Topology of the Fermi surface of AuAl2

Volume 25A, number 10

TOPOLOGY

P HY S I C S L E T T E R S

OF

THE

J. T. L O N G O

FERMI

SURFACE

** and P. A. S C H R O E D E R

20 November 1967

OF

AuAI

2 *

**

Department of Physics. Michigan State University, East Lansing. Michigan. USA and D. J. SE LLMYER ***

Massachusetts Instilute of Technology, Cambridge, Massachusetts, USA Received 1 November 1967

This paper compares experimentally determined topological properties of the Fermi surface of AuA12 with those predicted by a computer analysis of the nearly free electron model.

We have i n v e s t i g a t e d the m a g n e t o r e s i s t a n c e of the m e t a l l i c compound AuA12 in f i e l d s up to 140 kG. The s a m p l e s w e r e sufficiently p u r e [p(295°K)/p(4.2°K) = 400 550] that the h i g h - f i e l d condition was s a t i s f i e d . We c o m p a r e our e x p e r i m e n t a l r e s u l t s with those p r e d i c t e d by a c o m p u t e r a n a l y s i s of the MR e x p e c t e d f r o m a n e a r l y f r e e e l e c t r o n m o d e l . In g e n e r a l t h e r e i s q u a l i t a tive a g r e e m e n t with one notable exception. P r e l i m i n a r y w o r k on AuGa 2 and AuIn 2 c r y s t a l s with r e s i s t a n c e r a t i o s of 200 and 60, r e s p e c t i v e l y , i s a l s o c o n s i s t e n t with the m a g n e t o r e s i s t a n c e p r o p e r t i e s of a n e a r l y f r e e e l e c t r o n model. All t h r e e compounds c r y s t a l l i z e in the f.c.c. f l u o r i t e s t r u c t u r e with t h r e e a t o m s p e r p r i m i t i v e c e l l . The n e a r l y f r e e e l e c t r o n F e r m i s u r f a c e s , a s s u m i n g seven n e a r l y f r e e e l e c t r o n s p e r p r i m i tive c e l l , a r e shown in a p a p e r by Jan et al. [1], who i n v e s t i g a t e d t h e s e compounds with the de H a a s - v a n Alphen effect. We have a n a l y z e d the n e a r l y f r e e e l e c t r o n s u r f a c e s with the a i d of a c o m p u t e r p r o g r a m which g i v e s the d i r e c t i o n of open o r b i t s and the t h i c k n e s s of the band of open o r b i t s , m e a s u r e d p a r a l l e l to B . The a n a l y s i s i n d i c a t e s that the 4111) d i r e c t e d necks in the t h i r d zone hole s u r f a c e s u p p o r t p r i m a r y open o r b i t s along 41115 d i r e c t i o n s and s e c o n d a r y open o r b i t s along 41005 and 4110) d i r e c t i o n s . The 41005 d i r e c t e d a r m s of the fourth zone e l e c t r o n s u r * This work was performed in part at the National Magnet Laboratory which is supported by the U.S.A.F.O.S.R. ** Supported by the National Science Foundation. *** Supported by the Advanced Research Projects Agency.

face s u p p o r t p r i m a r y , s e c o n d a r y , and t e r t i a r y open o r b i t s in the (1005, (110), and (1115 d i r e c tions, r e s p e c t i v e l y . A l s o on the fourth zone a r m s a r e (1005 d i r e c t e d open o r b i t s when B//(l105 and, for B/l(211), n o n i n t e r s e c t i n g bands of open o r b i t s along (1115 and (1105 d i r e c t i o n s . Since the n e a r l y f r e e e l e c t r o n m o d e l a s s u m e s an odd n u m b e r of v a l e n c e e l e c t r o n s , AuA12 should be u n c o m p e n s a t e d . T h e s e r e s u l t s , when c o m bined with the t h e o r y of h i g h - f i e l d g a l v a n o m a g netic effects, then i m p l y a s a t u r a t i n g f i e l d d e pendence for a g e n e r a l f i e l d d i r e c t i o n and for B//(lO05, (1115, and (2115; a q u a d r a t i c f i e l d d e pendence i s e x p e c t e d for B//(l105 and for B in

