CORE LEVEL PHOTOEMISSION IN SOLIDS

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CORE LEVEL PHOTOEMISSION IN SOLIDS

A. Kotani

To cite this version:

A. Kotani. CORE LEVEL PHOTOEMISSION IN SOLIDS. Journal de Physique Colloques, 1987, 48

(C9), pp.C9-869-C9-877. �10.1051/jphyscol:19879156�. �jpa-00227268�

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Tome 48, dbcembre

CORE LEVEL PHOTOEMISSION IN SOLIDS

A . KOTANI

Department of Physics, Faculty of Science, Tohoku University, Sendai 980, Japan

A b s t r a c t

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Many body e f f e c t s i n c o r e l e v e l p h o t o e m i s s i o n a r e d i s c u s s e d f o r r a r e e a r t h systems, e s p e c i a l l y f o r La and Ce compounds b o t h i n m e t a l l i c and i n s u l a t i n g forms. The 3d c o r e photoemission spectrum o f t h e s e m a t e r i a l s i s analyzed by u s i n g t h e i m p u r i t y Anderson model i n c o r p o r a t e d w i t h a c o r e h o l e p o t e n t i a l t o t h e 4 f s t a t e . I m p o r t a n t i n f o r m a t i o n s on t h e m e t a l l i c mixed valency, as w e l l as on t h e i n s u l a t i n g covalency, a r e d e r i v e d f r o m t h e a n a l y s i s . The r e l a t i o n s h i p o f s p e c t r a between t h e 3d c o r e photoemission and t h e 2p c o r e p h o t o a b s o r p t i o n i s discussed.

I

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INTRODUCTION

I n t h e f i n a l s t a t e o f c o r e l e v e l photoemission, a c o r e h o l e i s l e f t behind. W i t h i n t h e Hartree-Fock approximation, t h e Koopmans theorem h o l d s , so t h a t t h e c o r e l e v e l photoemission spectrum i s d e s c r i b e d by d i s c r e t e l i n e s whose b i n d i n g energy corresponds t o t h e Hartree-Fock energy e i g e n v a l u e ^E o f c o r e e l e c t r o n s . H i s t o r i c a l l y , t h e c o r e l e v e l photoemi s s i o n i n s o l i d s hasCbeen developed f r o m t h e e x p e r i m e n t a l d e t e r m i n a t i o n o f E i n v a r i o u s systems. Since t h e v a l u e o f E i n s o l i d s i s n o t v e r y d i f f e r e n t f r o m t h e gorcesponding f r e e atom value, which i s c h a g a c t e r i s t i c i n each element, t h e c o r e l e v e l photoemission i s u s e f u l as a t o o l o f e l e m e n t a r y a n a l y s i s . Furthermore, a small d e v i a t i o n o f E from i t s f r e e atom value, i.e. t h e chemical s h i f t , p r o v i d e s us w i t h t h e i n f o r m a t i & on t h e chemical bonding o f o u t e r e l e c t r o n s .

However, t h e Koopmans theorem does n o t g e n e r a l l y h o l d because o f t h e many body e f f e c t beyond t h e Hartree-Fock approximation. When a c o r e h o l e i s c r e a t e d i n t h e f i n a l s t a t e o f photoemission, o u t e r e l e c t r o n s ( i . e . v a l e n c e e l e c t r o n s ) a r e p o l a r i z e d b y t h e c o r e h o l e p o t e n t i a l and screen t h e c o r e h o l e charge. T h i s corresponds t o t h e r e d i s t r i b u t i o n o r r e l a x a t i o n of o u t e r e l e c t r o n s t a t e s , and t h e dynamics o f many body response o f o u t e r e l e c t r o n s t o t h e c o r e h o l e a r e s e n s i t i v e l y r e f l e c t e d i n t h e s t r u c t u r e o f photoemission spectrum. Owing t o t h e r e c e n t p r o g r e s s i n e x p e r i m e n t a l technique, t h e many body e f f e c t i n t h e p h o t o e m i s s i o n spectrum can be observed w i t h s u f f i c i e n t accuracy as an asymmetry o f s p e c t r a l shape and as a s a t e l l i t e s t r u c t u r e . Furthermore, i t has been w e l l r e c o g n i z e d t h a t t h e c o r e l e v e l photoemission i s one o f t h e most p o w e r f u l t o o l s i n t h e s t u d y o f many body e f f e c t s o f o u t e r e l e c t r o n s / I / . A well-known example, which demonstrates t h e importance o f t h e many body e f f e c t o f o u t e r e l e c t r o n s , i s t h e s i n g u l a r i t y i n c o r e l e v e l p h o t o e m i s s i o n spectrum o f s i m p l e metals. I n t h e f i n a l s t a t e o f c o r e photoemission i n s i m p l e metals, c o n d u c t i o n e l e c t r o n s screen t h e c o r e h o l e charge, and t h i s many body response o f c o n d u c t i o n e l e c t r o n s g i v e s r i s e t o an asymmetric photoemission l i n e shape d i v e r g i n g a t t h e

