PHASE DIAGRAM OF 3He AT MELTING PRESSURES AND HIGH MAGNETIC FIELDS

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PHASE DIAGRAM OF 3He AT MELTING PRESSURES AND HIGH MAGNETIC FIELDS

H. Godfrin, G. Frossati, A. Greenberg, B. Hebral, D. Thoulouze

To cite this version:

H. Godfrin, G. Frossati, A. Greenberg, B. Hebral, D. Thoulouze. PHASE DIAGRAM OF 3He AT

MELTING PRESSURES AND HIGH MAGNETIC FIELDS. Journal de Physique Colloques, 1980,

41 (C7), pp.C7-125-C7-127. �10.1051/jphyscol:1980719�. �jpa-00220156�

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JOURNAL DE PHYSIQUE CoZZoque C7, supple'ment au n o 7 , Tome 41, juiZZet 1980, page C7-125

PHASE DIAGRAM OF

3 H e

AT MELTING PRESSURES AND HIGH MAGNETIC FIELDS

H. Godfrin, G. Frossati, A.S. Greenberg

* ,

^B.Hebral and D. Thoulouze

Centre de Recherches sur Zes Tr2s Basses Temp&ratures, C.N.R.S., B.P. 166 X , 38042 GrenobZe Cedex, France.

RQsum&.- Nous pr6sentons des mesures de pression sur 3 ~ e solide dans une cellule Pomeranchuk prg- refroidie P T % 3 3, dans des champs magn6tiques jusqulS 7,2 T.

Nous avons mesure les pressions B l'lquilibre des transitions A et A2 de 3 ~ e superfluide ; nous trouvons une correction nggative P la variation linsaire de P P vs.H, correspondant B l'ordre

magnltique de 3 ~ e solide

.

₃ ^A2 ^A1

Nous avons obtenu le diagramme de phases P(H) de He solide ; le diagramme H(T) P fort champ peut 8tre d6duit en employant une thermomstrie basGe ur les transitions A I * A2

.

Les rlsultats du modlle d16change multiple dans 'He solide sont en ban accord avec nos mesures

.

Abstract.- We report pressure measurements on melting 3 ~ e in a Pomeranchuk cell precooled to temperatures T % 3 3, in magnetic fields up to 7.2 T

.

The equilibrium pressures of the A1 and A phase transitions of superfluid 3 ~ e have been measured ; we have found a ne ative deviation from tie linear P

-

PAl vs.H splitting, due to the magnetic

ordering of solid 5He

.

^A2

We have obtained the magnetic P(H) phase diagram of solid 3 ~ e ; the H(T) phase diagram in high fields can be deduced by using a thermometry based on the AI-A2 splitting

.

Our results are in agreement with the multiple spin exchange model of solid 3 ~ e

.

Nuclear magnetic ordering of solid 3 ~ e at zero field was first observed by Halperin et al. (1)

.

Several groups have studied the effect of magnetic fields on the ordering(2-6). In a recent paper (6) we have shown experimentally that the "backstep", a new feature discovered by Schuberth et on the pressurization curve of 3 ~ e in a Pomeranchuk cell, was due to magnetic irreversibility, and closely related to the ideas of C. Lhuillier,

F. ~ a l o ~ ( ~ ) and B. Castaing, P. Nozi~res'~) on 3~e+-.

The "backstep", studied theoretically by Delrieu (9)

,

and Yu and ~nderson(lO), is shown to be due to non equilibrium magnetization of solid 3 ~ e .

In Pomeranchuk experiments, very slow compression rates are required to obtain equilibrium pressures (6). Therefore, it is convenient to

precool the experimental cell to the temperatures of interest (T % 3 mK), and to form small amounts of solid. This has been achieved by using a plastic Pomeranchuk cell located in the mixing chamber of a

( 6 ) dilution refrigerator working below 3 rnK

.

A -A? Pressure Splitting : -1-

We have observed the A1 and A2 features on the pressure vs. time curves during compressions, decompressions, and also heating the cell after the maximum pressure was reached. For sufficiently slow variations (<< 100 pK/mn), we obtained the pressure differences AP =

PA^ -

^PA~)VSH shown in fig. _{I .}

For H < 2T, AP = 220H Pa/T. Gully et al.(ll) found AP = 200H Pa/T (H < % 1 T) : Osheroff and Anderson (I2) : 220H Pa/T (H % 0.5 T) and 2398 Pa/T

(H = 0.74 T) ; Kummer et al. (2)

.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1980719

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JOURNAL DE PHYSIQUE

AP % 220H Pa/T(H < 1.2 T.).

