HIGHLY POLARIZED LIQUID 3He : SOME EXPERIMENTAL ASPECTS OF FAST MELTING OF POLARIZED SOLID 3He

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HIGHLY POLARIZED LIQUID 3He : SOME

EXPERIMENTAL ASPECTS OF FAST MELTING OF POLARIZED SOLID 3He

D. Thoulouze, G. Bonfait, Y. Chabre

To cite this version:

D. Thoulouze, G. Bonfait, Y. Chabre. HIGHLY POLARIZED LIQUID 3He : SOME EXPERIMEN-

TAL ASPECTS OF FAST MELTING OF POLARIZED SOLID 3He. Journal de Physique Colloques,

1980, 41 (C7), pp.C7-111-C7-117. �10.1051/jphyscol:1980717�. �jpa-00220154�

JOURNAL DE PHYSIQUE

CoZZoque C7, sqpZ&ment au n o 7 , Tome 41, jztiZZet 1980, page

C7-111

HIGHLY POLARIZED LIQUID

3 ~ e

: SOME EXPERIMENTAL ASPECTS OF FAST MELTING OF POLARIZED SOLID

3 ~ e

D. Thoulouze, G. Bonfait and Y. ~habre*

Cent-re de Recherches sur Zes Tr2s Basses Tempdratures, C. N.R. S., B. P. 266X, 38042 GrenobZe Cedex, France.

*

Laboratoire de Spectrome'trie Physique, U.S. G. M., B. P. 53X, 38041 GrenobZe Cedex, France.

Rlsum6.- Nous prdsentons ici quelques aspects ex Qrimentaux de la prQparation df3He liquide forte- ment polarisd

:

polarisation initiale du solide 3He, temps de relaxation dens le liquide et le solide. Ensuite on donne l'ordre de grandeur de quelques propri6tds caract5ristiques de ce liquide polaris6

:

courbe de fusion, champ interne ..., ddduites de certaines donnges expdrimentales de la fusion rapide.

Abstract.- We present here some experimental aspects concerning the production of highly polarized liquid 3 ~ e

:

previous polarization of the solid, relaxation times in the liquid and in the solid 3 ~ e . Then rough measurements of some characteristic properties of this polarized liquid, melting curve, internal field, are deduced from the main experimental features of the fast melting.

The idea of the possible existence of a "new

1 .

Initial polarization in the solid phase and quantum fluid", namely polarized 3 ~ e fluid

(

3 He+), relaxation processes

:

as well as its main physical properties have been In the initial method, solid He was formed at

³

discussed two years ago by C. Lhuillier and about 1.5

K ,

under a pressure of 50 bars, correspon- F. aloe"), and by Castaing and Nozisres (2) . ^{ding to}

^a

molar volume Vm

5

23.6 cm3/mole. Then it F. Laloe and

C .

Lhuillier proposed to ~olarize the was cooled by a dilution refrigerator in an external 3 ~ e atoms by optical pumping in the vapour phase, field formerly of 3.5 T, and then 7.3 Teslas.

while Castaing and Nozieres suggested the possibi- The heat transfer was insured by 100 copper lity of polarizing liquid 3 ~ e by fast decompression wires

(@ = 0.01

cm) of total surface

3

cm2 (fig.

1 ) .

of polarized solid 3 ~ e . The efficiency of this The 3 ~ e temperature inside the cell was measured by method and the existence of such a polarized liquid

^a

carbon resistor previously calibrated at thermal state was proved experimentally some months later equilibrium against the nuclear susceptibility of

( 4 )

in ren noble'^) and in Copenhagen . the solid 3 ~ e in the same magnetic field. 'Ihe He ³ We should like to present and discuss here some magnetization was measured by

NMR

at 114.8 MHz, and experimental aspects associated to the obtention of then 235 MHz, with a coherent pulsed NMR spectrome- highly polarized liquid 3 ~ e by fast melting of ter. The free decay of the signal was observed with previously polarized solid

$8.

The most important very small angle pulses (0.2' in solid He at the 3

parameters for the success of the experiment are lowest temperatures).

the initial polarization and the relaxation The pressure was measured at room temperature processes. Then, we shall write the thermodynamical with a fast response gauge.

balance of the decompression from solid to liquid The initial conditions before a decompression and of the magnetization relaxation in the liquid were the following

:

state, which will lead to the most typical proper- T.