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19879156

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C9-870 JOURNAL DE PHYSIQUE

t h r e s h o l d , due t o t h e s o - c a l l e d o r t h o g o n a l i t y c a t a s t r o p h e /2,3/. More i n t e r e s t i n g i s t h e r e c e n t development i n t h e s t u d y o f many body e f f e c t s i n magnetic m a t e r i a l s , which c o n t a i n i n c o m p l e t e l y f i l l e d d o r f e l e c t r o n s /I/. The r e l a x a t i o n o f d o r f e l e c t r o n o r b i t a l on t h e c o r e h o l e s i t e causes t h e s p l i t t i n g o f c o r e photoemission spectrum, and we can o b t a i n v e r y i m p o r t a n t i n f o r m a t i o n on t h e d o r f e l e c t r o n s t a t e f r o m t h e a n a l y s i s o f photoemission spectrum. I n t h e p r e s e n t paper, we r e v i e w t h e development i n t h e o r e t i c a l s t u d y o f c o r e l e v e l p h o t o e m i s s i o n o f r a r e e a r t h compounds, e s p e c i a l l y La and Ce compounds b o t h i n m e t a l l i c and i n s u l a t i n g forms.

I 1

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La and Ce METALS AND THEIR INTERMETALLIC COMPOUNDS

I n t h e 3d c o r e p h o t o e m i s s i o n spectrum (3d-XPS) o f La m e t a l /4,5/, as shown i n t h e i n s e t o f F i g . 1 /5/, a weak s a t e l l i t e peak i s observed on t h e l o w e r b i n d i n g e n e r g y s i d e o f t h e main peak. The energy s e p a r a t i o n between t h e s a t e l l i t e and t h e main peak i s about 3.4 eV. The i n t e n s i t y o f t h e s a t e l l i t e becomes v e r y l a r g e i n some i n t e r m e t a l l i c La compounds, f o r i n s t a n c e i n LaPd /5/. The mechanism o f t h i s s a t e l l i t e was f i r s t p o i n t e d o u t b y Toyozawa and t d e p r e s e n t a u t h o r more t h a n t e n y e a r s ago /6,7,8/. As a model s i m u l a t i n g t h e La m e t a l , l e t us c o n s i d e r a system which c o n s i s t s o f a c o n d u c t i o n band, w e l l - l o c a l i z e d 4 f s t a t e s and c o r e s t a t e s , as shown i n F i g . 1. We t a k e account o f a h y b r i d i z a t i o n V between 4 f and c o n d u c t i o n e l e c t r o n s . I n t h e i n i t i a l s t a t e o f photoemission, t h e 4 f l e v e l E~~ i s w e l l above t h e Fermi l e v e l E so t h a t we have no 4 f e l e c t r o n occupied i n t h e 4 f l e v e l , c o r r e s p o n d i n g t o 4 f 0 ground s t a t e o f La. However, i n t h e f i n a l s t a t e o f photoemission, 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 ^EFdue t o t h e a t t r a c t i v e p o t e n t i a l o f t h e c o r e h o l e . Then, we expect t o have two c l a s s e s o f f i n a l s t a t e s , c o r r e s p o n d i n g t o two d i f f e r e n t c o n f i g u r a t i o n s o f 4 f s t a t e . I n one c l a s s , a c o n d u c t i o n e l e c t r o n near 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 (see

F

F i g . I ) , w h i l e i n t h e o t h e c l a s s l t h e 4 f l e v e l i s s t i l l empty even a f t e r b e i n g p u l l e d down below ^{E ~ .} The f o r m e r ( 4 f c o n f i g u r a t i ~ n ) ~ g i v e s r i s e t o t h e s a t e l l i t e peak o f t h e photoemission spectrum, w h i l e t h e l a t t e r ( 4 f c o n f i g u r a t i o n ) t h e main peak. I n t h e former, t h e c o r e h o l e charge i s screened b y t h e 4 f e l e c t r o n , so t h i s f i n a l s t a t e i s c a l l e d t h e w e l l - s c r e e n e d s t a t e , w h i l e t h e l a t t e r f i n a l s t a t e i s denoted b y t h e p o o r l y - s c r e e n e d s t a t e . I n LaPd

,

t h e i n t e n s i t y o f t h e s a t e l l i t e becomes l a r g e r , s i n c e t h e e f f e c t o f h y b r i d i z a t i o g V becomes l a r g e r due t o t h e e x i s t e n c e o f Pd 4d c o n d u c t i o n band.

