s o d i u m ions are r e s p o n s z b l e for the v e r y h i g h v a l u e of E~ m u s t be e l i m z n a t e d . The c o m p l e t e lack of f r e q u e n c y d e p e n d e n c e m e n t i o n e d a b o v e , t o g e t h e ~ w l t h the fact that the v a l u e of E 1 r e m a l n s h z g h r l g h t d o w n to h e l i u m t e m p e r a tures, s u g g e s t s that thls is not the case. F u r t h e r m o r e , it £s n o t at all c l e a r that the s o d i u m Ions s h o u l d m a k e thezr m a j o r c o n t r l b u t z o n p a r a l lel to the b - a x l s , b e c a u s e a l t h o u g h the t u n n e l s w h z c h a c c o m m o d a t e t h e m run in thls d i r e c t i o n , e a c h Na Ion o c c u p l e s only one of a pazr of a v a i l a b l e sites is the a-c p l a n e , so that they m ~ g h t be e x p e c t e d to be m o r e w e a k l y b o u n d in th£s d l r e c tlon and so c o n t r l b u t e i n s t e a d to E~. We t h e r e f o r e c o n c l u d e that the h i g h v a l u e of eli at low t e m p e r a t u r e s is £ n d e e d e l e c t r o n i c in orlgin. Such a h l g h v a l u e is s u g g e s tlve of a n a r r o w gap s e m i c o n d u c t o r . The p r o p a b l e o r i g i n of thls gap w i l l be d i s c u s s e d b e l o w . A c c o r d i n g to K h a n n a et al. 9, the d £ e l e c t r l c c o n s t a n t for a o n e - d l m e n s l o n a l s e m l c o n d u c t o r is EJI 1 = I + 0.65 ~ p 2 / ~ g 2 Takznge the low f r e q u e n c y v a l u e of 460 for E 1 at 300 t e m p e r a t u r e and w l t h the p l a s m a f r e q u e n c y ~ as f o u n d f r o m the o p t i ~ l r e f l e c t l v i t y 3 of 3 . 0 5 x l O l S s -I i g i v e s a v a l u e for ~g of 1 . 1 5 x l O 1 4 s -I and h e n c e an e n e r g y gap E g ( T = O ) = ~ g of 76 meV. The i n i t i a l t e m p e r a t u r e d e p e n d e n c e of E~ seen in Fig. 2 s u g g e s t s that the gap s h r i n k s as the t e m p e r a t u r e rises. The s u b s e q u e n t d e c r e a s e in El~ a b o v e 120 K w o u l d r e s u l t f r o m the i n c r e a s i n g l y important (negatzve) contrlbutlon from carrlers thermally excited a c r o s s the gap. The m i c r o w a v e c o n d u c t i v i t y m e a s u r e m e n t s s h o w n in Fzg. i are c l e a r l y not, h o w e v e r , c o m p a t l b l e w l t h a r e a l gap in the d e n s i t y of s t a t e s , s i n c e t h e r e is no a c t z v a t l o n e n e r g y at low t e m p e r a t u r e s . In f a c t , the d l s p e r s l v e c o n d u c t l v l t y seen in Fig. i s u g g e s t s that the c o n d u c t l v l t y is b y h o p p i n g b e t w e e n l o c a l t s e d s t a t e s at the F e r m i level. In thls case w e s h o u l d e x p e c t 15 the a.c. c o n d u c t i v i t y ori(~) to be p r o p o r t i o n a l to k T { N ( E F ) } 2 . At low t e m p e r a t u r e s oi|(I0 GHz) has the r e q u i r e d p r o p o r -
157
158
PROPERTIES OF Na0.33V205
t z o n a l i t y to T, as s h o w n in the i n s e t to F i g . i. T h u s , t h e r e c a n be no r e a l g a p in t h e d e n s i t y of s t a t e s , but instead a pseudogap with a finite density of l o c a l i z e d states at the F e r m l l e v e l . T h i s is to be expected in a q u a s l - o n e - d l m e n s l o n a l s y s t e m w h e r e a n y k l n d of d i s o r d e r Is k n o w n to p l a y a d o m i n a n t role. These localized states will also contribute to the d i e l e c t r i c constant, although it is d i f f i c u l t to e s t i m a t e their importance with any certainty. The salient features of the above results, t h a t Is, a h i g h l y anzsotropzc dielectric constant wlth a l a r g e v a l u e of EJ~ w h i c h increases with