Study of the T⊗t Jahn-Teller effect: ESR of Ag2+ in the alkaline earth fluorides

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Reference

Study of the T⊗t Jahn-Teller effect: ESR of Ag2+ in the alkaline earth fluorides

BILL, Hans, LOVY, Dominique, HAGEMANN, Hans-Rudolf

Abstract

ESR results are reported on the Ag2+ ion introduced into alkaline earth fluoride crystals. In SrF2 (as in CaF2) a trigonal centre is present which tunnels between four equivalent C3 directions as shown by ESR under uniaxial stress. A T2g ⊗ t2g Jahn-Teller model describes adequately the paramagnetic and stress effects when the strong coupling case is considered.

Ag2+ in BaF2 forms a static tetragonal cluster similar to Ag2+ and Cu2+ in SrCl2.

BILL, Hans, LOVY, Dominique, HAGEMANN, Hans-Rudolf. Study of the T⊗t Jahn-Teller effect:

ESR of Ag2+ in the alkaline earth fluorides. Solid State Communications , 1989, vol. 70, no.

5, p. 511-516

DOI : 10.1016/0038-1098(89)90941-1

Available at:

http://archive-ouverte.unige.ch/unige:3072

Disclaimer: layout of this document may differ from the published version.

1 / 1

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Printed in Great Britain. Pergamon press plc

S T U D Y O F T H E T ~ t J A H N - T E L L E R E F F E C T : E S R O F A g 2+ IN T H E A L K A L I N E E A R T H F L U O R I D E S

H. Bill, D. L o v y a n d H. H a g e m a n n

30,

Dept. of P h y s i c a l C h e m i s t r y S c i e n c e s II, U n i v . o f G e n e v a ,

q u a i E r n e s t - A n s e r m e t , 1211 G e n e v a 4 S w i t z e r l a n d ( R e c e i v e d J a n u a r y 31, 1989 b y R. H. Silsbee)

E S R r e s u l t s a r e r e p o r t e d on t h e A g 2+ ion i n t r o d u c e d into a l k a l i n e e a r t h f l u o r i d e c r y s t a l s . In S r F 2 (as in CaF2) a t r i g o n a l c e n t r e is p r e s e n t w h i c h t u n n e l s b e t w e e n f o u r e q u i v a l e n t C 3 d i r e c t i o n s as s h o w n b y E S R u n d e r u n i a x i a l s t r e s s . A T 2 a ~ t 2 a J a h n - T e l l e r m o d e l d e s c r i b e s a d e q u a t e l y t h e ~ a r a m a g n ~ t i c a n d s t r e s s e f f e c t s w h e n t h e s t r o n g c o u p l i n g c a s e is c o n s i d e r e d . A g 2+ in B a F 2 f o r m s a s t a t i c t e t r a g o n a l c l u s t e r s i m i l a r to A g 2+ a n d C u 2 + i n S r C I 2 •

C o m p a r a t i v e l y f e w e x p e r i m e n t a l E S R s t u d i e s h a v e b e e n p u b l i s h e d o n J a h n - T e l l e r ( J T ) - s y s t e m s w h i c h i n v o l v e a T 2 a ~ t 2 a s i t u a t i o n . L o o k i n g f o r p o ~ s i b l e ~ c a n d i d a t e s w e r e v i s i t e d t h e l o n g - s t a n d i n g p r o b l e m t o i n t r o d u c e s i l v e r a n d c o p p e r i n t o t h e a l k a l i n e e a r t h f l u o r i d e s . It t u r n s o u t t h a t t h e y e n t e r i n t o t h e l a t t i c e w h e n o x y g e n is a b s e n t d u r i n g c r y s t a l g r o w t h . T h i s l e t t e r r e p o r t s E S R r e s u l t s i n c l u d i n g u n i a x i a l s t r e s s m e a s u r e m e n t s o n t h e s e c r y s t a l s .

