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CYCLOTRON EFFECTIVE MASS AND
IDENTIFICATION OF CARRIERS ON THE FERMI SURFACE OF MOLYBDENUM
M. Surma, J. Lebech, K. Saermark
To cite this version:
M. Surma, J. Lebech, K. Saermark. CYCLOTRON EFFECTIVE MASS AND IDENTIFICATION
OF CARRIERS ON THE FERMI SURFACE OF MOLYBDENUM. Journal de Physique Colloques,
1978, 39 (C6), pp.C6-1091-C6-1092. �10.1051/jphyscol:19786483�. �jpa-00217965�
JOURNAL DE PHYSIQUE
Colloque-.C6, suppigment
auno 8, Tome 39, aoiit 1978,
pageC6-1091
CYCLOTRON E F F E C T I V E MASS AND I D E N T l F I C A T I O N OF CARRIERS ON THE F E R M I SURFACE OF MOLYBDENUM,
M. Surma, 'J. Lebech and K. Saermark
Jnstitubk o f Physics,
A.Mickiewicz University
60-780Pozna6, u l . Grunwaldzka
6,Poland.
Physics Laboratory
I ,The Technical University of Denmark,
DK-2800Lyngby, Denmark.
Rdsum6.- La r6sonance c y c l o t r o n i q u e e s t 6 t u d i d e p a r l a mdthode de t r a n s m i s s i o n dans des p l a q u e s de molybdsne m o n o c r i s t a l l i n de h a u t e p u r e t 4 , d'une d p a i s s e u r de 0,15 mm e t 0 , 2 5 mm, dans l e p l a n c r i s -
t a l l o g r a p h i q u e ( 1 1 0 ) , e n u t i l i s a n t un champ micro-ondes d e f r 6 q u e n c e 45 GHz. Le r a p p o r t s i g n a l l b r u i t o b t e n u e n t r a n s m i s s i o n f u t m e i l l e u r , d'un f a c t e u r de 10, que c e l u i de l a mdthode t r a d i t i o n n e l l e de r d f l e c t i o n . De nouveaux p o r t e u r s de c h a r g e , p r d s e n t a n t d e s rdsonances c y c l o t r o n i q u e s j u s q u ' 8 pr6- s e n t non d g t e c t s e s , s o n t o b s e r v 6 s . Leurs masses e f f e c t i v e s c y c l o t r o n i q u e s , a i n s i que c e l l e s d e s . p o r - t e u r s d 6 j a a n a l y s g s , s o n t ddtermindes. Les a u t e u r s p r o p o s e n t une l o c a l i s a t i o n de c e s p o r t e u r s de c h a r g e s u r l a s u r f a c e d e Fermi.
A b s t r a c t . - C y c l o t r o n resonance by t h e t r a n s m i s s i o n method i s s t u d i e d i n s l i c e s , 0.15 mm and 0.25 mm t h i c k , of h i g h p u r i t y molybdenum s i n g l e c r y s t a l i n t h e c r y s t a l l o g r a p h i c a l p l a n e (110) a p p l y i n g a 45 GHz microwave f i e l d . The s i g n a l / n o i s e r a t i o achieved i n t h e t r a n s m i s s i o n method was b e t t e r by a f a c t o r of 10 t h a n t h a t of t h e t r a d i t i o n a l r e f l e c t i o n method. New c a r r i e r s , w i t h h i t h e r t o u n d e t e c t e d c y c l o t r o n r e s o n a n c e , were observed. T h e i r e f f e c t i v e mass, a s w e l l a s t h e e f f e c t i v e mass of p r e v i o u s - l y a n a l y z e d c a r r i e r s , a r e determined. A l o c a l i s a t i o n of t h e c a r r i e r s o n MO Fermi s u r f a c e p o c k e t s i s given.