temperature and a conductivity at m i c r o w a v e frequencies much greater t h a n at d . c . , a r e r e m a r k a b l y similar to the p r o p e r t i e s of o t h e r h i g h l y conducting quasi-one-dimensional materials. In p a r t i c u l a r these results bear a strong resemblance to the b e h a v z o u r of t h e s o - c a l l e d complex 1:2 T C N Q 1 6 - 1 9 s a l t s ( s u c h as Ad(TCNQ) 2 and Qn(TCNQ)2) in w h i c h t h e r e is o n e e l e c t r o n f o r e v e r y two s i t e s on t h e T C N Q s t a c k . It h a s b e e n p r o p o s e d 20 t h a t in t h e s e m a t e r i a l s t h e r e m a y be a o n e - d i m e n s i o n a l pseudogap d u e to the t e n d e n c y of the electrons to o c c u p y the a v a i l a b l e s i t e s in s u c h a w a y as to m z n z m z s e their electrostatic energy, a posslbiIzty originally suggested by O v c h z n n z K o v 21. T h a t is, n o t o n l y d o e s the i n t r a - s z t e Coulomb repulsion U split the b a n d i n t o two H u b b a r d bands, but the i n t e r - s i t e Coulomb repulsion produces a f u r t h e r splitting of the l o w e r Hubbard b a n d . We b e l i e v e t h a t the s a m e m o d e l is a p p l i c a b l e to N a O $ 3 V 2 0 5 at low temperatures, as w a s o r i g i n a l l y suggested b y M o r t 22. In N a o . $ 3 V 2 0 5 t h e r e a r e t w i c e as m a n y V I s l t e s as Na a t o m s so t h a t a s i t u a t i o n analogous to t h a t in the c o m p l e x 1 2 TCNQ salts exists. Furthermore the observation of C u r z e - W e l s s paramagnetzsm
at h i g h t e m p e r a t u r e 23 i m p l i e s that the s t r o n g C o u l o m b l i m i t is a p p r o priate. One difference is t h a t the V 1 s i t e s do n o t o c c u r in s i n g l e linear chains but are arranged in z l g - z a g f o r m in d o u b l e - c h a l n s . T h e i d e a t h a t in N a x V 2 0 5 the electrons condense at l o w t e m p e r a tures has already been Invoked to explain recent ESR measurements 2,24, w h i c h s h o w t h a t b e l o w 150 K the electrons appear to u n d e r g o a second order phase transition, w i t h the spln susceptibility suggesting that at l o w t e m p e r a t u r e s one side only of e a c h V 1 d o u b l e - c h a l n is o c c u p i e d . We n o t e t h a t the t e m p e r a t u r e depend e n c e of the g a p i m p l i e d b y the variation of Ell, i n c l u d i n g the initial increase of ~ as the g a p shrinks followed b y its z e r o c r o s s i n g w h e n the f r e e c a r r i e r contrlbutlon becomes dominant, Is consistent wlth thls model on the contrary it is n o t c o n s i s t e n t wlth the a l t e r n a t i v e picture in w h i c h s t a t e s at the F e r m i l e v e l a r e localized simply by disorder without the i n t r o d u c t i o n of s t r u c t u r e In the density of s t a t e s . In c o n c l u s i o n , we belleve that the r e s u l t s reported here provide strong support for a m o d e l of N a o . 3 3 V 2 0 5 In w h i c h the l o w e r H u b b a r d band progressively undergoes a further splitting below 150 K d u e to i n t e r - s i t e Coulomb repulsion within the o n e dimensional V I double-chains. The small gap which results gives rise to the h i g h v a l u e of t h e r e a l p a r t of the d i e l e c t r i c constant E 1 in the c h a i n d i r e c t i o n , b u t E 2 is dominated by states wxthln the g a p ~knowledgments We w o u l d l i k e to thank Professor N . F . M o r t , Dr. D. K a p l a n a n d Dr. A. F r l e d e r z c h for numerous helpful discussions and J.L. P z n s a r d and D. S a u x f o r h e l p in p r e p a r i n g the s a m p l e s u s e d zn thls investigation
REFERENCES i. 2.
