RECENT EXPERIMENTS IN SUPERFLUID 3He

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RECENT EXPERIMENTS IN SUPERFLUID 3He

D. Osheroff

To cite this version:

D. Osheroff. RECENT EXPERIMENTS IN SUPERFLUID 3He. Journal de Physique Colloques,

1978, 39 (C6), pp.C6-1270-C6-1277. �10.1051/jphyscol:19786556�. �jpa-00218045�

JOURNAL DE PHYSIQUE

Colloque C6, suppl6ment au

no

8, Tome 39, aotit 1978, page C6-1270

RECENT EXPERIMENTS I N S U P E R F L U I D 3 ~ e

D.D. Osherof f

BeZ

Z

Laboratories, Murray H i Z

Z ,

New Jersey, U.S. A .

RdsumC.- On p r d s e n t e u n e r e v u e du t r a v a i l e x p 6 r i m e n t a l r d c e n t d a n s 1 1 ~ H e s u p e r f l u i d e c o n c e r n a n t l a r e s o n a n c e m a g n s t i q u e , l e s e f f e t s d ' o r i e n t a t i o n d e s d i s t o r s i o n s d a n s l e s n u a g e s G l e c t r o n i q u e s d e s atomes d V 3 H e q u i c o m p o r t e n t l e s p a i r e s d e Cooper, e t l e s e x p d r i e n c e s P h a u t e r d s o l u t i o n s u r p e n d u l e d e t o r s i o n , y c o m p r i s l e s m e s u r e s d e ps/p e t d e

n.

Un e f f o r t e s t f a i t pour d i s c u t e r d e q u e l l e f a p n l e s e x p d r i e n c e s d i v e r s e s s e r a p p o r t e n t l ' u n e 1 l ' a u t r e e t P n o t r e c o n n a i s s a n c e d e l r 3 H e s u p e r f l u i d e . A b s t r a c t . - A r e v i e w i s p r e s e n t e d o f r e c e n t e x p e r i m e n t a l work i n s u p e r f l u i d 3 ~ e i n v o l v i n g m a g n e t i c r e s o n a n c e , t h e o r i e n t i n g e f f e c t s o f d i s t o r t i o n s i n t h e e l e c t r o n c l o u d s of t h e 3 ~ e atoms c o m p r i s i n g t h e Cooper p a i r s , and t h e h i g h r e s o l u t i o n t o r s i o n a l pendulum e x p e r i m e n t s i n c l u d i n g measurements o f p s / p and 0 . An e f f o r t i s made t o d i s c u s s v a r i o u s e x p e r i m e n t s a s t h e y r e l a t e t o e a c h o t h e r and t o our u n d e r s t a n d i n g o f s u p e r f l u i d 3 ~ e .

INTRODUCTION.- I n t h i s a r t i c l e I w i l l d i s c u s s r e c e n t t h e s e o b s e r v a t i o n s had r e g a r d i n g t h e s u p e r f l u i d s e x p e r i m e n t s i n j u s t t h r e e a r e a s o f s t u d y , t r y i n g t o t h e m s e l v e s . S i n c e t h a t t i m e , s t u d i e s of n u c l e a r ma- r e l a t e them t o e a c h o t h e r and t o t h e f u l l e r u n d e r s - g n e t i c phenomena have c e n t e r e d around t h r e e m a j o r t a n d i n g of 3 ~ e we hope t o o b t a i n . These a r e a s a r e a r e a s : 1) A t t e m p t i n g t o r e s o l v e t h e d i s a g r e e m e n t s m a g n e t i c r e s o n a n c e , e l e c t r o n i c e f f e c t s i n v o l v i n g the which e x i s t e d when t h e B p h a s e s u s c e p t i b i l i t y was e l e c t r o n c l o u d s of t h e 3 ~ e atoms, and r e c e n t measu- measured s t a t i c a l l y and t h e n d y n a m i c a l l y . 2 ) S t u d i e s r e m e n t s of

n

and ps/p. I r e g r e t n o t b e i n g a b l e t o o f s p i n dynamics o f s p a t i a l l y non-uniform s a p l e s , a n d c o v e r more i n t h i s m a n u s c r i p t , and a p o l o g i z e t o tho- 3) S t u d i e s o f l o n g i t u d i n a l s p i n r e c o v e r y u s i n g t h e s e whose work i s n o t m e n t i o n e d . U n f o r t u n a t e l y , spa- p o w e r f u l SQUID-NMR t e c h n i q u e s . I n a d d i t i o n t o t h e s e c e i s t o o l i m i t e d , and t h e r e i s t o o much t o d i s c u s s . t h r e e m a j o r a r e a s of i n t e r e s t , e f f o r t s have c o n t i - A) N u c l e a r Magnetism.-

nued t o measure l o n g i t u d i n a l r e s o n a n c e f r e q u e n c i e s a s a f u n c t i o n o f p r e s s u r e and l i n e w i d t h s a s a func- i ) I n t r o d u c t i o n . - The u n u s u a l b e h a v i o r o f t h e nu- t i o n of t e m p e r a t u r e ; and I r e f e r t h e r e a d e r t o t h e c l e a r m a g n e t i c moments i n s u p e r f l u i d 3 ~ e was one o f v e r y b e a u t i f u l work by Avenel e t a l . / 7 / a l t h o u g h I t h e e a r l i e s t and most u s e f u l p r o b e s o f t h e n a t u r e w i l l n o t c o v e r i t h e r e .

of t h e o r d e r e d p h a s e s / I / . I n t e r p r e t e d t h r o u g h t h e t h e o r e t i c a l work o f A . J . L e g g e t t / 2 / , t h e s h i f t s i n t h e m a g n e t i c r e s o n a n c e f r e q u e n c i e s o f q u a s i - u n i f o r m s a m p l e s , a s w e l l a s t h e l o n g i t u d i n a l r e s o n a n c e modes f i r s t p r e d i c t e d by L e g g e t t / 3 / , a n d combined w i t h mea- s u r e m e n t s of t h e n u c l e a r m a g n e t i c s u s c e p t i b i l i t i e s / 4 / , h a v e a l l o w e d u s t o f i n g e r p r i n t t h e m i c r o s c o p i c i d e n t i t i e s o f t h e new s t a t e s w i t h i n t h e b r o a d mani- f o l d o f L = I s u p e r f l u i d s c o n s i d e r e d . The o b s e r v a - t i o n o f a t r a n s v e r s e r e s o n a n c e f r e q u e n c y s h i f t i n t h e A1 p h a s e /S/,combined w i t h t h e t h e o r e t i c a l work by N . D . Mermin / 6 / f u r t h e r enhanced t h e l i k e l i h o o d t h a t t h e A and B p h a s e s a r e L = 1 s u p e r f l u i d s b y e l i m i n a t i n g a s a p o s s i b l e c o n t e n d e r f o r t h e A, pha- s e t h e most l i k e l y L = 3 c a n d i d a t e .