C r y s t a l s w e r e o b t a i n e d u n d e r v e r y h i g h p u r i t y c o n d i t i o n s in a B r i d g m a n f u r n a c e . N o m i n a l d o p i n g c o n c e n t r a t i o n s w e r e 0.3 to 1 m o l e % of AgF. M u c h of t h e s i l v e r f l u o r i d e d e c o m p o s e s d u r i n g g r o w t h . F u r t h e r , t h e d i s t r i b u t i o n o f t h e A g ions in t h e a s - g r o w n c r y s t a l s w a s n o t h o m o g e n e o u s . S a m p l e s w e r e c l e a v e d o f f o r c u t w i t h a s t r i n g saw.

T h e y a r e c o l o u r l e s s a n d t r a n s p a r e n t a n d t h e i r a b s o r p t i o n s p e c t r u m p r e s e n t s t w o b a n d s in t h e UV. A t a n d a b o v e 4 . 2 K n o E S R s i g n a l r e l a t e d t o s i l v e r w a s o b s e r v e d . A f t e r e x p o s i n g t h e m to X- rays, f o r t y p i c a l l y 1 h (40 k V / 3 5 mA, r o o m t e m p e r a t u r e ) , a l l o f t h e s a m p l e s b e c a m e y e l l o w - b r o w n i s h . T h e o p t i c a l a b s o r p t i o n s p e c t r u m s h o w s s t r o n g n e w a b s o r p t i o n b a n d s in t h e v i s i b l e a n d n e a r U V . A t t h e s a m e t i m e a s t r o n g E S R s p e c t r u m is o b s e r v e d . W e a s s i g n it t o A g 2+ as w i l l b e s h o w n b e l o w . T h e

s p e c t r a o b s e r v e d in S r F 2 a n d C a F 2 a r e v e r y d i f f e r e n t f r o m t h o s e in B a F 2 a n d w e w i l l t r e a t e a c h c a s e in turn.

SrF2 : Ag2_~ +

T h e s e c r y s t a l s e x h i b i t a t 4 . 2 K a s t r o n g a n d a n i s o t r o p i c s p e c t r u m . I t s

a n g u l a r d e p e n d e n c e w a s i n v e s t i g a t e d as a f u n c t i o n of t h e o r i e n t a t i o n of t h e m a g n e t i c field. T h e s p e c t r a o b s e r v e d w i t h B a l o n g C4, C 3 a n d

C2

r e s p e c t i v e l y , a r e s h o w n i n ' F i g , i.

T h e i r s t r u c t u r e a n d t h e i n t e n s i t y d i s t r i b u t i o n of t h e c o m p o n e n t s a r e w e l l e x p l a i n e d b y a s s u m i n g a s p i n S = 1/2, w i t h an a s s o c i a t e d g - t e n s o r o r i e n t e d a l o n g a b o d y d i a g o n a l of t h e h o s t u n i t cell, w h i c h i n t e r a c t s s t r o n g l y w i t h t w o a l w a y s e q u i v a l e n t F- i o n s a n d l e s s w i t h s i x f l u o r i n e n u c l e i . T h e s e l a t t e r o n e s p r o d u c e m u t u a l l y e q u i v a l e n t s p l i t t i n g w h e n t h e m a g n e t i c f i e l d is p a r a l l e l to t h e p r i n c i p a l a x i s of g. In a d d i t i o n , S i n t e r a c t s w i t h o n e n u c l e a r s p i n I = 1/2 (the s i l v e r n u c l e u s ; tw°l~°t°peSul e x i s t

~ w e r e n o t r e s o l v e d : A g : 51.82%,

~ V = A g : 48.18%, b o t h I = 1/2). T h e o b s e r v e d l i n e s a r e s y m m e t r i c a l , of G a u s s i a n s h a p e w i t h a t y p i c a l w i d t h B D p ~ 2.6 Gauss. T h e r e l a x a t i o n t i m e s oT t h e c e n t r e a r e c o m p a r a t i v e l y s h o r t as t h e E S R s p e c t r u m b r o a d e n s a n d d i s a p p e a r s b e t w e e n 9 a n d 18 K. A b o v e 1 8 K no s i g n a l r e l a t e d to s i l v e r c o u l d be found.