= 18 mK

ties of this new polarized state. Hi

=

7.34 T

corresponding to a polarization of about 30

%.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1980717

JOURNAL DE PHYSIQUE

L q A r c l d i i e E2 Copner

C! s i n t e r e d s i l v e r

i a siycas:

FIG. I : Caption Experimental c e l l : V J : vacuum j a c k e t ; S : s h i e l d a t 0.5 K; 1I.C. : mixing chamber of d i l u t i o ~ l r e f r i g e r a t o r ; C . W . : copper w i r e s ; S.M. : superconducting magnet ; C : c e l l ; H.E. : h e a t exchanger ; F : f i l l i n g c a p i l l a r y ; N : NMR c o i l ; C.R. : carbon thermometer.

The f i n a l temperature of the 3 ~ e was l i m i t e d by t h e boundary Kapitza r e s i s t a n c e between t h e s o l i d

R~

3 ~ e and t h e copper w i r e s , and by t h e l a r g e h e a t c a p a c i t i e s mainly due t o t h e n u c l e a r Zeeman energy

-

⁵

s o t h a t t h e c o o l i n g time c o n s t a n t T = RK C a T

,

-3 2 4 -2 3

w i t h

q(

2 100 T cm K /W and C = T J K/cm

,

was becoming p r o h i b i t i v e l y l a r g e , l a r g e r t h a n 10 s e c . The number of w i r e s had been l i m i t e d t o 5 100 i n o r d e r t o l e a v e a mean f r e e d i s t a n c e 2 0.1 cm between t h e w i r e s i n t h e c e l l and t o p r e v e n t an e v e n t u a l r e l a x a t i o n by d i f f u s i o n t o t h e w i r e s , l e a d i n g t o a d e c r e a s e of t h e p o l a r i z e d l i q u i d l i f e time. I n f a c t , a s r e c e n t l y c a l c u l a t e d by Godfrin (5)

,

a 0.03 cm d i s t a n c e , w o u l d be enough t o i n s u r e a l o n g r e l a x a t i o n time i n t h e l i q u i d , a l l o w i n g t o i n c r e a s e t h e s u r f a c e by a f a c t o r almost 10, and t h e n t o decrease t h e f i n a l temperature t o about 12 mK. This type of v e r y simple c o n s t a n t volume c e l l may t h u s be i n t e r e s t i n g i n some s p e c i a l c a s e s but i t seems

d i f f i c u l t t o ~ r o v i d e a p o l a r i z a t i o n h i g h e r t h a n 40-50 %, u n l e s s very h i g h magnetic f i e l d s a r e used, w i t h o u t l e a d i n g t o a ~ o s s i b l e d e c r e a s e of t h e pola- r i z e d l i q u i d l i f e t i m e . Pomeranchuk c e l l s , a s designed by ~ r o s s a t i ( ~ ) j l ~ k o v i d e much h i g h e r p o l a r i z a t i o n s , b u t we have r e c e n t l y shown t h a t t h i s p o l a r i z a t i o n i s about 7 0 % i n 7 T e s l a s , a s a consequence of t h e ma- g n e t i c o r d e r i n g of s o l i d 3 ~ e , which appears a t about 3 mK i n f i e l d s of 7.3 T"). Furthermore, above 5 T , t h e s o l i d i s no more formed from s u p e r f l u i d l i q u i d , b u t from normal Fermi l i q u i d i n which,as we s h a l l s e e l a t e r , r e l a x a t i o n and d i f f u s i o n times a r e very l o n g a t m i l l i K e l v i n temperatures. I n t h a t c a s e t h e s o l i d has t o be grown very slowly i n o r d e r t o g e t t h e e q u i l i b r i u m m a g n e t i z a t i o n : i f t h e compression i s t o o f a s t , t h e poorly p o l a r i z e d l i q u i d (% 3 % f o r 7.3 T) has no time enough t o provide t h e s o l i d f o r i t s e q u i l i b r i u m p o l a r i z a t i o n , by r e l a x a t i o n e i t h e r a t t h e i n t e r f a c e o r f r o n t h e w a l l s . The s o l i d i s t h e n u n d e r p o l a r i z e d by a p r o c e s s analogous t o t h e r e v e r s e of t h e Castaing-Nozieres p r o p o s a l . I n t h e s u p e r f l u i d phase, t h e s u p e r c u r r e n t s seem t o t r a n s f e r enough magnetization,from t h e w a l l s a p p a r e n t l y , s o t h a t i r r e v e r s i b l e p r o c e s s e s have much l e s s impor- t a n c e . This l a r g e d i f f e r e n c e of behaviour a t the s u p e r f l u i d t r a n s i t i o n i s a t t h e o r i g i n c 8 ) of t h e s o c a l l e d "backstep" observed f o r t h e f i r s t time by