By t h e t i m e o f LT14 a c o n s i d e r a b l e amourltwas known b o t h a b o u t t h e s u p e r f l u i d s p i n d y n a m i c s , even i n t h e n o n - l i n e a r r e g i m e , and t h e i m p l i c a t i o n s t h a t

i i ) S t a t i c S u s c e p t i b i l i t i e s i n 3 ~ e ~ . - One o f t h e most u n s e t t l i n g c o n t r o v e r s i e s i n t h e f i e l d o f s u p e r - f l u i d i t y i n 3 ~ e h a s been t h e d i s a g r e e m e n t o f s t a t i c measurements o f t h e B p h a s e s u s c e p t i b i l i t y ,

xB,

S w i t h v a l u e s , X B , made u s i n g D NMR t e c h n i q u e s . G e n e r a l l y ,

S ' S

s t a t i c measurements a c t u a l l y r e c o r d

xN - xB,

w h e r e a s NMR measurements r e c o r d o n l y t h e n u c l e a r s u s c e p t i - b i l i t y d i r e c t l y . Although o n e d o e s n o t e x p e c t a change i n t h e n o n - n u c l e a r m a g n e t i c s u s c e p t i b i l i t y c o n t r i b u t i o n s i n t h e B p h a s e , p r e v i o u s e x p e r i m e n t s

S S D D

have c o n s i s t e n t l y found XN

- xB

= 1.5 (xN

-

xB) /8/.

One p o s s i b l e s o u r c e o f t h e a b o v e d i s a g r e e m e n t was l o n g b e l i e v e d t o b e t h e manner i n which t h e s t a - t i c SQUID m a g n e t o m e t e r s were c a l i b r a t e d . T o e l i m i n a - t e t h i s p o s s i b l e f a i l i n g o f t h e SQUID t e c h n i q u e , two s e p a r a t e e x p e r i m e n t s h a v e b e e n performed /9,10/ i n which t h e SQUID s y s t e m was c a l i b r a t e d by u s i n g a r e - s o n a n t r a d i o f r e q u e n c y ( r f ) p u l s e t o t i p t h e nuclea'r

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19786556

m a g n e t i z a t i o n by a known a n g l e , u s u a l l y 180°, and o b s e r v i n g t h e change i n t h e s t a t i c m a g n e t i z a t i o n i n t h e p r o c e s s . T h i s c a l i b r a t i o n was g e n e r a l l y p e r f o r - med j u s t above T

.

Once c a l i b r a t e d , t h e SQUID s y s -

tems were a b l e t o measure t h e changes i n s u s c e p t i - b i l i t y a t t h e A

2

B t r a n s i t i o n s and a s a f u n c t i o n of t e m p e r a t u r e by n o t i n g t h e changes i n m a g n e t i z a t i o n a s t h e y had measured them b e f o r e . I n work by Webb a t Argonne / 9 / , however, t h e r e c o v e r y of t h e B p h a s e m a g n e t i z a t i o n could b e o b s e r v e d f u l l y f o l l o w i n g a n r f p u l s e w h i l e i n t h e s u p e r f l u i d p h a s e , s o t h a t Webb was a b l e t o u s e h i s SQUID s y s t e m t o a c t u a l l y measure t h e dynamic s u s c e p t i b i l i t i e s a s w e l l a s t h e s t a t i c changes i n s u s c e p t i b i l i t y . T h i s e l i m i n a t e d t h e need t o a d j u s t thermometry s c a l e s i n o r d e r t o compare h i s r e s u l t s t o t h e dynamic measurements.

The r e s u l t s o f t h e s e e x p e r i m e n t s a r e s t i l l a mystery however : The s t a t i c s u s c e p t i b i l i t y d i f f e r e n c e s Webb measures a r e s t i l l n e a r l y 1.5 t i m e s a s l a r g e a s t h e d i f f e r e n c e s ,

xN - xB,

D D which he m e a s u r e s d y n a m i c a l l y .

I n work a t La J o l l a by S a g e r e t a l . / I 0 1 mea- s u r e m e n t s were made i n t h r e e d i f f e r e n t g e o m e t r i e s , a l t h o u g h no s i g n i f i c a n t dependence o n geometry was

S S

n o t e d . I n t h e La J o l l a work

xA - x

was r e c o r d e d a t B

*the thermodynamic B -+ A t r a n s i t i o n a s a f u n c t i o n of p r e s s u r e . T h e i r r e s u l t s show t h a t t h e s t a t i c s u s c e p - t i b i l i t y d i f f e r e n c e s a r e s t i l l c o n s i s t e n t l y l a r g e r t h a n t h e dynamic d i f f e r e n c e s , b u t t h a t t h e r a t i o o f t h e two v a l u e s a p p r o a c h e s u n i t y a s t h e p r e s s u r e ap- p r o a c h e s t h e m e l t i n g p r e s s u r e . T h i s f e a t u r e was n o t c l e a r i n t h e Argonne r e s u l t s , a l t h o u g h t h o s e r e s u l t s were o b t a i n e d o n l y a t 26.5 b a r and 18 b a r p r e s s u r e s . Because t h e La J o l l a group must compare t h e i r s t a t i c v a l u e s w i t h dynamic measurements made e l s e w h e r e ,

t h e r e i s s t i l l a q u e s t i o n c o n c e r n i n g thermometry s c a l e s , and hence some room f o r f u r t h e r a d j u s t m e n t I t seems h i g h l y u n l i k e l y , however, t h a t any s u c h m a n i p u l a t i o n w i l l e l i m i n a t e t h e s t i l l s u b s t a n t i a l d i s c r e p a n c y between t h e r e s u l t s o f t h e two d i f f e r e n t

t y p e s o f measurements a t lower p r e s s u r e s , and t h e n a t u r e of t h e d i s a g r e e m e n t i s s t i l l a fundamental q u e s t i o n we do n o t u n d e r s t a n d .

i i i ) S p i n Dynamics of Non-Uniform Samples.- E f f o r t s t o u n d e r s t a n d s u p e r f l u i d 3 ~ e s p i n dynamics i n t h e p r e s e n c e of non-uniform t e x t u r e s have r e p r e s e n t e d a major new t h n s t s i n c e LT14, and one which may w e l l b e e x p e c t e d t o c o n t i n u e f o r y e a r s t o come.

The f i r s t c a r e f u l e f f o r t t o u n d e r s t a n d s t a n - d i n g s p i n waves i n a known geometry was made a t B e l l Labs. / 1 1 , 1 2 / . I n t h a t work NMR s p e c t r a o f a sample

o f 3 ~between p a r a l l e l p l a t e s was s t u d i e d when t h e e ~ s t a t i c f i e l d was i n t h e p l a n e o f t h e p l a t e s . I n s u c h a geometry t h e a n i s o t r o p y a x i s i n 3 ~ e ~ , 3, i s f i x e d a l m o s t r i g i d l y a t t h e w a l l s t o l i e n e a r l y p e r p e n d i - c u l a r t o Ho, b u t bends upward between t h e p l a t e s t o

-+

-f

l i n e n e a r l y a l o n g Hn.