{100}, {110}, and { m } . Fig. 1 shows a r o t a t i o n plot along the path shown in the s t e r e o g r a m . Although h i g h e r p u r i t y s a m p l e s of AuGa 2 and AuIn 2 a r e r e q u i r e d , we have included t h e i r r o t a t i o n plots to show the s i m i l a r i t y to AuA12. As the f i e l d c r o s s e s { 100} and two c l o s e l y s p a c e d { 110} p l a n e s , we o b s e r v e p e a k s in the m a g n e t o r e s i s t a n c e which have a p proximate B 2 field dependences. For a general field d i r e c t i o n s a t u r a t i o n o c c u r s a s e x p e c t e d for an u n c o m p e n s a t e d m e t a l . As the f i e l d s w e e p s through {111}, n e a r a (2115 d i r e c t i o n , a peak i s not o b s e r v e d . The t r a n s v e r s e m a g n e t o r e s i s t a n c e plot for a n o t h e r c r y s t a l f o r B in { 111} shows an approximate B 2 behavior everywhere, except f o r B//42115 and {1105 w h e r e the m a g n e t o r e s i s tance s a t u r a t e s and i s p r o p o r t i o n a l to B0.8, r e s p e c t i v e l y . T h e r e f o r e , e x c e p t f o r the equivocal b e h a v i o r f o r B//4110), t h e s e r e s u l t s a g r e e with the n e a r l y f r e e e l e c t r o n p r e d i c t i o n s . F i g . 2 shows the m a g n e t o r e s i s t a n c e in a 747

Volume 25A. number 10

PHYSICS

LETTERS

20 November 1967

Ap/p P 100 t "

AuAIz

0(3}

(2.0 i.~)

l, 80 80

60 d-40

40 I I0}

12.0, .7J 1.6

AuAI~ 20

AuGa2

20"I~~.

is

i

,.-+ ~

15 °

30"

"

l

Auln 2 45 °

60 °

75 =

90 °

Fig. 1 Transverse-to-longitudinal magnetoresistance along the path shown in the 110 stereogram for all three compounds. B = 130 kG. { 100} plane f o r al l t h r e e compounds. The field d e p e n d e n c e , e x p r e s s e d as B n, is noted at v a r i o u s a n g l e s on the p l o t s . C l e a r l y AuA12 exhibits r a t h e r unusual b e h a v i o u r o v e r much of this plot, v i z . , w h e r e n d e c r e a s e s as the f i e l d i n c r e a s e s . T h i s i s e s p e c i a l l y t~ue f o r B / / < l l 0 ) w h e r e the m o d e l p r e d i c t s a B d e p e n d e n c e . One p o s s i b l e e x p l a n a t i o n i s that f o r B ~ 100kG, m a g n e t i c b r e a k d o w n is c l o s i n g open o r b i t s c a u s i n g the m a g n e t o r e s i s t a n c e to begin to s a t u r a t e . A knowl e d g e of c e r t a i n e n e r g y gaps o r f u r t h e r e x p e r i m e n t a l e v i d e n c e i s n e e d e d , h o w e v e r , to draw any c o n c l u s i o n s on this point. The c o m p u t e r a n a l y s i s a l s o h a s been u s e d to c o m p u t e the m a g n e t o r e s i s t a n c e to within a c o n -

748

\-\y / ,~"

do"

,8

odo)

A.in, ~o"

7'5"

(rio>

Fig. 2. Experimental transverse magnetoresistance in { 100} for all three compounds. B = 140 kG for AuA12, 130 kG for AuIn2 and AuGa 2. A single number indicate~ the exponent n at 140 kG; the first and second of a pair of numbers give n at 50 kG and 140 kG, respectively. stant f a c t o r f o r B in a { 100} plane, in a m a n n e r s i m i l a r to that of C o l e m a n et al. [2]. It is i n t e r e s t i n g that, in spite of the a s s u m p t i o n of a constant r e l a x a t i o n t i m e o v e r the F e r m i s u r f a c e , the cal cu l at i o n does r e p r o d u c e the g e n e r a l shape of the e x p e r i m e n t a l plots of fig. 2 f o r AuA12 and AuGa 2.

References 1. J. p. Jan, W. B. Pearson, Y. Saito and I. M. Templeton, Phil. Mag. 12 {1965) 1271. 2. R.V. Coleman, A.J. Funes, J.S. Plaskett and C. M. Tapp, Phys. Rev. 133 (1964) A521.