NMR ASPECTS IN HIGH FIELD 3He AT THE LIQUID SOLID TRANSITION (Pomeranchuk compression and Castaing-Nozières décompression

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NMR ASPECTS IN HIGH FIELD 3He AT THE

LIQUID SOLID TRANSITION (Pomeranchuk

compression and Castaing-Nozières décompression

M. Chapallier

To cite this version:

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JOURNAL DE PHYSIQUE CoZZoque C7, suppte'ment au n o 7 , Tome 41, juiZZet 1980, page C7-119

NMR ASPECTS

IN HIGH

FIELD

3 ~ e

AT

THE

LIQUID SOLID TRANSITION

(Pomeranchuk compression and Castaing-NoziSres decompression)

M. Chapellier

Universite' de P a r i s Sud, Laboratoire de Physique des SoZides, BEt. 510, 91405 Orsay Cedex, France.

Resume

-

La belle idee de Castaing et Nozieres d'effectuer des experiences pendant un temps court devant tous les temps de relaxation TI a permis la production d'helium 3 liquide polarise. La compression initiale peut dtre analysee en considerant tous les mecanismes de relaxation possibles. Elle peut conduire :

1) A des Bquilibres non-thermodynamiques dans le solide avec pour consequence une pression liquide- solide plus Blevee que la pression Z l'dquilibre thermodynamique.

2) En champ tres eleve, si les reservoirs d'echange et Zeeman sont completement decouples, on pourra observer un ordre nucleaire dans le solide avec une aimantation tres faible, le decou- plage empdchant l'obtention de polarisation proche de 1 par cette methode.

Des aspects divers de ces problsmes, incluant la relaxation dans le liquide et le solide seront discutes et compares avec les experiences.

Abstract

-

The beautiful idea of Castaing and Nozieres to do experiments in a time short compared with any relaxation time TI have led to a successful experiment in which polarized liquid He3 was produced. The initial compression processes have to be reanalyzed considering all possible TI me- chanisms and may :

1) Lead to non-thermodynamic equilibrium in the solid with as a consequence a higher pressure than the normal thermodynamic equilibrium;

2) In very high fields where exchange and Zeeman reservoirs may be completely decoupled, it could lead to ordering of the solid with a very low magnetization, and thus prevent us from obtaining a polarization near unity by this method.

Various aspects of these problems including relaxation processes in the liquid and the solid will be discussed and compared with experiments.

INTRODUCTION.- As soon as Nozieres and Castaing ex- Zeeman, defects ...) which determine TI.

plained their proposal/l/ to observe polarized li- Let us start backward and see how one describes a quid 3 ~ e by rapid melting of polarized solid, it solid in N M R and show that a solid with low en- was obvious that the reverse process, known as tropy in high field is not necessarily polarized. Pomerantchuk compression had to be also analyzed

SOLID 3 ~ e IN NMR IN HIGH FIELD.- The hamiltonian in high fields /2/ in terms of the growth of the

of the system is written% = Z

+

E

+

Sdip

where magnetization. One wants to obtainrhighly polari-

zed solid but starting with a poorly polarized li- =

'

W~ IZ the Zeeman quid. Nevertheless, it was known long ago that a _-_W1_-_{- 32,43 MHz/Tesla}

slow compression /3/ ( 3 hours) in a field of 54.5 2lr

k Gauss yield 47% of average polarization in the E is the exchange, of the order of 15 MHz /6/. solid. Let us then try to give ideas (and for the For o w purpose, the main property of E is that moment no answers) on the possible phenomenons

[.:,

E

J

= 0 , is a small perturbation of the

DlP

which appear in a Pomerantchuk compression in high Order of 10 kHz, but commutes neither with Z nor field, as sketched in fig.1. Our problem is to know With E.

where the magnetization is produced : m t ~ r h

a) If only up spins goes into the solid, then one needs to restore the magnetization in the liquid and therefore know how it relaxes /4/5/,

b) If the spins relax at the interface, one should know how they relax and if there is any H and T dependence,

c) If in fact the solid is formed unpolarized but relax after its T1

,

one has to describe the solid with all its compounds (phonons, exchange and

T?

5

Fig. 4

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JOURNAL DE PHYSIQUE

the broadening is a square for simplicity. p(E)is the probability of occupation of the sublevel of energy E.