T h e c e n t r e h ~ D 3 d s y m m e t r y . It c o n s i s t s of an A g lon s u b s t i t u t i n g f o r a h o s t c a t i o n in a c u b e f o r m e d b y e i g h t F- ions. T h i s s t r u c t u r e is t r i g o n a l l y d e f o r m e d in t h e s e n s e t h a t t w o o p p o s i n g f l u o r i n e i o n s on a b o d y d i a g o n a l a p p r o a c h t h e s i l v e r ion w h e r e a s t h e s i x o t h e r s s e e m to r e c e d e . T h e t w o f o r m e r o n e s h a v e e a c h l o c a l s y m m e t r y C 3 v (axial s h f tensor) a n d t h e l a t t e r o n e s h a v e C_ l o c a l s y m m e t r y _{• ~ • • "}

A t r l g o n a l s p l n H a m l l t o n l a n w a s u s e d to p a r a m e t r i z e t h e E S R s p e c t r a . A p r e l i m i n a r y f i r s t o r d e r a n a l y s i s y i e l d e d t h e a p p r o x i m a t e s t a r t i n g 511

512 STUDY OF THE ~ t JAHN-TELLER EFFECT vol. 70, No. 5

Fig.

~

B / / C 3

~

l I

2 5 0 0 3 0 0 0

M a g n e t i c F i e l d [G]

3500 i

i. E S R s p e c t r a of A g 2+ in S r F 2 o b s e r v e d w i t h B as noted. T = 4.2 K. M i c r o w a v e f r e q u e n c y : 9 . 1 0 1 G H z (C2,C4), 9 . 1 9 5 SHz (C3).

p a r a m e t e r s for o u r c o m p u t e r p r o g r a m s w h i c h a l l o w a c o m p l e t e s e c o n d o r d e r a n a l y s i s w i t h g r a p h i c a l r e p r e s e n t a t i o n o f t h e r e s u l t s . T h e p a r a m e t e r s t h u s o b t a i n e d a r e g i v e n in t h e T a b l e . Yet, t h e e x p e r i m e n t a l r e s u l t s a r e a l s o c o m p a t i b l e w i t h an A g 2+ i o n

s u b s t i t u t i n g for a f l u o r i n e i o n a n d b e i n g a s s o c i a t e d w i t h t w o F- ions, o n e i n t e r s t i t i a l a n d t h e o t h e r o n e b e i n g l o c a t e d on a S r c a t i o n site. It c a n a l s o b e v i e w e d as a A g F 2 m o l e c u l e i m b e d d e d i n t o t h e c r y s t a l .

C a F 2 : A g 2+ p r e s e n t s t h e s a m ~ s y m m e t r y p r o p e r t i e s as S r F 2 : A g 2+. I n t h e c o u r s e of t h i s w o r k w e b e c a m e a w a r e o f r e f [i] w h e r e E S R o f A g 2 + in C a F 2 a n d C d F 2 is r e p o r t e d . T h e s e d a t a a r e c o n s i s t e n t w i t h o u r r e s u l t s .

In o r d e r t o d e c i d e b e t w e e n t h e p o s s i b l e i n t e r p r e t a t i o n s w e p e r f o r m e d E S R u n d e r u n i a x i a l s t r e s s a p p l i e d t o t h e sample. B o t h c e n t r e s , C a F , : A g 2+ a n d S r F 2 : A g 2+ , d o n o t s h o w a n y e f f e c t w h e n s t r e s s is a p p l i e d a l o n g a [001] c r y s t a l axis. I m p o r t a n t m o d i f i c a t i o n s a r e seen, h o w e v e r , w h e n s t r e s s a l o n g [iii] is used. S t r o n g a n d f u l l y r e v e r s i b l e r e p o p u l a t i o n is f o u n d s u c h t h a t t h e t r i g o n a l a x i s of t h e c e n t r e is

p r e f e r e n t i a l l y o r i e n t e d p a r a l l e l t o t h e a p p l i e d s t r e s s . F i g u r e 2 s h o w s r e s u l t s f o r b o t h h o s t s o b t a i n e d u n d e r t h e g e o m e t r y e x p l a i n e d in t h e f i g u r e c a p t i o n .

