MANY BODY EFFECTS IN X-RAY ABSORPTION EDGES OF Ce COMPOUNDS

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MANY BODY EFFECTS IN X-RAY ABSORPTION EDGES OF Ce COMPOUNDS

A. Kotani, T. Jo

To cite this version:

A. Kotani, T. Jo. MANY BODY EFFECTS IN X-RAY ABSORPTION EDGES OF Ce COMPOUNDS. Journal de Physique Colloques, 1986, 47 (C8), pp.C8-915-C8-922.

�10.1051/jphyscol:19868177�. �jpa-00226082�

JOURNAL DE PHYSIQUE

Colloque C8, supplement au n o 12, Tome 47, dgcembre 1986

MANY BODY EFFECTS IN X-RAY ABSORPTION EDGES OF Ce COMPOUNDS

A. KOTANI and T. JO

Department of P h y s i c s , F a c u l t y of S c i e n c e , Osaka U n i v e r s i t y , Toyonaka 5 6 0 , Japan

R6sum6 - Nous f a i s o n s une a n a l y s e t h g o r i q u e du s e u i l d ' a b s o r p t i o n L dans l e s

-- composes s o i t m 6 t a l l i q u e s s o i t i s s o l a n t s du L a e t du Ce. Nous 6zudions l e s e f f e t s des i n t e r a c t i o n s d N c o r p s dans 1 'G t a t f i n a l e t dans 1 '@ t a t i n i t i a l $ l ' a i d e du mod6le dlAnderson Z 1 s i t e . Une i n t e r p r g t a t i o n c o h 6 r e n t e du s p e c t r e d ' a b s o r p t i o n L e t de p h o t o 6 m i s s i o n de 3d coeur r e q u i e n t de m a n i e r 6 e s s e n t i e l l e l a p r i s e en c8mpte de l ' i n t e r a c t i o n de Coulomb U ( e n t r e un G l e c t r o n 4f e t un ( l e c t r o n 5d p h o t o e x c i t e ) e t Udc ( e n t r e l ' 6 1 e c t r o n f ~ d e t l e t r o u de c o e u r ) . A b s t r a c t - T h e o r e t i c a l a n a l y s i s i s p r e s e n t e d f o r L a b s o r p t i o n edges o f b o t h i n s u l a t i n g and m e t a l l i c compounds o f La and Ce. ~ 3 f e c t s o f many body f i n a l s t a t e i n t e r a c t i o n s , as w e l l as i n i t i a l s t a t e i n t e r a c t i o n s , a r e s t u d i e d b y u s i n g t h e s i n g l e - s i t e Anderson model. I n o r d e r t o g i v e a c o n s i s t e n t i n t e r p r e t a t i o n f o r t h e L 3 a b s o r p t i o n and t h e 3d c o r e p h o t o e m i s s i o n s p e c t r a , i t i s e s s e n t i a l l y i m p o r t a n t t o t a k e account o f t h e Coulomb i n t e r a c t i o n s U (between a 4 f e l e c t r o n and a p h o t o e x c i t e d 5d e l e c t r o n ) and -Udc (between t h e f f d e l e c t r o n and .a c o r e h o l e ) .

I - INTRODUCTION

Core l e v e l s p e c t r o s c o p y i s one o f t h e most p o w e r f u l t o o l s o f s t u d y i n g t h e 4 f e l e c t r o n s t a t e o f r a r e e a r t h systems / I / . F o r t h i s purpose, e.g. f o r s t u d y i n g t h e mixed v a l e n c e s t a t e o f Ce compounds, t h e 2p c o r e p h o t o a b s o r p t i o n spectrum (denoted b y L3- XAS) and t h e 3d c o r e photoemission spectrum (3d-XPS) have been most e x t e n s i v e l y used.

I n L a and Ce compounds, however, t h e s e s p e c t r a r e f l e c t n o t o n l y t h e 4 f ground s t a t e c o n f i g u r a t i o n b u t a l s o i t s f i n a l s t a t e c o n f i g u r a t i o n s , because o f t h e l a r g e f i n a l s t a t e i n t e r a c t i o n s o r i g i n a t i n g f r o m a p h o t o c r e a t e d c o r e h o l e F o r i n s t a n c e , i n many La compounds, t h e 4 f ground s t a t e i s i n t h e almost p u r e 4 f b c o n f i g u r a t i o n , b u t t h e 3d-XPS e x h i b i t s two peaks ( a s i d e f r o m t h e 3d c o r e s p i n - o r b i t s p l i t t i n g ) c o r r e s p o n d i n g t o t h e 4f 0 and 4 f 1 c o n f i g u r a t i o n s i n t h e f i n a l s t a t e /2-6/. Therefore, t o a n a l y z e c o n s i s t e n t l y t h e s e s p e c t r a , i t i s i m p o r t a n t t o understand w e l l t h e mechanism o f t h e f i n a l s t a t e i n t e r a c t i o n , i n a d d i t i o n t o t h e i n i t i a l s t a t e i n t e r a c t i o n , i n b o t h o f t h e L3-XAS and 3d-XPS.

