FERMI SURFACE AND dHvA EFFECT IN THE NORMAL STATE OF HIGH Tc A-15 SUPERCONDUCTORS

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HAL Id: jpa-00218067

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FERMI SURFACE AND dHvA EFFECT IN THE NORMAL STATE OF HIGH Tc A-15

SUPERCONDUCTORS

A. Arko, D. Lowndes, A. van Kessel, H. Myron, F. Mueller, F. Muller, L.

Roeland, J. Wolfrat, G. Webb

To cite this version:

A. Arko, D. Lowndes, A. van Kessel, H. Myron, F. Mueller, et al.. FERMI SURFACE AND dHvA EF-

FECT IN THE NORMAL STATE OF HIGH Tc A-15 SUPERCONDUCTORS. Journal de Physique

Colloques, 1978, 39 (C6), pp.C6-1385-C6-1389. �10.1051/jphyscol:19786576�. �jpa-00218067�

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JOURNAL DE PHYSIQUE

Colloque C6, suppl~ment au no

8,

Tome

39,

aoiit

1978,

page C6-1385

FERN1

SURFACE

AND

dHvA EFFECT

IN

THE NORMAL STATE OF

H I G H

T c A-15 SUPERCONDUCTORS

+

++ ++ ++

^35%

A.J. ~ r k o ' , D.H. ~owndes', A.T. Van K e s s e l

,

H.W. Myron

,

F.M. Mueller

,

F.A. Muller

,

L.W. ~ o e l a n d ~ , J . W o l f r a t = , and G.W. webbtt

ateri rials Science Division, Argonne National Laboratory, Argonne, IL. 60439, U.S.A.

r ~ e ~ a r t m e n t o f Physics, University o f Oregon, Eugene,

OR

97403, U.S.A., and Physics Laboratory, University o f Nijmegen, Nijmegen, The Netherlands

++Physics Laboratory, University of Nijmegen, Nijmegen, The Netherlands

ssNatuurkundig Laboratoriwn, University o f Amsterdam, Amsterdam, The Netherlands

t t ~ n s t i t u t e for Pure and Applied Sciences, University of CaZifornia, San Diego, La JoZZa, CA

92093,

U.S.A.

RCsum6.- La s u r f a c e d e Fermi de Nb,Sn a C t C d e t e r m i n e e p a r d e s c a l c u l s d e bande d e t y p e APW. Des 0s- ,

c i l l a t i o n s d e Haas-van Alphen (dHvA) o n t 6tC o b s e r v 6 e s d a n s Nb Sn e t dans V3Si e n accord avec l a sur- f a c e d e Fermi c a l c u l 6 e . Pour c e s deux composCs,

B

1 ' Q t a t norma? d e s o s c i l l a t i o n s dHvA o n t S t 6 mesu- r 6 e s avec d e s monocristaux a y a n t un h a u t r a p p o r t d e r C s i s t i v i t C plongCs dans d e s champs magn6tique.s a l l a n t j u s q u ' l 400 kOe e t l e s nouveaux d e t a i l s de l a s u r f a c e d e Fermi o n t 6 t d mis e n dvidence e t en p a r t i c u l i e r une s t r u c t u r e e l l i p s o y d a l e o s c u l a t r i c e a u t o u r d e M e t une grande s t r u c t u r e cubique au- t o u r de

r.

A b s t r a c t . - The Fermi s u r f a c e of Nb,Sn h a s been d e r i v e d form an APW band c a l c u l a t i o n . d e Haas-van Alphen (dHvA) o s c i l l a t i o n s have been observed i n Nb,Sn and V3Si which g i v e a c o n s i s t e n t FS d e s c r i p - t i o n . Using s i n g l e c r y s t a l s of h i g h r e s i s t a n c e r a t i o ' s and magnetic f i e l d s up t o 400 kOe, dHvA os- c i l l a t i o n s have been s e e n i n t h e normal s t a t e f o r b o t h specimens. New f e a t u r e s of t h e Fermi s u r f a c e i n c l u d e o s c u l a t e d e l l i p s o i d a l s t r u c t u r e around M, and a l a r g e c u b i c a l s t r u c t u r e around

T.