In v i e w o f t h e s e f a c t s t h e

g e o m e t r i c a l s t r u c t u r e s h o w n in Fig. 3a is p r o p o s e d f o r S r F 2 : A g 2+ a n d

C a F 2 : A g 2+.

B a F 2 : A g 2+.

A s p e c t r u m is o b s e r v e d ( a m o n g w e a k e r ones) w h i c h i n v o l v e s a s p i n S = 1/2 i n t e r a c t i n g w i t h s e v e r a l F- n e i g h b o u r s a n d o n e s i l v e r n u c l e u s . B u t t h e s y m m e t r y of t h e g - t e n s o r is

t e t r a a o n a l . Fig. 4 p r e s e n t s E S R s p e c t r a r e c o r d e d w i t h B p a r a l l e l to a C4, C3, C 2 axis, r e s p e c t i v e l y . T h e d e t a i l e d a n a l y s i s of t h e a n g u l a r d e p e n d e n c e d i s c l o s e s a C 4 v s y m m e t r y of t h e p a r a m a g n e t i c c l u s t e r . R e s o l v e d h y p e r f i n e i n t e r a c t i o n w i t h t h e A g n u c l e u s ( t e t r a g o n a l s y m m e t r y ) a n d w i t h t w o s e t s of F- n e i g h b o u r s , e a c h

c o n t a i n i n g f o u r e q u i v a l e n t ions, is o b s e r v e d . E a c h of t h e s e l a t t e r n u c l e i h a s C s s y m m e t r y . T h e p a r a m e t r i z a t i o n p r o c e d u r e w h i c h is s i m i l a r t o t h e o n e d e s c r i b e d a b o v e (but u s i n g t h e

a p p r o p r i a t e s p i n H a m i l t o n i a n ) y i e l d e d t h e c o n s t a n t s g i v e n in t h e T a b l e , w h e r e a s Fig. 3b s h o w s t h e s t r u c t u r e of t h e c e n t r e w e p r o p o s e a n d d e f i n e s t h e o r i e n t a t i o n s of t h e t e n s o r s .

T h i s p a r a m a g n e t i c c e n t r e e x h i b i t s m u c h l o n g e r r e l a x a t i o n t i m e s t h a n S r F 2 : A g 2+ as its E S R s i g n a l s a r e o b s e r v e d at a n d a b o v e 78K. A t 4 . 2 K t h e y s a t u r a t e h e a v y l y e v e n at 10 -5 W a t t n o m i n a l m i c r o w a v e p o w e r . N o e f f e c t s d u e t o a p p l i e d s t r e s s w e r e o b s e r v e d on t h i s s y s t e m . A n E N D O R s t u d y is p l a n n e d .

T h e s t r u c t u r e of t h i s c e n t r e is

2+ 2+

s i m i l a r t o t h e A g a n d t h e C u in S r C I 2 [2,3] w h i c h e q u a l l y d i d n o t s h o w a n y s t r e s s e f f e c t s .

Vol. 70, No. 5 STUDY OF THE ~ JAHN-TELLER EFFECT T a b l e : E S R p a r a m e t e r s of t h e A g 2+ c e n t e r s .

513

h o s t

S r F 2 gll = 1 . 9 2 0 1 (5) A g n u c l e u s g ~ = 2 . 5 8 2 5 (8) All = 20.7 (3)

A 1 = 23,2 (3)

F1, F 2 All = 697.3 (259.2 G) A l = 24.78 ( 6 . 8 5 G )

F 3 - F 8 A l l = 41.3 A22 = 28.9 A33 = 86.2

; = 28 °

B a F 2 g| = 2 . 4 5 9 2 (8) A g n u c l e u s

gl = 2 . 0 8 3 6 (i0) A u = 98(3)

A 1 = 78(3)

s u p e r h y p e r f i n e s t r u c t u r e

S e t 1 S e t 2

A l l = 77 (8) A l l = 20(3)

A 2 2 = 102 (8) A22 = 20(3)

A33 = 648 (5) A33 = 5(2)

I ' = 7 0 ( 1 . 2 ) ~"= 520(3)

h f a n d s h f const, in [MHz]

D i s c u s s i o n .