F o r t h e 3d-XPS of La m e t a l , t h e mechanism o f t h e f i n a l s t a t e i n t e r a c t i o n was f i r s t g i v e n by Toyozawa and one o f t h e p r e s e n t a u t h o r s 71. I n t h e ground s t a t e o f L a (and a l s o i n m e t a l l i c La compounds), t h e 4 f l e v e l c f 6 i s w e l l above t h e Fermi l e v e l c F , b u t i n t h e f i n a l s t a t e , t h e 4 f l e v e l on t h e c o r e h o l e s i t e i s p u l l e d down below due t o t h e a t t r a c t i v e p o t e n t i a l -Ufc o f t h e c o r e h o l e . Then, we have two t y p e s EF

f i n a l s t a t e s : i n one t y p e a conducti,on e l e c t r o n jumps i n t o t h e 4 f l e v e l t h r o u g h t h e h y b r i d i z a t i o n V ( r e s u l t i n g i n t h e 4 f l c o n f i g u r a t i o n ) , and i n t h e o t h e r t y p e t h e 4 f l e v e l i s s t i l l empty ( 4 f 0 c o n f i g u r a t i o n ) even a f t e r p u l l e d down below EF. Therefore, t h e 3d-XPS e x h i b i t s two peaks c o r r e s p o n d i n g t o t h e two t y p e s o f t h e f i n a l s t a t e s . The two-peak s t r u c t u r e o f t h e 3d-XPS i n i n s u l a t i n g L a compounds can a l s o be e x p l a i n e d b y t h i s mechanism o n l y b y r e p l a c i n g t h e c o n d u c t i o n band w i t h a f i l l e d v a l e n c e band /7,8/. I n t h e LQ-XAS, on t h e o t h e r hand, a 2p c o r e e l e c t r o n i s p h o t o e x c i t e d t o t h e La 5d band. Thus, a c o r e h o l e i s a l s o c r e a t e d i n t h e f i n a l s t a t e , b u t t h e L3-XAS of La and i t s compounds have o n l y one peak /6,9-11/. The f i n a l s t a t e i n t e r a c t i o n i n t h e L3-XAS o f La compounds has r e c e n t l y been s t u d i e d b o t h t h e o r e t i c a l l y /12,13/ and

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19868177

C8-916 JOURNAL DE PHYSIQUE

e x p e r i m e n t a l l y /6,10,11/, b u t no q u a n t i t a t i v e l y s a t i s f a c t o r y i n t e r p r e t a t i o n seems t o be o b t a i n e d .

I n mixed v a l e n t Ce compounds, t h e observed 3d-XPS has t h r e e pea s /5,6,14/, whereas t h e La-XAS e x h i b i t s o n l y two peaks /6,9,11,14/. The 4 f l e v e l E? o f t h e s e systems i s

i n t h e v i c i n i t y o f EF, and due t o t h e h y b r i d i z a t i o n V t h e 4 4 and 4f1 c o n f i g u r a t i o n s a r e mixed w i t h each o t h e r i n t h e ground s t a t e . i n t h e f i n a l s t a t e o f t h e 3d- XPS, we have t h r e e t y p e s o f 4 f c o n f i g u r a t i o n s 4 6 r e n i f l and 4f2 h y b r i d i z e d w i t h each o t h e r , s i n c e t h e 4 f l e v e l i s p u l l e d down b y t h e c o r e h o l e p o t e n t i a l and an e l e c t r o n can t r a n s f e r f r o m t h e c o n d u c t i o n band. T a k i n g account o f

