ALTERNATIVE EXPLANATION FOR KONDO - LIKE DEVIATIONS OF THE LOCAL MAGNETIZATION FROM A FREE SPIN BEHAVIOUR AS FOUND IN DILUTE LOCAL MOMENT SYSTEMS

(1)

HAL Id: jpa-00219733

https://hal.archives-ouvertes.fr/jpa-00219733

Submitted on 1 Jan 1980

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

ALTERNATIVE EXPLANATION FOR KONDO - LIKE DEVIATIONS OF THE LOCAL

MAGNETIZATION FROM A FREE SPIN BEHAVIOUR AS FOUND IN DILUTE LOCAL

MOMENT SYSTEMS

F. Litterst, V. Gorobchenko, G. Kalvius

To cite this version:

F. Litterst, V. Gorobchenko, G. Kalvius. ALTERNATIVE EXPLANATION FOR KONDO - LIKE

DEVIATIONS OF THE LOCAL MAGNETIZATION FROM A FREE SPIN BEHAVIOUR AS

FOUND IN DILUTE LOCAL MOMENT SYSTEMS. Journal de Physique Colloques, 1980, 41 (C1),

pp.C1-207-C1-208. �10.1051/jphyscol:1980164�. �jpa-00219733�

(2)

JOURNAL DE PHYSIQUE Colloque C1, suppl6ment au n ^O1, Tome 41, janvier 1980, page C1-207

ALTERNATIVE WIANATION FOR KONDO

-

LIKE DNIATIONS OF M E LOCAL MAGNETIZATION FROM A FREE

SPIN

BEH4VIOUR AS FOUND I N DILUTE LOCAL MayENT SYSTEMS

F.J. Litterst, V.D. Gorobchenko and G.M.

+

Kalvius

Phys.ik Department der Teehnisehen Universitd't kftlnchen D-8046 Garching, Fed. Rep. Gemmy.

+Kurchatov I n s t i t z t e of Atomic Lkergy, Moscow, USSR.

MBssbauer s t u d i e s on d i l u t e 5 7 ~ e i n magne- t i c a l l y n o n - o r d e r e d h o s t m e t a l s have been e x t e n s i v e l y used f o r i n v e s t i g a t i n g t h e

m i -

c r o s c o p i c b e h a v i o u r of l o c a l m a g n e t i c mo- m e n t s . From t h e v a r i a t i o n o f t h e 5 7 ~ e mag- n e t i c h y p e r f i n e ( h f ) f i e l d a s f u n c t i o n o f t h e a p p l i e d e x t e r n a l f i e l d B and t h e tem- p e r a t u r e T a m i c r o s c o p i c m a g n e t i z a t i o n i s deduced I l l . O f t e n d e v i a t i o n s from f r e e - s p i n dynamics o f t h e l o c a l moments a r e f o u n d . F i e l d d e p e n d e n t s a t u r a t i o n hf fields

( a t low T) and a l o c a l s u s c e p t i b i l i t y f o l l o w i n g a C u r i e - W e i s s law w i t h n e g a t i v e

@ a r e t a k e n a s i n d i c a t i o n f o r a r e d u c t i o n o f t h e l o c a l moment by K o n d o - e f f e c t . Here we want t o show b r i e f l y how Kondo- l i k e d e v i a t i o n s of t h e l o c a l m a g n e t i z a t i o n from a f r e e - s p i n b e h a v i o u r may be c a u s e d by a c o m p a r a t i v e l y n a r r o w d i s t r i b u t i o n o f t h e m a g n e t i c f i e l d a c t i n g on t h e l o c a l moment. T h i s d i s t r i b u t i o n may be c a u s e d by i m p u r i t y - i m p u r i t y i n t e r a c t i o n (RKKY) o r by f l u c t u a t i o n s i n the c r y s t a l l i n e e l e c - t r i c f i e l d . I t s p r e s e n c e i s r e v e a l e d , f o r example i n t h e Mo(Fe) s y s t e m by a n o t i c e - a b l e b r o a d e n i n g o f t h e r e s o n a n c e l i n e s C21.