Fig. 2

AS it is well known /7/, when in a system the (Pulses experiments in which one changes TZ but TE hamiltonian is a sum of two commuting components, may be a very good way of investigating of the sys- with as a consequence no possible exchange of ener- tem as a test of differents coupling).

gy between the two, one can describe this system by two reservoirs /8/ at differents temperatures, which are coupled by the third hamiltonian. A simple way to visualize this situation is proposed in Fig.2a with two Zeeman levels broadened by exchange inte- ractions. If only one Boltzmann exponential describes the population of all levels, there is only one temperature (Fig. 2b). If on the other hand the sublevels are not populated with the same BoltZmann exponential as the Zeeman levels, one could have a pseudo equilibrium (obtain in a time % T2) with two different temperatures.

As an example of this situation which arise when E and Z are decoupled (or during times short compared to the coupling time between E and Z)

Fig. 2c represents a very hot (or infinite) TZ, with no magnetization, but lonr TE. This is what may happen during a quick compression in high fields.

A last example, is given in Fig. 2d, with negative TZ and positive TE. Such a situation will happen after a pulse of radio frequency of length

s applied to a system prepared with a single positive temperature (Fig. 2b)

.

REMARKS.- The reservoirs model may not be adequate for very high polarization. Nevertheless we think that it is a good and didactic way to describe the system simply. Of course one should have the upper restriction in mind, because obviously the phase space available for E will not be the same as the system becomes more and more polarized, which means that E and Z cannot be describe completely indepen- dantly.

The higher the field, the better the decoupling of Z and E. The exact dependance which is the

tail of a correlation function is still problem, both experimentally and theoretically, at least along the melting curve.

Before we look more carefully on how theses baths connect to the lattice and to the outside bath let us relate the pressure of equilibrium between liquid and solid and the behavior of E and Z . From Clapeyron's relation in field one has

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temperature t h e same p r e s s u r e a s i n z e r o f i e l d . I n f u l l e q u i l i b r i u m i n f i e l d p v a r i e d by

2

_AH _(mS-mL) _{and t h e h i g h e r t h e v a l u e of}_ms v -v S L t h e lower t h e v a l u e of p . A v a r i a t i o n i n p a t f i x e d T i s t h e n i n d i c a t i n g t h a t Z r e l a x e s t o E . We r e p r e s e n t i n F i g . 3 a l l t h e b a t h s represen- t i n g s o l i d 3 ~ e . Near t h e belting curve a t h i g h tem- p e r a t u r e t h e r e e x i s t ( a s i n a l l s o l i d s ) t h e r m a l l y e x c i t e d v a c a n c i e s which move i n s i d e t h e s o l i d , pro-

ducing a modulation of

qiP

with components a t t h e

Larmor frequency and hence r e l a x i n g Z d i r e c t l y .

When t h e number of v a c a n c i e s d e c r e a s e s by Lowerlng T. TI goes through a minimum a t which t h e c o r r e l a - t i o n time .r produced by t h e s e s v a c a n c i e s i s e x a c t -

-

1

l y e q u a l tocwI

.

A t t h i s temperature T1

2

w I 2 M-l where M2 i s t h e Van Vleck second moment o f t h e l i n e

(Fig.4) (roughly t h e s q u a r e of t h e d i p o l a r i n t e r a c - t i o n )

.

G34

When t h e number o f v a c a n c i e s f u r t h e r d e c r e a s e s by d e c r e a s i n g T t h e l a t t e r p r o c e s s become i n e f f i - c i e n t . One t h e n observes t h e c o u p l i n g o f Z t o E

by %dip, a p r o c e s s which i s temperature inde-

pendant. T h i s assumes t h a t E i s always t h e r m a l i z e d by t h e remaining v a c a n c i e s which s t r o n g l y couples E

and phonons. I f T i s decreased f u r t h e r one may a l s o l o o s e c o n t a c t between E and t h e o u t s i d e b a t h connec- t e d t h e n by t h e remaining phonons, themselves ha- ving a Kapitza r e s i s t a n c e which depends on s u r f a c e s and a c o u s t i c impedance. T h i s a r e a i s p a r t i c u l a r l y unknown and t h e time c o n s t a n t i s no l o n g e r a u s u a l T1.