Ag~$~ S r F 2 : A g 2+. T h e g r o u n d s t a t e of in c u b i c c o o r d i n a t i o n

t r a n s f o r m s as T 2 g a n d is t h u s J T - actif. W i t h i n t h e w e a k c o v a l e n c y

a p p r o x i m a t i o n t h e o r b i t a l p a r t c o n s i s t s e s s e n t i a l l y of (4dvz , 4 d ~ x , 4 d x v ) T h e e x p e r i m e n t s i n d i c a t ~ t h a £ - t h e

e l e c t r o n i c t r i p l e t c o u p l e s w i t h t r i g o n a l v i b r a t i o n s . W i t h i n a ( A g F 8 ) - c l u s t e r m o d e l t h e r e a r e t w o l o c a l v i b r a t i o n s t r a n s f o r m i n g as t2_. A g a i n t h e e x p e r i m e n t a l r e s u l t s t e n d t o s h o w t h a t t h e d o m i n a n t l y r a d i a l o n e (Fig. 1 f of [3]) is i m p o r t a n t . Thus, w e c a n

a p p l y the (cubic) T 2 u ~ t 2 u m o d e l [4]

t o t h i s centre. T h e f o u r a d i a b a t i c J T - p o t e n t i a l m i n i m a in t h e t h r e e -

d i m e n s i o n a l v i b r a t i o n a l s p a c e a r e d e e p e n o u g h (and e q u i v a l e n t w i t h i n o u r e x p e r i m e n t a l findings) to p r o d u c e a p s e u d o s t a t i c J T e f f e c t as i n d i c a t e d b y t h e f a c t t h a t t h e c e n t r e r e o r i e n t s , b u t h a s c o n v e n t i o n a l l i n e s h a p e s a n d

t r i g o n a l s y m m e t r y . It is t h e r e f o r e a p p r o p r i a t e to t r a n s f o r m f r o m t h e v i b r o n i c (Tlu + Au) q u a d r u p l e t s t a t e to e i g e n s t a t e s I o c a t ~ d in e a c h of t h e wells. Then, t h e t h e o r y of t h e g t e n s o r d e v e l o p p e d in [5] is a p p r o p r i a t e a f t e r

STUDY OF THE ]~t JAHN-TELLER EFFECT T = 4 . 2 K

&

f- .J

/

/ / +

(b)

I I

0 i. I I. E 7 2. EP 3. £ P

P [Ps]

Vol. 70, No. 5

Fig. 2. E f f e c t o f u n i a x i a l s t r e s s a p p l i e d a l o n g a [iii]

a x i s o f

(a) C a F 2 : A g 2+

(b) S r F 2 : A g 2+

a n d o b s e r v e d o n t h e E S R s p e c t r u m w i t h B il [~[2].

ni~ = i n t e n s i t y o f t h e s p e c t r a l c o m p o n e n t s a s s o c i a t e d w i t h pi IC3 a n d n 7 0 . 7 = s a m e q u a n t i t y b u t w i t h p a l o n g o n e o f t h e t h r e e o t h e r C 3 a x e s . T h e r a t i o ( s l o p e ( b ) ) / ( s l o p e (a)) = 1 . 4 7 ( 9 ) . T h e e x p e r i m e n t a l e n e r g y p e r u n i t s t r e s s (AEI) f o r t h i s g e o m e t r y is

C a F 2 A E 1 = 2 . 6 2 10 -6 [ c m - i / p a ] 5 . 2 0 4 10 - 2 9 [J/Pa]

S r F 2 A E 1 = 3 . 8 5 10 -6 [ c m - i / p a ] 7 . 6 5 10 - 2 9 [J/Pa]

