Magnetothermal oscillations in beryllium

V o l u m e 11, n u m b e r 2

PHYSICS

MAGNETOTHERMAL

LETTERS

OSCILLATIONS

15 July 1964

IN

BERYLLIUM

*

J. L E P A G E **, M. GARBER and F. J. B L A T T Michigan State University, East Lansing, Michigan Received 17 June 1964

Magnetothermal oscillations were first observed by Ku n zl er et al. 1) in bismuth. The l a r g e s t o s c i l l a t i o n s they o b s e r v e d had an amplitude of 0.003°K. The am p l i t u d e of the o s c i l l a t i o n s , at a given m a g n e t i c f i e l d s t r e n g t h , d e c r e a s e s r a p i d l y a s the e f f e c t i v e m a s s of the e l e c t r o n s involved i n c r e a s e s . Since the e f f e c t i v e m a s s e s of the e l e c t r o n s in m o s t m e t a l s a r e much l a r g e r than t h o s e in b i s m u t h , the use of t h i s te c h n i q u e m i g h t s e e m l i m i t e d . What one a c t u a l l y m e a s u r e s is the change in l a t t i c e t e m p e r a t u r e due to an exchange of e n e r gy between the l a t t i c e and the e l e c t r o n s y s t e m . Thus the amplRude of the o s c i l l a t i o n s o b s e r v e d will also depend on the r a t i o of the s p e c i f i c heat of the e l e c t r o n s y s t e m to the s p e c i f i c heat of the lattice. F r o m t h i s a s p e c t , b is m u th i s not p a r t i c u l a r l y f a v o u r a b l e since it has a l a r g e l a t t i c e s p e c i fic heat (0 D = 120°K). B e r y l l i u m , on the o t h e r hand, has a high Debye t e m p e r a t u r e (l150OK). Thus the magnitude of the effect should be g r e a t l y enhanced. We have o b s e r v e d m a g n e t o t h e r m a l o s c i l l a t i o n s in b e r y l l i u m at 0.9OK in f i e l d s up to 20 kganss. The l a r g e s t o s c i l l a t i o n s o b s e r v e d in b e r y l l i u m w e r e about t h r e e t i m e s a s l a r g e as th o s e o b s e r v e d in b i s m u t h under s i m i l a r e x p e r i m e n t a l conditions. In the f i r s t e x p e r i m e n t a 0.7 g single c r y s t a l of b e r y l l i u m was s u p p o r te d in vacuum by a thinw a l l e d g r a p h i t e tube. T h e t h e r m a l r e l a x a t i o n t i m e to the helium bath of t h i s a r r a n g e m e n t was 30 min. M e a s u r e m e n t s w e r e taken with the c - a x i s of the c r y s t a l p e r p e n d i c u l a r to the plane of r o t a t i o n of the m a g n e t i c field. When the field w a s swept b e tween 0 and 5 k g a u s s , at a r a t e of 400 g a u s s / m i n , eddy c u r r e n t heating p r o d u c e d t e m p e r a t u r e changes of the o r d e r of 0.1°K. F o r this r e a s o n data w e r e taken only above 5 k g a u s s , w h e r e eddy c u r r e n t heating was s m a l l at this sweep r a t e . The m a x i m um a m p l i t u d e of the o s c i l l a t i o n s was about 0.01°K. In a subsequent e x p e r i m e n t the r e l a x a t i o n t i m e * Supported by the National Science Foundation. ** National Science Foundation P r e d o c t o r a l Fellow.

102

was r e d u c e d to one minute to m i n i m i s e the effect of eddy c u r r e n t heating above 5 k g a u s s , so that f a s t e r sweep r a t e s could be used. With the s h o r t e r t i m e constant the amplitude of the l a r g e s t o s c i l l a tions was d e c r e a s e d about 50% f o r a sweep r a t e of 400 g a u s s / m i n . The t e m p e r a t u r e of the s a m p l e was m e a s u r e d u si n g a carbon r e s i s t a n c e t h e r m o m e t e r in an ac bridge. A m a t c h e d c a r b o n r e s i s t o r in good t h e r m a l contact with the helium bath constituted ano t h er a r m of the b r i d g e so a s to c o m p e n s a t e f o r m a g n e t o r e s i s t a n c e and t e m p e r a t u r e d r i f t s of the helium bath. The b r i d g e output was a m p l i f i e d , fed to a p h ase s e n s i t i v e d e t e c t o r and then to the y - a x i s of a M o s e l e y X - Y r e c o r d e r . The x - a x i s w as d r i v e n by the output of a Rawson r o t a t i n g - c o i l g a u s s m e t 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 is shown in fig. 1. The effect of eddy c u r r e n t heating can be seen as an i n c r e a s e in m e a n t e m p e r a t u r e below 6 kgauss. The d e g r e e of c o m p e n s a t i o n a c h i e v e d in the bridge can be seen as the m a g n e t o r e s i s t a n c e of the carbon r e s i s t o r used c o r r e s p o n d s to an app a r e n t t e m p e r a t u r e change of 0.01OK f o r the change in f i el d shown. The r e s u l t s of the p r e s e n t work a g r e e well with p u l s e d - f i e l d De H a a s - V a n Alphen m e a s u r e m e n t s by Watts 2). The F e r m i s u r f a c e of b e r y l lium as d e s c r i b e d by Watts has a " c o r o n e t " of

T

5 10 1'5 FIELD KGAUSS Fig. 1. M a g n e t o t b e r m a l oscillations in Be at 0.9OK. H![ [10T0] Sweep rate, 400 g a u s s / m i n .