When s t u d y i n g c y c l o t r o n resonance (CR) i n t h i n s l i c e s of MO / l / ; B i and BiSb a l l o y s / 2 / s i n g l e c r y s t a l s , r e s o n a n c e d e t e c t i o n was o b t a i n e d n o t o n l y a p p l y i n g t h e t r a d i t i o n a l r e f l e c t i o n method b u t , a s w e l l , by t r a n s m i s s i o n t e c h n i q u e 131. Moreover, MO s i n g l e c r y s t a l s l i c e s 0.15 mm and even 0.21 m t h i c k a r e f i r s t found t o be t r a n s p a r e n t f o r a microwave f i e l d .
Recording c y c l o t r o n r e s o n a n c e s i g n a l s by t h e t r a n s m i s s i o n method, new c a r r i e r s h i t h e r t o n o t ana- l y z e d by CR were o b s e r v e d i n MO i n t h e c o u r s e of t h i s s t u d y . R e c e n t l y , Lubzens e t a 1
141,
a p p l y i n g s i m i l a r t r a n s m i s s i o n t e c h n i q u e , observed s h a r p peaks of mi- crowave f i e l d t r a n s m i s s i o n by s l i c e s of copper s i n g l e c r y s t a l s i n c r y s t a l l o g r a p h i c a l d i r e c t i o n s d e f i n e d by open o r b i t s . W i t h r e g a r d tn R e f s / 1 , 2 , 3 / and 141, which r e p o r t microwave t r a n s m i s s i o n by s l i c e s of MO B i and Cu, we draw t h e c o n c l u s i o n t h a t , f o r p a r t i c u - l a r topography of t h e Fermi s u r f a c e (FS) of t h e me- t a l , i n p e c u l i a r c r y s t a l l o g r a p h i c a t d i r e c t i o n s , and under c o n d i t i o n s of CR, t h e e f f e c t i s e x t r a o r d i n a r i - l y s t r o n g . Under t h e s e c o n d i t i o n s , we performed and a n a l y s i s of Azbel-Kaner c y c l o t r o n r e s o n a n c e of c a r - r i e r s i n t h e (110) p l a n e o f MO. Our a n a l y s i s was c a r r i e d o u t f a r t h e d i r e c t i o n s of magnetic f i e l d B -fs u b t e n d i n g a n g l e of 0° ; 6" ; 45" ; 54.74" ; 82.6' 87' and 90' w i t h t h e c r y s t a l l o g r a p h i c a l <001> a x i s of h i g h p u r i t y MO s i n g l e c r y s t a l (RRR = 40,000), a t
t e m p e r a t u r e s r a n g i n g from 4,2 K t o 2 K, a p p l y i n g a microwave f i e l d o f 45 GHz.
The r e s u l t s of o u r measurements of t h e c y c l o - t r o n e f f e c t i i r e mass (CEM) of t h e c a r r i e r s observed a r e g i v e n i n t a b l e I.
F i g u r e 1 g i v e s a g r a p h i c a l comparison of t h e r e s u l t s of Herrmann / 5 / f o r t h e CEM mx/mo i n Mo/dots/
and t h o s e of t h e p r e s e n t work / c i r c l e s and d o t s / , f o r t h e i n d i c a t e d d i r e c t i o n s i n t h e (110) p l a n e .
F i g . 1 : C y c l o t r o n e f f e c t i v e Mass i n Molybdenum : dots-Herrmann r e s u l t s
151,
c i r c l e s and dots-pre- s e n t work.Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19786483
Table I. : C y c l o t r o n E f f e c t i v e Mass mX/mo a t (110) p l a n e of MO E l e c t r o n
0.338 r o . 0 0 8
Hole Octahedron
1 . 2 8 + 0 . 0 1 ( a ) 0.835
+
0.008(b)1 . 2 7 f 0 . 0 1 ( a ) 0.831 f 0.08 (b) 1 . 0 5 f 0 . 0 5 ( a ) 0 . 8 3 k 0 . 0 2 (b)
-
0.83
+
0.04 ( b ) 0.910 i 0.004(a) 0.917 f 0.005(a) 0.910 f 0.002(a)E l e c t r o n J a c k
Neck of t h e E l e c t r o n JacK
One n o t e s t h a t t h e e x p e r i m e n t s of Herrmann d e t e c t e d no c a r r i e r s w i t h mX<*0.33 m and o t h e r s c a r r i e r s ha- v i n g t h e CEM shown by c i r c l e s i n f i g u r e 1 .
