TWO-PHOTON INDUCED VIBRONIC SPECTRA OF LANTHANIDE(III) OCTAHEDRAL COMPOUNDS

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TWO-PHOTON INDUCED VIBRONIC SPECTRA OF LANTHANIDE(III) OCTAHEDRAL COMPOUNDS

J. Sztucki, W. Strek

To cite this version:

J. Sztucki, W. Strek. TWO-PHOTON INDUCED VIBRONIC SPECTRA OF LANTHANIDE(III) OCTAHEDRAL COMPOUNDS. Journal de Physique Colloques, 1987, 48 (C7), pp.C7-479-C7-481.

�10.1051/jphyscol:19877114�. �jpa-00226931�

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JOURNAL DE PHYSIQUE

Colloque C7, s u p p l h e n t au n 0 1 2 , Tome 48, dgcembre 1987

TWO-PHOTON INDUCED VIBRONIC SPECTRA OF LANTHANIDE(II1) OCTAHEDRAL COMPOUNDS

J. SZTUCKI and W. STREK

I n s t i t u t e

f o r

Low Temperature and S t r u c t u r e R e s e a r c h , P o l i s h Academy of S c i e n c e s , P.O. Box 937, PL-53529 Wroclaw, P o l a n d

A b s t r a c t .

The e x p r e s s i o n s for two-photon induced v i b r o n i c t r a n s i t i o n i n o c t a - h e d r a l systems a r e d e r i v e d w i t h i n t h e i n d e p e n d e n t s y s t e m s model.

The s e l e c t i o n s r u l e s a r e d i s c u s s e d .

I n t r o d u c t i o n

R e c e n t l y a g r e a t i n t e r e s t was concerned w i t h two-photon s p e c t r o - scopy of l a n t h a n i d e (111) systems [I -3 1. The experiments were performed on t h e noncentrosymmetric systems. McClure e t a l . [ 4 ] have r e p o r t e d i n a number of p a p e r s t h e v i b r o n i c s p e c t r a of t h e t r a n s i t i o n m e t a l o c t a - h e d r a l compounds.

I n t h i s p a p e r we a t t e m p t t h e problem o f v i b r o n i c t r a n s i t i o n s induced by two-photon e x c i t a t i o n i n l a n t h a n i d e (111) o c t a h e d r a l compounds.

Two mechanisms of t h e electron-phonon c o u p l i n g a r e d i s c u s s e d . The s t a t - i c and t h e dynamic p o t e n t i a l s produced by t h e l i g a n d s a r e changed due t o t h e v i b r a t i o n s o f complex which i n t u r n c a n i n f l u e n c e t h e e l e c t r o n - i c t r a n s i t i o n s . The v i b r o n i c s e l e c t i o n r u l e s coming from both mechanisms a r e p r e s e n t e d

.

Theory

The p o i n t c h a r g e s on l i g a n d s produce t h e s t a t i c p o t e n t i a l

where D ( t ) a r e t h e m e t a l i o n m u l t i p o l e o p e r a t o r s and T ( t ) i s d e f i n e d

M L

by

The dynamic p o t e n t i a l i s provided by t h e d i p o l e moments induced on l i g a n d s by t h e r a d i a t i o n f i e l d

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19877114

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C7-480 JOURNAL DE PHYSIQUE

Here

2

i s t h e l i g h t p o l a r i z a t i o n v e c t o r and aL i s t h e l i g a n d p o l a r i z - a b i l i t y t e n s o r .