A v e r y s i m i l a r s a t e l l i t e s t r u c t u r e i s a l s o o b s e r v e d i n t h e system c o n t a i n i n g t r i v a l e n t Ce /5,9/, such as y-Ce and CeAl

,

and i t can be e x p l a i n e d b y e s s e n t i a l l y t h e same mechanism as above. I n t h e t r i v g l e n t Ce, one 4 f e l e c t r o n i s a l r e a d y o c c u p i e d i n t h e

F i g . 1

-

Model o f o u r system d e s c r i b i n g t h e c o r e photoemission process i n La m e t a l . -mental d a t a o f 3d-XPS i n La and LaPd3 a r e shown i n t h e i n s e t .

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t r a n s f e r r e d f r o m t h e c o n d u ~ t i o n ~ b a n d i n t h e f i n a l s t a t e o f photoemission. Therefore, t h e s a f e l l i t e comes f r o m t h e 4 f w e l l - s c r e e n e d f i n a l s t a t e , w h i l e t h e main l i n e f r o m t h e 4 f p o o r l y - s c r e e n e d f i n a l s t a t e .

I 1 1

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MIXED VALENCE Ce COMPOUNDS

The 3d-XPS o f mixed v a l e n c e Ce compounds e x h i b i t s three-peak s t r u c t u r e ( a p a r t f r o m t h e s p i n o r b i t s p l i t t i n g ) . As an example, t h e 3d-XPS o f CePd3 i s shown i n t h e i n s e t o f F i g . 2 /5/. I n t h e ground s t a t e o f mixed v a l e n c e systems, t h e 4 f l e v e l ~ ~ 0 i s l o c a t e d c l o s e t o t h e Fermi l e v e l E ~ , S O t h a t t h e 4 f s t a t e h y b r i d i z e s w i t h t h e c o b d u c t i o n Iband and t h e ground s t a t e i s a quantum-mechanically mixed s t a t e between 4 f and 4 f c o n f i g u r a t i o n s . The occurrence o f t h r e e peaks i n 3d-XPS i s understood, a t l e a s t q u a l i t a t i v e l y , f r o m theOmechanism o f t h e s a t e l l i t e i n La and t r i v a l e n t Ce:

When we t a k e account o f t h e f f component o f t h e mixgd v a l e n c e ground s t a t e , we expect t o have w e l l - s c r e e n e d 4 f and p o o r l y - s c j e e n e d 4 f f i n a l s t a t e s , as i n t h e case o f La. Bu5, when we t a k e account o f t h e 4 f component, we e x p e c t t o have w e l l - screened 4 f and p o o r l y - s c r e e n e d 4 f 1 f i n a l s t a t e s , as i n t h e case o f t r i v a l e n t Ce.

T h ~ r e f o r y , combieing t h e two cases, we expect t o have t h r e e d i f f e r e n t c o n f i g u r a t i o n s , 4 f

,

4 f and 4 f

,

i n t h e f i n a l s t a t e , and t h e y g i v e r i s e t o t h e t h r e e peaks i n 3d- XPS.

As found f r o m t h e above mechanism, t h e s t u c t u r e o f 3d-XPS depends s e n s i t i v e l y on t h e h y b r i d i z a t i o n between 4 f and c o n d u c t i o n e l e c t r o n s b o t h i n t h e i n i t i a l and f i n a l s t a t e o f photoemission. T h i s means t h a t we can o b t a i n i m p o r t a n t i n f o r m a t i o n on t h e 4 f e l e c t r o n s t a t e b y a n a l y z i n g q u a n t i t a t i v e l y 3d-XPS data. Such a q u a n t i t a t i v e t h e o r e t i c a l a n a l y s i s was f i r s t made by Gunnarsson and SchSnhammer

/ l o /

w i t h t h e use o f t h e i m p u r i t y Anderson model. The f o l l o w i n g argument i n t h i s s e c t i o n i s based m a i n l y on t h e i r t h e o r y , w i t h some m i n o r m o d i f i c a t i o n . To make t h e model e x p l i c i t , we d e s c r i b e t h e H a m i l t o n i a n f o r 4 f and c o n d u c t i o n e l e c t r o n s . The H a m i l t o n i a n i s g i v e n b y

i n t h e i n i t i a l s t a t e o f photoemission, w h i l e i t i s changed i n t o

H = Ho

-

Ufc p f v a f v

+

^{( 2 )}

i n t h e f i n a l s t a t e . Here,

\

and

~~q

a r e e n e r g i e s o f t h e c o n d u c t i o n band and 4 f

F i g . 2

-

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 of CePd3.

