PRESSURE DEPENDENCE OF THE SUPERFLUID DENSITY IN 3He-B

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PRESSURE DEPENDENCE OF THE SUPERFLUID

DENSITY IN 3He-B

C. Archie, T. Alvesalo, J. Bethold, J. Reppy, R. Richardson

To cite this version:

JOURNAL DE PHYSIQUE Colloque C6, supplément au n° 8, Tome 39, août 1978, page C6-37

PRESSURE DEPENDENCE OF THE SUPERFLUID DENSITY IN

He-B

G.N. A r c h i e , T.A. A l v e s a l o , J . E . B e t h o l d , J . D . Reppy and R . C . R i c h a r d s o n Department of Physios, Cornell University, Ithaaa, New York 14853, U.S.A.

Résumé.- À l'aide d'un oscillateur de torsion, nous avons étudié la densité de la composante normale du superfluide 3He jusqu'à 1 mK de 5 bar à 29 bar. La dépendence en pression de la densité normale pour la phase B peut être expliquée par la théorie du liquide de Fermi, mais la dépendance en tempé-rature n'est pas en accord avec la théorie BCS.

Abstract.- Using a torsional oscillator, the density of the normal component of superfluid 3He is stu-died down to 1 mK from 5 bar to 29 bar. The pressure dependence of the normal density for the B pha-se can be accounted for by Fermi Liquid theory, but the temperature dependence disagrees with BCS theory.

Early measurements of the superfluid density in the A, Ai, and B phases of 3He have been conducted by fourth sound/1-2/ and various viscometry methods /3-7/. Such measurements were restricted to a narrow range in the pressure-temperature phase space due to the cooling techniques involved, either adiabatic demagnetization of CMN of compressional cooling. Using nuclear demagnetization of copper we have ex-tended these measurements to 1 mK over the pressure range zero to 29 bar.

Our principal results are that the observed pressure dependence to the superfluid density in the B phase scales as the Fermi Liquid molecular field corrections but the temperature dependence signifi-cantly disagrees with BCS theory.

The experimental cell was a torsional oscilla-tor similar to one used by Berthold et al./4/. The 3He was confined to a thin cylindrical slab with a thickness of 95y and a radius of 0.42 cm. The 3He slab, encased in epoxy, was suspended by a BeCu tube which acted as fill line and torsion rod. The oscillator was driven and detected electrostatical-ly. The amplitude of oscillation was kept constant by electronically controlling the drive power. Mea-surement of this drive level provides a precise mea-sure of the overall dissipation which was predomina-tely due to the 3He viscosity response.

Details of the analysis are given elsewhere/8/ but conceptually the behaviour of the He is simple. Using the two fluid model to characterize the hydro-dynamic response of the superfluid, the superfluid component fails to interact with the oscillating

Present address : Low Temperature Laboratory, Hel-sinki University of Technology, Otaniemi, Finland

walls so the 3He response is completely determined by the viscosity and the density of the normal

frac-tion, n and p /p., respectively. The thickness of the slab is smaller than the viscous penetration length,6 = /2n/p U) where OJ is the resonant frequen-cy of the device. The normal fraction is entrained and contributes to the total moment of inertial and hence affects the resonant frequency.

Shown in figure 1 are normal fraction versus reduced temeprature for several pressures : 29, 20,

10, and 5 bar. A clear pressure dependence is

pre-1 pre-1 pre-1 pre-1 ° 29 bar a 20 bar • 10 bar 1 0

" * 5 bar

^

a /

0 8 ° '

-o V

:'*

Fig. 1 : Normal f r a c t i o n , p /pjversus temperature,

T/T .

c

sent such that p /p decreases more quickly at lower

n

pressures.

We can attempt to account for the Fermi Liquid

molecular field effects by using an analysing first

suggested by Leggett/9/. Separating the interaction

between the 3 ~ e

quasiparticles into a part responsi-

ble for the superfluid pairing phenomenon and that

which remains, the latter can be characterized by

~andau's

Fermi Liquid theory (FLT). The former in-

teraction alone would produce a stripped normal

component density polp which is easily corrected

n

for FLT Leggett's agalysis yielded

(1 +

FI/~)P,/P

P,/P

I

113 FIP;/P

where F1 is the Fermi Liquid parameter related to

the effective mass of quasiparticle.

From an experimental point of view, we can

invert the equation and remove the FLT effect from

our data. Shown in figure 2 are p

p

:

/

for the same

pressures as in figure 1. Within the accuracy of our

Fig. 2

Stripped normal fraction, pO/p, versus

reduced temperature, TITc. Symbol idegtification

is the .same as figure

The solid line is the BCS

prediction.

prisingly little pressure dependence in the stripped

normal fraction of 3 ~ e - ~ .

This work has been supported by the National

Science Foundation through Grant No. DMR 75-15933

and DMR 75-08624 and by the National Science Founda-

tion through the Cornell Materials Science Center

Grant No. DMR 76-81083.

References

/I/

Yanof,A.W. and Reppy,J.D., Phys. Rev. Lett.

33

(1974) 631

/2/ Kojima,H., Paulson,D.N. and Wheatley,J.C., Phys.

Rev. Lett.

(1974) 141

/3/ Alvesalo,T.A., Collan,H.K., Loponen,M.T., Lou-

nasmaa,O.V. and Veuro,M.C., J. Low Temp. Phys.

19 (1975) 1

-

/4/ Berthold,J.E., Giannetta,R.W., Smith,E.N. and

Reppy,J.D., Phys. Rev. Lett.

37

(1976) 1138

151 Main,P.C., Kiewiett,C.W., Band,W.T., Hook,J.R.,

Sandiford,D.J.J. and Hall,H.E., J. Phys. C

9

(1976) 39

161 Guernsey,R.W., Mccoy,R.J., Steinback,M. and Ly-

den,J.K., Phys. Lett.

58A

(1976) 26

/7/ Parpia,J.M., Sandiford,D.J., Berthold,J.E. and

Reppy,J.D., Phys. Rev. Lett.

40

(1978) 565

181

Reppy,J.D., Proc. ULT Hakone Symposium (1977) 89

191 Leggett,A.J., Phys. Rev.

A140

(1965) 1869

/lo/ F values from Wheatley,J.C., Rev. Mod. Phys.

4 3

(1975) 415.

-