SKEW SCATTERING AND THE HALL EFFECT IN LIQUID METALS

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Submitted on 1 Jan 1980

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SKEW SCATTERING AND THE HALL EFFECT IN LIQUID METALS

L. Ballentine

To cite this version:

L. Ballentine. SKEW SCATTERING AND THE HALL EFFECT IN LIQUID METALS. Journal de

Physique Colloques, 1980, 41 (C8), pp.C8-458-C8-458. �10.1051/jphyscol:19808113�. �jpa-00220209�

JOURNAL DE PHYSIQUE CoZZoque C8, suppZdment au n o 8, Tame 41, aoiit 1980, page C8-458

SKEW SCATTER1 NG AND THE H A L L EFFECT I N L I Q U I D METALS

L.E.

B a l l e n t i n e

Department of Physics, Simon Fraser U n i v e r s i t y , Burnaby, B. C., Canada V5A IS6

A b s t r a c t .

-

Skew s c a t t e r i n g i s t h e l a c k o f symmetry o f t h e s c a t t e r i n g p r o b a b i l i t y between i n i t i a l a n d f i n a l s t a t e s . I t s e f f e c t i n t h e Boltzmann e q u a t i o n i s o f a s i m i l a r form t o t h a t of a m a g n e t i c f i e l d , and t h u s it c o n t r i b u t e s d i r e c t l y t o t h e H a l l c o e f f i c i e n t . The a n t i - s y m m e t r i c p a r t o f t h e s c a t t e r i r l g

+ + *

*

-t

p r o b a b i l i t y must b e p r o p o r t i o n a l t o a ' ( k ' x k ) , where k a n d k ' a r e t h e i n i t i a l a n d f i n a l momenta and + a i s some a x i a l v e c t o r . T h r e e d i f f e r e n t c h o i c e s f o r

Hf

a r e known t o b e r e l e v a n t .

+ +

a = o ( e l e c t r o n s p i n ) : S p i n - o r b i t s c a t t e r i n g i s r e s p o n s i b l e f o r t h e d e v i a t i o n s o f t h e H a l l c o e f f i c i e n t s of some s i m p l e m e t a l s from t h e f r e e e l e c t r o n v a l u e [I].

-*

-+

a = L ( o r b i t a l a n g u l a r momentum o f t h e o c c u p i e d s t a t e s ) : Exchange s c a t t e r i n g c a n b e i m p o r t a n t i n p a r t i a l l y f i l l e d n a r r o w b a n d s . I t s c o n t r i b u t i o n i n t r a n s i t i o n m e t a l s i s a n o r d e r o f m a g n i t u d e g r e a t e r t h a n t h a t o f s p i n - o r b i t S c a t t e r i n g . I t makes a s i g n i f i c a n t c o n t r i b u t i o n t o t h e H a l l c o e f f i c i e n t s o f l i q u i d t r a n s i t i o n m e t a l s , b u t d o e s n o t seem t o b e l a r g e enough t o a c c o u n t f o r t h e o b s e r v e d r e s u l t s 121.

-+ _{a =}

-* _n:

A m o d i r i c a t i o n o f t h e s c a t t e r i n g a m p l i t u d e by t h e Zeeman e n e r g y , f i r s t s u g g e s t e d by Chambers [3!, may b e a p p r e c i a b l e n e a r a s c a t t e r i n g r e s o n a n c e , b u t seems t o b e t o o small t o e x p l a i n t h e H a l l e t f e c t i n l j q u i d t r a n s i t i o n m e t a l s 141.

R e f e r e n c e s

[l] B a l l e n t i n e , L.E. a n d Huberman, M. ( 1 9 7 7 ) , J. Phys. C: S o l i d S t a t e P h y s . 1 0 , 4991-5002.

[2] B a l l e n t i n e , L.E. a d Huberman, M. ( 1 9 8 0 ) , J. Phys. C: S o l i d S t a t e Phys. ( i n p r e s s ) . [3] Chambers, W.G. ( 1 9 7 3 ) , J. P h y s . C: S o l i d S t a t e P h y s .

5.

2441-5.

[4] B a l l e n t i n e , L.E. (1980). c h a p t e r i n t h e commemorative book f o r t h e 1 0 0 t h a n n i v e r s a r y o f t h e H a l l e f f e c t , (Plenum P r e s s ) , e d i t o r C.L. C h i e n .

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19808113