t h k c

Also, i n an i n s u l a t i n g compound CeO t h e e x p e r i m e n t a l 3d-XPS has a three-peak s t r u c t u r e /6,16,17/ and t h e L3-XAS i;s a two-peak s t r u c t u r e /6,9,14,18/. I n t h e gr8und s t a t o f Ce02, 'i s f 0 i s l o c a t e d n e a r t h e t o p o f t h e v a l e n c e band, so t h a t t h e 4 f and 4 f c o n f i g u r a t i o n s a r e s t r o n g l y mixed t h r o u g h t h e h y b r i d i z a t i o n between t h e 4 f s t a t e and t h e f i l l e d v a l e n c e band /19,20/. M i z u t a , P a r l e b a s and t h e p r e s e n t a u t h o r s /20,21/ analyzed i n d e t a i l b o t h o f t h e 3d-XPS and L3-XAS i n Ce02 b y u s i n g t h e Anderson model w i t h a f i l l e d v a l e n c e band. They p o i n t e d o u t t h a t i n t h e f i n a l s t a t e o f L -XAS t h e Coulomb i n t e r a c t i o n s U (between 4 f and 5d e l e c t r o n s ) and -U (between t h e #d e l e c t r o n and t h e c o r e h o l e ) pf!y an e s s e n t i a l l y i m p o r t a n t r o l e i n a d i i t i o n t o t h e Coulomb i n t e r a c t i o n -Ufc. T h i s model i s a l s o a p p l i c a b l e t o t h e a n a l y s i s o f t h e 3d-XPS and L3-XAS o f v a r i o u s La and Ce compounds ( b o t h i n s u l a t i n g and m e t a l l i c compounds) /22/. I n t h i s paper, we show how we can o b t a i n a c o n s i s t e n t i n t e r p r e t a t i o n f o r t h e 3d-XPS and L3-XAS o f v a r i o u s La and Ce compounds.

I 1 - - MODEL

We use t h e Anderson model w i t h a f i l l e d v a l e n c e band as shown i n F i g . 1. Our system c o n s i s t s o f a f i l l e d v a l e n c e band ( t h e oxygen 2p band f o r L a o r Ce o x i d e ) w i t h e n e r g y

~ ~ ( k ) , a 4 f l e v e l E ~ O , a 5d band w i t h q ( k ) and a c o r e l e v e l ( t h e 3d o r 2p l e v e l o f La o r Ce) w i t h ^{E ~ .} We t a k e account o f t h e h y b r i d i z a t i o n V between t h e 4 f s t a t e and t h e v a l e n c e band, and t h e Coulomb i n t e r a c t i o n Uff between 4 f e l e c t r o n s . I n t h e ground s t a t e ( F i g . l ( a ) ) , t h e c o r e l e v e l i s occupied and t h e 5d band i s empty. I n t h e l i m i t o f V ⁺ 0, t h e v a l e n c e band i s f i l l e d and t h e 4 f l e v e l i s empty, b u t w i t h f i n i t e V t h e y a r e mixed t o g e t h e r and a f r a c t i o n a l 4 f e l e c t r o n occupancy o c c u r s e s p e c i a l l y i n t h e case o f Ce compounds. I n t h e f i n a l s t a t e o f t h e 3d-XPS, a c o r e e l e c t r o n i s removed, w h i l e i n t h e L3-XAS i t i s e x c i t e d t o t h e 5d band, as shown i n F i g . l ( b ) . I n

F i g . 1 - Model o f o u r system i n t h e ( a ) i n i t i a l and ( b ) f i n a l s t a t e s o f L3-XAS and 3d-XPS.

t h e s e f i n a l s t a t e s , t h e 4 f l e v e l i s assumed t o be p u l l e d down t o ~f = E ~ " - 4, due t o t h e c o r e h o l e p o t e n t i a l -4,. Furthermore, i n t h e f i n a l s t a t e o f t h e L3-XAS, t h e p h o t o e x c i t e d 5d e l e c t r o n i s assumed t o i n t e r a c t w i t h t h e 4 f e l e c t r o n t h r o u g h t h e Coulomb i n t e r a c t i o n Ufd and w i t h t h e c o r e h o l e t h r o u g h

-Udc.

The H a m i l t o n i a n o f o u r system i s d e s c r i b e d as

Here, nv(k,v), n d ( k ) , n f ( v ) and nc r e p r e s e n t t h e e l e c t r o n number o p e r a t o r s i n t h e v a l e n c e band, 5d band, 4 f l e v e l and c o r e l e v e l , r e s p e c t i v e l y , where k denotes t h e i n d e x o f energy l e v e l ( k = 1 a N) and v s p e c i f i e s b o t h t h e s p i n and o r b i t a l degeneracy ( v = 1 a Nf). The o p e r a t o r s ac(k,v) and a f ( v ) express t h e c r e a t i o n o f t h e v a l e n c e e l e c t r o n and t h e a n n i h i l a t i o n o f t h e 4 f e l e c t r o n , r e s p e c t i v e l y . I n t h i s model we c o n s i d e r t h e 4 f and c o r e s t a t e s o n l y on a s i n g l e a t o m i c s i t e , c o n f i n i n g o u r s e l v e s t o t h e s i n g l e - s i t e a p p r o x i m a t i o n . The s p i n and o r b i t a l degeneracy i n E, and each o f E d ( k ) a r e d i s r e g a r d e d , s i n c e t h e y a r e n o t e s s e n t i a l l y i m p o r t a n t i n t h e p r e s e n t problem.

