VIBRONIC COUPLING EFFECTS AT THE NEEL TEMPERATURE IN FeCO3

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VIBRONIC COUPLING EFFECTS AT THE NEEL TEMPERATURE IN FeCO3

D. Price

To cite this version:

D. Price. VIBRONIC COUPLING EFFECTS AT THE NEEL TEMPERATURE IN FeCO3. Journal

de Physique Colloques, 1979, 40 (C2), pp.C2-316-C2-319. �10.1051/jphyscol:19792111�. �jpa-00218481�

JOURNAL DE PHYSIQUE

Colloque C2, suppl6ment au n

^O

3, Tome 40, mars 1979, page

C2-316

V I B R 3 N I C C O U P L I N G E F F E C T S AT T H E NEEL T E M P E R A T U R E I N

? e C 0 3

D.C. P r i c e

Department o f S o l i d S t a t e Physics, Research School o f Physical Sciences, AustraZicin National Univer- s i t y , Canberra ACT 2600, Australia

Rdsum6.- L ' e x i s t e n c e p o s s i b l e d ' u n c o u p l a g e de r d s o n a n c e v i b r o n i q u e , a n a l o g u e q u a n t 1 l ' o r i g i n e au p r o c e s s u s de r e l a x a t i o n r d s o n a n t e de Orbach, e s t e n v i s a g d e . On montre que l e s d t a t s fondamentaux s d p a r d s de ~ e ' + d a n s FeCO p e u v e n t B t r e f o r t e m e n t c o u p l d s p a r ce mdcanisme, p a r t i c u l i s r e m e n t 1 d e s t e l n p g r a t u r e s p r o c h e s de T:, e t gue ce c o u p l a g e p o u r r a i t Z t r e B l ' o r i g i n e du comportement anormal de l ' i n t e r a c t i o n q u a d r u p o l a i r e du 7 ~ e d a n s c e domaine d e t e m p d r a t u r e .

A b s t r a c t . - The p o s s i b l e e x i s t e n c e o f a r e s o n a n t v i b r o n i c c o u p l i n g , s i m i l a r i n o r i g i n t o t h e Orbach r e s o n a n t r e l a x a t i o n p r o c e s s , i s d i s c u s s e d . I t i s shown t h a t t h e exchange s p l i t ground s t a t e s o f F e 2 + i n FeCO, may be s t r o n g l y coupled by t h i s mechanism, p a r t i c u l a r l y f o r t e m p e r a t u r e s c l o s e t o TN, and t h i s c o u p l i n g c o u l d p r o v i d e a n e x p l a n a t i o n f o r t h e anomalous b e h a v i o u r o f t h e 5 7 ~ e q u a d r u p o l e i n t e - r a c t i o n i n t h i s t e m p e r a t u r e r e g i o n .

1 . I n t r o d u c t i o n . - I n a r e c e n t p a p e r / I / , a f o r m a l i s m t h a t e n a b l e d a p p r o x i m a t e c a l c u l a t i o n of t h e e f f e c t s o f v i b r o n i c a d m i x t u r e between t h e low-lying e l e c t r o - n i c s t a t e s of m a g n e t i c i o n s i n c r y s t a l s on o b s e r v a - b l e s s u c h a s t h e X z s s b a u e r q u a d r u p o l e s p l i t t i n g was p r e s e n t e d . T h i s was b a s e d on t h e s p i n - l a t t i c e r e l a - x a t i o n work o f Orbach and coworkers (e.g. / 2 / , / 3 / , / 4 / ) . P a r t i c u l a r a p p l i c a t i o n was made t o t h e tempe- r a t u r e dependence o f t h e 5 7 ~ e 2 + q u a d r u p o l e s p l i t t i n g i n FeC3,. I t was shown t h a t v i b r o n i c a d m i x t u r e e f - f e c t s can be i m p o r t a n t and t h a t t h e y s h o u l d t h e r e - f o r e be c o n s i d e r e d i n any d i s c u s s i o n o f t h e tempera- t u r e dependence ( o r a b s o l u t e magnitude) o f t h e nu- c l e a r e l e c t r i c f i e l d g r a d i e n t ( e . f . g . ) and o f o t h e r o b s e r v a b l e s s u c h a s g f a c t o r s , m a g n e t i c h y p e r f i n e c o u p l i n g c o n s t a n t s , e t c .

