We have investigated persistent flow of superfluid 3He with an ac gyroscope filled with 20-μm powder. In 3He-B, currents circulate undiminished for 48 h at least; this implies a viscosity 12 orders of magnitude lower than in the normal fluid. In 3He-A, the current does not persist. The observed critical velocity in 3He-B at P12 bars there are two regimes in the B phase: For example, at 29.3 bars the ultimate critical velocities are 5.4 and 7.8 mm/s, respectively.Peer reviewe

Lounasmaa, O. V.

Nummila, K. K.

Packard, R. E.

Pekola, Jukka P.

Simola, J. T.

Physical Review Letters

Aaltodoc Publication Archive

This is an electronic reprint of the original article.This reprint may differ from the original in pagination and typographic detail.Author(s): Pekola, Jukka & Simola, J. T. & Nummila, K. K. & Lounasmaa, O. V.& Packard, R. E.Title: Persistent-Current Experiments on Superfluid 3He-B and 3He-AYear: 1984Version: Final published versionPlease cite the original version:Pekola, Jukka & Simola, J. T. & Nummila, K. K. & Lounasmaa, O. V. & Packard, R. E.1984. Persistent-Current Experiments on Superfluid 3He-B and 3He-A. Physical ReviewLetters. Volume 53, Issue 1. P. 70-73. ISSN 0031-9007 (printed). DOI:10.1103/physrevlett.53.70.Rights: © 1984 American Physical Society (APS). http://www.aps.org/All material supplied via Aaltodoc is protected by copyright and other intellectual property rights, andduplication or sale of all or part of any of the repository collections is not permitted, except that material maybe duplicated by you for your research use or educational purposes in electronic or print form. You mustobtain permission for any other use. Electronic or print copies may not be offered, whether for sale orotherwise to anyone who is not an authorised user.Powered by TCPDF (www.tcpdf.org)VOLUME 53, NUMBER 1 2 JULY 1984Persistent-Current Experiments on Superfluid 3He-B and 3He-AJ. P. Pekola, J. T. Simola, K. K. Nummila, and O. V. LounasmaaLow Temperature Laboratory, Helsinki University of TechnologyS, F-02750 Espoo 15, FinlandandR. E. PackardDepartment ofPhysics, University of California, berkeley, California 94720(Received 20 April 1984)We have investigated persistent flow of superfluid 'He with an ac gyroscope filled with 20-p, m powder, In He-8, currents circulate undiminished for 48 h at least; this implies aviscosity 12 orders of magnitude lower than in the normal fluid. In 'He-A, the current doesnot persist. The observed critical velocity in He-8 at P ~ 12 bars is independent of tempera-ture. At P ) 12 bars there are two regimes in the 8 phase: For example, at 29.3 bars the ul-timate critical velocities are 5.4 and 7.8 mm/s, respectively.PACS numbers: 67.5Q.Fi%e present in this Letter results of persistent-current experiments in He-8 and He-3; we haveobtained extensive data at eight different pressures.A comparison with the recent results of Gammel,Hall, and Reppy, ' at P=29 bars, reveals severalqualitative differences. For example, we see a re-versible response of the superfluid to subcriticalspeeds of rotation and have observed two regions inthe 8 phase with clearly different critical velocities;we have also extended persistent-current measure-ments from 1 to 48 h. By use of finer powder inthe experimental cell, critical velocities becamelarger and the scatter of the data was thus consider-ably reduced over the results of Ref. 1 ~Our experiments were carried out in a rotatingnuclear refrigerator. The basic measuring device,an ac gyroscope, is illustrated in Fig. 1. A metaltorus, packed with 20-p, m plastic powder, pfrms apath for the circulating superfluid. This ring(R = 22 mm, r = 3 mm) is supported by two sets ofmutually perpendicular hollow copper torsion tubes,also used as the filling capillaries for the He sam-ple. Torsional modes about the tubes are deter-mined by angles 8 and ItI. The device is ac-drivenabout 8 by a superconducting solenoid inside aniobium shield; capacitive detectors are used formonitoring the ItI motion.%hen the ring is driven about 0 at the resonantfrequenCy tog2Tr Of the It mOde, the reSpOnSe dueto the angular momentum L = z L of the circulatingsuperfluid is ItIO= Q&L8ofI&to& , here 8o is the am-.plitude of the drive motion and I@ and 0~ arerespectively the moment of inertia of the torus andthe quality factor of the resonance about the ItI axis.In our apparatus, 0&= 20000, I& —30 g cm2, and0I~/2n = 69.8 Hz; typically 8II —10 s rad givingTORSION MEMBERS— ~CAPACITIVE DETECTORTORUS FILLED WITHHe AND PLASTICPOWDER (-20 pm)4-AXISNb-SHIELDp//~SUPERCONDUCTINGSOLENOID'r////////Nb-PLATEAg SINTER1 CMVX////////////////////////////////////////////APt NMR —THERMOMETERFILLING CAPILLARYFIG. 