The s p e c t r a o f 3d-XPS and L3-XAS a r e expressed as

where

L ( x ) = r / [ n ( x 2 + r 2 ) 1 ,

Here, l g > i s t h e ground s t a t e ( w i t h energy Eg) o f H, I f > ' s a r e e i g e n s t a t e s ( w i t h e n e r g i e s E f l s ) o f H i n t h e e x i s t e n c e o f a c o r e nole, EB and w a r e t h e b i n d i n g e n e r g y and t h e i n c i d e n t photon energy, r e s p e c t i v e l y , and r r e p r e s e n t s t h e s p e c t r a l broadening due t o t h e l i f e t i m e o f t Q e c o r e hole, as w e l l as t h e e x p e r i m e n t a l r e s o l u t i o n . The o p e r a t o r s ac and a d ( k ) r e p r e s e n t t h e a n n i h i l a t i o n o f t h e c o r e e l e c t r o n and t h e c r e a t i o n of t h e 5d e l e c t r o n , r e s p e c t i v e l y .

The s p e c t r a FXpS and FXAS a r e a l c u l t e d b y x a c t l y d i a g o n a l i z i n g t h e H a m i l t o n i a n (1) 6 B 5

i n t h e sub-space c o n t a i n i n g 4 f , 4 f and 4 f c o n f i g u r a t i o n s and f o r a f i n i t e system where E V ( k ) and Ed(k) a r e t a k e n as

~ . ( k ) = E o ^{'i 'i} 1

i i - ~ + - , + k - = ) ( 5 )

w i t h k = 1, 2;..N and i = v o r d. The v a l u e N i s t a k e n t o be s u f f i c i e n t l y l a r g e so t h a t t h e c a l c u l a t e d s p e c t r a a r e w e l l converged.

0 .

When cf i s much h i g h e r t h a n ~ ~ ( k ) , t h e ground s t a t e i s anOalmost p u r e 4 f 0 s t a t e , and t h e n o u r model d e s c r i b e s i n s u l a t i n g La compounds. When i s l o c a t e d nea E ( k ) , on t h e o t h e r hand, t h e ground s t a t e i s t h e mixed s t a t e between t h e 4 f 6 a n d 4f1 c o n f i g u r a t i o n s , which corresponds t o i n s u l a t i n g i n t e r m e d i a t e v a l e n c e compounds, such as CeOp. Furthermore, t h e p r e s e n t model i s a l s o a p p l i c a b l e t o t h e m e t a l l i c L a and Ce compounds; when we r e g a r d s i m p l y t h e t o p o f t h e v a l e n c e band as t h e Fermi l e v e l of

C8-918 JOURNAL DE PHYSIQUE

t h e c o n d u c t i o n band, t h e p r e s e n t a n a l y s i s corresponds t o t h e l o w e s t o r d e r a p p r o x i m a t i o n o f l / N f expansion i n m e t a l l i c systems, as found f r o m t h e 1/N expansion t h e o r y b y Gunnarsson and Sch6nhammer 1151. S i n c e t h e v a l u e o f Nf (Nf = 1 4 1 i s l a r g e , t h e l o w e s t o r d e r a p p r o x i m a t i o n p r o v i d e s us w i t h s u f f i c i e n t l y r e l i a b l e r e s u l t s . Then, t h e main d i f f e r e n c e between t h e i n s u l a t i n g and m e t a l l i c systems comes f r o m t h e d i f f e r e n c e i n t h e parameter values V, Uff e t c . , as shown l a t e r .

111 - ANALYSIS FOR La COMPOUNDS

The importance o f f i n a l s t a t e i n t e r a c t i o n s b o t h i n t h e 3d-XPS and L3-XAS can be most c l e a r l y understood b y a p p l y i n g o u r model t o t h e a n a l y s i s f o r i n s u l a t i n g La compounds /22/. As a t y p i c a l example, we show h e r e t h e r e s u l t f o r La203. The c a l c u l a t e d 3d-XPS i s p l o t t e d i n F i g . 2 w i t h t h e s o l i d curve, where t h e o r i g i n o f EB i s t a k e n a t t h e higher-peak p o s i t i o n . The arame e r v a l u e s a r e chosen as f o l l o w s : V = 0.57eV, U - 10.5eV, Ufc = 12.7 eV, E ~ B - ^12.5 eY, Wv = 2 . 5 e V , r = l . O e V , and Nf i s p i { i s I 4 t h r o u g h o u t t h i s paper. These values a r e i n f a i r l y good agreement w i t h t h o s e e s t i m a t e d b y Schneider e t a l . /8/. F u r t h e r , t h e y a r e r a b h e r c l o s e t o t h o s used i n o u r p r e v i o u s a n a l y s i s o f t h e 3d-XPS o f Ce02 /20/ e x c e p t E~ . The v a l u e o f E %

