ORDER PARAMETER RELAXATION NEAR Tλ: AN HIGH FREQUENCY EXPERIMENTAL TEXT IN LIQUID HELIUM

(1)

HAL Id: jpa-00218348

https://hal.archives-ouvertes.fr/jpa-00218348

Submitted on 1 Jan 1978

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

ORDER PARAMETER RELAXATION NEAR Tλ: AN HIGH FREQUENCY EXPERIMENTAL TEXT IN

LIQUID HELIUM

F. Vidal, J. Tarvin, T. Greytak

To cite this version:

F. Vidal, J. Tarvin, T. Greytak. ORDER PARAMETER RELAXATION NEAR Tλ: AN HIGH

FREQUENCY EXPERIMENTAL TEXT IN LIQUID HELIUM. Journal de Physique Colloques, 1978,

39 (C6), pp.C6-153-C6-155. �10.1051/jphyscol:1978668�. �jpa-00218348�

(2)

JOURNAL DE PHYSIQUE Colloque C6, supplkment au

no

8, Tome 39, aozit 1978, page

C6-153

ORDER PARAMETER R E L A X A T I O N NEAR TI : AN H I G H FREQUENCY EXPERIMENTAL T E X T I N L I Q U I D H E L I U M

%

**

F. Vidal , J.A. Tarvin and T.J. ~ r e ~ t a k t

*

EsGrarpe de Physique A s Solides de lrE.N.S., 24, rue Lhomond, 75005 Paris, France Brookhaven National k b o r a t o q j , Upton, N.Y. 11973, U.S.A.

t

Department o f Physics and Centre for Materials Science and Engineering, M.I.T., Cambridge Massachussetts, 02139, U.S.A.

R6sum6.- Nous avons mesur6 l'att6nuation et la vitesse du premier son de haute fr6quence

(QJ 1

GHz) prPs de TA dans 1"He liquide sous pression. Nos r6sultats sont en d6saccord avec les analyses ph6- nom6nologiques valables aux basses frgquences, bas6s sur la relaxation du paramstre d'ordre.

Abstract.- We have measured the attenuation and the dispersion of high-frequency first sound

(%1 GHz)

near TI in liquid 'He under pressure. Our results disagree with the phenomenological treatments currently used to explain the low frequency data and based on the order parameter relaxation.

We present here some results, concerning the first sound of our measurements of the dynamic structure factor near the lambda temperature in li- quid helium. These measurements, performed with a Brillouin light scattering technique, combine for the first time the advantages of high-resolution Brillouin spectroscopy with a microdegree tempera- ture resolution /I/. Results on the first sound we- re obtained at four pressures

:

SVP and P

= 1.9,

23.1 and 28.5 bars

;

the corresponding sound fre- quencies at TA (P) were, respectively, of the order of

0.50, 0.66, 0.96

and

1

GHz. Values of qS, where q is the wave vector of the sound and 5 is the cor- relation length of the order parameter, fall bet- ween 2.4 x and

10

below TA and between 4.5 and

2

x above TA. This range involves all the dif- ferent dynamic regions associated with the first sound. This point is illustrated, for T

<

TA, in figure

1,

where the dynamic regions are obtained following the approximation of two mode intermedia-

te

states /2/.

The main purpose of this note is to use these experimental results to probe at high frequency one of the dissipation mechanisms currently proposed to explain the anomalous behaviour of the sound near a second order phase transition /2/

:

the linear cou- pling between the sound wave and the time average order parameter

J, = <$>.

This critical process,

0

first proposed by Landau and Khalatnikov to explain the experimental results of Chase, will be due to the relaxation of

J,

and can be represented by a

0

term of the form

J,;

<J,(t)

~ J I ( o ) > ,

where the expres-

Fig.

1 :

Sketch of the different dynamic domains below TI associated with the first sound. The top and bottom striped areas correspond to our data on, respectively, the first and the second sound.

sion between brackets denotes the time correlation function of the order parameter. Such an effect, as well as other ~ossible processes related to the non zero values of J,o, are now also predicted on the grounds of the mode coupling approaches

/ 2 / .