I n t h i s p a p e r t h e p o s s i b l e e x i s t e n c e of a r e - s o n a n t v i b r o n i c a d m i x t u r e between e x c h a n g e - s p l i t l e - v e l s w i l l be examined and i t w i l l be shown t o be ca- p a b l e o f p r o d u c i n g e f f e c t s s i m i l a r t o t h o s e t h a t have been o b s e r v e d i n t h e 5 7 ~ e q u a d r u p o l e s p l i t t i n g i n FeCO, n e a r t h e NBel t e m p e r a t u r e /S/, / 6 / . 2 . V i b r o n i c c o u p l i n g model.- T h i s s e c t i o n c o n t a i n s a b r i e f summary o f t h e n e c e s s a r y r e s u l t s o b t a i n e d i n / I / , and t h a t p a p e r s h o u l d be c o n s u l t e d f o r d e r i - v a t i o n s , f u r t h e r r e f e r e n c e s and j u s t i f i c a t i o n s .

The v i b r o n i c , o r o r b i t - l a t t i c e i n t e r a c t i o n between a p a r a m a g n e t i c i o n and t h e c l u s t e r o f s u r - r o u n d i n g l i g a n d s i s w r i t t e n i n t h e form

~ ( r , p ) a r e s t r a i n s c o r r e s p o n d i n g t o t h e normal modes o f t h e c l u s t e r t h a t t r a n s f o r m a c c o r d i n g t o t h e p t h

s u b v e c t o r of t h e i r r e d u c i b l e r e p r e s e n t a t i o n

r

of i t s symmetry group. The B

R

( r , p ) a r e a p p r o p r i a t e l y t r a n s - f o r m i n g l i n e a r c o m b i n a t i o n s o f t h e t e s s e r a l harmonics Zm and t h e b ( r ) a r e c o u p l i n g c o e f f i c i e n t s .

R

R

The b a s i s s t a t e s a r e t h e Born-Oppenheimer pro- d u c t s

where .I) i s a s o l u t i o n , w i t h e n e r g y Ei, o f t h e e l e c - t r o n i c S c h r o d i n g e r e q u a t i o n f o r t h e i o n and t h e N a ( k , s ) a r e t h e o c c u p a t i o n numbers o f t h e phonon s t a - -

t e s o f wave v e c t o r and p o l a r i z a t i o n i n d e x S : t h e i n d e x

a

r e l a t e s t h e p a r t i c u l a r s e t o f o c c u p a t i o n numbers t o t h e p r o d u c t s t a t e

m 0

P o s s i b l e d i f f i c u l -

ia'

t i e s i n h e r e n t i n u s i n g ( 2 ) a s b a s i s s t a t e s f o r a p e r t u r b a t i o n c a l c u l a t i o n a r e d i s c u s s e d i n / l / . The e n e r g y o f t h e s t a t e ( 2 ) i s :

E& = Ei ⁺

1

[ N f f ( k , s ) + f ; ] f i a ( k , s ) ( 3 ) k , s

-

P e r t u r b e d s t a t e s a r e c a l c u l a t e d by t h e u s u a l f i r s t o r d e r method, i . e .

where A i s t h e n o r m a l i z a t i o n c o n s t a n t . i a

The e x p e c t a t i o n v a l u e o f a n o p e r a t o r , s a y t h e e . f . g . o p e r a t o r

V,

- can be c a l c u l a t e d u s i n g t h e s e p e r t u r b e d s t a t e s . Terms t h a t a r e f i r s t o r d e r i n

$

OL a r e i d e n t i c a l l y z e r o , so, t o l o w e s t o r d e r :

s i n c e

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- i s a p u r e l y e l e c t r o n i c o p e r a t o r .