i s a d j u s t e d so as t o reproduce t h e e x p e r i m e n t a l 3d-XPS ( t h e i n s e t o f F i g . 2) g y Fuggle e t a l . /4/, which i s a l s o p l o t t e d w i t h t h e dashed c u r v e a f t e a background s u b t r a c t i o n . I n t h e f i n a l s t a t e o f h i s 3d-XPS, t h e Of l e v e l b E~ = s f 6 - Ufc i s c l o s e t o t h e c e n t e r o f t h e valence band ^E" , so t h a t t h e 4 f s t a t e i s coup ed s t r o n d l y w i t h t h e v a l e n c e band s t a t e t h r o u g h t h e h y b r i d i z a t i o n V, i.e., t h e 4 f and 4 f q f i n a l s t a t e s m i x s t r o n g l y w i t h each o t h e r . The two peaks 8 f t h e 3d-XPS correspond t o t h e bonding and a n t i b o n d i n g s t a t e s o f t h e h y b r i d i z e d 4 f and 4 f l c o n f i g u r a t i o n s i n t h e f i n a l s t a t e .

I n F i g . 3, we show t h e La-XAS.calculated b y u s i n g Wd = 6.0 eV, T = 2.0 eV and v a r i o u s v a l u e s o f Uf and Ud, ( t e o r i g i n o f w i s t a k e n a p p r o p r i a t e l y ) . The o t h e r parameter values a r e t i e same as t h o s e used i n t h e a n a l y s i s o f t h e 3d-XPS. I t i s f o u n d t h a t t h e l i n e shape o f t h e L3-XAS depends s t r o n g l y on t h e values o f Ufd and Udc. I n t h e case o f Ufd = 0 and Udc = 0, t h e L3-XAS i s g i v e n b y a s i m p l e c o n v o l u t i o n o f t h e 3d-XPS w i t h a one e l e c t r o n 2p ^-t 5d a b s o r p t t o n spectrum ( c o n t a i n i n g no many body e f f e c t ) , and t h e n t h e L3-XAS i s f o u n d t o become a v e r y broad peak w i t h t h e p r e s e n t values o f Wd and r ( o r i t has two peaks when Wd and 'l a r e t a k e n t o be s m a l l e r ) . However, w i t h i n c r e a s i n g U and U t h e w i d t h o f t h e peak decreases and t h e l i n e shape becomes asymmetric wfeh higic;nergy t a i l . The r o l e o f t h e a t t r a c t i v e p o t e n t i a l -Udc i s t o l o c a l i z e t h e e x c i t e d 5d e l c t r o n n e a r t h e c o r e h o l e s i t e , and t h e n b y t h e e f f e c t o f

t .

Ufd t h e energy o f t h e 4 f f i n a l s t a t e i s e l e v a t e d i n comparison w i t h t h e 4 O f i n a l s t a t e . I n o t h e r words, t h e energy s e p a r a t i o n between t h e 4 f l e v e l sf sf6- Ufc +

Fig. 2 - T h e o r e t i c a l ( s o l i d c u r v e ) F i g . 3 - T h e o r e t i c a l ( s o l i d c u r v e s ) and e x p e r i m e n t a l (dashed c u r v e and i n s e t ) and e x p e r i m e n t a l (dashed c u r v e and i n s e t ) r e s u T t s o f t h e 3d-XPS o f La203. r e s u l t s o f t h e L3-XAS o f La203.

F i g . 4 - T h e o r e t i c a l ( s o l i d c u r v e ) F i g . 5 - T h e o r e t i c a l and e x p e r i m e n t a l ( i n and e x p e r i m e n t a l (dashed c u r v e and t h e i n s e t ) r e s u l t s o f t h e L3-XAS o f LaPd3.

i n s e t ) r e s u l t s o f t h e 3d-XPS o f The second d e r i v a t i v e o f t h e spectrum i s

LaPd3. shown w i t h t h e d o t t e d curve.