Howe- ver, no detailed theoretical analysis of these va- rious effects has been done as yet. We are just going to present here, therefore, a comparison between our experimental results and the phenomeno- logical approach based on the Landau-Khalatnikov mechanism. In this approximation, this critical

effect is like a classical internal relaxation pro-

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1978668 Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1978668

(3)

c e s s i n which $o p l a y s t h e r o l e o f a c r i t i c a l r e l a - f i g u r e 2 ( a ) . Two main p o i n t s must be emphasised : x i n g degree of freedom. Following t h e well-known

thermodynamical f o r m u l a t i o n f o such a p r o c e s s , t h e e x p r e s s i o n of t h e a s s o c i a t e d a t t e n u a t i o n and d i s - p e r s i o n can be e a s i l y c a l c u l a t e d a s a f u n c t i o n of some c h a r a c t e r i s t i c r e l a x a t i o n time T of t h e o r d e r parameter / 3 / . Although T i s n o t w e l l d e f i n e d , there i s some s c a l i n g a s w e l l a s e m p i r i c a l arguments which l e a d t o propose ^T= T~ E E / u 2 , where u p i s the

second sound v e l o c i t y / 3 / . T h i s p i c t u r e h a s been ^-300 ¹ I I I 1 I I I confirmed by t h e low frequency measurements i n li-

C

quid helium / 4 , 5 / ( i n which q c << I ) , although some

+

^q⁰

-

⁸

8 o o A

⁴⁰

^... ^....

d i f f i c u l t i e s s t i l l remain

151.

I n c o n s t r a s t , t h e

... _...

I ---uw..,."-

v e r y few d a t a of t h e a t t e n u a t i o n a t high frequency '0

- e C

*-d&(~

('L 1 GHz) a v a i l a b l e u n t i l now appear t o be incom- _-100⁰ _-10 _-1

-

^a1 ^-a01

p a t i b l e w i t h such a p i c t u r e /6,7/, although some f -TA (P) (mK)

measurements a t s t i l l h i g h e r frequency ^(% 10 GHz) seem t o i n d i c a t e t h a t t h e above formalism may be s t i l l a p p l i e d i f a r e l a x a t i o n time of t h e form

T = T,

Elu,

(where ul is t h e f i r s t sound v e l o c i t y ) Fig. : An of Our data a t Ph = 23.1 bar.

The s o l i d c u r v e s a r e o u r experimental r e s u l t s . The i s used i n s t e a d of T, /8/. Note, however, t h a t t h e d o t t e d and dashed c u r v e s a r e t h e s h e o r e t i c a l e s t i - regime of v a l i d i t y of t h e phenomenological approach mations' obtained using ' 0 A

w i l l be l i m i t e d t o t h e hydrodynamic r e g i o n

1 3 1 ,

f i r s t l y , t h e above i n d i c a t e d treatment o r i g i n a t e s a i . e . f o r t h e domain where q

5

<< 1 , o r e q u i v a l e n t l y ,

n e g a t i v e p a r t of aR. The same d i f f i c u l t y appears where U T ~ << 1 . I n a d d i t i o n , any i n f o r m a t i o n i n li-

when t h e background a t t e n u a t i o n i s supposed t o be quid helium has n o t e x i s t e d u n t i l now concerning the

symmetric around TX, and a l s o a t a l l t h e p r e s s u r e s v e l o c i t y d i s p e r s i o n i n t h e r e g i o n around q E = 1 .