-

S i n c e t h e t r a n s v e r s e f r e q u e n - cy s h i f t i n 3 ~ i s ep r o p o r t i o n a l t o n 2 t h e s q u a r e ~

-L'+

of t h e component o f 6 ~ e r ~ e n d i c u l a r t o H o , a l a r g e v a r i a t i o n i n t h e l o c a l t r a n s v e r s e NMR f r e q u e n c y s h i f t r e s u l t e d . However, r a t h e r t h a n o b s e r v i n g a b r o a d NMR l i n e , t h e B e l l group i n s t e a d o b s e r v e d up

t o f o u r n e a r l y e q u a l l y spaced r e s o n a n c e p e a k s . To u n d e r s t a n d t h e above r e s u l t , c o n s i d e r t h e e q u a t i o n g o v e r n i n g t h e s p i n dynamics i n s u c h a geo- m e t r y :

E S+ = -

I R ~

^{f ( S )}

^-

d z d2

⁷

- :n ( z ) }

s

Here E i s t h e t r a n s v e r s e f r e q u e n c y s h i f t n o r m a l i z e d t o i t s v a l u e when n: = 1 , S i s t h e p r e c e s s i n g ma- g n e t i z a t i o n , RS i s t h e d i p o l a r h e a l i n g l e n g t h , and f ( 6 ) i s a s c a l a r of o r d e r u n i t y . T h i s e q u a t i o n r e

-

s e m b l e s a S c h r z d i n g e r e q u a t i o n w i t h E t h e e i g e n v a - l u e and n: a p o t e n t i a l e n e r g y term. I t i s assumed t h a t t h e v a r i a t i o n o f 6 i s a l o n g 2.

I n t h e geometry of t h e B e l l Labs. e x p e r i m e n t , n

: v a r i e s a p p r o x i m a t e l y q u a d r a t i c a l l y o v e r t h e 3 ~ e f i l l e d r e g i o n . Once t h i s v a r i a t i o n of n: i s s u b s t i t u - t e d i n t o e q u a t i o n 1 , one o b t a i n s t h e e q u a t i o n of a harmonic o s c i l l a t o r , i n which t h e s p i n wave m o d e s a r e t r a p p e d i n t h e q u a d r a t i c p o t e n t i a l w e l l c r e a t e d by t h e t e x t u r e .

By d e t e r m i n i n g t h e 6 t e x t u r e n u m e r i c a l l y on a computer and u s i n g t h a t t e x t u r e i n s o l v i n g equa- t i o n l , t h e B e l l group a r r i v e d a t r e s o n a n c e s which c l o s e l y matched t h e i r d a t a . These r e s u l t s h a v e g i v e n u s c o n f i d e n c e i n d e a l i n g w i t h t e x t u r a l induced d i s - t o r t i o n s i n NMR s p e c t r a .

At t h e time of LT14, Avenel e t a l .

/

131 ob- s e r v e d " s a t e l l i t e " r e s o n a n c e s i n l o n g i t u d i n a l NMR s p e c t r a i n jHe.A. We now b e l i e v e t h e s e s a t e l l i t e s a r e a s s o c i a t e d w i t h s p i n waves t r a p p e d i n a d i p o l a r p o t e n t i a l w e l l a s s o c i a t e d w i t h a p l a n a r s i n g u l a r i t y i n 3 ~which h a s been s t u d i e d e x t e n s i v e l y t h e o r e - e ~ t i c a l l y by Maki and Kumar / 1 4 , 1 5 / . These s i n g u l a r i - t i e s , t o p o l o g i c a l s o l i t o n s

,

r e s u l t when two r e g i o n s o f 3 ~ a r e j o i n e d t o g e t h e r i n which e ~

a

i s p a r a l l e l t o

^a

i n one o f t h e r e g i o n s and a n t i p a r a l l e l t o i n t h e o t h e r . Maki and Kumar d e t e r m i n e t h e t e x t u r e s f o r s u c h s i n g u l a r i t i e s i n s e v e r a l e x p e r i m e n t a l s i -

JOURNAL DE PHYSIQUE

t u a t i o n s by r n i n i m i ~ i n g t h e t o t a l f r e e energy asso- c i a t e d w i t h them. Then u s i n g a n e q u a t i o n s i m i l a r t o e q u a t i o n 1 , they d e t e r m i n e t h e bound s p i n waves as- s o c i a t e d w i t h t h e s o l i t o n s . I n g e n e r a l , t h e i r c a l c u - l a t i o n s f i t r e c e n t d a t a q u i t e c l o s e l y . I n f a c t , r e - c e n t l y Maki 1151 h a s f i t t h e t e m p e r a t u r e dependence of t h e r a t i o of t h e l o n g i t u d i n a l s a t e l l i t e r e s o n a n t frequency t o t h e main l o n g i t u d i n a l r e s o n a n t frequen- cy a s determined by Gould and Lee 1161 t o e s t i m a t e t h a t t h e Landau Fermi l i q u i d parameter Fa =

-

1.2.

1

A v e r y s i m i l a r v a l u e of Fa h a s a l s o been a r r i v e d a t 1

by Osheroff e t a l . 1121 who needed t o invoke a v a l u e of :F t o f i t t h e i r s p i n wave d a t a t o t h e o r y , and by P e t h i c k , Smith and B h a t t a c h a r y y a 1171 who needed i t t o f i t normal s t a t e v i s c o s i t y d a t a t o t h e i r t h e o r y . Perhaps we a r e a g a i n l e a r n i n g something about t h e normal Fermi l i q u i d by s t u d y i n g t h e s u p e r f l u i d pha- s e s .

There i s no u n i v e r s a l agreement t h a t t h e sa- t e l l i t e r e s o n a n c e s , s e e n i n b o t h l o n g i t u d i n a l and t r a n s v e r s e NMR e x p e r i m e n t s , c a n b e completely ex- p l a i n e d by t h e s o l i t o n p i c t u r e , a l t h o u g h I p e r s o n a l - l y am v e r y o p t i m i s t i c : I n work by Gould and Lee 1161 i t was observed t h a t r a p i d h e a t flow could c r e a - te t h e s a t e l l i t e r e s o n a n c e s , as i f

2

were b e i n g pul- l e d o u t of t h e p l a n e i n which

a

must r e s i d e d u r i n g t u r b u l e n t c o u n t e r f l o w , t h e r e b y a l l o w i n g a s o l i t o n t o b e formed. G i a n n e t t a , Smith and Lee 1181 showed t h a t s a t e l l i t e s of n e a r l y t o t a l l i n e i n t e n s i t y (no main peak) could b e formed i n p u l s e d e x p e r i m e n t s by

t i p p i n g t h e m a g n e t i z a t i o n , MZ, w e l l away from Ho.