Ufd and t h e v a l e n c e band ~ , ( k ) becomes l a r g e r , and t h e f i n a l s t a t e m i x i n g between 4 f 0 and 4 f l c o n f i g u r a t i o n s decreases. Then, t h e peak o f L3-XAS becomes s h a r p e r because i t o r i g i n a t e s m a i n l y f r o m t h e 4 f 0 f i n a l s t a t e , and t h e 4 f l f i n a l s t a t e c o n t r i b u t e s o n l y t o t h e h i g h energy t a i l o f t h e L3-XAS. (Mote t h a t o n l y t h e 4 f 0 c o n f i g u r a t i o n has t h e l a r g e o s c i l l a t o r s t r e n g t h because t h e ground s t a t e i s t h e almost p u r e 4 P c o n f i g u r a t i o n . ) The r e s u l t w i t h Uf 4 eV and Udc = 5 eV i s f o u n d t o be i n b e s t agreement w i t h t h e e x p e r i m e n t a l r e s u ( l t Z b y B i a n c o n i e t a l . /11/, which i s shown i n t h e i n s e t o f F i g . 3. F o r comparison, t h e e x p e r i m e n t a l spectrum i s a l s o p l o t t e d w i t h t h e dashed curve, where t h e i n t e n s i t y and energy p o s i t i o n o f t h e a b s o r p t i o n peak a r e a d j u s t e d so as t o f i t t o t h o s e o f t h e t h e o r e t i c a l c u r v e a f t e r s u b t r a c t i n g t h e background (as shown w i t h t h e c h a i n c u r v e ) .

Next we use o u r model t o analyze t h e s p e c t r a i n m e t a l l i c L a compound, LaPd3, s i n c e o u r model i s a l s o a p p l i c a b l e t o t h e m e t a l l i c system i n t h e l o w e s t o r d e r a p p r o x i m a t i o n o f l / N f expansion o n l y b y r e g a r d i n g t h e f i l l e d v a l e n c e band as t h e c o n d u c t i o n band below EF . The main d i f f e r e n c e between LaPd3 and La20g comes f r o m t h e d i f f e r e n c e i n parameter v a l u e s - we t a k e f o r LaPd3 t h e v a l u e s o f V = 0.53 eV, Uff = 6.0 eV, OUfc = 8.7 eV, cfO - ^E d= 7.5 eV, Wv = 3.0 eV, and r = 1.3 eV. Note t h a t t h e v a l u e s E~ , Uff and Uf, a r e s m a r l e r t h a n t h o s e f o r Lap03. The 3d-XPS c a l c u l a t e d w i t h t h e s e parameters i s shown i n F i g . 4, and i t i s i n good agreement w i t h t h e e x p e r i m e n t a l r e s u l t observed b y F u g g l e e t a l . /5/, I n t h i s case, t h e 4 f l e v e l w h i c h i s p l o t t e d i n t h e i n s e t and a l s o w i t h he dashed curve. E~ i n t h e f i n a l s t a t e i s l o w e r t h a n E 8 , so t h a t t h e phgtoemission peaks w i t h h i g h e r and l o w e r b i n d i n g e n e r g i e s corresp8nd m a i n l y t o t h e 4 f and 4 f l f i n a l s t a t e s , a l t h o u g h t h e s e c o n f i g u r a t i o n s are, t o some e x t e n t , mixed t h r o u g h V.

I n F i g . 5, t h e c a l c u l a t e d r e s u l t o f t h e L3-XAS i s shown w i t h t h e s o l i d c u r v e ( h e r e we i n c l u d e t h e background c o n t r i b u t i o n w h i c h i s assumed as t h e c h a i n c u r v e ) , where (Ufd, Udc! a r e t a k e n as (1.7, 2.0) eV and (0,O) w i t h Wd = 6.0 eV and r ⁼ 1.7 eV. The r e s u l t w i t h (Ufd, Udc) = (1.7, 2.0) eV i s i n good agreement w i t h t h e e x p e r i m e n t a l r e s u l t b y B i a n c o n i e t a l . / l o / , which i s p l o t t e d i n t h e i n s e t . On t h e o t h e r hand, t h e r e s u l t w i t h (Ufd, Udc) = (0, 0 ) i s i n l e s s agreement w i t h t h e experiment; t h i s can be

C8-920 JOURNAL DE PHYSIQUE

c l e a r l y seen b y t a k i n g t h e second d e r i v a t i v e o f t h e spectrum, as shown w i t h t h e d o t t e d curve. Therefore, we f i n d t h a t t h e e f f e c t o f Ufd and -Udc i s s t i l l i m p o r t a n t i n t h e m e t a l l i c system, a l t h o u g h i t i s weakened b y t h e m e t a l l i c s c r e e n i n g e f f e c t . I V - - Ce COMPOUNDS

Here, we f i r s t r e v i e w o u r p r e v i o u s a n a l y s i s f o r t h e i n s u l a t i n g Ce compound, Ce02 !20,21/. I n F i g . 6 t h e c a l c u l a t e d 3d-XPS i s shown, compared w i t h t h e e x p e r i m e n t a l r e s u l t b y W u i l l o u d e t a l . /17/ i n t h e i n s e t . Th parameter v a l u e s a r e t a k e n as V = 0.76 eV, Uff = 10.5 eV, Ufc = 12.5 eV, c f O - ^{:E =} 1.6 eV, Wv = 3.0 eV

F i g . 6 - T h e o r , e t i c a l ( s o l i d c u r v e ) and F i g . 7 - T h e o r e t i c a l ( s o l i d c u r v e s ) and e x p e r i m e n t a l ( i n s e t ) r e s u l t s o f t h e e x p e r i m e n t a l ( i n s e t ) r e s u l t s o f t h e 3d-XPS o f CeO

2' L3-XAS o f Ge02.