The c u r r e n t h i g h l e v e l of i n t e r e s t i n A-15 m a t e r i a l s i s due t o t h e r e c e n t c o n t i n u i n g discove- r i e s of t h e c o e x i s t e n c e of a v a r i e t y of anomalous normal s t a t e p r o p e r t i e s / I / a t b o t h h i g h and low t e m p e r a t u r e s , w i t h t h e h i g h e s t T m a t e r i a l s showing t h e most p u z z l i n g b e h a v i o r . It i s w i d e l y f e l t t h a t t h e u n d e r l y i n g p h y s i c a l f e a t u r e s l e a d i n g t o t h e s e unusual normal s t a t e p r o p e r t i e s a r e a l s o t h e c a u s e o f h i g h t r a n s i t i o n t e m p e r a t u r e s observed i n many A-15 s t r u c t u r e m a t e r i a l s . A v a r i e t y of p h y s i c a l models a s c r i b i n g s p e c i a l f e a t u r e s t o e i t h e r t h e phonon o r e l e c t r o n d i s t r i b u t i o n s have been invoked t o e x p l a i n t h e normal s t a t e p r o p e r t i e s . D e t a i l e d knowledge of t h e band s t r u c t u r e i s a n e c e s s a r y p r e c u r s o r and un- d e r p i n n i n g t o t h e i n c l u s i o n of t h e electron-phonon and e l e c t r o n - e l e c t r o n c o u p l i n g s and hence t o t h e t h e o r y of s u p e r c o n d u c t i v i t y i n t h e s e m a t e r i a l s . The o n l y p r i o r dHvA measurements on an A-15 a r e t h e re- c e n t r e s u l t s o f Arko e t a l . /2/ f o r Nb,Sb (TC%0.2 K).

Magnetothermal o s c i l l a t i o n s were p r e v i o u s l y observed / 3 / i n V3Ge (T % 6 K). R e c e n t l y (some of u s ) have r e p o r t e d / 4 / on t h e g l o b a l e n e r g y s t r u c t u r e of Nb3Sn. Here we now r e p o r t on band p r o p e r t i e s c l o s e

t o EF

-

t h e d e r i v e d Fermi s u r f a c e . B r i e f l y t h e c a l - +work s u p p o r t e d by t h e U. S

.

Department o f ~ n i r ~ ~ , t h e

N a t i o n a l S c i e n c e Foundation (USA), t h e S t i c h t i n g v o o r Fundamenteel Onderzoek d e r M a t e r i e (The N e t h e r l a n d s ) and NASA (U.S.A)

c u l a t e d e x t r e m a l c r o s s - s e c t i o n a l a r e a s a g r e e w i t h i n 3 t o 5% w i t h t h e dHvA d a t a p r e s e n t e d h e r e f o r s h e e t s n e a r M. I n a d d i t i o n we f i n d a v e r y l a r g e - m a s s e d

(m* = 2.3) c u b i c a l "box-like" s t r u c t u r e n e a r

r

^which

we i d e n t i f y w i t h b r e a k s i n t h e d e r i v a t i v e s of t h e p o s i t r o n a n n i h i l a t i o n d a t a of Samoilov and Weger /5/

on t h e i s o e l e c t r o n i c m a t e r i a l V3Si.

U n f o r t u n a t e l y , t h e v e r y f o r c e s which m a k e t h e h i g h Tc A-15's such i n t e r e s t i n g m a t e r i a l s had, u n t i l now, combined t o p r e v e n t dHvA measurements of t h e Fermi s u r f a c e , t h e o n l y p r i o r dHvA measurements being

t h e v e r y r e c e n t r e s u l t s f o r NbsSb / 2 / . The f o u r main l i m i t i n g e x p e r i m e n t a l f a c t o r s a r e :

1) C y c l o t r o n e f f e c t i v e masses a r e expected t o b e h i g h due t o t h e i n t r i n s i c a l l y f l a t e l e c t r o n i c band s t r u c t u r e and t o t h e s t r o n g electron-phonon coupling (1 1.4 f o r Nb3Sn) ;