-+

I n l a t e r s e c t i o n s of t h i s m a n u s c r i p t i t w i l l be shown how such a p r o c e s s can b e expected t o c r e a t e s o l i - tons. B o z l e r and B a r t o l a c 1191 have shown t h a t i n p u l s e d e x p e r i m e n t s , s a t e l l i t e r e s o n a n c e s a r e c r e a t e d w i t h i n a v e r y s h o r t time (- 20 ms) f o l l o w i n g a t i p - p i n g p u l s e . F i n a l l y , Kokko e t a l . 1201 have demons- t r a t e d t h a t t h e s a t e l l i t e s o r i g i n a t e from q u i t e lo- c a l i z e d r e g i o n s of t h e f l u i d , and t h a t t h e y r e q u i r e a s t a t i c f i e l d t o s t a b i l i z e them, a t l e a s t i n t h e i r p a r a l l e l p l a t e geometry. A l l t h e s e c h a r a c t e r i s t i c s a r e c o n s i s t e n t w i t h t h e s o l i t o n model.

Our a p p a r e n t a b i l i t y t o i d e n t i f y t e x t u r a l s i n g u l a r i t i e s i n 3 ~ e A by t h e i r NMR s i g n a t u r e s i s v e r y h e a r t e n i n g , and may e v e n t u a l l y prove i m p o r t a n t i n u n d e r s t a n d i n g t h e e f f e c t s o f f l o w i n 3 ~ e A , such a s t h e v e r y complex r e s u l t o b t a i n e d by Adams and coworkers a t t h e U n i v e r s i t y of F l o r i d a , / 2 1 / i n which a p p a r e n t d e c r e a s e s i n t h e A phase s u s c e p t i b i l i t y and a complex time dependent NMR s p e c t r a were observed

I n an a r e a r e l a t e d t o t h e s o l i t o n problem, groups a t Sussex 1221 and C o r n e l l 1231 have been s t u d y i n g NMR s p e c t r a of 3 ~c o n t a i n e d i n 2 e ~ vm d i a - meter c y l i n d r i c a l c h a n n e l s i n o r d e r t o u n d e r s t a n d

t h e e q u i l i b r i u m t e x t u r e s i n r e s t r i c t e d g e o m e t r i e s . I n such t i g h t s p a c e s

1

cannot remain everywhere pa- r a l l e l t o

2,

and hence t h e NMR r e s o n a n t f r e q u e n c y i s d e p r e s s e d r e l a t i v e t o t h e bulk. There i s , a s w e l l , t h e p o s s i b i l i t y t h a t t h e e q u i l i b r i u m t e x t u r e w i l l be dominated by a l i n e s i n g u l a r i t y which c a n b e d e t e r - mined from i t s NMR s i g n a t u r e . I t now a p p e a r s t h a t b o t h groups have s e e n two s e p a r a t e t e x t u r e s s t a b l e i n d i f f e r e n t t e m p e r a t u r e r e g i o n s , which t r a n s f o r m i n t o e a c h o t h e r on warming o r c o o l i n g v e r y s l o w l y . These o b s e r v a t i o n s w i l l undoubtedly produce a g r e a t d e a l of f u r t h e r e x p e r i m e n t a l and t h e o r e t i c a l work.

i v ) L o n g i t u d i n a l S p i n Recovery.- When t h e e q u i l i b r i m m a g n e t i z a t i o n , MZ, of t h e n u c l e a r s p i n system a l o n g t h e s t a t i c f i e l d i s d e s t r o y e d i n a p u l s e d NMR expe-

A

riment by t i p p i n g MZ w e l l away from Ho, s p i n noncon- s e r v i n g p r o c e s s e s must e v e n t u a l l y r e t u r n MZ t o i t s e q u i l i b r i u m v a l u e . The c h a r a c t e r i s t i c time f o r t h i s p r o c e s s t o occur i s u s u a l l y termed T I . I n 1975 C o r r u c c i n i and Osheroff 1241 showed t h a t v e r y unusu- a l r e c o v e r y mechanisms e x i s t i n b o t h s u p e r f l u i d pha- s e s of 3 ~ e , s u f f i c i e n t l y s t r a n g e t h a t even today we have no e x p l a n a t i o n f o r t h o s e o b s e r v a t i o n s , a l t h o u g h r e c e n t e x p e r i m e n t s a t La J o l l a 1251 and a t Argonne 1261 have g i v e n u s f u r t h e r c l u e s a s t o what may b e happening i n t h e s e i n h e r e n t l y n o n l i n e a r and s p a t i a l -

l y nonuniform p r o c e s s e s .

S h o r t l y f o l l o w i n g t h e p u b l i c a t i o n by C o r r u c c i n i and Osheroff 1241 (C-O) of t h e i r r e s u l t s showing t h a t MZ recovered n e a r l y l i n e a r l y w i t h time i n t h e A p h a s e , L e g g e t t and Takagi 127,281 (L-T) produced a t h e o r y p r e d i c t i n g a new m a g n e t i z a t i o n r e - covery mechanism i n which t h e d i p o l a r t o r q u e r e p r e - s e n t e d t h e s p i n nonconserving p r o c e s s . T h i s t h e o r y s u g g e s t e d t h a t t h e e x c e s s e n e r g y i n t h e s p i n system s h o u l d obey t h e r e l a t i o n s h i p :

Here t h e l e f t hand s i d e of t h e e q u a t i o n i s t h e time r a t e of change of t h e energy i n t h a s p i n system, w i t h ED t h e d i p o l a r e n e r g y , which we s h a l l i g n o r e a s b e i n g n e g l i g i b l e . (x/x,) i s t h e s u s c e p t i b i l i t y enhan- cement (xlx,

-

^{( I +}

^.L

4 ^Z 0

^I-',

^A

-

⁽⁼ .2 (Ao/kBTc) where A i s t h e maximum of t h e gap f u n c t i o n , 52 i s t h e

l o n g i t u d i n a l r e s o n a n t f r e q u e n c y , y i s t h e gyromagne- d u r i n g f l o w c o n d i t i o n s .

t i c r a t i o

,

and ¸ is t h e normal q u a s i p a r t i c l e s c a t - t e r i n g t i m e a t t h e Fermi s u r f a c e .

The L-T e q u a t i o n s u g g e s t s a r e l a x a t i o n t i m e T p r o p o r t i o n a l t o (I-T/T )3/2 n e a r t o Tc, i n which

1

M~ r e c o v e r s l i n e a r l y w i t h time. Because t h e t i m e s Z

f o r f u l l s p i n r e c o v e r y a r e p r o p o r t i o n a l t o H2 i n t h i s t h e o r y , o n e n e e d s t o s t u d y t h i s phenomenon i n v e r y low f i e l d s where more r a p i d p r o c e s s e s w i l l n o t d o m i n a t e t h e r e c o v e r y .

