HIGH FREQUENCIES CRITICAL ATTENUATION IN LIQUID HELIUM 4

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HIGH FREQUENCIES CRITICAL ATTENUATION IN LIQUID HELIUM 4

B. Lambert, R. Perzynski, D. Salin

To cite this version:

B. Lambert, R. Perzynski, D. Salin. HIGH FREQUENCIES CRITICAL ATTENUATION IN LIQUID HELIUM 4. Journal de Physique Colloques, 1978, 39 (C6), pp.C6-148-C6-150.

�10.1051/jphyscol:1978666�. �jpa-00218346�

JOURNAL DE PHYSIQUE Colloque C6, supplPment au no 8, Tome 39, aolit 1978, page C6-148

HIGH FREQUENCIES CRITICAL ATTENUATION IN LIQUID HELIUM 4

B.Lambert, R.Perzynski and D.Salin

Laboratoire d 'Ultrasons (a), UniversitB Pierre et Marie Curie, Tour 13, 4 place Jussieu, 75230 Paris Cedex 05, France.

Rbsum6.- Nous avons mesur6 l'attgnuation critique dans l'hglium liquide de 0,55 2 1,7 GHz. pour T < T X , nous analysons nos rgsultats comme la s o m e d'une fonction d'gchelle du type fluctuation du parambtre d'ordre et d'une faible contribution qui prgsente un maximum prbs de la transition.

Abstract.- We have measured the critical attenuation of liquid helium from 0.55 to 1.7 GHz. For T < T A , the results are analysed as the sum of a fluctuation type scaling function and a small contribution which has a maximum close to the transition.

For many years theoretical treatments /I/ of the attenuation a and dispersion D of first sound near TX in liquid helium is an open question. Recent experimental results /1/ at low frequencies (- w =

27T 2.3 to 623 kHz) allow the authors to clarify the behaviour of a and D near the superfluid transition TI. However at higher frequencies, c?ly few experi- ments have been performed /2,3,4/ and have not recei-

ved a satisfactory interpretation especially in the 1 GHz vicinity.

Here we report new quantitative results on the divergence of a in the high frequencies range from 550 MHz to 1700 MHz ; then we compare our re- sults with teh existing theoretical treatments. In the experiment, we use a classical ultrasonic trans- mission method through a 6 pm thick sample ; such a small thickness is required because of the large attenuation of helium at high frequencies. From the measurements of the relative intensity and phase of the signal received by the transducer, we get the value of the attenuation a and of the velocity of first sound versus the temperature (measured with an accuracy better than 1

a).

Before we examine our own experimental re- sults, let us recall the results obtained / 1 / at low frequencies.

-For T > T X , the critical attenuation a is due to the fluctuations of the order parameter with a characte- ristic time TZ Q, -where 5 cz is the velocity of

c2

second sound and 5 is the correlation length

( E = t o r -v ; ^E = 1 1

-61;

^{v = 0.675 : 5. = 1 ); ;}

X

*~ssociated with the Centre National de la Recher- che Scientifique.

with ~ ~ = T 2 0 E - ' ~ , w=0.387 and T ~ O = 2.01x10-'~ s for helium 4. The attenuation can be scaled with an unique scaling function of UTzover 4 decades of wrz ; the function normalized at TX takes the

a wr r

simple form

-

_ax ⁼

-

c + U T 2 ^{(1) with c = 0.506.}

-

For T <TX, a second additional mechanism takes place : the relaxation of the order parameter leads to an attenuation

%

^{= 1+(&2)}wT2- ( 2 ) .

%

has a maximum for wr2=1. For T < T X , the fluctuation part of the attenuation is also represented by (1).

The experiments we have performed from 550 MHz to 1.7 GHz show :

-There is no dispersion of sound (-2 Ac independent c 1

ofw) within the accuracy of our measurements 5

lo-'.

l o -

~ C R I T (lom3) I

el690 MHz

+775 MHz

2 2.1 ' TA 22 2.3 Fig.] : Critjcal attenuation (0 = i;)versus the a temperature; a background has been substracted (see text) ; the full line corresponds to expres- sion (1) with c = 1.

-

The critical attenuation is plotted in figures 1 and 2 ( 0 = a

-

⁼

x)

a better parameter than a be-

k w

cause the effect ofwon a is always greater than wl. In figures 1 and 2 wa have substrated a smoo-

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1978666

thly temperature dependent background (= 20% of the maximum total attenuation) ; its frequency dapenden- ce has been taken quadratic : this corresponds to this hydrodynamic behaviour of a (a a w2 )we observe far away from the transition (T %1.8 K). We have to notice that our experimental results are in reaso- nable agreement with these of reference / 3 / at 1 GHz.