As shown i n r'ef.3 i t i s r e a s o n a b l e i n d i - l u t e a l J o y s t o assume a L o r e n t z i a n d i s t r i - b u t i o n o f t h e f i e l d b a c t i n g on t h e e l e c - t r o n i c s p i n . The mean v a l u e of b must be

B ,

t h e h a l f - w i d t h o f t h e d i s t r i b u t i o n be 248. hen t h e a v e r a g e v a l u e of t h e z-com- p o n e n t o f t h e e l e c t r o n i c s p i n i s

<s%>-

$ ~ & i i ( ~ ~ h ~ ~ ~ 1

^-0o

-

- $ c o t h + )

( 1

1 w i t h x=gvBb/kT,

X , = ~ I . J ~ B / ~ T , dx=:Clgr~/ k ~ .

' ~ f t e r e x p a n d i n g t h e ~ r i l l o u i n f u n c t i o n and

w r i t i n g t h e L o r e n t z i a n i n complex n o t a t i o n we g e t _<'*)-+ 3m-glX-%-i.-inx -

^'OD

&< ^{{ x +} ⁱ ' ⁺

I n t e g r a t i o n y i e l d s

4

-

( 3 )

of t h e digamma f u n c t i o n

where y i s E u l e r ' s c o n s t a n t . I t f o l l o w s

2St6

<sJ* Y ( q + - ( ~ ~ + d ) -

- ¹

^7f

^{y ( l c}

⁽⁴

Eq.4 a s w e l l a s t h e f o l l o w i n g e x p r e s s i o n s a r e f o r m a l l y i d e n t i c a l t o t h o s e g i v e n by S c h o t t e and S c h o t t e t 4 1 f o r t h e Kondo-prob- lem. I n t h e i r d e r i v a t i o n t h e y had assumed t h a t r e s o n a n c e l e v e l s of t h e s p i n d e n s i t y e x i s t n e a r t h e Fermi e n e r g y w i t h a Lore*- i a n s h a p e and a w i d t h d - k T K o n d o . T h e i r

4

c o r r e s p o n d s t o o u r gpBdB.

I n t h e low t e m p e r a t u r e l i m i t we g e t

=tan

( B / a B )

< s 3 - , ⁽⁵

The m a g n e t i c s u s c e p t i b i l i t y i s o b t a i n e d from t h e m a g n e t i z a t i o n by d i f f e r e n t i a t i n g w i t h r e s p e c t t o B:

F o r h i g h t e m p e r a t u r e s t h i s becomes

( t h e z e t a f u n c t i o n 3 ( 3 ) = 1 . 2 0 2 ) which can be r e d u c e d t o a C u r i e - W e i s s law

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1980164

(3)

C1-208 JOURNAL DE PHYSIQUE

Thus t h e f u n c t i o n a l r e l a t i o n s f o r t h e s a - t u r a t i o n m a g n e t i z a t i o n ( e q . 5 ) a n d t h e i n i - t i a l s u s c e p t i b i l i t y ( e q . 8 ) w h i c h a r e c o n - s i d e r e d c h a r a c t e r i s t i c f o r t h e l o c a l magne- t i z a t i o n b e h a v i o u r o f Kondo s y s t e m s c a n e q u a l l y w e l l b e i n t e r p r e t e d b y a d i s t r i b u - t i o n o f t h e l o c a l f i e l d .

As a n e x a m p l e we w a n t t o c o n s i d e r t h e l o c a l m a g n e t i z a t i o n o f Fe i n t h e g i a n t m o m e n t s y s t e m ~ t ( ~

f 5 1 .