S a g e r e t a l . / 2 5 / a t La J o l l a , and ~ e b b / 2 6 / a t Argonne have employed SQUID NMR t o s t u d y t h e s e r e -

l a x a t i o n p r o c e s s e s . As i n t h e s t a t i c m a g n e t i z a t i o n s t u d i e s , t h e y have t i p p e d t h e m a g n e t i z a t i o n w i t h a r e s o n a n t r f p u l s e , and t h e n f o l l o w e d t h e r e c o v e r y of M

z

d i r e c t l y u s i n g SQUID magnetometers. T h i s t e c h n i - que h a s many v i r t u e s o v e r c o n v e n t i o n a l NMR i n t h i s p a r t i c u l a r a p p l i c a t i o n , i n c l u d i n g good s e n s i t i v i t y a t v e r y low f i e l d s , and t h e a b i l i t y t o r e c o r e t h e e n t i r e M

z

r e c o v e r y a f t e r a s i n g l e r f p u l s e . Both g r o u p s have b e e n a b l e t o o b s e r v e L-T r e c o v e r y i n b o t h s u p e r f l u i d p h a s e s , a l t h o u g h i n t h e La J o l l a s t u d y o n l y i n a narrow t e m p e r a t u r e r a n g e v e r y n e a r t o Tc, and i n f i e l d s of 30 Oe o r l e s s . I n t h e Argonne work, L-T r e l a x a t i o n was observed i n 3 ~i n f i e l d s e ~ a s h i g h a s 180 Oe f o r (1-TIT ) a s l a r g e a s 0.07, b u t n e v e r i n a f i e l d a s low a s 31 Oe. I n g e n e r a l , t h e measured r e l a x a t i o n r a t e s a p p e a r t o b e somewhat t o o h i g h i n 3 ~ e ~ , and i n 3 ~Sager e t a l . measure a e ~ ( I -TITc) t e m p e r a t u r e dependence i n s t e a d o f ( I - T I T ~ ) ~ ~ ? . It i s c l e a r , however, t h a t i n a t l e a s t c e r t a i n li- m i t s t h e L-T r e l a x a t i o n d o e s dominate a l l o t h e r pro-

c e s s e s .

The d i f f e r e n c e s between Webb's r e s u l t s and t h o s e of Sager e t a l . may l i e i n t h e d i f f e r e n c e s i n geometry, and perhaps i n t h e g r a d i e n t s i n Ho. The La J o l l a group s t u d i e d s p i n r e c o v e r y i n a n open ge- o m e t r y , and i n g e o m e t r i e s c o n t a i n i n g p a r a l l e l p l a t e s b o t h p a r a l l e l and p e r p e n d i c u l a r t o t h e s t a t i c f i e l d . The r e s u l t s showed s t r o n g dependences o f t h e c h a r a c - t e r of t h e r e c o v e r y p r o c e s s e s on geometry. L-T r e - l a x a t i o n was o n l y o b s e r v e d i n 3 ~i n t h e open and e ~ p a r a l l e l ( t o

H

⁾ p l a t e a r r a y . I n 3 ~ e ~ , L-T r e l a x a - t i o n was o n l y o b s e r v e d i n t h e open geometry.

Under o t h e r c o n d i t i o n s t h a n t h o s e d e s c r i b e d above, b o t h g r o u p s o b s e r v e d a v a r i e t y o f d i f f e r e n t r e l a x a t i o n b e h a v i o r s , i n c l u d i n g l i n e a r r e c o v e r y o f MZ w i t h t i m e v e r y s i m i l a r t o t h e C-0 r e s u l t s , and e x p o n e n t i a l r e c o v e r y i n t h e B p h a s e which may b e i n good a g r e e m e n t w i t h t h e b e h a v i o r C-0 o b s e r v e d i n t h e B p h a s e . (Because i n t h e B p h a s e C-0 o b s e r v e d a

s t r o n g dependence o f T I on g r a d i e n t s i n Ho, and s u c h g r a d i e n t s c o u l d n o t b e v a r i e d i n e i t h e r of t h e new e x p e r i m e n t s , t h i s agreement i s t i l l i n q u e s t i o n . )

Two of many new f e a t u r e s Sager e t a l . /25/

-

o b s e r v e d were t h a t i n t h e p e r p e n d i c u l a r ( t o Ho) p l a - t e a r r a y , r e l a x a t i o n i n 3 ~was much s l o w e r t h a n e ~ e i t h e r of t h e o t h e r two g e o m e t r i e s ; and t h a t t h e m a g n e t i z a t i o n i n t h e A phase d i d n o t a l w a y s r e c o v e r m o n o t o n i c a l l y . F r e q u e n t l y a r e v e r s a l i n t h e r e c o v e r y would b e o b s e r v e d i n which t h e m a g n e t i z a t i o n would d r o p f o r a w h i l e b e f o r e c o n t i n u i n g t o r e c o v e r . Sager e t a l . found t h e maximum o f t h i s r e v e r s a l t o b e com- p a r a b l e t o t h e s u s c e p t i b i l i t y a n i s o t r o p y i n 3 ~ e ~ , and i t s d u r a t i o n t o b e comparable t o t h e o r b i t a l r e l a x a t i o n t i m e .

Undoubtedly t h e most i n t e r e s t i n g new r e s u l t i n t h e Argonne work i s t h e e x i s t e n c e of a tempera- t u r e and f i e l d d e p e n d e n t c r i t i c a l t i p p i n g a n g l e f o r b o t h s u p e r f l u i d p h a s e s beyond which n o n e x p o n e n t i a l r e l a x a t i o n i s o b s e r v e d , and below which e x p o n e n t i a l r e l a x a t i o n i s o b s e r v e d . Webb f e e l s h i s r e s u l t s ex- p l a i n t h e v e r y d i f f e r e n t c h a r a c t e r of t h e A and B p h a s e r e c o v e r y mechanisms r e p o r t e d by C-0, b u t t h e dependence o f h i s c r i t i c a l t i p p i n g a n g l e s on geome- t r y and s t a t i c f i e l d g r a d i e n t a r e a s o f y e t unknown.

S i g n i f i c a n t l y , t h e s e c r i t i c a l t i p p i n g a n g l e s e x t r a - p o l a t e t o z e r o a t T f o r b o t h p h a s e s , s u g g e s t i n g t h a t t h e y a r e n o t r e l a t e d t o t h e c h a r a c t e r i s t i c ma- g i c a n g l e s ( s u c h a s cos-' (-114)) i n e i t h e r p h a s e .