1. The ac gyroscope. The foot is thermally con-nected to the nuclear refrigerator. For further explana-tions, see text.Ito=10 rad. In our mode of operation, withtoe )) co&, /II is insensitive to changes in theresonant frequencies. The response Qo is detectedcapacitively and the preamplifier output is fed backto a self-resonating drive circuit. This techniqueensures a constant-amplitude drive, strictly at theresonant frequency of the ItI mode. The minimumobservable change in L is 0.01 g cm2/s ( —102it )using 12-s integration time. Noise in the system ismostly of mechanical origin.The L sensitivity of the device can be calibratedby means of the Coriolis effect: This force pro-duces an additional torque about the It axis while1984 The American Physical SocietyVOLUME 53, NUMBER 1 PHYSICAL REVIEW LETTERS 2 JULY 1984the ring is b 'eing rotated. Th0, whereis the cryostat'se n is the calib' ration constant t flos angular velociw, with the crIn t i p aseshe superfluid hasesm met r The fr qyal to the superfl '"isakr uid fractionperature andpe T serve as calibrationfill d ihf'there is a spatially rand bth hp es. An indP=293 b b th f t thby reversible dea so1In our ex erimomentum L = MR (p ments we observe the anh'" Mgis the mass of He inis the average velocity of thethe"luin the rin asn a'g io o 0wh''n =maxin1umtainih h s was rotated. Tci yp g p e cryfLth tdbencd' ' n going Lt }. The difference,ur basic datum Precise0—~m 4—U A~ j' 2Ac, /0.2 0.4I I0 ~0 '1.0 1.20.6 0.8Ap (r ad/s}1.4FIG. 2.~ Persistent an ulagvelocity 0 of tvs thefh i }1o hst eidea ions, see text.sis oop. Forsignal istameasurements of Leing rotated because thun1 is —100se e CoriolisOt 1 thects.avr an the superfl 'dr uid ef-a te hher- angular mome made extensive measuremenP=3y : (I) fooM tMt th b h"'" w"h 0 =0Cnd Libra-}1'turn.m persistent angular mdent Ouru ar omen-dresults can be iat idealizednterpreted inh t i loo, hodb do ths a e premise that the re„—,=RI never exceeds thee iso a the ine owe at 0=—(u=—cu„becaused o 1hh fldid. flow ir ui component ex ' 'n- powderd d b h Ke elvin draia'1 d h e~—co differs from 0b-„and the true v =—R ' esextent from t, cuc deViateShe measured RA .ofoop have unit slo pe and corres ra ionThe sides of thflo b,---- Thee ysteresis a 'x creationtices become pinned to the owrises because th e vor-oopmeae. Our result 'is in markedby Rudnick et 14Q.their d ( Fi. 3 fRamrne}, Halli t eabsent.o ef. I) the clast's ic regime isIn Fig. 3, u, = L,/[MR ( ep$p Mo the reduced ternP=. . bars. The datamperature T/ Tc atman' ' ot oseinFi .'e inag,. The dataangu-are included fo p~ ~at v, is indeurthi bo t 10/o. In previous woper atureff' 'su icient tod- 0-' dA heck for possibled ' 3H 8 P=1in the riu ar momentum wasTh t hmeasured. Afteras t en brou ght to rest and LP C'~ er the cryostat had bewasen kept in theVOLUME 53, NUMBER 1 PHYSICAL REVIE% LETTERS 2 JULY 198406 —00 0 0 000 ~ 00 0 0 0~~ 0 0T„/T~ = 0.50/op000000O0004I0.5I0.6I0.7I0.8 0.9A B og ~+TRAN-SITION +P'T/ TL.FIG. 3. Critical velocity u, at P = 15.0 bars (open cir-cles) and 12.0 bars (filled circles) as a function of the re-duced temperature T/ T, . Lozenges are the data of Gam-mel, Hall, and Reppy (Ref. 1) at P = 29 bars, multipliedby 5, the ratio of the pore sizes [(100 p, m)/(20 p, m)];this reduction factor is only approximate because of dif-ferent types of geometries involved.B phase continuously for 48 h, L was again mea-sured. This value was then compared with that ob-tained after the cryostat was again rotated at thesame velocity as before and then stopped. Withinour experimental accuracy of 10% there was no de-cay in the signal. This gives for v, the relaxationtime of the superflow, a value in excess of 450 hand implies in the 8 phase an effective viscosity,q,rr= pd /r, which is at least 12 orders of magni-tude smaller than for the normal liquid at the sametemperature. Here d = 20 p, m is the average sizeof the interstitial pores.Measurements of L made after thermal cycling inthe region below T= 0.98 T, showed that the angu-lar momentum is a reversible function of tempera-ture. In addition to the fact that v, is independentof temperature, this demonstrates that, because ofmacroscopic quantization, circulation is conservedin 3He-8 as in He II.