Volume 11, number 2 23

~2L r~

PHYSICS LETTERS

zone with t h e i r m a j o r axes p a r a l l e l to the c - a x i s . T h i s p i c t u r e i s in s u b s t a n t i a l a g r e e m e n t with A. P . W . 3) and O. P. W. 4) c a l c u l a t i o n s . In t h i s i n i t i a l study, the a r e a s of the n e c k s of the c o r o n e t of h o l e s have been m e a s u r e d over an a n g u l a r r a n g e of 50 o. The r e s u l t s a r e shown in fig. 2. F u r t h e r work is in p r o g r e s s and a c o m plete study will be p r e s e n t e d e l s e w h e r e .

P R E S E N T WORK x - I MIN T I M E CONSTANT " - 3 0 MIN T I M E CONSTANT o-WATTS'

DATA

I

O >(,9

I

o •

U-

eX eXo

15 June 1964

The a u t h o r s a r e indebted to the F r a n k l i n Institute for the loan of the b e r y l l i u m single c r y s t a l which was p r e p a r e d u n d e r a p u r i f i c a t i o n c o n t r a s t f r o m the Bureau of Naval Weapons. We a r e g r a t e ful to Dr. P. A. Schroeder for m a n y helpful d i s cussions.

%

q( 9(

3' 4'0 ,~5~o1 ~b 2b [t~o]

5'0

6'0

ANGLE IN DEGREES

Fig. 2. Frequency versus rotation. H± [0O01]. The area can be obtained from the Onsager relation f = PicA/2~e.

References

1) J.E. Kunzler, F.S.L. Hsu and W. S. Boyle, Phys. Rev. 128 (1962) 1084. 2) B.R.Watts, Physics Letters 3 (1963) 284. 3) J.H.Terrell, Physics Letters 8 (1964) 149. 4) T. L. Loucks and P.H.Cufler, Phys. Rev. 133 (1964) A819.

holes in the second zone lying in the b a s a l plane. The " b e l l i e s " of the c o r o n e t have d i a m e t e r s about 10 t i m e s those of the " n e c k s " . The e l e c t r o n s u r f a c e s a r e " c i g a r s '~ in the double t h i r d and fourth * * * * *

SCHNELLE

KAPAZITJ~TSMESSUNGEN

AN DER

GRENZFLJ~CHE

Ge/H2SO 4

H. GOBRECHT und O. MEINHARDT II. P h y s i k a l i s c h e n Institut d e r Technischen Universit~it, B e r l i n

Eingegangen am 15. Juni 1964

Der theoretische Verlaul der Randschichtkapazitat nach Bolmenlmmp und Engell I) ist mit Wechselstrom-Messbrtlcken nut sehr angen~daert zu messen. Eine gute b'bereinstimmung konnte erst durch Verwendung schnellerer Messverfahren 2-5) gefunden werden, wobei die zeitliche Aufll~sung in der Gr0ssenordnung yon 1 s lag. Wir haben eine Apparatur nach d e m Prinzip der phasenempfindlichen Gleichrichtung verwendet, die e s gestattet, den Real- und Irnaginarteil eines komplexen Widerstandes glelchzeitig und kontinuierlich bei Frequenzen yon 40 Hz his 60 kHz zu messen. Dabei liegt die zeltllche AullSsung mater 1 ms. Bei der Auswertung haben wir in Tjbereinstimmung mit 2) das in Fig. 1 angegebene Ersatzschaltbild zugrunde gelegt. Das Potential der Ge-Elektrode V E setzt sich aus d e m Oberll~tchenpotential q~s und der HelmhoRzspannung V H zusammen:

150

cp

•theor. ~

'c 100 ":

Rp

'

'; /.---S kH 10 kH ~ kH

~ so g -¢~)o -z~)o -2~o -loo Etektrodenpotlmtiot Vz [ mY ]

Fig. 1. Ersatzschaltbfld und Parallelkapazitttt Cp einer Ge-Elektrode bet verschied~nen Frequenzen (p-Ge 28 Ohm. cm in -i-ffn H2SO4).

V E = -~Ps + V H + const. W e n n A V E nicht allzugross (< 200 m V ) und die zeitliche Anderung A V E / A t >> A V H / A t ist, dann 103