2) HC2 i s l a r g e , s o t h a t e x c e p t i o n a l l y h i g h magnetic f i e l d s a r e needed, simply t o r e a c h t h e normal s t a t e ; 3) S i n g l e c r y s t a l s tend t o grow n o n s t o i c h i o m e t r i c a l - l y s o t h a t TD, t h e D i n g l e t e m p e r a t u r e , would be ex- p e c t e d t o b e l a r g e . The A-15's tendency toward i n - t r i n s i c d e f e c t f o r m a t i o n i s presumably a l s o accom- p a n i e d by h i g h dHvA D i n g l e t e m p e r a t u r e s ;

4) C r y s t a l s undergo m a r t e n s i t i c t r a n s f o r m a t i o n i n c o o l i n g from room t o helium t e m p e r a t u r e , s o t h a t s u p p r e s s i o n of t h e dHvA s i g n a l due t o i n t e r f e r e n c e of o s c i l l a t i o n s and t o p h a s e smearing between t e t r a -

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19786576

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JOURNAL D E PHYSIQUE

g o n a l l y d i s t o r t e d subdomains i s expected. Both pha- s e smearing and s c a t t e r i n g (Dingle temperature) c o n t r i b u t e t o an e x p o n e n t i a l a t t e n u a t i o n of t h e dHvA amplitude, w i t h phase smearing becoming more pronounced a s t h e dHvA frequency i n c r e a s e s .

The Nb Sn c r y s t a l s were grown over a p e r i o d o f f o u r months by c l o s e d tube vapor t r a n s p o r t w i t h io- d i n e a s t h e t r a n s p o r t i n g a g e n t . An i n d u c t i v e measu- rement of t h e a c t u a l dHvA c r y s t a l showed a Tc of

17.8 K and a width (10 %

-

90 %) of 0.07 K. Resis- t i v l t y measurements confirm t h a t t h e samples undergo a m a r t e n s i t i c t r a n s f o r m a t i o n a t 51 K. Assumingan, approximate e x t r a p o l a t i o n f u n c t i o n / 6 / we e s t i m a t e R (300 K)

/

R (0 K) = 5 0 and R (0 K) = 1.5 )1Qcm

171.

From t h i s r e s i d u a l r e s i s t i v i t y we e s t i m a t e an e l e c -

e

t r o n mean f r e e p a t h of about 500 A and

w

T > 1 i n

C -

magnetic f i e l d s above 230 kOe, where

w

i s t h e cy- c l o t r o n frequency and T i s a mean s c a t t e r i n g time.

This c o n s i d e r a t i o n i s s u g g e s t i v e of t h e s c a t t e r i n g time being high enough t o s e e t h e dHvA e f f e c t .

The V S i specimen was grown using a f l o a t i n g molten zone technique w i t h i n d u c t i o n h e a t i n g i n a pure argon atmosphere. The zone was passed a l o n g t h e rod (obtained by m e l t i n g t h e c o n s i s t e n t m e t a l s i n a s i l v e r b o a t ) a t t h e r a t e of % 2 cm/h. A m u l t i - g r a i n e d sample was o b t a i n e d which had a l a r g e cen- t r a l g r a i n t h e l e n g t h of t h e sample

(a

1/8" d i m . ) . No r e s i s t a n c e r a t i o o r T measurements were made.

However, i t i s known t h a t V S i i s l e s s s u s c e p t i b l e t h a n NbsSn t o t h e A-15 tendency toward d e f e c t f o r - mation, w h i l e t h e amplitude o f t h e dHvA s i g n a l s ma- k e s i t c l e a r t h a t t h e t o t a l s c a t t e r i n g r a t e i n V3Si must be a t l e a s t comparable t o t h a t of Nb3Sn. The q u a l i t y of both t h e Nb,Sn and V3Si c r y s t a l s was ve- r y g o o l , a s i n d i c a t e d by examination of t h e room temperature d i f f r a c t i o n s p o t s i n Laue back-reflec- t i o n x-ray p i c t u r e s . Both t h e Nb3Sn and V3Si c r y s - t a l s were c u t by s p a r k e r o s i o n i n t o specimens