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19792111

T h i s can be r e d u c e d t o ( s e e / I / ) :

where

and

i f i t i s assumed t h a t t h e phonon s p e c t r u m i s i s o t r o - p i c .

E q u a t i o n (6) shows q u i t e c l e a r l y how t h e v i - b r o n i c a l l y i n d u c e d t e m p e r a t u r e dependence a r i s e s a s

a r e s u l t o f t h e t e m p e r a t u r e dependence of t h e phonon o c c u p a t i o n numbers N ( k ) . Assuming t h a t r e l a x a t i o n

a

between t h e s t a t e s $. i s s u f f i c i e n t l y r a p i d , t h e ob- s e r v e d e . f . g . i s t h e n o b t a i n e d f r o m a n ensemble ave- r a g e of t h e i n ( 6 ) .

3. Resonant V i b r o n i c Admixture.- When t h e s p l i t t i n g o f two e l e c t r o n i c s t a t e s $ i and $ j i s l e s s t h a n t h e maximum phonon e n e r g y t h e e x p r e s s i o n f o r t h e phonon term C! i n ( 6 ) c o n t a i n s a d i v e r g e n c e . A way o f dea-

J j

l i n g w i t h t h i s i s t o a d o p t t h e a p p r o a c h of Orbach / 2 / i n h i s t r e a t m e n t o f r e s o n a n t r e l a x a t i o n and a s - s i g n t o t h e u p p e r s t a t e $ a l i f e t i m e T which c a n

j j

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

qi

and $ a r e m a g n e t i c a l l y s p l i t l e v e l s , T may b e

j j

q u i t e l o n g and t h e c o r r e s p o n d i n g n e a r - d i v e r g e n c e may d o m i n a t e t h e summation o v e r i n C i T h i s w i l l b e

j j ' i l l u s t r a t e d i n t h e n e x t s e c t i o n .

One consequence of t h i s i s t h a t , owing t o t h e f a c t t h a t t h e d e n s i t y o f s t a t e s i s e n e r g y depen- d e n t , t h e m a g n i t u d e of C . . ( T ) may depend s e n s i t i v e l y i

J

!

o n Ei-E and i f t h i s s p l r t t i n g i s due t o a n exchan- j '

g e i n t e r a c t i o n o r t o an a p p l i e d m a g n e t i c f i e l d , t h e n

< l > i may show a s t r o n g t e m p e r a t u r e dependence n e a r t h e m a g n e t i c t r a n s i t i o n t e m p e r a t u r e o r a s t r o n g ap- p l i e d f i e l d dependence.

4. A p p l i c a t i o n t o FeC03.- FeCO i s a u n i a x i a l a n t i - f e r r o m a g n e t w i t h a Ndel t e m p e r a t u r e TN-38 K. The Fe2+ i o n s i t e is t r i g o n a l ( p o i n t g r o u p S 6 = C 3 X i) and t h e l o w e s t c r y s t a l f i e l d m u l t i p l e t i s ^5~ T h i s

g' i s s p l i t i n t o a s e r i e s of d o u b l e t s and s i n g l e t s by

s p i n - o r b i t c o u p l i n e and (below T N ) by t h e exchange i n t e r a c t i o n . The s p l i t t i n g o f t h i s m u l t i p l e t i s shown s c h e m a t i c a l l y i n f i g u r e 1.