( 9 ) A d a m s e t a l .

.

F i n a l l y , a b e t t e r knowledge of t h e s o l i d 3 ~ e p r o p e r t i e s i s n e c e s s a r y t o o b t a i n ~ o l a r i z a t i o n n e a r

100 %. I n t h e framework of t h e m u l t i p l e s p i n

exchange model o f D e l r i e u , Roger and ~ e t h e r i n g t o 6 10) which e x p l a i n s most of t h e very low temperature- magnetic f i e l d p r o p e r t i e s of s o l i d 3 ~ e n e a r t h e t r a n s i t i o n , two ways appear l o g i c a l l y : e i t h e r p r e c o o l i n g t h e l i q u i d below 1 mK under high a p p l i e d magnetic f i e l d and t h e n form s o l i d 3 ~ e , b u t i n t h e o r d e r e d phase i t w i l l be very d i f f i c u l t t o g e t high

m a g n e t i z a t i o n s , o r a p p l y i n g very h i g h magnetic f i e l d s , about 15 T, t o reach t h e (H,T) r e g i o n i n which t h e o r d e r i n g temperature would d e c r e a s e and

tend t o zero.

A second c l a s s of parameters which p l a y a very important r o l e i n our s t u d y concerns t h e r e l a x a t i o n times i n t h e c e l l . One may t h i n k a p r i o r i of t h r e e main types of r e l a x a t i o n s : i n t h e s o l i d d u r i n g t h e m e l t i n g , i n t h e l i q u i d a f t e r m e l t i n g , and a t t h e s o l i d - l i q u i d i n t e r f a c e .

I n o r d e r t o d e f i n e t h e dynamical p r o p e r t i e s of o u r system, we have measured t h e r e l a x a t i o n times i n t h e c e l l where t h e p o l a r i z e d l i q u i d was produced.

A s p r e v i o u s l y d e s c r i b e d , t h e r e l a x a t i o n time i n t h e l i q u i d s t a t e was measured by t h e t y p i c a l following procedure : t h e e q u i l i b r i u m m a g n e t i z a t i o n was f i r s t t i p p e d t o an a n g l e of about 60° by a p p l y i n g a sequence of 6' p u l s e s of ¹⁰ ps l e n g t h and r e p e t i t i o n r a t e of 2 p e r second ; t h e recovery of t h e l o n g i t u - d i n a l magnetization was observed by a p p l y i n g succes- s i v e 0.2' p u l s e s every 20 s . I n f a c t , t h e l e n g t h of t h e p u l s e s , t h e i r r e p e t i t i o n r a t e and t h e recovery p u l s e r a t e were v a r i e d not t o d i s t u r b t h e l o c a l e q u i l i b r i u m .

The experimental r e s u l t s f o r T I a r e given i n f i g . 2 , i n t h e temperature range 50 mK

-

1 . 5 K, f o r b o t h f i e l d s 3.5 T and 7.3 T . I n t h e l i m i t of low temperature, they tend t o follow t h e T - ~ law expec- t e d f o r q u a s i - p a r t i c l e s c a t t e r i n g . Between 200 mK and 1 R, a r a t h e r f l a t minimum depends on t h e p r e s s u r e , r a n g i n g from 130 s e c . a t 22 b a r t o 330 s e c a t 0 b a r . AS expected, they do not depend upon t h e a p p l i e d f i e l d , w i t h i n t h e experimental e r r o r . These values a r e more thoroughly analyzed i n t h e i s s u e by ~ o d f r i n " ) t o g e t h e r w i t h previous w a l l r e l a x a t i o n r e s u l t s which a r e found t o be n e g l i g i b l e i n our c a s e .