s t u d i e d . Such a n e g a t i v e aR, t h a t has indeed no phy- I n comparing t h e experimental r e s u l t s with

t h e t h e o r y , the main d i f f i c u l t y i s t h e e s t i m a t i o n of t h e n o n c r i t i c a l o r background c o n t r i b u t i o n t o e a c h t r a n s p o r t c o e f f i c i e n t . I n a d d i t i o n , one must sepa- r a t e r h e r e l a x a t i o n c o n t r i b u t i o n form the o t h e r c r i t i c a l p r o c e s s a c t i n g on t h e sound and a r i s i n g from n o n l i n e a r c o u p l i n g between t h e sound and t h e expontaneous thermal f l u c t u a t i o n s of t h e o r d e r parameter. We have e s t i m a t e d t h e background c o n t r i b u - t i o n t o t h e a t t e n u a t i o n using the3hydrodynamic equa- tions and t h e d a t a a v a i l a b l e i n t h e l i t e r a t u r e of the k i n e t i c c o e f f i c i e n t s . The c r i t i c a l sound d i s p e r s i o n was o b t a i n e d by comparing our r e s u l t s w i t h t h e low frequency d a t a 1.51. To s e p a r a t e t h e two c r i t i c a l c o n t r i b u t i o n s , we u s e t h e assumption, f i r s t proposed by Rudnick and coworkers / 4 , 6 / , t h a t t h e f l u c t u a t i o n p r o c e s i i s symmetric around TI, whereas t h e r e l a x a - t i o n p r o c e s s a p p e a r s o n l y below TX. This h y p o t h e s i s

s i c a l s i g n i f i c a n c e , a p p e a r s a l s o i n p r e v i o u s high frequency measurements a t SVP / 6 , 7 / . Secondly, i t i s e v i d e n t from t h i s f i g u r e t h a t t h e t h e o r e t i c a l o _R

'

c a l c u l a t e d u s i n g T~ o r ^t2,d i s a g r e e s w i t h t h e measured a t t e n u a t i o n . A s c a n be seen i n f i g u r e 2 ( b ) , t h i s disagreement i s confirmed by t h e v e l o c i t y d i s - p e r s i o n d a t a , a l t h o u g h some ambiguity a r i s e s from t h e comparison w i t h t h e c a l c u l a t e d DR u s i n g T ~ .

The main c o n c l u s i o n i s , t h e r e f o r e , t h a t t h e same phenomelogical t r e a t m e n t of t h e c r i t i c a l beha- v i o u r of t h e sound n e a r TX (P) i n l i q u i d helium a s t h a t a t t h e lower f r e q u e n c i e s does n o t seem a p p l i - c a b l e a t h i g h e r f r e q u e n c i e s , More meaningful compa- r i s o n w i l l n o t b e p o s s i b l e u n t i l t h e microscopic t h e o r y i s extended t o t h e h i g h frequency r e g i o n , where q

5

1 .

was confirmed by t h e mode coupling approach 121.

An example of o u r r e s u l t s on t h e a t t e n u a t i o n cxR due t o t h e r e l a x a t i o n mechanism i s shown i n

(4)

R e f e r e n c e s

/ I / T a r v i n , J . A . , V i d a l , F. and G r e y t a k , T . J . , Phys.

Rev. B

2

(1977) 4193

/ 2 / Kawasaki, K . , i n Phase T r a n s i t i o n s and C r i t i c a l Phenomena (Academic, N . Y . ) 1976, Vol. 5 a , p. 165 / 3 / Hohenberg, P . C . , i n C r i t i c a l Phenomena (Academic,

N.Y.) 1971, p. 285

141 W i l l i a m s , R.D. and Rudnick, I . , Phys. Rev. L e t t . 25 (1970) 276

-

/ 5 / Carey, R., Buchal, Ch. and P o b e l l , F . , Phys. Rev.

B

16

(1977) 3133

/ 6 / Cummins, D.E., and Rudnick I . , LT 13 ( B o u l d e r ) 1972 Vol. 1 , p . 356

/ 7 / Ikushima, A. and Tozaki, K . , LT 14 ( H e l s i n k i ) 1975, Vol. 1 , p. 231

181 J o f f r i n , J., Lambert, B . and S a l i n , D., J . Physique L e t t . ( P a r i s )

37

(1976) 255