~ The temperature reversibilitywas used to study the stability of persistent currentsin the immediate vicinity of T, . These experimentsshowed that above T=0.98T, the critical velocitydecreases markedly; at T=0.989T„ for example,u, is (50 + 5)% of its Iow-temperature value.Figure 4 shows a plot of L, vs p, /p at 29.3 and12.0 bars. The slope of the linear regime betweenT„=0.56T, and Tzz in the 29.3-bar data corre-sponds to v, =7.8 mm/s. The critical velocity isdifferent below T„; at low temperatures v, 5.4mmls. This value is close to that measured atP ~ 12 bars. The change in v, at T„was not seenby Gammel, Hall, and Reppy' because an experi-mental artifact prevented accurate observationsnear T=0.57T, .72I0.2I I0.4 0.6ps pI0.8FIG. 4. Saturated angular momentum I., as a functionof p, /p at P= 29.3 bars (open circles) and P = 12.0 bars(filled circles, crosses, two different experiments). Thestraight line corresponds to v, = 7.8 and 5.6 mm/s for the29.3- and 12.0-bar data, respectively (to compare the twocritical velocities one should divide the slopes by the den-sity of 'He at each pressure). The nonzero L, in 2 phaseis an experimental artifact that was removed in later runs(see Fig. 5).Experiments are in progress to test the possiblerelation of the change in ~, at T=0.56T, with thevortex-core transition observed in NMR experi-ments at T=0.6T, .6Data in Fig. 5 illustrate that currents in He-A donot persist, at least under zero magnetic field. Thisconclusion is supported by an experiment in whichthe maximum L = L, was first created and mea-sured in He-B, whereafter the torus was thermallycycled to the 3 phase and then back to the 8 liquidagain: The signal had completely disappeared dur-ing this sequence. The upper limit for the super-flow decay in He-3 is less than 1 min, which wasthe transient time for the signal to recover from theCoriolis shift after the cryostat had been stopped.Because of the anisotropic nature of He-A, the su-percurrent might persist in some geometry differentfrom our packed powder.Critical velocities of the order of a few millime-ters per second seem to be associated with vorticityin confined geometries from 10 to 100 p, m. For theemission of a vortex ring with diameter do,u, —(t/m3de) ln(da/(a), where m3 is the bare massof the 3He atom and (e= 20 nm is the coherencelength. If the vortex rings have a diameter equalto the pore size, the calculated critical velocity is 7VOLUME 53, NUMBER 1 PHYSICAL REVIE% LETTERS 2 JULY 19840.50.1It-T/Tc0.2yoro0~o oe~r'O0~ yA~9T RANSIT ION0.3I ppressure dependence is due to (o in the logarithmicfactor.The authors wish to express their gratitude toProfessor J. D. Reppy's group at Cornell for usefuldiscussions. We thank Matti Krusius and PerttiHakonen for experimental advice, and Sandy Fetterand David Judd for theoretical help. Two of us(O.V.L. and R.E.P.) thank, respectively, membersof the Berkeley Physics and Chemistry Depart-ments and of the Otaniemi Low TemperatureLaboratory for their hospitality during the evolutionof this experiment. Our work was supported by theAcademy of Finland, by the Wihuri Foundation,and by the U. S. National Science Foundation underGrant No. DMR-81-19542.0 +—+ q~ PS/PI0.2 0.3mm/s in our experimental setup, quite close to theobserved values 4.7—7.8 mm/s. Additional confir-mation of this model is provided by the tempera-ture independence of the measured v, . The weakFIG. 5. L, vs p,/p around the 8 A transition atP = 29.3 bars. Different symbols correspond to differentpreparation angular velocities: open circles, O,~= 1.16rad/s; filled circles, 0.86 rad/s; plusses, 0.57 rad/s. Notethat the reduced temperature scale at the top is non-linear.~P. L. Gammel, H. E. Hall, and J. D. Reppy, Phys.Rev. Lett. 52, 121 (1984).2P. J. Hakonen, O. T. Ikkala, S. T. Islander, T. K.Markkula, P. M. Roubeau, K. M. Saloheimo, D. I. Gari-bashvili, and J. S. Tsakadze, Cryogenics 23, 243 (1983).3C. N. Archie, T. A. Alvesalo, J. D. Reppy, and R. C.Richardson, Phys. Rev. Lett. 43, 139 (1979).I. Rudnick, H. Kojima, %. Veith, and R. S. Kagiwada,Phys. Rev. Lett. 23, 1220 (1969).sJ. D. Reppy, Phys. Rev. Lett. 14, 733 (1965).6P. J. Hakonen, M. Krusius, M. M. Salomaa, J. T.Simola, Yu. M. Bunkov, V. P. Mineev, and G. E. Volo-vik, Phys. Rev. Lett. 51, 1362 (1983).7See for example A. L. Fetter, in The Physics of Liquidand Solid Helium, Part I, edited by K. H, Bennemann andJ. B. Ketterson (Wiley, New York, 1976), p. 207.73