For t h e s o l i d 3 ~ e (23.6 cm /mole) two d i f f e r e n t 3

F i g . 2 : S p i n - l a t t i c e r e l a x a t i o n times i n 3 ~ e : s o l i d 23.6 cm3/mole 0 H = 7.3 T

0 H = 3.5 T l i q u i d : H = 3 , 5 T A P = 0 b a r

and 7,34T f l P = 2 2 b a r

curves a r e o b t a i n e d f o r 3.5 T and 7 T , p r e s e n t i n g t h e same g e n e r a l behaviour. For t h e lowest f i e l d , t h r e e r e g i o n s may be c l a s s i c a l y d i s t i n g u i s h e d i n terms of t h e 3 b a t h s model (11)

-

above 800 mK, t h e observed r a t e s a r e determined by t h e modulation of t h e d i p o l a r f i e l d r e s u l t i n g

from t h e d i f f u s i o n of t h e r m a l l y a c t i v a t e d vacan- c i e s . The minimum value i s o b t a i n e d when t h e hopping r a t e -rL i s of t h e o r d e r of t h e Larmor frequency wo : wo r L 2. 1 .

-

below 800 mK, t h e vacancies a r e f r o z e n o u t , and t h e Zeeman energy i s no l o n g e r d i r e c t l y coupled t o t h e l a t t i c e . One then observes t h e Zeeman- exchange c r o s s r e l a x a t i o n which g i v e s r i s e t o temperature independant r e l a x a t i o n r a t e s .

-

a t temperatures lower t h a n 300-400 ^ml(, t h e t h e r - mal e x c i t a t i o n of t h e v a c a n c i e s i s t o o low t o i n s u r e r e l a x a t i o n of t h e exchange, and an

C7-114 JOURNAL DE P H Y S I Q U E

e x c h a n g e - l a t t i c e r e l a x a t i o n b o t t l e n e c k appears. 1 t h e n i n c r e a s e s by o r d e r s of magnitude. I n f a c t , f o r t h e two l a s t regimes, t h e t h e o r y i s not c l e a r l y understood.

-

t h e f i r s t regime i s well-defined f o r b o t h f i e l d s , w i t h a minimum a t 0.85 K f o r t h e h i g h e s t f i e l d , corresponding t o 0.94 E f o r 110 MHz i n e x c e l l e n t agreement w i t h t h e parameters f o r t h i s molar volume ( a c t i v a t i o n energy

0

= 6.5 K ; half-band w i d t h w3 = 3 1;). However t h e v a l u e s of TI a r e

l a r g e r t h a n expected from t h e c l a s s i c a l t r e a t m e n t , which y i e l d s T I minimum ² 4 s e c a t 234 MHz and

2 s e c a t 110 MHz.

Then, t h e Zeeman exchange c r o s s r e l a x a t i o n p l a - t e a u T1 ?. 12 s e c measured a t 110 MHz i s c o n s i s t e n t w i t h the v a l u e s r e p o r t e d by S u l l i v a n and

c h a p e l l i e r ( 1 2 ) , b u t i t does n o t appear a t 234 MHz, w h i l e t h e p r e v i o u s a u t h o r s would l o c a t e i t around T ^?. 250 s e c . The disappearance of t h i s p l a t e a u

1

may be understood a s a r e d u c t i o n from b o t h ends : i n o u r f i e l d , t h e "high temperature" l i m i t happens a t lower temperature, i n such a way t h a t t h e phonon b a t h (and thus t h e vacancies) does no more s t a y t h e r a i n energy r e s e r v o i r , and becomes comparable t o the Zeeman b a t h . On i t s "low temperature ^" l i m i t t h e e x c h a n g e - l a t t i c e b o t t l e n e c k i s s h i f t e d towards h i g h e r temperatures s i n c e t o g e t t h e same r e l a x a -

t i o n r a t e , t h e e x c h a n g e - l a t t i c e coupling must b e i n c r e a s e d , f o r l a r g e r f r e q u e n c i e s .