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C9-872 JOURNAL DE PHYSIQUE

l e v e l , r e s p e c t i v e l y and a+ and a$v a r e e l e c t r o n c r e a t i o n o p e r a t o r s i n t h e s e s t a t e s , where t h e {ndex k d k x o t e s t h e energy l e v e l o f c o n d u c t i o n e l e c t r o n s (k = 1 1.

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 ^QNf). I n t e r a c t i o n s V, Uff and -U r e p r e s e n t , r e s p e c t i v e l y , t h e h y b r i d i z a t i o n between 4 f and c o n d u c t i o n band s t a t e s , f f h e Coulomb i n t e r a c t i o n between 4 f e l e c t r o n s and t h e c o r e h o l e p o t e n t i a l . I t i s c o n v e n i e n t t o c a l c u l a t e t h e p h o t o e m i s s i o n spectrum b y u s i n g t h e l/Nf expansion method (N b e i n g t h e degeneracy o f 4 f l e v e l ) . I n 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 Ho o r H, i t f s t o be n o t e d t h a t t h e c o u p l i n g among t h e s t a t e s A, B and C o f F i g . 3 occurs w i t h i n t h e l o w e s t o r d e r o f l / N f , b u t t h e c o u p l i n g o f t h e s e s t a t e s w i t h t h e o t h e r ones, D, E, F, e t c . , occurs o n l y as a h i g h e r o r d e r c o r r e c t i o n w i t h r e s p e c t t o 1/N S i n c e t h e v a l u e N i s l a r g e (we u s u a l l y t a k e Nf = 14), t h e l o w e s t o r d e r a p p r o x i & t i o n p r o v i d e s us Z i t h s u f f i c i e n t l y r e 1 ia b l e r e s u l t s . Once we d i a g o n a l i z e Ho and H, t h e c o r e p h o t o e m i s s i o n spectrum i s c a l c u l a t e d b y

where l g > i s t h e ground s t a t e o f H w i t h energy E

, Ir>

' s a r e e i g e n s t a t e s o f H w i t h e n e r g i e s E I s , E i s t h e b i n d i n g en?rgy, and

r

r e p p 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 g t i m e

gf

t h e c o r e h o l e , 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 . I n F i g . 2, we show 3d-XPS o f CePd c a l c u l a t e d w i t h 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 /11/. I n orde? t o reproduce t h e e x p e r i m e n t a l 3d-XPS, we used t h e f o l l o w i n g parameter values: V = 0.38, U = 8.3, U = 10.5, E O

-

cF = -2.0 and

r

⁼^{1.6 i n}

u n i t s o f eV. With t h e s e paramgfers, t h e a t g r a g e i f e l e l t r o n number nf i n t h e ground s t a t e i s e s t i m a t e d as nf = 0.86.

Gunnarsson and SchBnhammer /5,10/ performed s y s t e m a t i c a n a l y s i s o f 3d-XPS i n v a r i o u s Ce compounds, and r e v e a l e d t h a t t h e i n t e r m e t a l l i c Ce compounds w i t h Ni, Co,

.

Ru e t c . a r e i n t h e mixed v a l e n c e s t a t e ( w i t h f r a c t i o n a l v a l u e o f n ), a l t h o u g h t h e s e compounds were t r a d i t i o n a l l y c o n s i d e r e d t o be i n t h e t e t r a v a l e n t f t a t e ( w i t h nf = 0 ) .

F i g . 3

-

Schematic r e p r e s e n t a t i o n o f b a s i s s t a t e s used i n d i a g o n a l i z i n g t h e HamilTonian H o r H. The c o u p l i n g t h r o u g h V i s shown w i t h arrows. O n l y t h e s t a t e s A, 6 and C a r ? c o u p l e d w i t h i n t h e l o w e s t o r d e r o f l / N f expansion.