%

1 mm3 and s u r f a c e damage etched away. O r i e n t e d s i n g l e c r y s t a l samples were mounted i n a s p i r a l gear d r i v e n r o t a t o r w i t h t h e magnetic f i e l d w i t h i n about

l o of a (110) p l a n e ; t h e accuracy w i t h which orien- t a t i o n s a r e known i n t h e (1 10) plHne i s a l s o e s t i - mated t o b e about l o .

The experiments were conducted a t t h e Univer- s i t y of Amsterdam's 400 kOe "slow pulsed f i e l d " f a - c i l i t y u s i n g t h e magnet i n t h e f r e e i n d u c t i v e decay mode t o minimize n o i s e 181. The o u t p u t of a compen-

s a t e d dHvA pickup c o i l was d i f f e r e n t i a t e d twice, f i l - t e r e d t o t a k e o u t some of t h e dc v o l t a g e r e s u l t i n g from incomplete c o i l compensation, a m p l i f i e d and

d i s p l a y e d d i r e c t l y on t h e r e c o r d e r . A t y p i c a l r e - c o r d e r t r a c i n g i s shown i n f i g u r e I .

Nb3 Sn 75' FROM [loo]

Fig. 1 : Dual t r a c e s of a t y p i c a l high speed c h a r t r e c o r d i n g f o r Nb,Sn, showing t h e decay of a 40 T magnetic f i e l d p u l s e and t h e simultaneous r e c o r d i n g

of dHvA o s c i l l a t i o n s followed by t h e superconduc- t i n g t r a n s i t i o n a t H v e r s u s time. The a p p a r e n t o s c i l l a t i o n s below H" a r e n o i s e generated i n t h e pickup c o i l due t o e$%y c u r r e n t s , f l u x jumps, e t c .

.,

and

not

p e r i o d i c i n 1/H.

The dHvA o s c i l l a t i o n s were analyzed by marking t h e p o s i t i o n s of s u c c e s s i v e o s c i l l a t i o n peaks and making a p l o t of o s c i l l a t i o n number v e r s u s 1 / H ; t h e

s l o p e of t h i s "number p l o t " g i v e s t h e dHvA frequency d i r e c t l y and was g e n e r a l l y found t o be a good s t r a i g h t l i n e . Beat s t r u c t u r e , w h i l e obviously pre- s e n t a t some o r , i e n t a t i o n s , was d i f f i c u l t t o r e s o l v e because of t h e few o s c i l l a t i o n s . N e v e r t h e l e s s , i t i s p o s s i b l e t o r e s o l v e s e v e r a l branches i n t h e Nb3Sn d a t a . Figure 2 d i s p l a y s t h e dHvA f r e q u e n c i e s (open c i r c l e s ) found f o r Nb3Sn i n t h e (110) p l a n e , while t h e l i m i t e d d a t a f o r V3Si a r e g i v e n i n Table I. The t y p i c a l e r r o r e s t i m a t e s i n d i c a t e d i n f i g u r e 2 a r e c o n s e r v a t i v e , based on a maximum p o s s i b l e counting e r r o r of one-half o s c i l l a t i o n .

T a b l e I

dHvA Frequencies f o r V3Si

O r i e n t a t i o n Frequency

( l o 6 gauss)

[loo] 6.24

U n t i l r e c e n c l y t h e i n t r i n s i c r e s o l u t i o n of band t h e o r e t i c a l c a l c u l a t i o n s f o r m a t e r i a l s a s com-,

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p l e x a s t h e A-15's was no b e t t e r t h a n about 4,000 K / 1 , 9 / p r e c l u d i n g d i r e c t t h e o r e t i c a l e x p l o r a t i o n of e l e c t r o n i c a l l y - d r i v e n models f o r t h e many i n t e r e s - t i n g A-15 anomalies. However, we w i l l i n t e r p r e t our experimental r e s u l t s h e r e by comparing them w i t h t h e Fermi s u r f a c e p r e d i c t e d by a new h i g h p r e c i s i o n energy band model f o r Nb3Sn, f o r which t h e i n t r i n - s i c r e s o l u t i o n i s l e s s t h a n 500 K 141.