A t lower temperature, T 1 seems t o s a t u r a t e b e t - ween 1000 and 2000 seconds.In f a c t , i t i s d i f f i c u l t

t o a s c r i b e a p h y s i c a l meaning t o t h e s e v a l u e s , s i n c e below 300 mK t h e Zeeman h e a t c a p a c i t y (which i s h e r e 30 times l a r g e r t h a n t h e exchange one) becomes l a r g e r t h a n t h e l a t t i c e one. Then t h e Zeeman t h e r m a l i z a t i o n p r o c e s s t a k e s p l a c e e i t h e r by coupling w i t h t h e d i l u t i o n mixing chamber through the l a t t i c e and Kapitza r e s i s t a n c e o r by s p i n

d i f f u s i o n and r e l a x a t i o n on t h e w a l l s .

Concerning t h e s o l i d - l i q u i d i n t e r f a c e , we s h a l l s e e l a t e r t h a t a s h o r t time c o n s t a n t may p o s s i b l y b e a s s o c i a t e d t o i t s movement, b u t no p r e c i s e mea- surements have been performed up t o now and only o r d e r s of magnitude may be sketched a p r i o r i (2)

.

2. Plelting of s o l i d and r e l a x a t i o n of t h e p o l a r i z e d l i q u i d : f i n a l temperature, l i f e time, and energy r e l a x a t i o n

We know how t o o b t a i n e x p e r i m e n t a l l y p o l a r i z e d s o l i d He, w i t h p o l a r i z a t i o n s of t h e o r d e r of 30 t o 3

70 % ; furthermore t h e r e l a x a t i o n i n t h e s o l i d and i n t h e l i q u i d , which a r e t h e i n t r i n s i c dynamical p r o p e r t i e s of t h e c e l l , a r e t y p i c a l l y of t h e o r d e r o f 100 s e c (20 s e c minimum) and make t h e experiment p o s s i b l e . Now, we s h a l l c o n s i d e r some a s p e c t s concerning t h e r e s u l t s a f t e r t h e m e l t i n g , which i s o p e r a t e d by connecting t h e c e l l t o a tank a t room temperature.

A t y p i c a l r e c o r d of a f a s t decompression i s

shown i n f i g . 3. Let us n e g l e c t i n a f i r s t s t e p t h e i n i t i a l t r a n s i e n t regime. A f t e r some seconds t h e p r e s s u r e s t a y s a b s o l u t e l y c o n s t a n t a t a v a l u e f i x e d from oucside, 22 b a r s i n t h i s c a s e , w h i l e t h e tempe- r a t u r e reaches a value very c l o s e t o 0.3 K which i s t h e temperature of t h e minimum of t h e m e l t i n g curve.

This i s t o be expected, f o l l o w i n g a p r o c e s s r e v e r s e of t h e Pomeranchuk e f f e c t . During t h a t time, t h e m a g n e t i z a t i o n d e c r e a s e s w i t h a unique time c o n s t a n t

% 140 s e c , e q u a l t o t h e T, measured a t t h e same temperature i n t h e l i q u i d 3 ~ e . This l i f e t i m e T , * e f f e c t i v e l y f o l l o w s t h e v a l u e s measured f o r l i q u i d 3 ~ e a t e q u i l i b r i u m , r e a c h i n g 340 seconds f o r a f i n a l p r e s s u r e about 0 b a r . This confirms t h a t t h e system i s i n t h e l i q u i d phase, and t h a t t h e magnetization i s d i r e c t l y t r a n s f e r e d f r a n t h e s o l i d a t 18 mK t o t h e l i q u i d a t 0.3 K. This a l s o shows t h a t even i n

f a s t decompressions w i t h and without a p p l i e d magne- t i c f i e l d . The mean v a l u e f o r 6 decompressions gives ATf Q

-

15 mK once s u b s t r a c t e d t h e rnagneto- r e s i s t a n c e of t h e thermometer, i . e . from about 0.31 K t o 0.295 K.

This v a l u e i s s m a l l e r t h a n t b a t which may be c a l c u l a t e d assuming f a s t m e l t i n g i s an a d i a b a t i c

(2)

.

process

.

ssolid(Ms) =

s

l i q u i d ( T f i n a l ' '\)

w i t h M = M . s i n c e t h e magnetization i s conservative.