F i g . 8 - T h e o r e t i c a l and e x p e r i m e n t a l ( i n s e t ) r e s u l t s o f t h e 3d-XPS o f CePd 3'

F i g . 9 - T h e o r e t i c a l and e x p e r i m e n t a l ( i n s e t ) r e s u l t s o f t h e L3-XAS o f CePd3:

The second d e r i v a t i v e o f t h e spectrum i s shown w i t h t h e d o t t e d curve.

and r = 1.0 eV. Since t h e 4 f l e v e l sf0 i s v e r y c l o s e t o t h e t o p o f t h e valence band, t h e 4 f s t a t e h y b r i d i z e s s t r o n g l y w ' t h t h e alence band, and t h e ground s t a t e o f Ce02

d Y

i s t h e mixed s t a t e between t h e 4 f and 4 f c o n f i g u r a t i o n s ( t e avera e 4 f !

2

t h e bonding and antibonding s t a t e s o f t h e s t r o n g l y mixed 4 f and 4 f c o n f i g u r a t i o n s On t h e o t h e r hand, t h e h i g h e s t b i n d i n g energy peak corresponds t o t h e almost pure 4 f b c o n f i g u r a t i o n .

The L3-XAS i s shown i n Fig. 7, where we take Wd = 6.0 eV and 'I = 1.0 eV. ( I n our previous c a l c u l a t i o n o f L3-XAS /21/ t h e value o f Nf i s l i m i t e d t o 2, b u t here i t i s extended t o Nf 7 14.) With vanishing Ufd and Udc, t h e L3-XAS has three-peak s t r u c t u r e , which i s n o t h i n g b u t t h e broadened v e r s i o n o f t h e 3d-XPS, b u t i t i s q u i t e d i f f e r e n t from t h e experimental two-peak s t r u c t u r e /18/ p l o t t e d i n t h e i n s e t . When we take account o f U and -U t h e energies o f t h e f i n a l s t a t e c o n f i g u r a t i o n s 4 f 1 and 4 f 2 (measured f&!m t h a t %'the 4 f 0 c o n f i g u r a t i o n ) are pushed up by Ufd and 2Ufd, r e s p e c t i v e l y , and thus t h e i r m i x i n g decreas s. 6 As 7 r e s u l t , L -XAS c o n s i s t s o f on1 two peaks, m a i n l y corresponding t o t h e 4 f and 4 f configuragions, w h i l e t h e 4f 3

f i n a l s t a t e has o n l y a very weak i n t e n s i t y because t h e 4 f 2 c o n f i g u r a t i o n i s scarecely included i n t h e ground s t a t e . The c a l c u l a t e d r e s u l t w i t h (U U ) = (4.0,- 5.0) eV i s found t o be i n s a t i s f a c t o r y agreement w i t h t h e experime%'bo!!h i n t h e r e 1 a t i v e i n t e n s i t y and t h e energy separation o f t h e two peaks.

We next show t h e r e s u l t s c a l c u l a t e d f o r t h e m e t a l l i c compound CePd3 i n Fig. 8 (3d- XPS) and F i g . 9 (L -XAS). The parameter values are taken as f o l l o w s : V = 0.38 eV, Uff

= 8.3 eV. Uf = 18.5 eV, sf0 - ^{O,r = -0.5 eV, W, =} 3.0 eV, Wd = 4.0 eV. T(3d-XPS) = 1.6 eV and T ? L ~ - ~ A S ) = 2.0 eY. The ground s t a t e i s t h e mixed valence s t a t e between t h e i f 0 and 4 f c o n f i g u r a t i o n s {nf = 0.86), and t h e t h r e e peaks o f t h e 3d-XPS corresponds m a i n l y t o t h e 4f0, 4 f and 4 f 2 o n f i g u r a t i o n s i n t h e order o f decreasing F

b i n d i n g energy. The m i x i n g between t h e 4 f and 4 f 2 c o n f i g u r a t i o n s i s much smaller than t h a t i n Ce02 because o f t h e smaller h y b r i d i z a t i o n V, and t h i s i s t h e reason t h a t t h e i n t e n s i t y o f t h e middle peak i s l a r g e s t whereas i t i s s m a l l e s t i n Ce02.