I V

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INSULATING COMPOUNDS

Much i n t e r e s t has r e c e n t l y been t a k e n i n t h e i n s u l a t i n g Ce compounds CeOZ.. CeO was t r a d i t i o n a l l y c o n s i d e r e d t o be t e t r a v a l e n t , b u t t h e 3d-XPS o f Ce02 e x h i b ~ t s Zhree-

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t o t h a t o f mixed v a l e n c e Ce i n t e r m e t a l l i c s . Even i n i n s u l a t i n g Ce compounds, i t can be shown t h a t i f t h e 4 f l e v e l E~ 0 i s l o c a t e d c l o s e t o t h e f i l l e d v a l e n c e band t h e ground s t a t e i s d e s c r i b e d by a m i x t u r e between 4 f and 4 f c o n f i g u r a t i o n s /14,15,16,17/. We can use H a m i l t o n i a n s ( 1 ) and ( 2 ) o n l y by r e g a r d i n g E as t h e f i l l e d v a l e n c e band o f oxygen 2p s t a t e s . I n t h i s case, V r e p r e s e n t s t h e c o v a l e n c y m i x i n g b e t w e ~ n 4 f anq v a l e n c e band s t a t e s . T h e r e f o r e , i f t h e ground s t a t e c o n t a i n s b o t h o f 4 f and 46 c o n f i g u r a t i o n f , i t i s p o s s i b l e t o have t h r e e d i f f e r e n t f i n a l c o n f i g u r a t i o n s , 4 f

,

4 f and 4 f

,

because a charge t r a n s f e r can o c c u r f r o m t h e valence band t o t h e 4 f s t a t e i n t h e f i n a l s t a t e . We show t h e c a l c u l a t e d 3d-XPS o f Ce02 i n F i g . 4 /11/, where t h e parameter v a l u e s a r e t a k e n as V = 0.76, U = 10.5,

= 12.4, cfO

-

^EO= 1.6 and l. = 1.0 i n u n i t s o f eV /11,17/ ( € 0 b e i n g t h g c e n t e r o f

:fig

v a l e n c e band)! I n t h i s c a l c u l a t i o n H a m i l t o n i a n s ( 1 ) and Y2) a r e d i a g o n a l i i e d n u m e r i c a l l y f o r a f i n i t e system where ek i s t a k e n as

w i t h k = 1, 2;..N. The band w i d t h W i s chosen as 3.0 eV, and t h e v a l u e o f 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 spectrum converges w e l l . From t h i s c a l c u l a t i o n t h e avera8e 4 f e l y c t r o n number i n t h e ground s t a t e o f CeO i s f o u n d t o be about 0.5, so t h a t 4 f and 4 f c o n f i g u r a t i o n s a r e f o u n d t o be mixed v g r y s t r o n g l y . Very r e c e n t l y , e x p e r i m e n t a l o b s e r v a t i o n o f 3d-XPS has been made f o r a n o t h e r

" n o m i n a l l y t e t r a v a l e n t " i n s u l a t i n g Ce compound CeF4 /18/. As shown i n t h e i n s e t o f F i g . 5, t h e 3d-XPS o f CeF has t h r e e peaks, whose energy spacings and r e l a t i v e i n t e n s i t i e s a r e somewhat d i f t e r e n t f r o m t h o s e o f CeO

.

T h e o r e t i c a l a n a l y s i s o f t h i s spectrum i s a l s o made by u s i n g t h e same model as ~ e 6 and b y somewhat m o d i f y i n g t h e parameter v a l u e s /19/. The r e s u l t i s shown i n F i g .

g,

where we used t h e parameters o f V = 0.76, Uff = 8.5, Ufc = 12.0, c f O - & O= 4.0, W = 3.0 and

r

⁼1.0 i n u n i t s o f eV. The background spectrum B ( E ) i s a l s o Kaken i n t o account, as p l o t t e d w i t h t h e dashed curve, where i t i s assumed f o be g i v e n b y

B ( E ~ ) = c

f

E~ F ~ ~ ~ ( E ~ ' )

aB'

(5) w i t h a c o n s t a n t C as an a d j u s t a b l e parameter. The agreement between t h e c a l c u l a t e d and observed s p e c t r a i s s a t i s f a c t o r y .

The most e s s e n t i a l d i f f e r e n c e i n t h e e s t i m a t e d parameter values between CeFq and Ce O2 i s t h a t t h e v a l u e o f ^EO

-

^EOin CeF4 i s much l a r g e r t h a n t h a t i n CeO

,

c o r r e s p o n d i n g t o l a r g e r e l e c f r o n e g $ t i v i t y o f t h e f l u o r i n e i o n . Compared w i t h t i e

F i g . 4

-

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 of Ce02.

