ELECTRON-PHONON COUPLING IN THE NONTRANSITION METAL CADMIUM

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ELECTRON-PHONON COUPLING IN THE

NONTRANSITION METAL CADMIUM

B. Dorner, A. Chernyshov, V. Pushkarov, A. Rumyantsev, R. Pynn

To cite this version:

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JOURNAL DE PHYSIQUE

CoZZoque C6, suppZe'ment au n o 12, Tome 42, de'cernbre 1981 page C6-365

ELECTRON-PHONON COUPLING I N THE N O N T R A N S I T I O N

METAL

CADMIUM

B . Dorner, A.A. ~hernyshov*, V.V. ~ushkarev*, A.Yu. ~umyantsev* and R. Pynn

ILL GrenobZe, France

*Kurtchatou I n s t . , Moscow, U. S. S. R.

A b s t r a c t .

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By i n e l a s t i c neutron s c a t t e r i n g we observed s e v e r a l anomalies i n t h e group v e l o c i t i e s of t h e phonon d i s p e r s i o n curves. They could a l l be a l l o c a t e d on t h e Fermi s u r f a c e . S t r e n g t h s and shape of t h e anomalies d i f f e r c o n s i d e r a b l y from t h e o r e t i c a l pre- d i c t i o n s .

A f t e r measuring t h e phonon d i s p e r s i o n curves of Cd a t 80 K by i n e l a s t i c neutron s c a t t e r i n g /I/ we c o n c e n t r a t e d on t h e Kohn anomalies / 2 / i n t h e d i s p e r s i o n curves. S e v e r a l anomalies ( A N ' S ) l i k e Fig. 1 were de- t e c t e d and a l l o c a t e d on t h e Fermi s u r f a c e . From c a l c u l a t i o n s i n per- t u r b a t i o n t h e o r y , i n c l u d i n g second-order terms i n t h e Heine Abarenkov / 3 / model p o t e n t i a l , i t was expected t h a t t h e group v e l o c i t y

a t

an AN should e x h i b i t a s i n g l e maximum o r a s i n g l e minimum depending on whether t h e phonon d i s p e r s i o n i s followed from i n s i d e t h e Fermi s u r - f a c e towards o u t s i d e o r v i c e v e r s a /4/. I n Fig. 1 anomaly No. 4 should be a mamimum and No. 5 , p r a c t i c a l l y c o i n c i d i n g , a minimum. The calcu- l a t i o n shows a s a r e s u l t a n t of both e f f e c t s a maximum, w h i l e t h e

Fig. 1: a )

...

Transverse

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phonon d i s p e r s i o n curve. 0.75 5 0 0 0 measured phonon group

o v e l o c i t y .

2

b ) P r e d i c t e d group v e l o c i t y 0-50

$2Q

w i t h numbered anomalies /4/. I5 3 0 1 .2 .3 .4 .S P

-.

K T' M q +

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C6-366 JOURNAL DE PHYSIQUE

e x p e r i m e n t a l o b s e r v a t i o n r e v e a l s a s t r o n g maximum a t t h e p r e d i c t e d p o s i t i o n and a s t r o n g unexpected minimum f o r s m a l l e r q - v a l u e s .

F i g . 2: Measured c a l c u l a t e d ( b , d ) v e l o c i t y . (open d o t s ) a n d phonon group [2X/c] PHONON WAVEVECTOR [ L n l f l a l

F i g . 2 shows c a l c u l a t e d and measured A N ' S /5/ f o r two l o n g i t u d i - n a l d i s p e r s i o n c u r v e s i n 10051 and 1~001 d i r e c t i o n s i n v o l v i n g t h e r e -

+

c i p r o c a l l a t t i c e v e c t o r s T = (002) and = ( l o o ) , r e s p e c t i v e l y . Both c a l c u l a t e d A N ' s and t h e e x p e r i m e n t a l one i n 15001 d i r e c t i o n s a r e com- p a r a b l e i n s t r e n g t h , b u t t h e o b s e r v e d one i n [0051 d i r e c t i o n i s much s t r o n g e r . Both A N ' s a r e r e l a t e d t o e l e c t r o n t r a n s i t i o n s between s p h e r i - c a l p a r t s o f t h e Fermi s u r f a c e , t h e r e f o r e t h e band s t r u c t u r e s h o u l d b e s i m i l a r . But t h e s t r o n g a n i s o t r o p y o f t h e Cd s t r u c t u r e ( c / a = 1.886 i n s t e a d o f 1.633 f o r i d e a l h . c . p . ) produces p r o b a b l y an a n i s o t r o p y i n t h e e l e c t r o n phonon i n t e r a c t i o n and i n t h e e l e c t r o n s u s c e p t i b i l i t y v i a a n a n i s o t r o p y i n t h e c o n d u c t i o n e l e c t r o n wave f u n c t i o n and i n t h e e l e c - t r o n i o n p o t e n t i a l .

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_'r=

₍₁₀₁₁

F i g . 3: P l a n e i n r e c i p r o c a l s p a c e p e r p e n d i c u l a r t o 1100] W e i n v e s t i g a t e d t h e A N ' s o u t o f symmetry d i r e c t i o n s a s w e l l /5/ and c o u l d s e p a r a t e some which c o i n c i d e f o r symmetry d i r e c t i o n s . Par- t i c u l a r a t t e n t i o n was ? a i d t o e l e c t r o n t r a n s i t i o n s between f l a t p a r t s

( s u r f a c e o f t h e second B r i l l o u i n zone) o f t h e Fermi s u r f a c e w i t h 3

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would occur in the case of a spherical Fermi surface. The points in Fig. 3 indicate observed AN'S. For the symmetry direction T, where the AN coincides with q = o, we found a strong variation of the phonon group velocity for small q.

Fig. 4: Anomalous behavior of the phonon group velocity in T direction for small q's. a) Kohn anomaly in case of a spherical Fermi surface. b-d) Case of a flat Fermi surf ace T = ( 1 0 1 )

.

b: E = 0.01; C: E = 0.02; d: E = 0.03.

PHONON WAVEVECTOR

A calculation /5/ shows that some kind of

AN appears even for

flat parts of the Fermi surface, if the gap is sufficiently small. Yet, it is not a Kohn AN, as the slope of the electron susceptibility at 2 kF (2kF being the distance between opposite parts of the Fermi surface) is finite and not infinite. The calculated effect on the group velocity for small q's in T-direction is presented in Fig. 4. Case b resembles the observed behavior. The gap which is 2 V; was character- ized by the parameter E = v;/~EO(T/~) where V; is the value of the

model potential at the point (101 ) and ~O(r/2) is the energy of an un- perturbed state at the zone boundary.

/I/ B. Dorner, A.A. Chernyshov, V.V. Pushkarev, A.Yu. Rumyantsev and R. Pynn; J. Phys. F.

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11, 365 (1981)

/2/ W. Kohn; Phys. Rev. Lett.

2,

393 (1959)

/3/ I.V. Abarenkov and V. Heine; Phil. Mag.

2,

529 (1965)

/4/ A.A. Chernyshov, V.V. Pushkarev, A.Yu. Rumyantsev, B. Dorner and

R. Pynn; J. Phys. F

2,

1983 (1979)