Persistent-Current Experiments on Superfluid 3He-B and 3He-A

Pekola, J. P.

Persistent-current experiments on superfluid 3He-B and 3He-A

Aaltodoc

This is an electronic reprint of the original article.
This reprint may differ from the original in pagination and typographic detail.
Author(s): Pekola, Jukka & Simola, J. T. & Nummila, K. K. & Lounasmaa, O. V.
& Packard, R. E.
Title: Persistent-Current Experiments on Superfluid 3He-B and 3He-A
Year: 1984
Version: Final published version
Please cite the original version:
Pekola, Jukka & Simola, J. T. & Nummila, K. K. & Lounasmaa, O. V. & Packard, R. E.
1984. Persistent-Current Experiments on Superfluid 3He-B and 3He-A. Physical Review
Letters. Volume 53, Issue 1. P. 70-73. ISSN 0031-9007 (printed). DOI:
10.1103/physrevlett.53.70.
Rights: © 1984 American Physical Society (APS). http://www.aps.org/
All material supplied via Aaltodoc is protected by copyright and other intellectual property rights, and
duplication or sale of all or part of any of the repository collections is not permitted, except that material may
be duplicated by you for your research use or educational purposes in electronic or print form. You must
obtain permission for any other use. Electronic or print copies may not be offered, whether for sale or
otherwise to anyone who is not an authorised user.
Powered by TCPDF (www.tcpdf.org)
VOLUME 53, NUMBER 1 2 JULY 1984
Persistent-Current Experiments on Superfluid 3He-B and 3He-A
J. P. Pekola, J. T. Simola, K. K. Nummila, and O. V. Lounasmaa
Low Temperature Laboratory, Helsinki University of TechnologyS, F-02750 Espoo 15, Finland
and
R. E. Packard
Department ofPhysics, University of California, berkeley, California 94720
(Received 20 April 1984)
We have investigated persistent flow of superfluid 'He with an ac gyroscope filled with 20-
p, m powder, In He-8, currents circulate undiminished for 48 h at least; this implies a
viscosity 12 orders of magnitude lower than in the normal fluid. In 'He-A, the current does
not persist. The observed critical velocity in He-8 at P ~ 12 bars is independent of tempera-
ture. At P ) 12 bars there are two regimes in the 8 phase: For example, at 29.3 bars the ul-
timate critical velocities are 5.4 and 7.8 mm/s, respectively.
PACS numbers: 67.5Q.Fi
%e present in this Letter results of persistent-
current experiments in He-8 and He-3; we have
obtained extensive data at eight different pressures.
A comparison with the recent results of Gammel,
Hall, and Reppy, ' at P=29 bars, reveals several
qualitative differences. For example, we see a re-
versible response of the superfluid to subcritical
speeds of rotation and have observed two regions in
the 8 phase with clearly different critical velocities;
we have also extended persistent-current measure-
ments from 1 to 48 h. By use of finer powder in
the experimental cell, critical velocities became
larger and the scatter of the data was thus consider-
ably reduced over the results of Ref. 1 ~
Our experiments were carried out in a rotating
nuclear refrigerator. The basic measuring device,
an ac gyroscope, is illustrated in Fig. 1. A metal
torus, packed with 20-p, m plastic powder, pfrms a
path for the circulating superfluid. This ring
(R = 22 mm, r = 3 mm) is supported by two sets of
mutually perpendicular hollow copper torsion tubes,
also used as the filling capillaries for the He sam-