I t h a s l o n g b e e n b e l i e v e d t h a t t h e l i n e a r r e c o v e r y o f MZ w i t h time may b e due t o c o u n t e r f l o - wing m a g n e t i z a t i o n s u p e r c u r r e n t s c a u s e d by t h e d i f - f e r e n c e s i n l o c a l c h e m i c a l p o t e n t i a l o f t h e s p i n s y s t e m f o l l o w i n g a n r f p u l s e . I f s o , we would e x p e c t t h e

a

v e c t o r t o t w i s t u p i n s p a c e , s i n c e i t i s r e - l a t e d t o t h e r e l a t i v e p h a s e s o f t h e up and downspi"

s y s t e m s , and m a g n e t i z a t i o n s u p e r f l o w i s r e l a t e d t o s p a t i a l g r a d i e n t s i n t h a t r e l a t i v e phase. Such a t w i s t i n g would r e s u l t i n t h e ( a t l e a s t ) t e m p o r a r y f o r m a t i o n of

2

s o l i t o n s i n 3 ~and e 8 ~s o l i t o n s i n 3 ~ e ~ , p r o v i d e d t h e g r a d i e n t s w e r e s u f f i c i e n t l y l a r - g e . We t h e r e f o r e c a n n o t d i s c u s s m a g n e t i z a t i o n s u p e r - c u r r e n t s w i t h o u t c o n s i d e r i n g s o l i t o n s a s w e l l . How t h e s e i d e a s must b e m o d i f i e d by t h e r e s u l t s o f B o z l e r and B a r t o l a c / 9 / i s u n c l e a r a t t h i s t i m e , b u t c e r t a i n l y such s t u d i e s which p r o b e t h e n a t u r e o f t h e d i s e q u i l i b r i u m s t a t e f o l l o w i n g a n r f p u l s e w i l l pro- v i d e i m p o r t a n t new i n f o r m a t i o n i n o u r e f f o r t s t o u n d e r s t a n d T p r o c e s s e s i n s u p e r f l u i d 3 ~ e .

1

C6-

1274 ^{JOURNAL D E PHYSIQUE}

B) E l e c t r o n i c E f f e c t s . -

i ) I n t r o d u c t i o n . - We n o r m a l l y t h i n k of s u p e r f l u i d 3 ~ e as b e i n g composed o f c h a r g e l e s s p a r t i c l e s w i t h s p i n 112. R e c e n t l y , however, L e g g e t t h a s s u g g e s t e d 1291 t h a t we s h o u l d be aware o f p o s s i b l e e f f e c t s on t h e s u p e r f l u i d s caused by a r e d i s t r i b u t i o n o f e l e c - t r o n j c c h a r g e by atoms forming a Cooper p a i r . T h i s r e d i s t r i b u t i o n might r e s u l t i f t h e atoms were t o form a n unbound dimer i n r e s p o n s e t o c o n v e n t i o n a l c h e m i c a l e n e r g y c o n s i d e r a t i o n s . Two p o s s i b l e con- s e q u e n c e s of such a c h a r g e r e d i s t r i b u t i o n m i g h t b e t h e e x i s t e n c e o f a m a g n e t i c moment a s s o c i a t e d w i t h t h e

?

v e c t o r i n 3 ~ e A , and a p e r h a p s s u b s t a n t i a l a l - t e r a t i o n of t h e o r i e n t a t i o n a l e f f e c t s an e l e c t r i c f i e l d /30/ might have on t h e a n g u l a r momentum o f t h e Cooper p a i r s .

i i ) O r i e n t a t i o n i n a n E l e c t r i c F i e l d . - D e l r i e u 1301 -+

showed i f a n e l e c t r i c f i e l d E i s a p p l i e d a c r o s s a sample of 3 ~ e A , t h e

2

v e c t o r s h o u l d f e e l a t o r q u e

-f

t e n d i n g t o a l l i g n i t normal t o E. T h i s i s d u e t o t h e e l e c t r i c d i p o l e e n e r g y o f t h e p o l a r i z e d 3 ~ e atoms i n d i r e c t anology w i t h t h e m a g n e t i c d i p o l e e n e r g y . However, p r e v i o u s e x p e r i m e n t s 131,321 have f a i l e d t o o b s e r v e s u c h a n e f f e c t . I n an e x p e r i m e n t a t C o r n e l l 1311 t h e r e a p p e a r e d t o e v e n b e a s l i g h t tendancy f o r ?t o a l l i g n p a r a l l e l t o E. Although i + i t was b e l i e v e d t h e a b s e n c e o f t h i s e f f e c t m i g h t b e a Fermi l i q u i d l i k e e f f e c t , it c o u l d p e r h a p s b e due t o a r e d i s t r i b u t i o n o f e l e c t r i c c h a r g e f o r s m a l l s e p a r a t i o n s of t h e atoms of t h e Cooper p a i r s d u e t o dimer e f f e c t s j u s t where t h e l a r g e s t c o n t r i b u t i o n t o t h e e l e c t r i c d i p o l e e n e r g y s h o u l d o c c u r .

Two g r o u p s have r e c e n t l y t r i e d t o measure t h e e l u s i v e e l e c t r i c f i e l d e f f e c t . At La J o l l a , P a u l s o n and Wheatley 1331 have used t h e a n i s o t r o p y i n t h e a t t e n u a t i o n o f z e r o sound a s a p r o b e 1351 t o m o n i t o r t h e o r i e n t a t i o n of

2

i n j ~ e ~ , While o b s e r - v i n g t h e a t t e n u a t i o n , a, t h e two a p p l i e d a f i e l d of -lkV/cm a c r o s s t h e i r z e r a sound c e l l and looked f o r

a change i n t h e a t t e n u a t i o n due t o a r e o r i e n t a t i o n

..

of t h e i r 9, t e x t u r e . They c a l i b r a t e d t h e i r s y s t e m t o

..

s m a l l t o r q u e s on .9 b y a p p l y i n g and t h e n r o t a t i n g a s m a l l (300-600 mG) m a g n e t i c f i e l d . Except f o r a t r a n s i e n t , and a s t a t i c e f f e c t which o c c u r r e d e v e n i n t h e normal p h a s e , P a u l s o n and Wheatley o b s e r v e d no o r i e n t i n g e f f e c t s of t h e e l e c t r i c f i e l d what s o e v e r . They e s t i m a t e t h a t i f i t e x i s t s , t h e e l e c t r i c f i e l d o r i e n t a t i o n a l e n e r g y must b e a t l e a s t 1000 t i m e s s m a l l e r t h a n D e l r i e u e s t i m a t e d .

At B e l l Labs., P a a l a n e n e t a1.1341 looked f o r a n o r i e n t i n g e f f e c t of t h e

ii

v e c t o r i n 3 ~ e ~ . By

l o o k i n g f o r a n e f f e c t i n 3 ~ e ~ , t h e B e l l group c o u l d work a t much lower sample p r e s s u r e s , where Fermi l i q u i d e f f e c t s s h o u l d b e s m a l l e s t . I n t h e i r e x p e r i - ment, changes i n t h e o r i e n t a t i o n of t h e 6 t e x t u r e upon t h e a p p l i c a t i o n o f an e l e c t r i c f i e l d a s h i g h a s 35 kV/cm were m o n i t o r e d by m e a s u r i n g t h e s p i n - wave s p e c t r a i n a p a r a l l e l p l a t e a r r a y . The expe- r i m e n t a l geometry was n e a r l y i d e n t i c a l t o t h a t used p r e v i o u s l y i n t h e B p h a s e spinwave s t u d i e s 1121.