+ 1100 MHz 550 MHz 5 -

n

Fig. 2 : See caption of figure 1.

-

For T >Ti, as it is mentioned in reference /2/, there is a scaling function of wT, from low to high frequencies. We verify that the form of the scaling function is given by by expression (1).

-

^{For T =} Ti, the value of the attenuati~ncl~at the transition is an interesting result /1,2/. If at low frequencies (2.3 kHz to 600 kHz),aXa wl'l fits the result /I/, a fit up to I GHz /2/ need clXa w1'33 our results above 1 GHz move up this frequency de- pendence ; this effect is enhanced at 9 GHz.

-

For T <TX, the attenuation exhibits a small maxi- mum close to the transition _; this maximum moves off

the transition as w increases (from 2 mK at 550 MHz to 5 mK at 1700 MHz). Because this maximum is small, we fit our results (except for this small maximum) with a fluctuation scaling function of the type (1);

as one can see on figures the full lines fit our results except in the vicinity of the maximum : the full lines correspond to the expression (1) with c = 1 ; such an expression is in good agreement with reference /5/ ; the result at 163 MHz /2/ gi- ves a numerical constant c between the two values c = 1 and c = 0.506 at low frequencies. The resi- dual attenuation (Oexperimental

-

full lines) has a nearly constant intensity in

.

We have then to interpret this maximum of a the intensity of which

is approximatively proportional to w and which moves off the transition with increasing w : if we examine all the experimentally investigated frequen- cies ( 2.3 kHz to 9 GHz), we can follow this maxi- mum from 2.3 kHz to 1.7 GHz (at 9 GHz it would be

too tiny to be measurable because the other parts of the attenuation increase faster thanw). At low frequencies (k < 3 MHz), this maximum is obtained

2a

by the symmetrization of the fluctuations around TX (this procedure is explained in /I/ ; the remaining peak is interpreted as a relaxation one (1) and it peaks at = 1. For intermediate frequencies

(18.4 MHz and 163 MIz 2), such symmetrization is no more working because the two branches T> TI and T < T intersect. At our frequencies, the maxi-

X

mum ofamoves off the transition more slowly than the condition mT2 = 1 predicts it (at 1 GHz,TX-TMax

% 4 or 5 mX instead of % 40 mK forwT2 = l).Rthough we can follow this peak from low to high frequencies we cannot call it a relaxation peak. Some workers have tried to explain this high frequency behaviour at very high frequencies, when w ~ , >> 1, the criti- cal variation in helium is described _{/ 6 /} by a new relaxation time T I %

-

4 (c,,velocity of first sound) sounds) ; such a time fits the results at 9 GHz /4/

but are not able to fit ours. An alternative expla- nation has been proposed in a recent paper / 7 / . It predicts a maximum of attenuation for k

5

^{% 1 (or}

w T,?. 1) with a strong frequency dependence (ci aw3) of its amplitude. But we do see a linear dependence of the maximum in w and we are in the frequency range where k 5 = 1 at

I T -

^T~

I <

^{0.5 mK} ; thus such a theory does not fit our results.

tion in liquid helium 4 in the vicinity of I GHz.

The clearest point is that for T < T X our measure- mento are fitted by a fluctuation scaling function with a characteristic time T 2 %

-. 4

The evolution of a small maximum close to TX is observed but not explained.

References

/I/ A good bibliography is given in these two papers Buchal, Ch. and Pobell,F.Phys.Rev.

B.14

(1976) 1103;

Carey,R. Bucha1,Ch. and Pobel1,F. Phys.Rev.

B.16

(1977) 3133.

/2/ Tozaki, K.and Ikushima,A. Phys-Lett.

53

((1977) 458 /3/ Comrnins,D.E. and Rudnick,I., in Proc.13th 1nternat.Conf.

Low Temp.Phys.(Roulder) 1972, Vol.1, p.356.

/ 4 / Joffrin,J., Lambert,B. and Salin,D., J.Physique Lett.2

( 1976) L-255.

/5/ Ahlers,G. J.low Temp. Physics L(1969) 609.

161 Swift, J. and Kananoff,L. Annals of Physics.

50

(1968)312.

171 Liuksyutov,I.F. and Pokrowskii,V.L., JEPT Lett.2 (1977) 391.