For b o t h H = 0 and H # 0 , one may w r i t e :

assuming C c o n s t a n t f o r s m a l l AT and low p o l a r i z a - t i o n

C ". 2.5 J/mole 8 . For H = 7 T and Ti = 18

Tf ^Q 0.3 K

would l e a d t o ATf =

-

50 mK.

An o t h e r e s t i m a t e o f t h i s AT c o n s i s t s i n assu- ming AT t o be p r o p o r t i o n n a l t o t h e square of t h e m a g n e t i z a t i o n , a s most of t h e p h y s i c a l p r o p e r t i e s of t h i s f l u i d (2) :

A T = - m x ' 0 . 3 K 2

f o r m Q, 25 %, t h i s g i v e s AT Q

-

^{19 mK.}

This number i s i n b e t t e r agreement w i t h t h e measured one. However, such small AT a r e only twice t h e experimental e r r o r and f u r t h e r experiments a r e b e i n g performed, with l a r g e r p o l a r i s a t i o n s , s o a s t o prowmore e v i d e n t l y a n e v e n t u a l lowering of t h e n e l t i n g curve.

For d i s c u s s i n g t h e "long" time p a r t of t h e decompression, we have n e g l e c t e d f o r t h e moment t h e m e l t i n g process i t s e l f . Two main f e a t u r e s appear from f i g . 3 : t h e temperature g i v e n by t h e carbon r e s i s t o r r i s e s i n a few t e n t h s of a second up t o about 0.5 K, s t a y s t h e r e some time and t h e n

d e c r e a s e s down t o t h e e q u i l i b r i u m temperature T f Q 0 . 3 I( where a l l s o l i d i s molten. During t h a t time, t h e 3 ~ e m a g n e t i z a t i o n d e c r e a s e s quickly, w i t h a time c o n s t a n t of about 1.8 s e c , b e f o r e r e a c h i n g t h e long T I time c o n s t a n t . For f a s t mel-

*

t i n g t i m e s , l 5 t o 30 % of t h e magnetization a r e l o s t i n t h a t way ( e v i d e n t l y t h e 15 % atoms l o s t when m e l t i n g from s o l i d (vs = 2 3 . 6 cm3/mole) t o l i q u i d

(vL = 27.3 cm3/mole) have been deduced) ; f o r slower decompressions, 10 t o 20 seconds, up t o 75 % of t h e m a g n e t i z a t i o n may be l o s t , w i t h d i f f e r e n t time c o n s t a n t s

,

mainly i n 3.5 T f i e l d s . I n 7.3 T, no more t h a n 30 % were l o s t even f o r very slow decompressions.

The very f a s t temperature r i s e i s probably due t o t h e f a c t t h a t , below 100

a,

t h e h e a t c a p a c i t y of t h e s o l i d He phonons 3 i s very smal1,much lower

t h a n t h a t of t h e magnetic terms, exchange and Zeeman. Thus, a s soon a s t h e f i r s t l i q u i d 3 ~ e dro- p l e t i s formed, i t h e a t s t h e s e phonons which propa- g a t e b a l i s t i c a l l y i n t o t h e s o l i d 3fie. I t i s more d i f f i c u l t t o understand why t h e phonons a r e h e a t e d up t o 0.5 K and n o t t o 0.3 K which i s t h e f i n a l temperature of t h e l i q u i d and i s mostly determined by t h e magnetic e n t r o p i e s . The same o v e r h e a t i n g appears when t h e decompression i s stopped b e f o r e a l l t h e s o l i d i s molten b u t i t comes back t o ^d f i n a l temperature much lower t h a n 0.3 K, t y p i c a l l y 60 mK, a s a r e s u l t of thermal e q u i l i b r i u m between t h e l i q u i d formed a t about 0.3 K and t h e remaining s o l i d which s t a y s cold.The same f a s t h e a t i n g o f t h e phonons appears i n a Foneranchdccell , b u t no such o v e r h e a t i n g i s t h e n observed. This d i f f e r e n c e may f i n d i t s o r i g i n i n t h e mechanical work1 PIY a s s o c i a t e d t o t h e decompression of t h e s o l i d 3 ~ e from t h e o v e r p r e s s u r e corresponding t o a molar volume of 23.6 cm /mole t o t h e m e l t i n g curve 3

(vs % 25 cm3/mole).

