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Submitted on 1 Jan 1978
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OBSERVATION OF THE COMPLETE DECAY OF
PERSISTENT CURRENTS IN UNSATURATED
SUPERFLUID 4He FILMS
D. Ekholm, R. Hallock
To cite this version:
JOURNAL DE PHYSIQUE
Colloque
C6, supplPment au no
8, Tome 39, aoat 1978, page
C6-306
OBSERVATION OF THE COMPLETE DECAY OF PERSISTENT CURRENTS I N UNSATURATED SUPERFLUID 4He FILMS=
D.T. Ekholm and R.B.Hallock+
Department of Physics and Astronomy, University of Massachussets, Amherst, Massachusetts,
USARCsum6.- Nous avons 6tudi6 la d6croissance
B
long terme des courants permanents dans des films non satur6s de 4 ~ e d'gpaisseur 8,1 couches atomiques, B 1,5K,
5 l'aide de techni-ques bas6es sur le temps de parcours moyen d'impulsions de troisisme son. On observe que la vitesse tend
2
s'annuler et que sa d6pendance fonctionnelle d6vie fortement de la d6pen- dance en log t, observ6e prbc6demment dans des expsriences sur des films et sur le solide dans des g6om6tries restreintes.Abstract.- We have studied the long term decay of persistent currents in unsaturated 4 ~ e superfluid films of thickness 8.1 atomic layers at 1.5
K
using pulsed third sound time of flight techniques. The velocity is observed to decay to zero and the functional dependence deviates strongly from the log t behavior observed previously in both film and bulk res- tricted geometry experiments.One of the remarkable features of super- fluid 4 ~ e is its ability to attain a state of macroscopic persistent flow. In the past, experi- mental studies of the decay of this persistent flow /1,2/ has usually been limited to cases in which the film flow velocity changed by only a
small amount during the course of a measurement. In these studies it is generally observed that the superfluid velocity decays in time according to the functional form
v (t) = a
-
,3 log t (1where t is the time v (t) dependent superfluid velocity and a and ,3 are empirical parameters which depend on the experimental conditions. The above form was also seen to be an acceptable des- cription of the film observations of Telschow and Hallock /3/ where substantial velocity changes were reported for several persistent current de- cays. We report here film persistent current de- cay measurements for which the final persistent current velocity is close to zero. For these de- cays the previously observed decay rule, eq. (I), is inadequate and a more complicated form is neces- sary. We compare our results with two theoretical predictions and comment on deviations of the theo- ry from the observations in each case.
*Supported by the National Science Foundation DMR 76-08260.
+~ddress until September 1978 : Laboratory of Ato- mic and Solid State Physics, Cornell University, Ithaca, N.Y. 14853, U.S.A.
The measurements we report here were carried out in an improved version of the basic apparatus originally described by Telschow and Hallock 1 3 1 . The persistent current velocity is determined from
the Doppler shift of third sound using time of flight techniques. An example of a complete decay of a persistent current is shown in figure 1 for the case of a superfluid 4 ~ e film of thickness, d, equal to 8.1 atomic layers at a temperature of 1.50
K.
Film thickness values are determined from measurements of the relative pressure PIPo in the usual way.Fig. 1 : Typical decay of a persistent current at d = 8.1 layers, T = 1.50
K.
Here we display(AC3/2) = <ps vs/p vs. time. The smooth curves are fitted to the data using functional forms as discussed in the text.
Here P i s t h e p r e s s u r e i n t h e experimental chamber and P i s t h e s a t u r a t e d vapor p r e s s u r e a t f h e opera- t i n g temperature. Thickness v a l u e s determined i n t h i s way a r e c o n s i s t e n t w i t h t h o s e o b t a i n e d from t h e observed v e l o c i t y of t h i r d sound / 4 / . P l o t t e d on t h e v e r t i c a l a x i s i s AC3/2 t h e d i f f e r e n c e between t h e downstream and the upstream t h i r d sound v e l o c i t y . T h i s i s r e l a t e d t o t h e v e l o c i t y vs o f t h e p e r s i s t e n t c u r r e n t by AC3/2 = <ps>vs/p where <ps>/p i s t h e reduced 151 s u p e r f l u i d f r a c t i o n i n t h e f i l m . For d a t a taken a t times g r e a t e r t h a n 60s a f t e r t h e c r e a t i o n of a p e r s i s t e n t c u r r e n t each p o i n t r e p r e s e n t s t h e average of two aC3/2 measu- rements. Each measurement r e q u i r e s % I0 s . Data f o r t 2 6 0 s h a s a somewhat l a r g e r e r r o r s i n c e o n l y one d e t e r m i n a t i o n of AC3/2 was made f o r each d a t a p o i n t .