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C9-874 JOURNAL DE _PHYSIQUE

case o f CeO

,

t h e r e f o r e , t h e h y b r i d i z a t i o n between 4 f and v a l e n c e band s t a t e s i n t h e ground s t a g e o f CeF becomes s m a l l e r , and t h e average 4 f e l e c t r o n number n i s e s t i m a t e d t o be about 8.29, which i s c o n s i d e r a b l y s m a l l e r t h a n t h a t o f CeO

. of

t h e t h r e e peaks o f 3d-XPS bott) i n CeF4 and CeO t h e h i g h e s t b i n d i n g en8rgy peak corresponds m a i n l y t o t h e 4 f f i n a l s t a t e l w2;le2the m i d d l e and t h e l o w e s t b i n d i n g energy peaks a r e mixed s t a t e s between 4 f and 4 f f i n a l s t a t e s . The f r a c t i o n a l i n t e n s i t y o f t h e h i g h e s t b i n d i n g energy peak i s l a r g e r i n CeF t h a n i n Ce02, which i s caused b y t h e l a r g e r w e i g h t 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 g80und s t a t e .

I n t h i s way, t h e c o r e photoemission g i v e s t h e i n f o r m a t i o n on t h e c o v a l e n c y m i x i n g between d i f f e r e n t 4 f c o n f i g u r a t i o n s i n i n s u l a t i n g compounds. The mechanism o f t h e s a t e l l i t e i s e s s e n t i a l l y t h e same between i n s u l a t i n g and m e t a l l i c systems. The c h a r a c t e r i s t i c f e a t u r e i n m e t a l l i c systems i s t h e e x i s t e n c e o f e l e c t r o n h o l e p a i r e x c i t a t i o n s i n t h e c o n d u c t i o n band, as shown i n D, E, F, e t c . i n F i g . 3, i n c o n t r a s t t h a t t h e y a r e absent i n i n s u l a t i n g systems. However, t h e c o n t r i b u t i o n o f t h e s e s t a t e s w i t h e l e c t r o n h o l e p a i r s (D, E, F, e t c . ) t o t h e photoemission s p e c t r a i s much s m a l l e r t h a n t h o s e w i t h no e l e c t r o n h o l e p a i r (A, B, C), as mentioned b e f o r e . T h e r e f o r e , when we r e g a r d t h e f i l l e d v a l e n c e band i n i n s u l a t i n g systems as t h e c o n d u c t i o n band below cF i n m e t a l l i c systems, t h e f o r m a l t h e o r e t i c a l procedure i n c a l c u l a t i n g 3d-XPS i s e s s e n t i a l l y t h e same between i n s u l a t i n g and m e t a l l i c systems.

The d i f f e r e n c e i n t h e s p e c t r a l f e a t u r e s i n d i f f e r e n t systems comes o n l y f r o m t h e d i f f e r e n c e i n t h e parameter v a l u e s i n c l u d e d i n t h e model system. I n t h i s sense, we can say t h a t CeO and CeF4 aye a l s o i n t h e "mixed v a l e n c e " s t a t e , and we cannot d i s t i n g u i s h betwee$ t h e m e t a l l ~ c mixed v a l e n c y and t h e i n s u l a t i n g c o v a l e n c y f r o m c o r e photoemission data.

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 s e t ) r e s u l t s o f t h e 3d-XPS o f CeF4.

V

-

RELATION BETWEEN 3d-XPS AND L2-XAS

I n t h e 2p c o r e p h o t o a b s o r p t i o n ( L -XAS) o f Ce compounds, a 2p e l e c t r o n i s e x c i t e d t o t h e Ce 5d c o n d u c t i o n band, a2 shown i n F i g . 6 f o r t h e case o f i n s u l a t i n g Ce compounds. Therefore, we have a c o r e h o l e l e f t b e h i n d i n t h e f i n a l s t a t e , and t h e c o r e h o l e p o t e n t i a l -U i s expected t o cause t h e f i n a l s t a t e i n t e r a c t i o n v e r y s i m i l a r t o t h a t o f 3 d - x p s f c A c c o r d i n g t o e x p e r i m e n t a l data, however, c h a r a c t e r i s t i c f e a t u r e s o f L3-XAS i n v a r i o u s Ce compounds a r e u s u a l l y d i f f e r e n t f r o m t h o s e o f 3d- XPS. The d i f f e r e n c e between 3d-XPS and L3-XAS i s observed most c l e a r l y i n i n s u l a t i n g Ce compounds CeO and CeF

.