Another unknown i s t h e number and temperature behavior of v a c a n c i e s i n t h e c o l d s i d e of t h e mel- t i n g curve on which d e c r e a s i n g T t r a n s f o r m t h e so- l i d i n t o l i q u i d ( 1 f it e x i s t t h e r m a l l y a c t i v a t e d v a c a n c i e s t h e i r energy formation should b e n e g a t i v e t o i n c r e a s e t h e i r number when lowering t h e tempe- r a t u r e ) . I t i s c r u c i a l t o know T1 along t h e m e l t i n g curve t o determine i f d u r i n g a compression t h e so- l i d i s formed p o l a r i z e d immediately o r i f o n l y E i s cooled down and t h e n r e l a x e t o a common temperature w i t h Z .

A l a s t important f e a t u r e i n TI p r o c e s s e s even a t high t e m p e r a t u r e s (T>50 mK) is what happen a f t e r a decompression of a p o l a r i z e d s o l i d . I f t h e tempe- r a t u r e o f t h e l i q u i d t h e n produced i s t o o l a r g e

(which happens i f a complete c e l l i s melted s t a r - t i n g from high b u t n o t very high p o l a r i z a t i o n

P

2

70%) t h e n t h e remaining s o l i d heated by t h e li-

q u i d w i l l r e l a x and l o s e i t s p o l a r i z a t i o n , preven- t i n g any o b s e r v a t i o n of reduced m e l t i n g p r e s s u r e .

A s a concluion a b e t t e r knowledge o f T I i s needed a s w e l l a s a t r i a l compression i n very high f i e l d s H > 12 T t o s e e how good o r how poor t h e 2-E c o u p l i n g i s . I f t h e coupling i s t o o weak t h e n t h i s method w i l l f a i l i n producing very high pola- r i z a t i o n s . One may be tempted t o overcome t h i s s i t u a t i o n by b r u t e f o r c e c o o l i n g of 3 ~ e a t a h i g h e r p r e s s u r e than t h a t a l o n g t h e m e l t i n g curve /9/. A t

t h e same time one w i l l i n c r e a s e t h e t h e o r e t i c a l po- l a r i z a t i o n which i s l i m i t e d by t h e i n t e r a c t i o n s i n f i e l d of 7 T b u t i n t h e same time t h i s i n c r e a s e t h e decoupling between E and Z . T h i s should i n f a c t be t r i e d .

A FEW EXPERIMENTAL ASPECTS OF NMR I N SOLID.-

-

v t h e c e n t r a l frequency i s unchanged a t f i e l d

0

> 0 . 5 T /10/;P maximum p o l a r i z a t i o n o b t a i n e d a t 7T

i s l i m i t e d by o r d e r i n g a t about 70% /11/ ; Av i s

v e r y s m a l l because t h e l i n e i s L o r e n t z i a n w i t h a l a r g e 4 t h moment and a small 2nd moment (exchange

narrowing) Av i s always determined by t h e

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JOURNAL DE P H Y S I Q U E

magnet at low polarization.

At higher polarization a demagneting field produced by m itself further increases the width of the line

.

The line also starts to be very peaky, which is due to the resonance of highly polarized solid which do not have the same frequency (Fiq. 5 ) .

I

Ha=

37

46arccr

Just after a quick decompression the shape is conserved in the liquid until diffusion and convection smooth the resonance line of the liquid which we shall now treat.

LIQUID.- The magnetization is pressure dependant hV

and is given along the melting curve by th

7

2kT,

with T: = 0,177-K. At 23 k Gauss this gives

-T = T for intrinsic process which means a very 2 1

narrow line. Again it is the inhomogeneity of the magnet which determine

Av.

-T 1

a) Intrinsic relaxation is produced by modulation of the dipole-dipole interaction and fhllowing BPP -

-

where D is the self diffusion coeffi-

4142

and C1 is given by N/v nb bf atom 5 v a

per unit volumeia atomic diameter; y gyromagnetic ratio.

T 2 T 2

1 .

For p = 0 and 27 atm -is respectively -and

-

1 30 1 t 5

for temperature < 0,l K

If m is large the available phase space is not limited by T~ and T1 correspond roughly to T1 (T) for T = TF. One finds 2

-

6 mn for p = 0

-

29 atm.

b) Walls : See also /13/

Containing paramagnetic impurities which produce fluctuating field they can relaxe the liquid in near contact. The efficiency will depend on the possible coating of the wall.