Also shown on t h e f i g u r e a r e two computer generated f i t s t o t h e d a t a . The s o l i d l i n e r e p r e - s e n t s t h e I o r d a n s k i /6/-Langer-Fisher /7/ r e l a t i o n
where r a t h e r than expanding / I / t h e a c t i v a t i o n energy Ea, (which would r e s u l t t o f i r s t o r d e r i n eq. ( I ) , we have adopted f u l l y t h e v e l o c i t y depen- dence i n t h e model of v o r t e x l i n e p a i r s o r i e n t e d p e r p e n d i c u l a r t o t h e p l a n e of t h e f i l m . For such a case we have / I /
~ P ~ K ~
Ea =
-
2T {En(- 27rvsa1 - 1 1
I n eqs. (2) and (3) K i s t h e quantum of c i r c u l a - t i o n , Af t h e c r o s s - s e c t i o n a l a r e a of t h e f i l m i n t h e d i r e c t i o n of t h e flow, v t h e a t t e m p t frequen- c y , k t h e Boltzman c o n s t a n t and a t h e r a d i u s of t h e v o r t e x c o r e . D i r e c t i n t e g r a t i o n r e s u l t s i n a time dependent v e l o c i t y o f t h e form v = v
S 0
p
+
G(t-to) -Jn.The dashed curve i s a l e a s t s q u a r e s f i t t o t h e experimental d a t a of t h e f u n c t i o n a l form v = A Rn [ ( I
+
~ e - ' ~ ) / ( l-
which a r i s e s /8/ from t h e competing b a r r i e r model proposed by Donnelly and Roberts (DR) 191. I n t h i s model A i sr e l a t e d t o t h e momentum of t h e c r i t i c a l e x c i t a t i o n w h i l e t h e product AC i s r e l a t e d t o t h e energy of t h e c r i t i c a l e x c i t a t i o n .
Although i t i s r i s k y t o draw c o n c l u s i o n s from f u n c t i o n s w i t h so many a d j u s t a b l e parameters,
seems t o r e p r e s e n t t h e d a t a r a t h e r w e l l a t l a r g e times. A t small v a l u e s of t h e time our e r r o r s a r e l a r g e r b u t t h e
DR
f u n c t i o n seems c o n s i s t e n t l y b e t t e r t h e r e .F u r t h e r s t u d i e s of t h e temperature dependen- c e and i n p a r t i c u l a r t h e t h i c k n e s s dependence of t h e s e decays t o e x t i n c t i o n should shed v a l u a b l e l i g h t on t h e c h a r a c t e r of t h e decays and provide q u a n t i t a t i v e comparison t o t h e p r e d i c t i o n s of t h e t h e o r y . We should a l s o b e a b l e to s t u d y t h i n n e r f i l m s a t lower temperatures.
We g r a t e f u l l y acknowledge numerous produc- t i v e c o n v e r s a t i o n s w i t h J . D . Reppy and R.J. Donnel-
IY
References
/ I / Langer, J.S. and Reppy, J . D . , P r o g r e s s i n Low
T e m p . s .
/ 2 / Kojima, H . , Veith,W., GUYON,E. and Rudnick, I. i n Low Temperature Physics
-
LT 13, ed. K.D. Timmerhaus e t a l . (Plenum, New York) 1974, Vol. 1 , p. 279./ 3 / Telschow, K.L. and Hallock, R . B . , Phys. Rev. L e t t .
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(1976) 1484./ 4 / See, f o r example, A t k i n s , K.R. and Rudnick, I. i n P r o g r e s s i n Low Temperature P h y s i c s , ed. C.J. G o r t e r (North Holland, Amsterdam) 1970, Vol. 6, Ch. 2.
151 S h o l t z , J.H., McLean, E.D., and Rudnick, I.
Phys. Rev. L e t t .
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(1974) 147./ 6 / I o r d a n s k i , S.V., Zh. Eksp. Theor. F i z . 48 (1965) 708 (Sov. Phys. JETP
2
(1965) 4 m ) . / 7 / Langer, J . S . and F i s h e r , M.E., Phys. Rev. Lett.19 (1967) 560.
/8/ Donnelly, R. J . ( p r i v a t e communication)
.
191 Donnelly, R.J. and Roberts, P.H. Proc. R.Soc.(London)