Our low f i e l d v a l u e s f o r AP a r e t h e n i n good agreement w i t h p r e v i o u s r e s u l t s . For f i e l d s 2 < H < 5T, we f i n d t h a t AP r e a c h e s a maximum a t H % 3.5 T, AP = (500 i: 10)Pa. Above 5T, t h e o r d e r i l g t r a n s i t i o n TN o f s o l i d He o c c u r s a t t e m p e r a t u r e s 3

above T A ~ and T A ~ ( s e e f i g . 1) ; t h e m e l t i n g c u r v e h a s a s m a l l e r t e m p e r a t u r e dependence below TN, which e x p l a i n s t h e n e g a t i v e d e v i a t i o n s from t h e l i n e a r behaviour of AP vs.H. We found no evidence f o r t h e p o s i t i v e d e v i a t i o n r e p o r t e d by r e f . 3 a t 3T.

P r e s s u r e v s . magnetic f i e l d phase diagram o f s o l i d and s u p e r f l u i d 3 ~ e :

The p r e s s u r e s of t h e A , and A2 t r a n s i t i o n s PA 1 and PA2 and t h e maximum p r e s s u r e i n t h e c e l l PS a r e shown i n f i g u r e 2. For r e v e r s i b l e compressions, PS(H) does n o t depend o n t h e compression r a t e . Although PS i s n o t t h e p r e s s u r e PN of t h e r e a l magnetic t r a n s i t i o n , i t p r o v i d e s a good e s t i m a t e of PN, s i n c e t h e e n t r o p y d e c r e a s e a t TN o c c u r s i n a s m a l l t e m p e r a t u r e r a n g e even i n h i g h

.

I n moderate f i e l d s (H % 3 T ) , we observed a change of d P / d t ( p r e s s u r i z a t i o n r a t e ) a t p r e s s u r e s

% 200 Pa below Ps, b u t t h i s f e a t u r e d i d n ' t show up s y s t e m a t i c a l l y i n o u r p r e s s u r i z a t i o n c u r v e s . H-T p h a s e diagram o f s o l i d 3 ~ e :

I t i s c l e a r from t h e r e s u l t s shown i n f i g u r e 2 t h a t t h e o r d e r i n g t e m p e r a t u r e o f t h e s o l i d becomes h i g h e r t h a n TA1 and TA* when t h e f i e l d i s i n c r e a s e d above 5 T. We u s e t h e Al-A2 s p l i t t i n g , a s a thermo- meter : we assume t h a t t h e l i n e a r s p l i t t i n g AT = (TA2

-

T A ~ ) = 64 H uK/T measured a t lower

field^'^^'^'^)

i s

s t i l l

l i n e a r and a p p r o x i m a t l y symmetric up t o ST. We c a n t h e r e f o r e e s t i m a t e t h e o r d e r i n g t e m p e r a t u r e s i n h i g h magnetic f i e l d s

( f i g u r e 3 ) . A t 7.2 T, o r d e r i n g o c c u r s a t t h e tempe- r a t u r e of t h e mixing chamber of t h e d i l u t i o n r e f r i g e r a t o r ; t h i s h i g h f i e l d ~ o i n t a g r e e s w e l l

FIG. 1 : AI-A2 p r e s s u r e s p l i t t i n g vs.magnetic f i e l d . a

-

Osheroff and Anderson( l 2,

b

-

~ u l l y e t a 1 . ( 1 ' ) +

-

Kmmer e t a1. ( 2 )

-

t h i s work.

w i t h t h e r e s u l t s o b t a i n e d f o r H < 5T by assuming a l i n e a r t e m p e r a t u r e s p l i t t i n g AT(H).

The m u l t i p l e exchange model :

M. Roger, J.M. D e l r i e u and J.H. H e t h e r i n g t o n p r o v i d e a t h e o r e t i c a l i n t e r p r e t a t i o n o f o u r d a t a , assuming t h a t m u l t i p l e s p i n exchange i n t e r a c t i o n s a r e r e s p o n s i b l e f o r t h e magnetic o r d e r i n g . Three s p i n exchange and f o u r s p i n p l a n a r exchange a r e t h e dominant mechanisms. A comparison o f t h e c a l c u - l a t i o n s w i t h o u r e x p e r i m e n t a l r e s u l t s ' 13) shows t h a t t h i s two p a r a m e t e r s model r e p r o d u c e s a l l t h e e s s e n t i a l f e a t u r e s o f t h e P-H and H-T phase d i a - grams we have o b t a i n e d .

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+

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-

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