The i n t e r p r e t a t i o n of t h e c a r r i e r s observed by u s on t h e FS o f MO i s based on our s t u d i e s of CR supplemented by t h e r e s u l t s of o t h e r s d e r i v e d from s t u d i e s of t h e de H a a s v a n Alphen e f f e c t ( d ~ v A ) 161, r a d i o - f r e q u e n c y
-
s i z e e f f e c t / 7 / and a n a l y s e s of t h e e l e c t r o n s t r u c t u r e of MO 181. I n supplementa- t i o n of our p r e v i o u s l y p u b l i s h e d i n t e r p r e t a t i o n / l / of t h e h o l e e l l i p s o i d s and e l e c t r o n l e n s e s of t h e FS o f MO, we a s s i g n t h e new CEMs r e p o r t e d i n t h e p r e s e n t p a p e r t o t h e f o l l o w i n g MO Fermi s u r f a c e po- c k e t s .1 . E l e c t r o n b a l l . The a n i s o t r o p y of CEM i s shown i n Table I. For a n g l e s (B, <001>) l a r g e r t h a n 82.6', -t
CR s i g n a l d i s a p p e a r e d . No CR s i g n a l i s p r e s e n t f o r t h e d i r e c t i o n < I l l > . I n t h i s d i r e c t i o n , t h e dHvA e f f e c t e x h i b i t s an extrenum of dHvA o s c i l l a t i o n f r e q u e n c y from b r a n c h X 161. Assuming m X = 0.338 m. and an e l e c t r o n b a l l r a d i u s of k = 0.31
L-'
161,F
we o b t a i n a Fermi v e l o c i t y of e l e c t r o n s of vF = 1.06 X 106m/s.
2. Hole octahedron. The a n i s o t r o p y of CEM i s shown i n T a b l e I. Here, two groups ( a ) and ( b ) of c a r - r i e r s a r e found t o be p r e s e n t .
3. E l e c t r o n j a c k . CR i s observed f o r t h e o r b i t (d)
comprising two b a l l s f o r a n g l e s (B,<001>) + = 82.6' 87' and 90" o n l y . The CEM a n i s o t r o p y i s shown i n Table I. Another group o f c a r r i e r s ( c ) g i v e s CR f o r a n g l e s (B,<001>) -t = 90' and 54.74' a l s o .
4. Neck o r b i t of t h e j a c k . The CEM a n i s o t r o p y i s shown i n T a b l e I.
5. The i d e n t i f i c a t i a n of t h e c a r r i e r s w i t h CEM g i - v e n i n t h e l a s t l i n e of T a b l e I i s d i f f i c u l t , and w i l l r e q u i r e an e l u c i d a t i o n o f t h e dimensions of t h e i r o r b i t s by t h e method of CR s i g n a l c u t - o f f .
R e f e r e n c e s
/ l / Surma, M . , Lebech, J. and Saermark, K., S o l i d S t a t e Commun.
17
(1975) 1359; i b i d . 0 - ( 1 9 7 6 ) 493.121 Braune, W., Lebech, 3. and Saermark, K., i n p r e s s / 3 / Lebech, J., Surma, M. and Saermark, K., Phys.
L e t t . (1975) 211.
141 Lubzens, D., Grunzweig-Genossar, J. and S c h u l t z , S., Phys. Rev.
B16
(1977) 2474./ 5 / Herrmann, R., Phys. S t a t . S o l .
2
(1968) 427.161 H o e k s t r a , J.A. and S t a n f o r d , J . L . , Phys. Rev.
(1973) 1416.
/ 7 / C l e v e l a n d , J.R. and S t a n f o r d , J.L., Phys. Rev.
(1971) 311.
/ 8 / K o e l l i n g , D.D., M u e l l e r , F.M. and Arko, A . J . , Phys. Rev. B= (1974) 4889.