W i t h : A E 1 = K_~ in (n,,/n70.7) P

a f e w m i n o r m o d i f i c a t i o n s ( u n d e r p r o g r e s s ) . T h e s t r o n g l y n e g a t i v e v a l u e

git

T h e f a c t t h a t n o m o t i o n a l l y

a v e r a g e d s p e c t r u m w a s f o u n d is p r o b a b l y d u e t o t h e ( s t r o n g l y q u e n c h e d ) s p i n -

o r b i t c o u p l i n g b e i n g i m p o r t a n t in t h e r e o r i e n t a t i o n p r o c e s s b e t w e e n t h e d i f f e r e n t p o t e n t i a l s h e e t s [6]. A s a r e s u l t t h e s p a t i a l r e o r i e n t a t i o n

p r o d u c e s i m p o r t a n t c o n t r i b u t i o n s t o t h e s p i n r e l a x a t i o n [7].

v o l . 7 0 , N o . 5 STUDY OF THE ~ t JAHN-TELLER EFFECT

a) b)

i 2

515

Fig. 3. a) G e o m e t r i c a l m o d e l of A g 2+ in S r F 2.

T h e A g 2+ i o n is at t h e c e n t e r o f t h e cube.

FI, 2 a r e t h e a x i a l f l u o r i n e ions. T h e s h f t e n s o r a x e s of F 3 a r e shown. T h e o t h e r s a r e o b t a i n e d b y a p p l y i n g t r a n s f o r m a t i o n s {R}~D3d.

b) S t r u c t u r e o f A g 2+ in B a F 2. T h e A g 2+ a p p r o a c h e s t h e b a s e p l a n e . T h e s h f t e n s o r a x e s of o n e f l u o r i n e i o n o f e a c h s e t a r e shown. T h e a x e s l a b e l e d 1 a n d 3, r e s p e c t i v e l y , a r e l o c a t e d in t h e v e r t i c a l d i a g o n a l p l a n e .

i i

2500 3O00 3~00

Magnetic ]Field [G]

Fig. 4. E S R s p e c t r a of A g 2+ in B a F 2. B o r i e n t e d as n o t e d . M i c r o w a v e f r e q u e n c y : 9 . 2 5 8 GHz.

516

B. T h e s i l v e r c e n t e r in B a F 2 :its s t r u c t u r e is r e m a r k a b l y d i f f e r e n t f r o m t h e o n e s o b s e r v e d in S r F 2 a n d C a F 2. It f o r m s an a l m o s t f l a t q u a d r a t i c p y r a m i d w i t h t h e s i l v e r i o n b e i n g l o c a t e d a t t h e apex. C h o o s i n g a x e s p a r a l l e l t o t h e f o u r f o l d c r y s t a l a x e s o n e h a s

e s s e n t i a l l y a 4d x. o r b i t a l of t h e m a g n e t i c e l e c t r o n [ T h e w e l l - k n o w n r e l a t i o n t h a t gll - 2 . 0 0 2 3 > g m - 2 . 0 0 2 3 c o m p l i e s 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 s . It is p o s s i b l e t h a t t h e d i f f e r e n t b e h a v i o u r is d u e t o t h e l a r g e r u n i t cell, a n d t h e s m a l l e r i o n i c r a d i u s o f

STUDY OF THE ~ c JAHN-TELLER EFFECT Vol. 70, No. 5

A g 2+ as c o m p a r e d to Ba 2+, r e s u l t i n g in a m u c h s m a l l e r t r i g o n a l J T c o u p l i n g c o n s t a n t (the t e t r a g o n a l o n e is a n y h o w small), w h i c h l e a d s to an " a d s o r p t i o n "

of t h e s i l v e r ion on a s u r f a c e of t h e s u r r o u n d i n g f l u o r i n e cube. N o t e t h a t t ~ i s c o o r d i n a t i o n is t y p i c a l for m a n y d = c o o r d i n a t i o n c o m p l e x e s .

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