Fig. 3 : The Fermi s u r f a c e of Nb3Sn. The band in- dexing f o l l o w s r e f e r e n c e 141. Note t h a t t h e p o s i - t i o n s o f t h e l a b e l s f o l l o w s t h e f i l l i n g of

2

space volumes s o t h a t band 20 n e a r

r

i s an e l e c t r o n p i e c e and band 15 n e a r M i s a h o l e p i e c e .

10 2 0 3 0 4 0 50 6 0 70 8 0

[OOII [I

111

^IIlOI

MAGNETIC FIELD DIRECTION

Fig. 2 : dHvA f r e q u e n c i e s f o r NbeSn i n t h e (110) p l a n e . The s o l i d c i r c l e s (and t y p i c a l e r r o r b a r s ) a r e t h e experimental r e s u l t s . Accuracy of o r i e n t a - t i o n i n t h e (1 10) p l a n e i s I D . The f r e q u e n c i e s a t a g i v e n o r i e n t a t i o n a r e r e p r o d u c i b l e t o w i t h i n a few

%. The s o l i d l i n e s a r e generated from t h e Fermi sur- f a c e model and band s t r u c t u r e c a l c u l a t i o n of r e f e - r e n c e 141

I n f i g u r e 3 we p r e s e n t t h e Fermi s u r f a c e of Nb,Sn ( i n t e r s e c t i n g bands 15-21) i n t h e p r i n c i p a l symaetry planes. The Fermi energy was determined e x a c t l y from t h e d e n s i t y of s t a t e s 141 and no ad- j u s t a b l e parameters were used. Because of t h e sen- s i t i v i t y o f f i g u r e 3 t o s m a l l energy s h i f t s (espe- c i a l l y bands 19 and 20) we have used t h e ( l a r g e r t h a n 300th o r d e r ) APW s e c u l a r m a t r i x i t s e l f a s a n i n t e r p o l a t i o n scheme t o make t h e p l o t .

Two f e a t u r e s a r e noteworthy compared t o t h e p r e v i o u s V,Sk i s o e l e c t r i c Fermi s u r f a c e of Mattheiss I 9 1 :

1) t h e g r e a t e r confluence o f o s c u l a t e d s t r u c t u r e a t M ;

2 ) t h e f l a t "box-like" s t r u c t u r e s c e n t e r e d a t

T.

G l o b a l l y t h e Nb,Sn band s t r u c t u r e was t h e same a s t h a t of M a t t h e i s s . Making a microscopic com- p a r i s o n n e a r EF between h i s 191 f i g u r e 6(d) and f i - gure 1 of r e f e r e n c e 141, we f i n d t h a t t h e main r e - s u l t i s t h a t

rI2

h a s "dropped" by about 30 mRy r e - l a t i v e s e t s of l e v e l s a t M

-

a r e s u l t e a s i l y under- stood i n t h a t we have included an e x t r a ( n e g a t i v e ) p o t e n t i a l i n s i d e t h e muffin-tin-spheres ( p r i m a r i l y Nb-along-the-"chains") r e l a t i v e t o M a t t h e i s s . Hence

t h e d - l i k e Nb bonding s t a t e TI2 n e a r EF

-

which i s maximally s e n s i t i v e t o such e f f e c t s

-

"drops" r e l a - t i v e t o t h e i n s e n s i t i v e l e v e l s a t M. Since t h e F e d l e v e l f o l l o w s t h e heavy massed I'12 s t a t e , t h e l ' l i g h t "

massed M-centered h o l e - l i k e l e v e l s seen i n f i g u r e 3

"pop-up" through EF. The s t r u c t u r e n e a r R a l s o h a s a l i g h t mass. We have f i t t e d t h e v a l u e s of t h e