JOURNAL DE PHYSIQUE

M

(arb. units)

-

-0.4 -0.3 30--0.2

-

0 3 6 9 1 2 1 5 l B i O 1 2

3

4

5

seconds minutes

Fig. 3 : Typical diagrams f o r a decompression a ) f a s t decompression

b) slow decompression

h i g h l y p o l a r i z e d l i q u i d T I s t a y s c o n s t a n t . Let us c o n s i d e r now t h e h e a t d i s s i p a t i o n asso- c i a t e d t o t h i s s p i n r e l a x a t i o n . The magnetic work w i l l be AQ =

I

K d

M

where K i s t h e i n t e r n a l f i e l d

defined by Castaing and ~ o z i e r e s ' ~ ) . For s m a l l p o l a r i z a t i o n s , we can w r i t e R = mHmax

w i t h 0 c m < I and M = ml4

sat mf

s o t h a t ₌ 'sat 'ma

Jmi ^ma.

Knowing M % 6.5 cgslmole, such a measurement s a t

of t h e h e a t d i s s i p a t i o n AQ p r o v i d e s a value f o r t h e i n t e r n a l f i e l d and t h e n a way t o g e t t h e whole magnetization curve M(H) of l i q u i d 3 ~ e ( 2 ) . However i t i s n o t easy t o e v a l u a t e t h e d i s s i p a t e d h e a t AQ, s i n c e t h e experimental c e l l i s n o t completely i s o - l a t e d from t h e c o l d s o u r c e , and i t begins t o c o o l soon a f t e r t h e decompression. A good way t o evalua- t e t h e energy r e l a x e d i s t o compare t h e temperature

d r i f t s i n high f i e l d and i n zero f i e l d , j u s t a f t e r decompression, when AQ i s d e v e l o p p e d , a d a f t e r r e l a x a t i o n , so a s t o normalize t h e d r i f t s and t a k e i n t o account any v a r i a t i o n of o t h e r experimental parame- t e r s .

I n those c o n d i t i o n s , one f i n d s an o r d e r of magni- tude :

AQ = 25-35 mJ/mole,

f o r p o l a r i z a t i o n r e l a x i n g from t y p i c a l l y 23 % t o 15 %, which g i v e s :

Emax 1 1,5

-

^{2 , 5 x lo6 Gauss.}

This v a l u e may b e compared t o t h a t c a l c u l a t e d i n a l i n e a r approximation :

"sat =

%

'max

w i t h

5

^{= 2 . 5 x and Msat = 6.5 cgs}

g i v i n g E = 2.5 x lo6 gauss.

max

These a r e o n l y rough p r e l i m i n a r y e s t i m a t e s of t h e i n t e r n a l f i e l d v a l u e s . Higher p o l a r i z a t i o n s , and perhaps s h o r t e r r e l a x a t i o n time c o n s t a n t s , a s w e l l a s simultaneous measurement of t h e s p e c i f i c h e a t of t h e p o l a r i z e d l i q u i d , would b e n e c e s s a r y t o draw t h e m a g n e t i z a t i o n curve of l i q u i d 3 ~ e .

L e t us cone back t o t h e f i n a l temperature T f , j u s t a f t e r t h e m e l t i n g has been completed. We have noted t h a t t h e temperature i n c r e a s e on a d i a b a t i c m e l t i n g is j u s t t h e r e v e r s e of t h e Pomeranchuk c o o l i n g . The f i n a l s t a t e i n zero f i e l d corresponds t o t h e p o i n t where t h e e n t r o p y of t h e s o l i d i s equal t o t h a t o f t h e l i q u i d , i . e . , t h e minimum of t h e m e l t i n g c u r v e . I f now, a s p r e d i c t e d by L h u i l l i e r ,

aloe") ,

C a s t a i n g and iJozieres")

,

t h e m e l t i n g curve i s lowered f o r p o l a r i z e d l i q u i d 3 ~ e , t h e minimum temperature w i l l be s h i f t e d towards lower t e m p e r a t u r e s . I n t h a t c a s e , t h e measurement of t h i s f i n a l temperature w i l l be an i n d i c a t i o n of an even- t u a l lowering of t h e m e l t i n g curve.