Both p o t e n t i a l s c a n b e expended i n normal c o o r d i n a t e s around t h e e q u i l i b r i u m p o s i t i o n Qo :

where Vr a r e e q u a l t o t h e d e r i v a t i v e s

- av

t a k e n a t Qo and I a r e t h e i r r e p i n d e x e s d e f i n i n g t h e symmetry p r o p e r t i e s of t h e normal c o o r d i - aQr

n a t e s . O p e r a t o r s Qr a r e r e s p o n s i b l e f o r t h e v i b r a t i o n a l t r a n s i t i o n s w h i l e t h e expansion c o e f f i c i e n t s Vr a c t between t h e e l e c t r o n i c s t a t e s . Consequently t h e t e r m

r e s u l t s i n v i b r o n i c t r a n s i t i o n s . I n two-photon c a s e t h e s e t r a n s i t i o n s a r e d e s c r i b e d i n t h e l o w e s t o r d e r of t h e p e r t u r b a t i o n t h e o r y by two terms ^:

r

<slt.i3\n><nlv:ib jm><mlt.dlf> E - I E

-

I

ng mg ( 6 )

n ,m

Using t h e w e l l developed methods o f o n e and two-photon t h e o r e t i c a l s p e c t r o s c o p y of t h e l a n t h a n i d e systems 151 we g e t from ( 6 ) and ( 7 ) t h e f o l l o w i n g f i n a l e x p r e s s i o n s

even

where t h e f i e l d - p o l a r i z a t i o n t e n s o r F ( ~ ) i s d e f i n e d by

aF

.

The i n i t i a l and f i n a l s t a t e s < ~ a

I

and

I

a r e o h a r -

and F;

= -

a

Qr

a c t e r i z e d by t h e t o t a l a n g u l a r momenta J 1 J 1 and t h e i r r e p l a b e l s alf3

.

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The v i b r o n i c i n t e g r a l <Q

r

> f o r one-phonon t r a n s i t i o n w i t h i n t h e harmo- n i c a p p r o x i m a t i o n i s e q u a l t o

[

^4n: ^where^{d r} ^{i s}t h e c i r c u l a r f r e - quency of t h e r t h normal mode.

When t h e i n v e s t i g a t e d complex i s of o c t a h e d r a l symmetry o r , more g e n e r - a l , it i s a c e n t r o s y m m e t r i c s y s t e m t h e e l e c t r o n i c s t a t e s h a v e t h e d e - f i n i t e p a r i t y . S i n c e w e c o n s i d e r t h e f - f t r a n s i t i o n s t h e ground and f i n a l s t a t e s a r e o f t h e same p a r i t y and, c o n s e q u e n t l y , U'') must b e even. Moreover an o p e r a t o r

[

( E ( I ) 6 " ) ) (m) T;' ( k ) -

1")

^{h a s}^{t o}t r a n s £ orm i n t h e same way a s

u ' ' )

b e c a u s e t h e y form a s c a l a r . The t e n s o r p r o d u c t

( E " ) E ( ' ) ) (m) of t h e t r u e v e c t o r s

2

i s o f e v e n p a r i t y ( 6 ) , h e n c e t h e T i ( k ) must a l s o be symmetric u n d e r t h e i n v e r s i o n . F i n a l l y , s i n c e t h e . T+ o p e r a t o r t r a n s f o r m s u n d e r t h e same r e p r e s e n t a t i o n a s Q r o n l y t h e even modes c a n c o n t r i b u t e t o t h e two-photon v i b r o n i c t r a n s i t i o n s . S i m i l a r d i s c u s s i o n c a n b e c a r r i e d o v e r f o r t h e dynamic mechanism

(Ff o p e r a t o r s )

.

Ref e r e n c es

1. M.C. Dowher and A. B i v a s , P h y s . Rev. B g (1983) 3 6 7 7 . 2. P . C . Becker e t a l . , Phys. Rev. B g (1985) 81 02.

3 . B.R. Judd and J . P o o l e r , J . Phys. C x (1982) 591.

4. D.S. McClure, A c t a Phys. P o l o n . A= (1 987) 787 (see r e f e r e n c e s t h e r e i n )

.

5. J. S z t u c k i and W. S t r e k , Phys. Rev. B e (1986) 3120.

6.

J.

Jerphagnon, D . Chemla and R. B o n n e v i l l e , Adv. Phys.

27 (1978) 609.

-