~ ~ The s a t u r a t i o n h f e ) f i e l d i s d e p e n d e n t o n t h e a p p l i e d f i e l d B ( F i g . 1 ) w h a t c a n b e e x p l a i n e d a s a f i e l d d e p e n d e n t moment c o m p e n s a t i o n b y K o n d o - e f f e c t . T h i s , h o w e v e r , l e a d s t o t h e b a s i c d i f f i c u l t y t h a t t h e c o u p l i n g o f t h e l o c a l moment t o t h e c o n d u c t i o n e l e c t r o n s m u s t b e a t t h e same t i m e b o t h f e r r o m a g n e t i c t o p r o - d u c e a g i a n t moment a n d a n t i f e r r o m a g n e t i c t o p r o d u c e Kondo c o m p e n s a t i o n . A l t h o u g h t h e r e e x i s t s u g g e s t i o n s ( 5 1 how t h i s c o - e x i s t e n c e i s p o s s i b l e , t h e d i f f i c u l t y c a n a l t o g e t h e r b e a v o i d e d b y t h e e x p l a i n i n g ^' t h e d a t a w i t h i n t h e m o d e l o f a d i s t r i b u - t i o n o f t h e l o c a l f i e l d . As shown i n F i g . ? , t h e d a t a c a n b e s a t i s f a c t o r i l y e x p l a i n e d b y u s i n g e q . 5 w i t h d B = 0 . 0 2 T 9 a f u l l y r e a s o n - a b l e v a l u e . I n summary we w i s h t o p o i n t o u t , t h a t t h e p r e s e n c e o f a f i e l d d e p e n d e n t l o c a l m a g n e t i z a t i o n i s i n i t s e l f n o t a c r u - c i a l t e s t f o r t h e e x i s t e n c e o f a Kondo- e f f e c t . F i n a l l y , t h e d e r i v a t i o n p u t f o r - w a r d i n t h i s n o t e may e a s i l y b e m o d i f i e d

t o c a l c u l a t e t h e m a g n e t i z a t i o n i n c o n c e n - t r a t e d s y s t e m s l i k e s p i n g l a s s e s o r amor- p h o u s m a g n e t s o n c e t h e a p p r o p r i a t e d i s t r i - b u t i o n f u n c t i o n f o r t h e l o c a l f i e l d h a s b e e n c h o s e n .

A c k n o w l e d g e m e n t : T h e a u t h o r s a r e g r a t e f u l t o t h e D e u t s c h e F o r s c h u n g s g e m e i n s c h a f t a n d t h e Academy o f S c i e n c e s o f t h e U.S.S.R.

who made p o s s i b l e t h e c o o p e r a t i o n b y t h e i r s u p p o r t .

R e f e r e n c e s

/I]

STEINER P. a n d HUFNER S., Phys.Rev.

( 1 9 7 4 ) 4 0 3 8

[2] PEREZ-RAMIREZ J.G., THOMAS L.K. a n d

STEINER P., J.Low Temp.Phys.

2

( 1 9 7 7 ) 8 3

131

HELD C. a n d KLEIN M.W., P h y s . R e v . L e t t . 3 5 ( 1 9 7 5 ) 1 7 8 3

141 SCHOTTE K.D. a n d SCHOTTE U., P h y s . L e t t . 55A ( 1 9 7 5 ) 3 8

-

151 SCHERG W., SEIDEL E.R., LITTERST F.J.,

GIERISCH W . a n d KALVIUS G.M., J .Physique 35C6 ( 1 9 7 4 ) 527

B (Tesla)

F i g . 1 : Low t e m p e r a t u r e s a t u r a t i o n h f f i e l d a t t h e F e n u c l e u s i n P t ( F e ) a s a f u n c t i o n o f t h e e x t e r n a l m a g n e t i c f i e l d 6. S o l i d c u r v e : eq.5 w i t h pB=0.02 T e s l a a n d h i g h

h f

f i e l d B s a t = - 3 1 . 4 T e s l a l 5 1 .