ple. Torsional modes about the tubes are deter-
mined by angles 8 and ItI. The device is ac-driven
about 8 by a superconducting solenoid inside a
niobium shield; capacitive detectors are used for
monitoring the ItI motion.
%hen the ring is driven about 0 at the resonant
frequenCy tog2Tr Of the It mOde, the reSpOnSe due
to the angular momentum L = z L of the circulating
superfluid is ItIO= Q&L8ofI&to& , here 8o is the am-.
plitude of the drive motion and I@ and 0~ are
respectively the moment of inertia of the torus and
the quality factor of the resonance about the ItI axis.
In our apparatus, 0&= 20000, I& —30 g cm2, and
0I~/2n = 69.8 Hz; typically 8II —10 s rad giving
TORSION MEMBERS
— ~CAPACITIVE DETECTOR
TORUS FILLED WITH
He AND PLASTIC
POWDER (-20 pm)
4-AXIS
Nb-SHIELD
p//
~SUPERCONDUCTING
SOLENOID
'r////////
Nb-PLATE
Ag SINTER
1 CM
VX////////////////////////////////////////////A
Pt NMR —THERMOMETER
FILLING CAPILLARY
FIG. 1. The ac gyroscope. The foot is thermally con-
nected to the nuclear refrigerator. For further explana-
tions, see text.
Ito=10 rad. In our mode of operation, with
toe )) co&, /II is insensitive to changes in the
resonant frequencies. The response Qo is detected
capacitively and the preamplifier output is fed back
to a self-resonating drive circuit. This technique
ensures a constant-amplitude drive, strictly at the
resonant frequency of the ItI mode. The minimum
observable change in L is 0.01 g cm2/s ( —102it )
using 12-s integration time. Noise in the system is
mostly of mechanical origin.
The L sensitivity of the device can be calibrated
by means of the Coriolis effect: This force pro-
duces an additional torque about the It axis while
1984 The American Physical Society
VOLUME 53, NUMBER 1 PHYSICAL REVIEW LETTERS 2 JULY 1984
the ring is b 'eing rotated. Th
0, where
is the cryostat's
e n is the calib' ration constan
t t flo
s angular veloci
w, with the cr
In t i p aseshe superfluid hases
m met r The fr qy
al to the superfl '"
isak
r uid fraction
perature and
p
e T serve as calibration
fill d ihf'
there is a spatially ran
d bth hp es. An ind
P=293 b b th f t th
by reversible d
ea so
1
In our ex eri
momentum L = MR (
p ments we observe the an
h'" M
g
is the mass of He in
is the average velocity of the
the
"lu
in the rin as
n a
'g io o 0
wh'
'
n =maxin1um
tain
ih h s was rotated. T
ci y
p g p e cry
fL
th tdb
enc
d' ' n going Lt }. The difference,
ur basic datum Precise
0—
~
m 4—
U A~ j' 2Ac
, /
0.2 0.4
I I0 ~
0 '1.0 1.20.6 0.8
Ap (r ad/s}
1.4
FIG. 2.~ Persistent an ulag
velocity 0 of t
vs the
f
h i }1o hst eide
a ions, see text.
sis oop. For
signal is
ta
measurements of L
eing rotated because th
un1 is —100
se e Coriolis
Ot 1 th
ects.
av
r an the superfl 'dr uid ef-
a t
e h
her- angular mom
e made extensive measuremen
P=3
y : (I) fo
oM tMt th b h"'" w"h 0 =0C
nd L
ibra-
}1
'
turn.
m persistent angular m
dent Our
u ar omen-
d
results can be i
at idealized
nterpreted in
h t i loo, ho
db do ths a e premise that the re
„—,=RI never exceeds the
e iso a th
e ine ow
e at 0=—(u=—cu„because
d o 1
hh fld
id. flow i
r ui component ex ' '
n- powder
d d b h Ke elvin dra
ia
'1 d h e
~
—co differs from 0
b-
„and the true v =—R ' es
extent from t
, cuc deViateS
he measured RA .
of
oop have unit slo pe and corres ra ion
The sides of th
flo b
,---- Th
e
e ysteresis a '