3. 4. 5. 6. 7. 8 9.
Vol. 26, No. 3
W A L L I S R.H. , SOL N. , a n d Z Y L B E R S Z T E J N A. , S o l i d S t a t e Comm., 23, 5 3 9 ( 1 9 7 7 ) . FRIEDERICH A. , K A P L A N D. , S O L N. , W A L L I S R . H . , a n d ZYLBERSZTEJN A. , P r o c . 1 3 t h Int. C o n f . on P h y s i c s of Semiconductors, R o m e , 1 9 7 6 , p. 357. K A P L A N D. , a n d Z Y L B E R S Z T E J N A. , J. de P h y s . , 3 7 , L 1 2 3 (1976). SPERLICH G. , L A Z E W . D . , a n d B A N G G. , S o l i d S t ~ e Comm., 16, 4 8 9 ( 1 9 7 5 ) . FRIEDERICH A. , K A P L A N D. , and SOL N , S o l i d S t a t e C o m m . , 2 5 , 633 ( 1 9 7 S ) . GENDELL J. , C O T T S R. , a n d S I E N K O M . J . , J. C h e m . P h y s . , 37, 2 2 0 ( 1 9 6 2 ) . WADSLEY A . D . , A c t a C r y s t . , 8, 695 ( 1 9 5 5 ) . GOODENOUGH J . B . , J. S o l i d S t a t e C h e m . , I, 3 4 9 ( 1 9 7 0 ) . KHANNA S.K. , E H R E N F R E U N D E. , G A R I T O A . F ~ , and H E E G E R A . J . , P h y s . Rev. B, I O , 2 2 0 5 ( 1 9 7 4 )
Vol. 26, No. 3 i0. ii. 12. 13. 14. 15.
16. 17. 18. 19. 20. 21. 22. 23.
24.
PROPERTIES OF Na 0. 33V205
COHEN M., K H A N N A S.K., GUNNING W.J., GARITO A.F., and H E E G E R A.J., Solld State Comm., 17, 367 (1975). KHANNA S.K., CHIANG C.K., GARITO A.F., and HEEGER A.J., Solld State Comm., 18, 1405 (1976). Z Y L B E R S Z T E J N A., P A N N E T I E R B., and M E R E N D A P., Phys. Letters, 54A, 145 (1975). W H E E L E R H.A., IEEE Trans. M i c r o w a v e Theory and Technlques, 13, 172 (1965). ~-hls value of ~p £s (Ecore) I/2 greater than that given £n ref. 3 because of the d e f i n l t l o n of ~p used there. AUSTIN I.G. , and MOTT N.F. , Advances in Physics, 18, 41 (1969). SHCHEGOLEV I . F . , Phys. Star. Solid1 (a), 12, 9 (1972). GOGOLIN A . A . , ZOLOTUKHIN S . P . , MEL'NIKOV V.I., RASHBA E . I . , a n d SHCHEGOLEV I . F . , JETP Letters, 22, 278 (1975). MIHALY G . , ROLCZER K . , PINTER K . , JANOSSY A . , GRUNER G. , a n d MILJAK M . , S o l i d S t a t e C o m m . , 1 7 , 1OO7, ( 1 9 7 5 ) . MIHALY G . , RITVAY-EMANDITY K . , JANOSSY A . , HOLCZER K . , a n d GRUNER G . , S o l i d S t a t e C o m m . , 2 1 , 721 ( 1 9 7 7 ) . MICHALY G . , RITVAY-EMANDITY K . , a n d GRUNER G . , J . P h y s . C8, L361 (1975). OVCHINNIKOV A . A . , S o v i e t Physics J E T P , 3 7 , 176 ( 1 9 7 3 ) . MOTT N.F., " M e t a l - I n s u l a t o r Transltlonslr-(Taylor and Francls, London, 1973), pp.160-63. See ref. 5.Detalled calculatlons show that the a l t e r n a t l v e suggestlon made in ref. 5, that the C u r l e - W e i s s llke suscept£b11£ty could arlse from a very n a r r o w o n e - d £ m e n s l o n a l band wlthout correlatlon, cannot correctly d e s c r l b e the data. F R I E D E R I C H A., and KAPLAN D., to be publlshed.
159