I n t h e f i n a l s t a t e o f t h e L3-XAS, t h e e f f e c t o f Ufd and -U i s much smflller t h a t h a t o f t h e i n s u l a t i n g compound C e 0 2 . Concerning t h e c o n t r i g u t i o n from 4 f and 4 f n +?

( n = 1) f i n a l states, t h e s i t u a t i o n i s v e r y s i m i l a r t o t h e case o f LaPd3 ( n = 0).

Although t h e c a l c u l a t i o n o f t h e L3-XAS i n Fig. 9 i s r a t h e r p r e l i m i n a r y , t h e importance o f t h e e f f e c t o f Ufd and -Ud can 'be seen from comparison w i t h experimental d a t a (The data i n t h e i n s e t s o f p i g s . 8 and 9 are observed by Fuggle e t a l . /5/ and Bianconi e t a l . / l o / , r e s p e c t i v e l y . ) .

V - CONCLUDING REMARKS

I n t h i s paper, we disregarded t h e e f f e c t o f 4 f c o n f i g u r a t i o n i n t h e f i n a l s t a t e , 3 c o n f i n i n g ourselves t o t h e sub-space c o n t a i n i n g 4f0, 4 f l and 4 f 2 c o n f i g u r a t i o n s . Very r e c e n t l y , t h e present authors /23/ p o i n t e d o u t a p o s s i b l e r o l e o f t h e 4 f c o n f i g u r a t i o n i n t h e f i n a l s t a t e o f t h e d-XPS (see Ref. 23 f o r d e t a i l s ) . 3 I n t h e L3- XAS, on t h e o t h e r hand, t h e e f f e c t o f 4 f c o n f i g u r a t i o n i s n e g l i g i b l y small.

Some experimental observations o f t h e 3d core photoabsorption spectra (3d-XAS) have r e c e n t l y been made i n a d d i t i o n t o t h e 3d-XPS and L3-XAS. According t o t h e experimental data /24/, t h e l i n e shapes o f 3d-XAS i n m e t a l l i c (e.g. CeRh3) and i n s u l a t i n g (Ce02).mixed v a l e n t compounds are s i m i l a r t o each other, having a s t r o n g peak and a weak h i g h energy s a t e l l i t e , although t h e i r l i n e shapes i n 3d-XPS a r e v e r y d i f f e r e n t as shown i n I V . Our t h e o r y can also be a p p l i e d t o t h e a n a l y s i s o f t h e 3d- XAS, and t h e present authors have given an i n t e r p r e t a t i o n f o r t h e s i m i l a r i t y i n t h e 3d-XAS between t h e m e t a l l i c and i n s u l a t i n g mixed v a l e n t systems (see a l s o Ref. 23).

As shown i n t h i s paper, t h e e f f e c t o f U and -Udc i s e s s e n t i a l l y important i n t h e L3-XAS o f i n s u l a t i n g compounds o f La and Ee, although D e l l e y e t a l . /25/ analyzed t h e

C8-922 JOURNAL DE PHYSIQUE

L3-XAS o f Ce02 b y d i s r e g a r d i n g Ufd and -Udc. I n m e t a l l i c compounds, Ufd and Udc a r e s m a l l e r t h a n t h o s e o f i n s u l a t i n g compounds, so t h a t an a n a l y s i s w i t h d i s r e g a r d i n g them may be u s e f u l as a f i r s t a p p r o x i m a t i o n /8,12/, b u t t h e i r e f f e c t i s s t i l l i m p o r t a n t i n more d e t a i l e d a n a l y s i s . The t h e o r e t i c a l c a l c u l a t i o n s f o r v a r i o u s m e t a l l i c Ce compounds w i l l be made w i t h t h e p r e s e n t model i n t h e near f u t u r e .

ACKNOWLEDGMENTS

The a u t h o r s would l i k e t o express t h e i r thanks t o M r . M. Okada, Mr. H. M i z u t a and Dr. J.C. Parlebas f o r t h e i r c o l l a b o r a t i o n i n t h e p r e s e n t study. The f i n i s h o f t h i s paper was made d u r i n g one o f t h e a u t h o r s (A.K.) s t a y e d i n U n i v e r s i t a d i Roma "La Sapienza" and he would l i k e t o thank P r o f e s s o r A. Bianconi f o r v a l u a b l e d i s c u s s i o n s and h o s p i t a l i t y . T h i s work i s p a r t l y supported b y The K u r a t a Research Grant and b y a G r a n t - i n - A i d f o r S c i e n t i f i c Research f r o m t h e M i n i s t r y o f Education, Science and C u l t u r e i n Japan.

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