x creation
tices become pinned to the ow
rises because th e vor-
oop
mea
e. Our result 'is in marked
by Rudnick et 14Q.
their d ( Fi. 3 fR
amrne}, Hall
i t e
absent.
o ef. I) the clast's ic regime is
In Fig. 3, u, = L,/[MR ( ep$p M
o the reduced tern
P=
. . bars. The data
mperature T/ Tc at
man
' ' ot oseinFi .
'
e ina
g
,. The data
angu-
are included fo p
~ ~
at v, is inde
ur
thi bo t 10/o. In previous wo
per ature
ff' 'su icient tod
- 0-
' d
A heck for possible
d ' 3H 8 P=
1
in the ri
u ar momentum was
Th t h
measured. After
as t en brou ght to rest and L
P C'
~ er the cryostat had be
was
en kept in the
VOLUME 53, NUMBER 1 PHYSICAL REVIE% LETTERS 2 JULY 1984
0
6 —00 0 0 000 ~ 00 0 0 0
~
~ 0 0
T„/T~ = 0.5
0/op
0
00
0
00
O0
0
04
I
0.5
I
0.6
I
0.7
I
0.8 0.9
A B og ~+
TRAN-
SITION +P'
T/ TL.
FIG. 3. Critical velocity u, at P = 15.0 bars (open cir-
cles) and 12.0 bars (filled circles) as a function of the re-
duced temperature T/ T, . Lozenges are the data of Gam-
mel, Hall, and Reppy (Ref. 1) at P = 29 bars, multiplied
by 5, the ratio of the pore sizes [(100 p, m)/(20 p, m)];
this reduction factor is only approximate because of dif-
ferent types of geometries involved.
B phase continuously for 48 h, L was again mea-
sured. This value was then compared with that ob-
tained after the cryostat was again rotated at the
same velocity as before and then stopped. Within
our experimental accuracy of 10% there was no de-
cay in the signal. This gives for v, the relaxation
time of the superflow, a value in excess of 450 h
and implies in the 8 phase an effective viscosity,
q,rr= pd /r, which is at least 12 orders of magni-
tude smaller than for the normal liquid at the same
temperature. Here d = 20 p, m is the average size
of the interstitial pores.
Measurements of L made after thermal cycling in
the region below T= 0.98 T, showed that the angu-
lar momentum is a reversible function of tempera-
ture. In addition to the fact that v, is independent
of temperature, this demonstrates that, because of
macroscopic quantization, circulation is conserved
in 3He-8 as in He II.~ The temperature reversibility
was used to study the stability of persistent currents
in the immediate vicinity of T, . These experiments
showed that above T=0.98T, the critical velocity
decreases markedly; at T=0.989T„ for example,
u, is (50 + 5)% of its Iow-temperature value.
Figure 4 shows a plot of L, vs p, /p at 29.3 and
12.0 bars. The slope of the linear regime between
T„=0.56T, and Tzz in the 29.3-bar data corre-
sponds to v, =7.8 mm/s. The critical velocity is
different below T„; at low temperatures v, 5.4
mmls. This value is close to that measured at
P ~ 12 bars. The change in v, at T„was not seen
by Gammel, Hall, and Reppy' because an experi-
mental artifact prevented accurate observations
near T=0.57T, .
72
I
0.2
I I
0.4 0.6
ps p
I
0.8
FIG. 4. Saturated angular momentum I., as a function
of p, /p at P= 29.3 bars (open circles) and P = 12.0 bars
(filled circles, crosses, two different experiments). The
straight line corresponds to v, = 7.8 and 5.6 mm/s for the
29.3- and 12.0-bar data, respectively (to compare the two
critical velocities one should divide the slopes by the den-
sity of 'He at each pressure). The nonzero L, in 2 phase
is an experimental artifact that was removed in later runs
(see Fig. 5).
Experiments are in progress to test the possible