T r i g o n a l F i e l d + S p i n - o r b i t Coupling + Exchange

-

¹¹⁾

80,

00,

XL.$ J S,

F i g . I : S p l i t t i n g o f t h e ground 'E m u l t i p l e t o f F e 2 + i n a t r i g o n a l l y e l o n g a t e d o c t a i e d r a l c r y s t a l f i e l d b y t h e s p i n - o r b i t c o u p l i n g and a n a x i a l ex- change i n t e r a c t i o n . The p a r a m e t e r s u s e d f o r t h e pu- r e l y i l l u s t r a t i v e p u r p o s e s of t h i s d i a g r a m were B: = -100 cm-', X = -100 cm-', J = -16 c m - ' w h i c h a r e of t h e c o r r e c t o r d e r o f magnitude f o r ~ e i n ~ + FeCO, / 7 / .

The f i r s t e x c i t e d m u l t i p l e t i s 'A a t -1000-1500cm-' 'g

above t h e ground s t a t e / 7 / , / 8 / . The 'E and 'A

1 g s t a t e s a r e d e r i v e d from t h e o c t a h e d r a l 'T m u l t i p l e t .

2 g As t h e t e m p e r a t u r e a p p r o a c h e s TN from below t h e r e i s a s h a r p i n c r e a s e i n t h e "Fe q u a d r u p o l e in- t e r a c t i o n ,

f;

eQVzZ, o f - 0 . 0 7 mms-'/5/ t h a t h a s been s p e c u l a t i v e l y a t t r i b u t e d t o t h e e f f e c t of magnetos- t r i c t i o n on t h e s t a t i c c r y s t a l f i e l d / 6 / ( s e e F i g . 2 ( a ) ) . Above TN t h e q u a d r u p o l e s p l i t t i n g d e c r e a s e s a l m o s t l i n e a r l y w i t h t e m p e r a t u r e .

I n / I f i t was shown t h a t "spin-allowed" cou- p l i n g w i t h i n t h e o c t a h e d r a l 'T m u l t i p l e t mixes t h e

8

s t a t e l a b e l l e d 19 > i n f i g u r e 1 and a s t a t e from t h e

5~ m u l t i p l e t i n t o t h e ground s t a t e ( l a b e l l e d

)

1 >

'g

i n f i g u r e l ) , and t h i s r e s u l t s i n a s i g n i f i c a n t de- c r e a s e i n t h e o b s e r v e d q u a d r u p o l e s p l i t t i n g , e v e n a t TQO, b e c a u s e t h e e . f . g . p r o d u c e d b y t h e 'A s t a t e s

l g

i s o p p o s i t e i n s i g n t o t h a t o f t h e lower 'E s t a t e s . g

For t h i s c o u p l i n g , t h e e l c t r o n i c m a t r i x e l e m e n t s a r e l a r g e b u t t h e phonon t e r m s

~ i .

a r e r e l a t i v e l y s m a l l

J J

c2-3

18 JOURNAL DE PHYSIQUE

( ~ l ~ - * ( c m - ' ) - ~ f o r T

-

^TN). s o t h a t (8) becomes

1 .-261

The r e v e r s e s i t u a t i o n i s e n c o u n t e r e d , however, (T)

' -

⁼

^-

^{1 .-A12/kgT}

i f c o u p l i n g between t h e e x c h a n g e - s p l i t s t a t e s

I

^{I >}

^{5' 5}

and from ( 7 ) and 12> i s c o n s i d e r e d . The e l e c t r o n i c m a t r i x e l e -

D ' (T) : e -A1z/kBT ments a r e p r e d o m i n a n t l y s p i n - f o r b i d d e n and a r e

-

^{10 2 2}

-100 t i m e s s m a l l e r t h a n t h e s p i n - a l l o w e d o n e s . How- e v e r , b e c a u s e t h e i r s p l i t t i n g i s o n l y 5 7 0 cm-' / g / , / 1 0 / , which i s c o n s i d e r a b l y l e s s t h a n t h e maximum phonon e n e r g y / 7 / , t h e r e may be a r e s o n a n t c o u p l i n g g i v i n g a g r e a t l y enhanced phonon term. T h i s w i l l be c o n f i r m e d s e m i - q u a n t i t a t i v e l y below. The f a c t t h a t t h e e l e c t r o n i c m a t r i x e l e m e n t s c o u p l i n g t h e s t a t e s a r e s m a l l i s h e l p f u l h e r e a s i t r e d u c e s t h e d e c a y r a t e o f t h e e x c i t e d s t a t e 12 > t o t h e ground s t a t e

1 1

^>.