Again, no e f f e c t was o b s e r v e d which c o u l d b e i n t e r - p r e t e d a s e v i d e n c e of a n e l e c t r i c f i e l d o r i e n t i n g e f f e c t . A t 32 b a r , t h e B e l l group e s t i m a t e t h e o r i e n t a t i o n a l e n e r g y t o b e a t l e a s t 3000 t i m e s l e s s t h a n s i m p l e t h e o r y p r e d i c t e d , and a t 0 b a r a t l e a s t 700 t i m e s l e s s .

Exept f o r t h e 0 b a r r e s u l t by t h e B e l l group, none of t h e s e r e n o r m a l i z a t i o n f a c t o r s i s l a r g e r t h a n t h o s e e x p e c t e d from a new t h e o r y I 3 6 1 which e s t i m a t e s Fermi l i q u i d r e n o r m a l i z i n g e f f e c t s . T h i s i s n o t t o s a y t h a t c h e m i c a l e f f e c t s d o n o t e x i s t i n t h e o r i e n t a t i o n a l e l e c t r i c f i e l d e n e r g y , b u t t h a t i f t h e y a r e i n d e e d p r e s e n t , we w i l l have t o work much, much h a r d e r t o measure them.

i i i ) E l e c t r o n i c O r b i t a l Ferromagnetism i n 3 ~ e ~ . - 3 ~h a s been termed a n " o r b i t a l f e r r o m a g n e t " /37/ e ~ b e c a u s e t h e o r b i t a l a n g u l a r momenta of a l l t h e Cooper p a i r s p o i n t i n t h e same d i r e c t i o n . I f t h e s o r t o f c h e m i c a l e f f e c t s L e g g e t t h a s c o n s i d e r e d were t o change t h e e l e c t r o n i c c h a r g e d i s t r i b u t i o n of t h e Cooper p a i r s , t h e y c o u l d p o s s e s s o r b i t a l ma- g n e t i c moments, and h e n c e t h e e n t i r e f l u i d could p o s s e s s a s p o n t a n e o u s m a g n e t i z a t i o n a l o n g t h e d i - r e c t i o n o f

2

1381. L e g g e t t h a s e s t i m a t e d t h a t t h i s m a g n e t i z a t i o n a t 9Tc c o u l d b e a s l a r g e a s t h e nu- c l e a r m a g n e t i z a t i o n i n an a p p l i e d f i e l d o f 1 mG.

Such a m i n u t e m a g n e t i z a t i o n a s t h e above might b e o b s e r v a b l e i n t h e z e r o sound e x p e r i m e n t s /33/of P a u l s o n and Wheatley. I n s i m i l a r e x p e r i m e n t s 1391, t h e y h a v e found t h a t when t h e y j u s t r e v e r s e d t h e s i g n o f t h e i r a p p l i e d 300 mG f i e l d , t h e y mea- s u r e d a change i n a , i n d i c a t i n g a r e o r i e n t a t i o n o f

x.

Such a r e o r i e n t a t i o n c o u l d b e e x p e c t e d i f

%

had a s s o c i a t e d w i t h i t a m a g n e t i c moment. It a l s o could r e s u l t , however, i f t h e f i e l d t h e y r e v e r s e d were n o t t h e t o t a l f i e l d a c r o s s t h e i r sample. To l i m i t t h i s second p o s s i b i l i t y , P a u l s o n and Wheatley c a r e - f u l l y s h i e l d e d t h e i r sound chamber from s t r a y ma- g n e t i c f i e l d s . S t i l l , t h e y e s t i m a t e t h a t p e r h a p s a r e s i d u a l f i e l d of

-

2 mG remained. T h i s i s t h e magnitude o f t h e t r a p p e d f i e l d n e c e s s a r y t o produce

t h e a v e r a g e s h i f t i n

?.

o b s e r v e d .

The o r i e n t i n g e f f e c t due t o a s p o n t a n e o u s m a g n e t i z a t i o n a l o n g

x

would depend upon which d i r e c - t i o n

x

p o i n t e d r e l a t i v e t o t h e a p p l i e d f i e l d . I f upon warming above T and c o o l i n g back t h e

2

t e x t u r e were t o e x a c t l y r e v e r s e i t s s e n s e , t h e n t h e change i n a caused by t h e m a g n e t i z a t i o n would a l s o r e v e r s e . I n f a c t , P a u l s o n and Wheatley d i d o b s e r v e s c a t t e r i n t h e i r changes i n a upon r e p e a t e d c y c l i n g above and below Tc, and a n a p p a r e n t c l u s t e r i n g a b o u t two d i s - t i n c t s e t s o f v a l u e s ; a n e n c o u r a g i n g s i g n .

U n f o r t u n a t e l y , t h e t e x t u r e s i n t h e sound c e l l a r e n o t w e l l known, and p r o b a b l y change w i t h t e m p e r a t u r e . I n any e v e n t , t h e changes i n a above and below t h e v a l u e a t t r i b u t e d t o t h e r e s i d u a l f i e l d showed c o n s i d e r a b l e s c a t t e r , and n o t t h e t e m p e r a t u r e dependence which i s a s s o c i a t e d w i t h t h e e f f e c t s o f t h e s p o n t a n e o u s m a g n e t i z a t i o n . On t h e o t h e r h a n d , t h e m a g n i t u d e of t h e s c a t t e r was f a r l a r g e r t h a n t h e two c o u l d a t t r i b u t e t o any known e x p e r i m e n t a l a r t i - f a c t , and i n d e e d v e r y n e a r l y e q u a l t o t h e m a g n i t u d e of t h e change i n o r i e n t a t i o n e x p e c t e d from t h e spon- t a n e o u s m a g n e t i z a t i o n .

I t a p p e a r s q u i t e l i k e l y t h a t t h e La J o l l a p a i r have i n d e e d d e t e c t e d s p o n t a n e o u s m a g n e t i z a t i o n a l o n g

3 ,

a l t h o u g h a s t h e y a r e q u i c k t o p o i n t o u t , t h e i r e x p e r i m e n t i s o n l y q u a l i t a t i v e and from i t n o v a l u e o f t h e moment c a n b e e x t r a c t e d . I f we a r e i n - d e e d t o u n d e r s t a n d L e g g e t t ' s c h e m i c a l e f f e c t s , more c a r e f u l e x p e r i m e n t s w i l l be needed. I n p a r t i c u l a r , i t w i l l b e n e c e s s a r y t o r e d u c e t h e m a g n i t u d e o f t h e r e s i d u a l f i e l d s o t h a t i t s e f f e c t s a r e no l o n g e r comparable t o t h e s c a t t e r which r e p r e s e n t t h e e f f e c t s of t h e s p o n t a n e o u s m a g n e t i z a t i o n o n t h e o r i e n t a t i o n of

z.