"light-massed" bands 15-19 a t 10 p o i n t s near M t o t h e lowest 7 M-harmonics by a l e a s t squares proce- d u r e :

R ~ P

En(k) = C

cn

x y z

R ~ P ⁽¹⁾

where E (k) i s t h e energy of band n a t p o i n t

k,

t h e n

-

C 1 s a r e t h e expansion c o e f f i c i e n t s and x , y , z a r e t h e components of t h e k - v e c t o r d i f f e r e n c e from M , i n atomic u n i t s . A l l terms through q u a r t i c ( i . e . z 4 ) were used. These were used t o o b t a i n t h e a r e a s and masses, m %i = (l/~r)dA/dE l i s t e d i n t a b l e 11. I n gene- r a l , t h e correspondence between t h e observed and c a l c u l a t e d dHvA f r e q u e n c i e s ( f i g u r e 2 and t a b l e 11) i s good. (The experimental l a b e l i n g and i d e n t i f i - c a t i o n was based on t h e a n g u l a r dependence of t h e a r e a s ) . We have l i s t e d i n t a b l e I1 t h e masses f o r t h e M-centered p i e c e s a s a guide t o understanding t h e experimental d a t a . Very low dHvA f r e q u e n c i e s we-

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C6-1388

JOURNAL DE PHYSIQUE

r e d i s c r i m i n a t e d a g a i n s t i n t h e pulsed f i e l d expe- r i m e n t s , both because t h e i r p e r i o d i n H was t o o l o n g and f o r o t h e r experimental r e a s o n s / l o / . Most o t h e r M-centered "missing" o r b i t s probably had too h i g h a mass t o be observed (m f

%

2.4 taband), a l t h o u g h it i s s u r p r i s i n g t h a t 17(z) a t [ l l a were m i s s i n g . I n e=P view of t h e d i f f i c u l t y of t h e measurements and c a l - c u l a t i o n s t h e o v e r a l l agreement i s s a t i s f a c t o r y a n d we conclude t h a t t h e dHvA o s c i l l a t i o n s we have seen a r e c o n s i s t e n t w i t h a s e r i e s of o s c i l a t e d e l l i p s o i d s a t M. Guided by Mattheiss'band c a l c u l a t i o n s / 9 / , both Graebner and Kunzler /3/ ( f o r V3Ge) and Arko, F i s k and Mueller /2/ ( f o r Nb3Sb) have a l s o i n t e r p r e - t e d t h e i r d a t a i n terms of M-centered s t r u c t u r e s , although t h o s e i n t e r p r e t a t i o n s r e q u i r e d r i g i d s h i f - t i n g of EF upward.

Table I1

Areas and masses i n t h e [00

ll

and [ l l q d i r e c t i o n s i n atomic u n i t s .

The convention of M l a b e l i n g i s a s i n f i g u r e 2.

Direct ion

coo ^Cl

n b a Cll01

*

^b

Symetry 'expa '*theory mtheory *exp Atheom t h e o r y m

M-centered o r b i t s

15 (2) 0.47 0.23 1.16 0.42

16(z) 0.74 0.64 2.02 0.97

17(2) 1.43 0.43

18(z) 1.58 1.61 0.46

15(x,y) 1.12 1.17 0.35 0.65 0.32

I ~ ( x , Y ) 2.01 1.03 0.99 0.77

1 7 ( x , ~ ) 1.59 1.66 0.49

P c e n t e r e d ' o r b i t s

a ) e x p e r i m e n t a l d a t a . f

b, mtheory should b e m u l t i p l i e d by (1 + A ) % 2.4 t o o b t a i n experimental masses.