I t can be s e e n from e q u a t i o n ( 6 ) t h a t t h e c o u p l i n g o f 12> and

I

^{I >} w i l l i n c r e a s e a s t h e s p l i t - t i n g A I , = E t

-

E , d e c r e a s e s b u t w i l l f a l l t o z e r o f o r A 1 2 = 0 s i n c e t h e d e n s i t y o f phonon s t a t e s w i t h z e r o e n e r g y i s z e r o . S i n c e

<E>:

^Z

<g>:,

a l a r g e cou- p l i n g of 12> and

)

l > w i l l r e d u c e t h e e f f e c t on o f c o u l i n g t o t h e 'A s t a t e s , i . e . a s t h e c o u p l i n g

'g

of 12> and

I

^{I >} i n c r e a s e s t h e e . f . g . w i l l i n c r e a s e . An o r d e r of magnitude e s t i m a t e of t h i s change can be made. For C 3 i symmetry i t c a n be shown ( s e e / ] / ) t h a t Di i s o n l y n o n - z e r o f o r j = j l . L e t :

j j l

D : ~ ( T ) =

c

c : ~ ( T ) (7)

s o t h a t

5'

depends o n l y on e l e c t r o n i c c o o r d i n a t e s . F o l l o w i n g Orbach ( / 2 / , / 4 / ) t h e e n e r g y of s t a t e 12>

now becomes E2 + i r / 2 w i t h

r - H / T ~ .

Assuming a Debye model f o r t h e phonon s p e c t r u m 171 and t a k i n g t h e Na(k) t o b e t h e t h e r m a l e q u i l i b r i u m v a l u e s a t tempe- r a t u r e T, C;,(T) becomes, f o r s m a l l v a l u e s o f

where 6 , = A12/2kgT and p , v a r e t h e l a t t i c e d e n s i t y and (average) v e l o c i t y o f sound.

An e s t i m a t e o f

r

(and h e n c e o f y) c a n be ob- t a i n e d i f i t i s assumed t h a t 12> d e c a y s predominan- t l y by a d i r e c t s p i n - l a t t i c e p r o c e s s t o

I

I >

.

^{T h i s}

i s p r o b a b l y n o t t r u e , p a r t i c u l a r l y f o r T T N s i n c e f o r i?e2+:i!nco3 two-phonon p r o c e s s e s have b e e n shown t o be dominant / 7 / . However, i n t h i s t e m p e r a t u r e r e - g i o n t h e d i r e c t p r o c e s s d e c a y r a t e i s w i t h i n one o r two o r d e r s o f magnitude o f t h e two-phonon r a t e f o r A I , # 0 s o t h e c o n c l u s i o n s drawn below w i l l n o t be a f f e c t e d . T h e r e f o r e , a lower l i m i t f o r

r

w i l l be g i v e n by / 2 / :

The a p p r o x i m a t i o n s (8) and ( 9 ) a r e o n l y v a l i d f o r A12not t o o c l o s e t o z e r o (compared w i t h T): when A , , = 0 t h e d i v e r g e n c e d i s a p p e a r s and t h e c o u p l i n g i s g r e a t l y r e d u c e d .

A s T a p p r o a c h e s TN from below, A I 2 d e c r e a s e s r a p i d l y towards z e r o s o D:,(T) i n c r e a s e s s h a r p l y : t h e o t h e r c o u p l i n g c o e f f i c i e n t s

D!.

w i l l v a r y o n l y slow-

J J

l y i n t h i s t e m p e r a t u r e r a n g e . E q u a t i o n ( 6 ) shows t h a t t h e r e w i l l be an a s s o c i a t e d s h a r p change i n t h e q u a d r u p o l e s p l i t t i n g f o r T L TN.