relation of the change in ~, at T=0.56T, with the
vortex-core transition observed in NMR experi-
ments at T=0.6T, .6
Data in Fig. 5 illustrate that currents in He-A do
not persist, at least under zero magnetic field. This
conclusion is supported by an experiment in which
the maximum L = L, was first created and mea-
sured in He-B, whereafter the torus was thermally
cycled to the 3 phase and then back to the 8 liquid
again: The signal had completely disappeared dur-
ing this sequence. The upper limit for the super-
flow decay in He-3 is less than 1 min, which was
the transient time for the signal to recover from the
Coriolis shift after the cryostat had been stopped.
Because of the anisotropic nature of He-A, the su-
percurrent might persist in some geometry different
from our packed powder.
Critical velocities of the order of a few millime-
ters per second seem to be associated with vorticity
in confined geometries from 10 to 100 p, m. For the
emission of a vortex ring with diameter do,
u, —(t/m3de) ln(da/(a), where m3 is the bare mass
of the 3He atom and (e= 20 nm is the coherence
length. If the vortex rings have a diameter equal
to the pore size, the calculated critical velocity is 7
VOLUME 53, NUMBER 1 PHYSICAL REVIE% LETTERS 2 JULY 1984
0.5
0.1
I
t-T/Tc
0.2
yo
ro0
~
o oe
~r'O
0
~ y
A~9
T RANSIT ION
0.3
I p
pressure dependence is due to (o in the logarithmic
factor.
The authors wish to express their gratitude to
Professor J. D. Reppy's group at Cornell for useful
discussions. We thank Matti Krusius and Pertti
Hakonen for experimental advice, and Sandy Fetter
and David Judd for theoretical help. Two of us
(O.V.L. and R.E.P.) thank, respectively, members
of the Berkeley Physics and Chemistry Depart-
ments and of the Otaniemi Low Temperature
Laboratory for their hospitality during the evolution
of this experiment. Our work was supported by the
Academy of Finland, by the Wihuri Foundation,
and by the U. S. National Science Foundation under
Grant No. DMR-81-19542.
0 +—+ q
~ PS/P
I
0.2 0.3
mm/s in our experimental setup, quite close to the
observed values 4.7—7.8 mm/s. Additional confir-
mation of this model is provided by the tempera-
ture independence of the measured v, . The weak
FIG. 5. L, vs p,/p around the 8 A transition at
P = 29.3 bars. Different symbols correspond to different
preparation angular velocities: open circles, O,
~
= 1.16
rad/s; filled circles, 0.86 rad/s; plusses, 0.57 rad/s. Note
that the reduced temperature scale at the top is non-
linear.
~P. L. Gammel, H. E. Hall, and J. D. Reppy, Phys.
Rev. Lett. 52, 121 (1984).
2P. J. Hakonen, O. T. Ikkala, S. T. Islander, T. K.
Markkula, P. M. Roubeau, K. M. Saloheimo, D. I. Gari-
bashvili, and J. S. Tsakadze, Cryogenics 23, 243 (1983).
3C. N. Archie, T. A. Alvesalo, J. D. Reppy, and R. C.
Richardson, Phys. Rev. Lett. 43, 139 (1979).
I. Rudnick, H. Kojima, %. Veith, and R. S. Kagiwada,
Phys. Rev. Lett. 23, 1220 (1969).
sJ. D. Reppy, Phys. Rev. Lett. 14, 733 (1965).
6P. J. Hakonen, M. Krusius, M. M. Salomaa, J. T.
Simola, Yu. M. Bunkov, V. P. Mineev, and G. E. Volo-
vik, Phys. Rev. Lett. 51, 1362 (1983).
7See for example A. L. Fetter, in The Physics of Liquid
and Solid Helium, Part I, edited by K. H, Bennemann and
J. B. Ketterson (Wiley, New York, 1976), p. 207.
73


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