For t h e r-centered s h e e t , we have found i t im- p o s s i b l e t o make a s a t i s f a c t o r y expansion of t h e

19th band energy s t r u c t u r e i n a few c u b i c harmonics / I l l , analogous t o e q u a t i o n ( 1 ) . The a r e a s and mas- s e s l i s t e d i n t a b l e I1 f o r t h e r-centered s h e e t were d e r i v e d n u m e r i c a l l y from k v e c t o r s found from t h e

+

APW s e c u l a r m a t r i x . The e r r o r s of t h e two 19th band masses a r e r e l a t i v e l y l a r g e because they were found

by numerical d i f f e r e n t i a t i o n . (The e f f e c t i v e ener- g i e s used were spaced 0.5 mRy a p p a r t . ) We have g i - ven M-centered and r-centered masses a l s o t o stimu- l a t e measurements of t h e c y c l o t r o n mass. The massof t h e r-centered p i e c e normal t o [001] i s r a t h e r cons- t a n t f o r d i f f e r e n t v a l u e s of k

.

Hence most of t h a t Fermi s u r f a c e s h e e t should c o n t r i b u t e a t a s i n g l e v a l u e of m f

.

T h i s should h e l p t o make t h e r a t h e r h i g h v a l u e of c y c l o t r o n mass of about 5 o b s e r v a b l e . Although o u r p r e d i c t e d Fermi s u r f a c e i s somewhat complicated, t h e r e a r e c l e a r open and c l o s e d d i r e c - t i o n s . We a s k t h a t h i g h f i e l d magneto-resistance experiments be considered a s a f u r t h e r t e s t of our Fermi s u r f a c e topology.

We now f o c u s on an unexpected f e a t u r e of f i - g u r e 3 : t h e two c u b i c a l "box-like" s t r u c t u r e s of band 20 and 19 c e n t e r e d a t

r

and i n t e r s e c t i n g t h e

r

t o X ([loo]) l i n e a t 0.15 and 0.64 ~ / a u n i t s r e s - p e c t i v e l y , and t h e I' t o M ([llo]) l i n e a t 0.15 and 0.62 ~ / a u n i t s , r e s p e c t i v e l y . These f e a t u r e s were i n v a r i a n t t o s l i g h t s h i f t s (+ 3 mRy) of EF, a l t h o u g h t h e e x a c t i n t e r s e c t i o n d i s t a n c e s v a r i e d s l i g h t l y w i t h EF. R e c e n t l y Samoilov and Weger have r e p o r t e d

/ 5 / p o s i t r o n a n n i h i l a t i o n experiments i n iso-elec- t r o n i c VsSi i n t h e [loo] d i r e c t i o n , and we have en- hanced t h e s e n s i t i v i t y of t h e i r d a t a t o Fermi s u r f a - c e e f f e c t s by means of a n o v e l "folding" technique.

Although t h e r e s o l u t i o n of t h e i r experiment was li- mited t o 0.5 m i l l i r a d i a n s ( o r 0.196 ~ / a u n i t s ) , t h e y

f i n d ( t h e i r f i g u r e 2) d e r i v a t i v e s t r u c t u r e w i t h 3 peaks a l o n g [loo] a t 0.185, 0.635 and 0.844 ~ / a u n i t s . C l e a r l y t h e r e i s good agreement between t h e f l a t band 20 and 19 i n t e r s e c t i o n s of

[~oo]

and t h e i r f i r s t two peaks. Band 20 i s a p o s s i b l e c a n d i d a t e f o r t h e i r t h i r d peak s t r u c t u r e

-

p a r t i c u l a r l y t h e f l a t s t r u c t u r e c e n t e r e d around X i n confluence w i t h t h e m u l t i p l e s t r u c t u r e a t M. But t h e s e t h i r d peak iden-

t i f i c a t i o n s a r e t e n t a t i v e . We have assumed an inva- r i a n c e between t h e d e t a i l e d band s t r u c t u r e shape n e a r EF of V3Si and Nb3Sn. Comparing f i g u r e s 6a-6d of M a t t h e i s s /9/ t h e r e i s a c l o s e f a m i l y ressemblarr c e

-

b u t m i c r o s c o p i c a l l y our Nb Sn bands a r e more l i k e h i s V3Si bands t h a n h i s Nb3Sn bands. Samoilov and Weger have i n t e r p r e t e d /5/ t h e i r d a t a i n terms of t h e independent band model / I / wh:se c h i e f d i f - f e r e n c e n e a r EF from o u r model i s t h a t t h e y f i n d t h a t E F i n t e r s e c t s t h e

rZ5

l e v e l s and t h a t t h e i r

I'12

l e v e l s a r e above EF. Our r e s u l t s s u p p o r t Samoilov and Weger's main c o n c l u s i o n of t h e impor- t a n c e of p l a n a r Fermi s u r f a c e s t r u c t u r e s along [ I O ~

(6)

in A-15 materials although our interpretation and wave functions near EF is different from theirs.