The 3d-XPS o f t h e s e systems has t h r e e peaks as shown b e f o r e , whereas {he L - X A ~ has o n l y two peaks /13,18,20,21,22/. Experimental d a t a o f L -XAS i n CeF i s saown i n t h e i n s e t o f F i g . 7 /18/. The energy s e p a r a t i o n o f two peak2 i n L ~ - X A ? i s about 6 eV i n CeF4 and about 8 eV i n Ce02, whereas t h e energy

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SeB2 (see i n s e t s o f F i g s . 4 and 5). T h i s r e s u l t suggests t h a t 44 c o n f i g u r a t i o n s i n f i n a l s t a t e s of 3d-XPS and L -XAS a r e d i f f e r e n t . As an o r i g i n o f t h i s d i f f e r e n c e , two p o s s i b l e mechanisms cad be c o n s i d e r e d : ( i ) A d i f f e r e n c e i n t h e c o r e h o l e p o t e n t i a l -U between 2p and 3d c o r e h o l e s . ( i i ) The e x i s t e n c e o f a p h o t o e x c i t e d 5d e l e c t r o n i n f 6 e f i n a l s t a t e o f L ~ - X A S .

Jo and t h e p r e s e n t a u t h o r /11,23/ c o n s i d e r e d t h a t t h e p o i n t ( i i ) i s e s s e n t i a l l y i m p o r t a n t , and proposed a mechanism b y which t h e 3d-XPS and L -XAS i n CeO a r e e x p l a i n e d c o n s i s t e n t l y . A s i m i l a r c a l c u l a t i o n has a l s o been mads f o r CeF /197. I n t h e s e c a l c u l a t i o n s , t h e i n t e r a c t i o n U between t h e p h o t o - e x c i t e d 5d e l e c t 9 o n and t h e 4f e l e c t r o n , as w e l l as t h e a t t r a c t i t $ p o t e n t i a l -U o f t h e c o r e h o l e a c t i n g on t h e 5d e l e c t r o n , a r e t a k e n i n t o account, as shown i n

FQG.

^6. On t h e o t h e r hand, i t i s assumed t h a t t h e c o r e h o l e p o t e n t i a l -U a c t i n g on t h e 4 f e l e c t r o n i s t h e same f o r t h e 3d and 2p c o r e holes, w i t h d i s r e g a F S i n g t h e p o s s i b i l i t y ( i ) . The r o l e o f t h e p o t e n t i a l -U i s t o l o c a l i z e t h e 5d e l e c t r o n near t h e c o r e h o l e s i t e , and t h e n due t o t h e i n t d t i a c t i o n U t h e 4 f e l e c t r o n 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 o f L3-XAS become d i f f e r e n t fromff!hose o f 3d-XPS. As an example, we show i n F i g . 7 /19/ t h e r e s u l t o f L3-XAS o f CeF which i s c a l c u l a t e d b y u s i n g t h e parameter v a l u e s determined from t h e a n a l y 2 i s o f 3d-XPS and b y assuming t h e 5d band w i d t h o f 6.0 eV and

r

⁼2.5 eV. The v a l u e s o f U and Udc a r e changed as parameters. I t i s f o u n d t h a t when we use U = 4.0 eV 686 U = 5.0 eV t h e c a l c u l a t e d L3-XAS ( t h e s o l i d c u r v e ) i s i n good a g r & $ m e n t j w i t h t h e e x g g r i m e n t a l r e s u l t b o t h i n t h e energy s e p a r a t i o n and t h e r e l a t i v e i n t e n s i t y o f two peaks ( b y t a k i n g account o f t h e background as shown w i t h t h e dashed c u r v e i n t h e i n s e t o f F i g . 7 ) . On t h e o t h e r hand, when we d i s r e g a r d t h e e f f e c t o f U and U as shown b y t h e dashed curve, t h e L3-XAS i s a s i m p l e c o n v o l u t i o n o f

5d-XPS

d $ i h t h e d e n s i t y o f s t a t e s o f 5d band, and t h e o b t a i n e d spectrum i s q u i t e d i f f e r e n t f r o m t h e e x p e r i m e n t a l r e s u l t . The importance o f U and

-U

was a l s o c o n f i r m e d i n t h e a n a l y s i s o f L3-XAS i n Ce02 /11,22,23/ a i d i n i n & l a t i n g La compounds, La2O3 and LaF3 /24/.