C) _ T o r s i o n a l Pendulum E x p e r i m e n t s P l u s . - Of p a r t i - c u l a r u s e f u l l n e s s i n t h e p a s t and w i t h even more p r o m i s e f o r t h e f u t u r e h a s been t h e t e c h n i q u e o f u s i n g t h e A n d r o n i k a s h v i l i o s c i l l a t i n g - p e n d u l u m , o r t o r s i o n a l pendulum t o measure s u p e r f l u i d p r o p e r t i e s o f 3 ~ e s u c h a s p s / p , t h e r e l a t i v e s u p e r f l u i d d e n s i - t y , and

n,

t h e v i s c o s i t y . Main e t a l . 1401 w e r e t h e f i r s t t o u s e t h e t e c h n i q u e t o show c o n c l u s i v e l y t h e a n i s o t r o p y o f p / p i n 3 ~ e ~ , w h i l e B e r t h o l d e t a l . /41/ have g o t t e n c r e d i t f o r t h e f i r s t a c c u r a t e mea- s u r e m e n t s o f t h a t a n i s o t r o p y . R e c e n t l y , P a r p i a e t a l . 1421 h a v e a g a i n u s e d s u c h a t e c h n i q u e t o m e a s u r e t h e normal and s u p e r f l u i d v i s c o s i t i e s o f 3 ~ e a t a number of p r e s s u r e s , w i t h p a r t i c u l a r emphasis b e i n g

g i v e n t o t h e r e g i o n v e r y n e a r t o Tc.

I n t h e i r new r e s u l t s , P a r p i a e t a l . f i n d t h a t Aq/n v a r i e s a s ( ~ - T / T ~ ) ' / ~ o n l y w i t h i n a b o u t

5 x lo-" o f Tc. T h i s i s s i g n i f i c a n t b e c a u s e i t was o r i g i n a l l y b e l i e v e d All/rl, s h o u l d b e p r o p o r t i o n a l t o t h e e n e r g y gap o n l y n e a r Tc, b u t presumably o v e r a s u b s t a n t i a l t e m p e r a t u r e i n t e r v a l . The new C o r n e l l r e s u l t s u p p o r t s a t h e o r e t i c a l p r e d i c t i o n by Ono e t a l . 1431. I n a d d i t i o n , P a r p i a e t a l . f i n d a s u b s - t a n t i a l

-

^1.4

^X

d r o p i n q o v e r a 5 pK t e m p e r a t u r e i n t e r v a l

above

Tc, and i n d i c a t e t h a t o v e r t h i s same t e m p e r a t u r e i n t e r v a l a n anomalous r i s e i n t h e pe- r i o d of t h e i r pendulum was o b s e r v e d . The a u t h o r s s u g g e s t t h a t t h e s e e f f e c t s may be d u e t o a f l u c t u - a t i o n p r e c u r s o r s u c h a s Emery 1441 h a s p r e d i c t e d . R e c e n t l y P a u l s o n and Wheatley 1 4 5 1 h a v e r e p o r t e d what t h e y b e l i e v e t o b e p r e c u r s o r y b e h a v i o r o v e r a much b r o a d e r t e m p e r a t u r e i n t e r v a l above T i n t h e

a t t e n u a t i o n of z e r o sound.

I n s t i l l u n p u b l i s h e d work a t C o r n e l l 1461, h i g h r e s o l u t i o n s t u d i e s of p / p i n 3 ~h a v e been e ~ made a t a l a r g e number of d i f f e r e n t sample p r e s s u r e s u s i n g p l a t i n u m NMR thermometry. The d a t a h a s been a n a l y z e d t o e x t r a c t t h e "weak c o u p l i n g " p n , t h e Yoshida f u n c t i o n . I n t h i s a n a l y s i s , v a l u e s o f m f / m p u b l i s h e d by W h e a t l e y 1471 h a v e b e e n u s e d t o e l i - m i n a t e t h e Fermi l i q u i d e f f e c t s . Once c o m p l e t e , t h i s a n a l y s i s shows t h e Yoshida f u n c t i o n i n 3 ~t o e ~ be a s i n g l e f u n c t i o n of TITc, i d d e p e n d e n t o f p r e s - s u r e . From t h e i n i t i a l s l o p e o f p / p n e a r Tc

,

t h e C o r n e l l g r o u p c a n e s t i m a t e

Ac/AcBCS

⁼ 1.39 a t a l l p r e s s u r e s . T h i s i s i n good agreement w i t h t h e measurements by H a l p e r i n 1481 a t m e l t i n g p r e s s u r e , b u t t h e f a i l u r e o f t h e s t r o n g c o u p l i n g e f f e c t s t o d e c r e a s e w i t h d e c r e a s i n g p r e s s u r e i s n o t e x p e c t e d . Yet i t seems u n l i k e l y t h a t t h e p l a t i n u m thermometry c o u l d b e wrong by more t h a n t e n p e r c e n t a t m o s t , and o n e would e x p e c t t h a t t h a t e r r o r s h o u l d be a c o n s t a n t m u l t i p l i c a t i v e f a c t o r a t a l l t e m p e r a t u r e s .

Using t h e i r new Lanthinum d i l u t e d CMN t h e r - mometry s c a l e , Wheatley and coworkers 1 4 9 1 h a v e r e c e n t l y r e a n a l y z e d p r e v i o u s z e r o sound d a t a o f P a u l s o n e t a l . / 5 0 / t o e s t i m a t e AC/ACBCS. They n o t e t h a t t h e z e r o sound a b s o r p t i o n peak i n 3 ~ i s e r e - ~ l a t e d t o t h e e n e r g y g a p , and u s e t h e p o s i t i o n of t h e peak a s a f u n c t i o n o f t e m p e r a t u r e t o o b t a i n t h e i r r e s u l t s . I n s t r o n g c o n t r a s t t o t h e C o r n e l l r e s u l t , t h e La J o l l a r e s u l t shows AC/ACBCS a l m o s t e q u a l t o u n i t y from 12 b a r t o 20 b a r sample p r e s - s u r e . Although t h e l a c k of a t e m p e r a t u r e dependence

c6-1276 JOURNAL DE PHYSIQUE agrees with the Cornell result, the value of AC/ACBCS

is nearly 40

%

lower than the Cornell result. This strong disagreement is well outside the errors in thermometry, and, according to Serene 1511 appears beyond the range which "non-trivial" strong coupling effects could produce, at least those which influ- ence ps/p. It goes without saying that new, highly reliable measurements of the heat capacity jump are desperately needed.

ACKNOWLEDGEMENTS.- The author whishes to thank Mikko Paalanen, Bob Richardson and Mike Cross for many substantive discussions of the content of this ma- nuscript and the ideas which are presented there.

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