For r e a s o n a b l e e s t i m a t e s of t h e p a r a m e t e r s b L ( r ) ( s e e / I / ) :

5'

⁼

1 2

< l I b e ( r > B e ( r S p ) 12><21be, ( r ) B e , (T.P)

1

L,%'

r * ~

^=2,b ~ ~ ~ ( c m - ~ ) 2 .

and

r

d e c r e a s e s from -0.5 cm-' f o r T<<TN t o <10-'an-' f o r T j u s t below TN. Thus, t h e a s s u m p t i o n o f y being v e r y s m a l l a p p e a r s t o b e w e l l j u s t i f i e d , p a r t i c u l a r - l y i n t h e r e g i o n of i n t e r e s t n e a r TN, and t h e e s t i - mate (10) f o r D:,(T) f o r T L T N i s v a l i d .

For c o m p a r i s o n , f o r T-TN, t h e

cjfj

t e r m s t h a t d e s c r i b e t h e s p i n - a l l o w e d c o u p l i n g t o s t a t e ) 9 > ( F i g .

I ) and t o t h e 5 ~ l g m u l t i p l e t a r e ' 1 0 - ~ ( c m - ' ) - ~ giving D!.(TN) v a l u e s

-<o.

^{l .} T h e r e f o r e , a s t h e t e m p e r a t u r e

1 1

r i s e s from z e r o t o - T t h e c o u p l i n g between s t a t e s N

/ I > and

Iz>

changes from b e i n g much s m a l l e r t o se- v e r a l t i m e s l a r g e r t h a n t h a t t o t h e s p i n - a l l o w e d s t a t e s and c o n s e q u e n t l y t h e low t e m p e r a t u r e r e d u c t i o n i n t h e e.E.g. i s d i m i n i s h e d by a l m o s t a f a c t o r o f two ( s e e e q u a t i o n ( 6 ) ) .

From / l / i t can be s e e n t h a t t h e low t e m p e r a t u r e v i - b r o n i c r e d u c t i o n i n e Q <VZZ>' may be a t l e a s t 0 . 1 m / s , d e p e n d i n g on t h e v a l u e s t a k e n f o r t h e cou- p l i n g p a r a m e t e r s b L ( r ) . The c o n t r i b u t i o n (10) t o D:, t h e n i m p l i e s t h a t t h i s q u a n t i t y w i l l i n c r e a s e n e a r TN by a s i m i l a r amount t o t h a t o b s e r v e d ( F i g . 2 ( a ) ) .

When A l z i s z e r o , however, t h e d i v e r g e n c e i n t h e i n t e g r a l f o r c : ~ ( T ) d i s a p p e a r s and s o t o o , the- r e f o r e , d o e s t h e a s s o c i a t e d l a r g e r e s o n a n t c o n t r i b u - t i o n ( 1 0 ) t o D:,

.

I t might . t h e r e f o r e be e x p e c t e d t h a t t h e i n c r e a s e i n t h e q u a d r u p o l e s p l i t t i n g t h a t i t p r o d u c e s s h o u l d d i s a p p e a r f o r T>TN, c o n t r a r y t o what i s o b s e r v e d . However, a l t h o u g h t h e exchange s p l i t - t i n g o f

)

I > and 12> h a s a mean v a l u e o f z e r o f o r T>TN, i t w i l l s t i l l have a non-zero a v e r a g e o v e r t i - mes o f t h e o r d e r o f t h e ~ e ' + r e l a x a t i o n t i m e , which,

a t l e a s t f o r t e m p e r a t u r e s up t o 100 K o r more, i s l o n g e r t h a n t y p i c a l phonon l i f e t i m e s / 5 / , / 7 / . Hence, t h e phonon s y s t e m w i l l "see" s m a l l q u a s i - s t a t i c s p l i t t i n g s e v e n above TN and D:,(T) w i l l s t i l l be l a r g e . As t h e F e 2 + r e l a x a t i o n r a t e i n c r e a s e s , how- e v e r , t h i s e f f e c t w i l l g r a d u a l l y d i s a p p e a r and t h e A , , = 0 s i t u a t i o n w i l l p r e v a i l .