On t h e p o s s i b i l i t y o f ( i ) , a t h e o r e t i c a l c a l c u l a t i o n b y H e r b s t and W i l k i n s /25/

i n d i c a t e s t h a t U o f 3d c o r e h o l e i n Ce m e t a l i s l a r g e r t h a n t h a t o f t h e 2p c o r e h o l e by 1.3 eV, b 6 f no c a l c u l a t i o n has been made f o r i n s u l a t i n g systems. A c c o r d i n g t o r e c e n t 3p c o r e s p e c t r o s c o p i e s i n Leo2, i t i s c o n f i r m e d t h a t t h e p o i n t ( i ) i s l e s s

F i g . 6

-

Model o f L3-XAS i n CeF4.

--

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C9-876 JOURNAL DE PHYSIQUE

i m p o r t a n t t h a n ( i i ) . The 3p-XAS of CeO observed b y K a i n d l e t a1

.

^/26/ i s v e r y s i m i l a r t o L3-XAS, a l t h o u g h t h e s p e c t r a l a i d t h i s l a r g e r . Furthermore, t h e 3p-XPS, which has v e r y r e c e n t l y been observed b y B i a n c o n i e t a l . /27/, can a l s o be reproduced f a i r l y w e l l from t h e 3d-XPS by i n c r e a s i n g t h e s p e c t r a l w i d t h and by adding a .background c o n t r i b u t i o n . T h e r e f o r e , we can conclude t h a t t h e v a l u e o f U i s almost t h e same f o r 2p, 3p, and 3d c o r e h o l e s . The d i f f e r e n c e i n t h e experime&al s p e c t r a between 3 p - x ~ S and 3p-XAS can be e x p l a i n e d o n l y b y t h e e f f e c t o f U and -U A l t h o u g h t h e r e remains a p o s s i b i l i t y o f t h e d i f f e r e n c e i n U between

5$

and 3d

f8r

2p) c o r e h o l e s by about 1 eV due t o t h e e x p e r i m e n t a l u n c e r t a f k t y , t h e 1 eV d i f f e r e n c e i n Ufc i s t o o s m a l l t o e x p l a i n t h e d i f f e r e n c e between 3 d ( o r 3p)-XPS and 2 p ( o r 3p)- XAS

.

I n mixed v a l e n c e Ce i n t e r m e t a l l i c s , L -XAS has a l s o two peaks /13,20,21/, b u t t h e d i f f e r e n c e between 3d-XPS and L -XAS i$ n o t so remarkable as t h a t i n Ce02 and CeF4.

A p r e l i m i n a r y a n a l y s i s o f L

AS

i n CePd3 /11,28/ suggests t h e importance o f t h e e f f e c t o f U and -U b u t ghe v a l u e s o f U and U seem t o be much s m a l l e r t h a n t h o s e o f i n f i l a t i n g &'compounds. More d e t z f l e d i n d g s t i g a t i o n s w i l l be needed i n a n a l y z i n g L3-XAS o f m e t a l l i c mixed v a l e n c e compounds.

V I

-

CONCLUDING REMARKS

We have d i s c u s s e d many body e f f e c t s i n c o r e l e v e l photoemission i n s o l i d s c o n t a i n i n g i n c o m p l e t e l y f i l l e d 4f s t a t e s . I t i s shown t h a t t h e a n a l y s i s o f 3d-XPS w i t h t h e i m p u r i t y Anderson model p r o v i d e s us w i t h i m p o r t a n t i n f o r m a t i o n on t h e 4 f s t a t e . I n a d d i t i o n t o t h e m a t e r i a l s t r e a t e d i n t h i s paper, t h e o r e t i c a l and/or e x p e r i m e n t a l s t u d i e s have been made f o r Ce 03, Pro

,

Tb02 and so on /29,30/. I t i s t o be mentioned t h a t t h e i m p u r i t y ~ n 2 e r s o n mogel has a l s o been used s u c c e s s f u l l y i n t h e a n a l y s i s o f c o r e l e v e l photoemission o f t r a n s i t i o n m e t a l compounds /31/.

The a u t h o r would l i k e t o express h i s t h a n k s t o P r o f . T. Jo, P r o f . A. Bianconi, Dr. J.C Parlebas, Dr. A. M a r c e l l i , Dr. K. Okada, Dr. T. Nakano, and Mr. M. Okada f o r v a l u a b l e d i s c u s s i o n and f r u i t f u l c o l l a b o r a t i o n . T h i s work i s p a r t l y s u p p o r t e d b y The K u r a t a Research Grant, t h e France-Japan C o l l a b o r a t i o n P r o j e c t on Magnetism, and 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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