Another mechanism is the fluctuation seen by 3 ~ e atom when moving /14/ in the inhomogeneous field produce by the magnet and the walls, even

diamagnetic. One has to look at the ruggeness of the wall.

If, for any reason the walls are relaxing all incoming 3 ~ e then for a spherical chamber of radius

One would expect a T~ which decreases with T.

In our plastic without silver exchanger cell, at 30 mK, 80 MHz and 30 atm

,

in a radius R ;\: 0,65 cm we have observe a T = 1200 sec.

1

In a smaller cell R % C),2 cm T was in the same ₁ conditions T1 = 420 sec.

We have then the feeling that plastic walls are not very effective to relaxe 3 ~ e which for the bigger cell correspond nearly to the intrinsic TI. One could say also that this relaxation is too small to restore the needed magnetization in Pomerantchuk compression.

C) A last way to increase the rate of relaxation is to reduce the effective length of the cell by convection which appear when temperature is no longer homogenous. For a vertical gradient AT on a

oc

AT^"

length P. convection starts if Ra = 1707 < L _?f-' for !L = 1 cm this give T~ AT = 7106 T, AT in

m~ for a critical situation

.

Convection will be difficult below 20 mK but very easy above 200 mK

where one ensafter a sudden decompression of polarized solid.

d) Warning to "dilutors"

A last point in seeing what happens in time shorter than T is to see how dilution works in

1

high field /lS/.(~nother external interesting para- meter non treated in dilution problem is the gravity ! ) . A simple answer is to notice that if

3 ~ e arrived in the mixing chamber in a non polarized state, its relaxation will produce heat. It is then advisable to put relaxing surfaces in contact with 3 ~ e before it enters the mixing chamber.

More experiments are needed !!

ACKNOWLEDGEMENTS.- We would like to acknowledge N. Sullivan for critical reading of the manuscript and J.M. Delrieu, G. Frossati, H. Godfrin,

A.Landesman and F.B.Rasmussen for passionate and helpful discussions.

*

-7 -2 Experimentally measured at 27 atm D =1,2 1 0 T at

m

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References

/1/ Noziares P . and C a s t a i n g B., Seminar a t CRTBT

,

Grenoble, A p r i l 1978; and C a s t a i n g B. e t Nozieres P., Le J o u r n a l d e Physique,

40,

257 (1979).

/2/ C h a p e l l i e r M . , L e t t e r t o P . Nozigres, May 1978

/3/ R.T. Johnson, D.N. Paulson, R.P. G i f f a r d ,

and J . C . Wheatley, J . Low Temp. Phys.

lo,

35(1973)

/4/ J . M . D e l r i e u , p r i v a t e l e t t e r t o E.D. Adams and E.A. Schuberth. T h i s l e t t e r Septembelr 1978, u n l u c k i l y unpublished ( p e r i s h i f p u b l i s h !) con- t a i n s i n t e r e s t i n g remarks on Pomerantchuk com- p r e s s i o n i n h i g h f i e l d .

/5/ C. Yu and P.W. Anderson,Phys. L e t t . 74 A,236(1979) /6/ M. Roger, J . M . D e l r i e u , t h i s conference.

/ 7 / See f o r i n s t a n c e M. Goldman, Spin t e m p e r a t u r e and n u c l e a r magnetic resonance, Clarendon P r e s s .

/8/ R.L. Garwin and A. ~ a n d e s m a n , Phys. Rev.l33,A, 1503 (1964)

.

/9/ D . Thoulouze, T h i s conference.

/ l o / E.D. Adams, E . A . Schuberth, G.E. Haas,

D.M. Bakakyar, Phys. Rev. L e t .

44,

789 (1980). /11/ H.Godirin, G. F r o s s a t i , A.S.Greenberg, B.Hebra1

and D. Thoulouze, p r e p r i n t and t h i s conference.

/ 1 2 / L.R. C o r r u c c i n i , D.D. Osheroff, D.M. Lee and R.C. Richardson, J o u r n . Low Temp. Phys.

8,

229

(1972).

/13/ H. Godfrin, G. F r o s s a t i , B. Hebral and D . Thoulouze, T h i s conference.

/14/ V. Lefevre, T h i s conference