(If we artifically modify the potential to place E F at rp,,,we loose agreement with the M-centered dHvA data.) Weger has suggested

/

121 a high magnetic field NMR experiment as a definitive test of Tl,vs.

r25, .

We ask that experimentalists also consider further high resolution positron annihilation work in A-15 materials along other high symmetry direc- tions as a test of band models. We predict that there should be a smaller but similar break along

[llq -

we believe that the Samoilov-Weger model would predict smooth behavior in that direction.

The correspondance between the observed frequencies and those labeled 15(xy), 182 and 17(xy) is good. We conclude that the observed frequencies are consistent with a set of nested ellipsoids at M, similar to observations in Nb,Sb 121 and V , G e 131.

The very low dHvA frequencies are discriminated against in pulsed field experiments, it is reasona- ble that we do not observe the lowest predicted branches of figure 2.

Finally, our present data clearly do not al- low us to determine whether the disappearance ofthe higher frequency oscillations as a result of ther- mal cycling was due to the (progressive) disappearance of a piece of Fermi surface, accompanying the structural transformation, or simply due to an in- crease in Dingle temperature (electronic scattering rate) due to strain. The change in the lattice pa- rameter accompanying the transformation is only of order 1 % so that a major change in the band struc- ture is not expected. One would expect the degene- racy of the branches to be lifted, but our data are not sufficiently accurate to determine any minor splittings in the dHvA frequency branches. However, it does seem clear from our measurements that the effects of the martensitic transformation are rever- sible, and that it will be possible to use the dHvA effect as a detailed probe, in kspace, of the electronic consequences of the A-15 structural transformation.

We would like to acknowledge the help provided by Dr. Sven Hornfeldt in connection with the sample rotator deAgn, by Mr. Weizenbeek in connection with

References

/1/ For a review see : Weger, M.,and Goldberg, I.B., in Solid State Physics, H. Ehrenreich and D. Turnbull, eds. (Academic Press, N.Y.), 1973, vol. 28 ; Testardi, L.R. in Physical Accoustics, W.P. Mason and R.N. Thurston, eds. (Academic Press, N.P.), 1973, vol. 10

/2/ Arko, A.J., Fisk, Z.,and Mueller, F.M., Phys.

Rev. B

3

(1977) 1387

/ 3 / Graebner, J.E. and Kunzler, J.E., J. Low Temp.

Phys.

1

(1969) 443

/4/ Kessel van, A.T., Myron, H.W., Mueller, F.M.

(these ~roceedings)

/5/ Samoilov, S. and Weger, M., Solid State Commun.

24 (1977) 821

-

/6/ Webb, G.W., Fisk, Z., Engelhardt, J.J. and Bader, S.D., Phys. Rev. B

15

(1977) 2624 /7/ Woodard, D.W. and Cody, G.D., Phys. Rev.

136

(1964) A166

181 Gesdorf, R., Muller, F.A.,and Roeland, L.W., Rev. Sci. Instrum.

3

(1965) 1100.

/9/ Mattheiss, L.F., Phys. Rev. B

2

(1975) 2161 /lo/ Arko, A.J., Lowndes, D.H., Muller, F.A.,

Roeland, L.W., Wolfrat, J.W., van Kessel, A.T., Myron, H.W., Mueller, F.M., and Webb, G., Phys.

Rev. Lett. (1978) 1590

/11/ Lage vd, F.C., and Bethe, H.A., Phys. Rev.

2

(1974) 612

/12/ Weger, M. (private communication)

data logging, and the generous support provided to 9

one of us (DHL) by the University of Nijmegen during the time these experiments were being conducted.