however, t h i s mechanism can a l s o p r o v i d e a n e x p l a n a - t i o n f o r t h e s h a r p s h i f t i n t h e e n e r g y of t h e 438cm-' Raman t r a n s i t i o n n e a r TN t h a t was o b s e r v e d by Popkov e t a l . / I I / . T h i s w i l l be e l a b o r a t e d upon i n a f u t u r e p u b l i c a t i o n .

P r e l i m i n a r y measurements i n d i c a t e t h a t e f f e c t s of m a g n e t o s t r i c t i o n a r e s m a l l . F u r t h e r d e t a i l s w i l l be g i v e n l a t e r .

F i g . 2 : Temperature dependence o f t h e q u a d r u p o l e s p l i t t i n g ' h e ~ v , ~ f o r 5 7 ~ e 2 + i n FeCO,.

( a ) E x p e r i m e n t a l v a l u e s from r e f . / 5 / ( b ) A s c h e m a t i c i n d i c a t i o n of t h e c o n t r i b u - t i o n t h a t m i g h t r e s u l t from t h e r e s o n a n t v i b r o n i c c o u p l i n g mechanism d i s c u s s e d h e r e . P,, i s t h e v a l u e i n t h e a b s e n c e o f any v i b r o n i c a d m i x t u r e and PS, i s t h e r e d u c e d v a l u e when t h e s p i n - a l l o w e d c o u p l i n g i s c o n s i d e r e d . The r e l a t i v e l y weak t e m p e r a t u r e depen- d e n t r e d u c t i o n of b o t h o f t h e s e q u a n t i t i e s due t o t h e o c c u p a t i o n of e x c i t e d s t a t e s h a s b e e n i g n o r e d . F i g u r e 2 ( b ) shows s c h e m a t i c a l l y t h e way i n which !l2 eQ <V,,>1 m i g h t v a r y w i t h t e m p e r a t u r e ac- c o r d i n g t o t h e arguments p r e s e n t e d above and t h i s compares f a v o u r a b l y w i t h t h e measured v a r i a t i o n o f

eQ <<V,,>> t a k e n from / 5 / and shown i n f i g u r e 2(a).

5 . ' C o n c l u s i o n s . - The p o s s i b i l i t y of a r e s o n a n t v i - b r o n i c c o u p l i n g w i t h a s i m i l a r o r i g i n t o t h e Orbach r e s o n a n t r e l a x a t i o n p r o c e s s h a s b e e n p o i n t e d o u t a n d , on t h e b a s i s of f a i r l y q u a l i t a t i v e a r g u m e n t s , shown t o b e a p o s s i b l e e x p l a n a t i o n f o r t h e anomalous

5 7

v a r i a t i o n o f t h e Fe q u a d r u p o l e i n t e r a c t i o n n e a r TN i n FeC03. More d e t a i l e d c a l c u l a t i o n s would b e re- q u i r e d b e f o r e a more p o s i t i v e i d e n t i f i c a t i o n o f t h e o r i g i n o f t h i s anomalous b e h a v i o u r c o u l d b e made.

Using s i m i l a r arguments t o t h o s e g i v e n above,

Acknowledgements.- I t i s a p l e a s u r e t o acknowledge t h e c o n t i n u e d encouragement w i t h t h i s work g i v e n by D r D.J. Newman and t o thank him and Dr A . Edgar f o r h e l p f u l comments on t h e m a n u s c r i p t .

R e f e r e n c e s

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