As p r e v i o u s l y , i t i s d i f f i c u l t t o g e t a b s o l u t e v a l u e s of t h i s s h i f t , b u t i t i s p o s s i b l e t o compare

The f a s t i n i t i a l r e l a x a t i o n a p p e a r s t o b e a s s o - c i a t e d w i t h o v e r h e a t i n g ; a s may b e s e e n f r o m f i g . 3 , t h e y p r e s e n t t h e same b e h a v i o u r f o r f a s t and s l o w d e c o m p r e s s i o n s . F u r t h e r m o r e , t h i s r e l a x a t i o n s t o p s a t t h e same t i m e a s t h e o v e r h e a t i n g i n a p a r t i a l d e c o m p r e s s i o n where p a r t o f t h e s o l i d r e m a i n s i n t h e c e l l . T h i s s u g g e s t s t h a t his f a s t r e l a x a t i o n i s r e l a t e d e i t h e r t o t h e moving l i q u i d - s o l i d i n t e r f a c e , o r t o d e f e c t s a s s o c i a t e d t o t h e under- p r e s s u r i z e d m e l t i n g s o l i d 3 ~ e , o r f i n a l l y t o t h i s o v e r h e a t i n g o f t h e phonons, which i n c r e a s e s t h e r e l a x a t i o n r a t e i n t h i s o u t o f e q u i l i b r i u m s y s t e m .

A s a c o n c l u s i o n , we h a v e g i v e n and d i s c u s s e d some e x p e r i m e n t a l v a l u e s o f t h e p a r a m e t e r s c o n c e r - n i n g t h e c o n d i t i o n s o f p r o d u c t i o n and o f e x i s t e n c e o f t h e p o l a r i z e d l i q u i d 3 ~ e p h a s e , which we h o p e t o

(1 3 ) produce s o o n w i t h p o l a r i z a l i o n s up t o 7 0 %

.

We have a l s o d i s c u s s e d some a s p e c t s c o n c e r n i n g t h e t e m p e r a t u r e a f t e r m e l t i n g and t h e e n e r g y r e l a x a t i o n , a s s o c i a t e d w i t h t h e i n t r i n s i c p h y s i c a l p r o p e r t i e s o f t h e p o l a r i z e d s t a t e : m e l t i n g c u r v e , n a g n e t i z a - t i o n c u r v e o f t h e l i q u i d , i n t e r n a l f i e l d . . . More p r e c i s e e x p e r i m e n t a l v a l u e s w i l l b e p r o v i d e d i n

t h e n e x t f u t u r e by s t a r t i n g from h i g h e r p o l a r i z a - t i o n s .

We a r e g r a t e f u l t o P. Averbuch, B. C a s t a i n g , M. C h a p e l l i e r , J.11. D e l r i e u , 2 . J o f Z r i n , A. Landesnan and P. N o z i S r e s f o r f r u i t f u l d i s c u s s i o n s .

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257 ( 1 9 7 9 ) .

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G. Schumacher a n d D. Thoulouze, i n P h y s i c s of U l t r a l o w T e m p e r a t u r e s , e d i t e d by T. Sugawara e t a l . ( P h y s i c a l S o c i e t y o f J a p a n , Tokyo 1978), p.294. G. F r o s s a t i , t h e s i s , U n i v e r s i t y o f G r e n o b l e , 1978.

( 7 ) 11. G o d f r i n , G. F r o s s a t i , A . Greenberg, B. H e b r a l and D. Thoulouze, Phys. Rev. L e t t . t o b e p u b l i s h e d , and t h i s i s s u e .

( 8 ) C. Yu and P.W. Anderson, P r i v a t e Communica- t i o n . P h y s i c s L e t t e r s

*,

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H e t h e r i n g t o n , J . P h y s i q u e L e t t r e s

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532 (1971).

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5 3 ( 1 9 7 3 ) . PI. C h a p e l l . i e r , t h i s i s s u e .

0 2 ) N.S. S u l l i v a n and M. C h a p e l l i e r , J. P t ~ y s . C 7, L 195 ( 1 9 7 4 ) .

-

( 1 3 ) G. F r o s s a t i , t h i s i s s u e . F.B. Rasmussen, t h i s i s s u e .