The phase diagram of quantized vortices in 3He-B has been obtained with two techniques. Our NMR measurements show that magnetization displays a pressure-dependent first-order phase change at TV(P). Our gyroscopic experiments reveal a transition curve TG(P) which marks an abrupt change in the critical velocity. Both curves show a weak magnetic field dependence, run similarly in the (P, T) plane, and seem to mark the same vortex-core transition.Peer reviewe

Hakonen, Pertti J.

Krusius, M.

Lounasmaa, O. V.

Mamniashvili, G.

Nummila, K. K.

Packard, R. E.

Pekola, Jukka P.

Simola, J. T.

Volovik, G. E.

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. & Hakonen, P. J. & Krusius, M. &Lounasmaa, O. V. & Nummila, K. K. & Mamniashvili, G. & Packard,R. E. & Volovik, G. E.Title: Phase Diagram of the First-Order Vortex-Core Transition in Superfluid3He-BYear: 1984Version: Final published versionPlease cite the original version:Pekola, Jukka & Simola, J. T. & Hakonen, P. J. & Krusius, M. & Lounasmaa, O. V. &Nummila, K. K. & Mamniashvili, G. & Packard, R. E. & Volovik, G. E. 1984. PhaseDiagram of the First-Order Vortex-Core Transition in Superfluid 3He-B. Physical ReviewLetters. Volume 53, Issue 6. P. 584-587. ISSN 0031-9007 (printed). DOI:10.1103/physrevlett.53.584.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 6 PHYSICAL REVIEW LETTERS 6 AUGUST 1984Phase Diagram of the First-Order Vortex-Core Transitionin Superflnid 3He-BJ. P. Pekola, J. T. Simola, P. J. Hakonen, M. Krusius, 0. V. Lounasmaa, and K. K. NummilaLow Temperature Laboratory, Helsinki University of Technology, SF 0215-0 Espoo 15, FinlandandG. MamniashviliInstitute ofPhysics, Georgian Academy ofSciences, 380077 Tbilisi,Union ofSoviet Socr'alist RepublicsandR. E. PackardDepartment ofPhysics, University of California, Berkeley, California 94720andG. E. VolovikL Dlandau . .l.nstitute for Theoretical Physics, U. S.S.R. Academy of Sciences, 117334 Moscow,Union ofSoviet Socialist Republics(Ret:eived 13 3'une 1984)The phase diagram of quantized vortices in 'He-B has been obtained with two techniques.Our NMR measurements show that magnetization displays a pressure-dependent first-orderphase change at Tr(P). Our gyroscopic experiments reveal a transition curve To(P) whichmarks an abrupt change in the critical velocity. Both curves show a weak magnetic fielddependence, run similarly in the (P, T) plane, and seem to mark the same vortex-core transi-tion.PACS numbers: 67.50.FiEarlier measurements' at P =29.3 bars and0= 284 6 revealed a discontinuity in the rotation-induced NMR frequency shift at T& =0.6T, , identi-fied as a first-order phase transition in the corestructure of quantized vortices. We have now ex-tended these experiments to other pressures andfields to establish the curve separating the two dif-ferent types of vortices in the (P, T) plane. Wehave also continued our gyroscopic experimentsand now can make a rather detailed report on thephase transition, manifested by a discontinuouschange in the critical flow velocity v, and by a largelatent heat.Our measurements were carried out in a rotatingnuclear demagnetization refrigerator. 5 The NMRcel1 of open cylindrical geometry is 5 mm in diame-ter and 30 mm long. The heart of the gyroscope ex-periment4 is a torus, of radius 8 = 22 mm, packedwith 20-p, m plastic powder.An NMR result is illustrated in Fig. 1. Therotation-induced frequency shift Au exhibits adiscontinuity at T&=0.6T, =1.6 mK. The jump inhv is proportional to 0, the angular velocity of ro-tation, while T& is independent of O. Such abehavior rules out all textural tran. sitions in thebulk liquid, leaving only a phase change inside thevortex cores as an explanation. The latter is insen-sitive to 0 because only at 0 & 10 rad/s does thedistance between vortices become small enough todisturb the core structure, while the jump in 4v isproportional to the density of vortices nz= (4m3/h) A.The influence of the vortex cores on the NMRshifts, observed both in aixal, H Il 0, and in tiltedmagnetic fields, are well accounted for by the extravortex terms, —', a) (f),;RkHk) and —', ate(A;Rkx Hh), in the textural free energy. Here a is a mea-sure of the small magnetic anisotropy energy inbulk liquid, —a (n H), and R,k(n ) is a matrixrepresenting a rotation around the anisotropy axis nby the angle cos '( ——,). Phenomenological con-stants P and K, associated with the large magneticanisotropy and with the spontaneous magnetization.in the vortex-core region, respectively, are mani-fested by odd and even NMR shifts, in respect to Hand 0, .Prominent discontinuities, 5X = (0.1—0.25) Qs/rad and 15tr/H = —(0.002—0.02) 0 s/rad, wereobserved during warmup at the vortex-core transi-tion. . The magnitudes of these discontinuities scale584 1984 The American Physical SocietyVOLUME 53, NUMBER 6 PHYSICAL REVIEW LETTERS 6 AUGUsT 1984pOOOg0.15—OOOOo iooiOO.IOthDz)0 20—CL0.0 5—0.5 0,6 0.7 0.8FIG. 1. The NMR frequency change hv (normalizedby the maximum frequency shift in 'He B) as -a functionof the reduced temperature. In this measurement, atP = 29.3 bars, H = 284 G, and / ( 0, A) = 25', the cryo-stat was continuously rotated at 0=1.4 rad/s duringcooldown (open circles) and warmup (closed circles).The inset shows an example of the primary NMR absorp-tion data at rest (left) and under rotation from which AviS Obtained. Thermal hySteresis near TI —0.6T, becomesevident when the data points are compared with the solidcurve showing the measured equilibrium behavior.with 0 but the transition temperature Tt is in-dependent of Q.s The phase boundary Tt (P), de-fined by the jump in hv, is shown in Fig. 2. Mostof our NMR measurements were carried out at0=284 G. Experiments were also made at 500 6under P = 25.0 bars and an increase of about 1% inTv/T, was seen. At the lowest pressure, P =17.1bars, the transition line was crossed twice, which in-dicates that Tv (P) tends to curve towards higherpressures when approaching the superfluid phasetransition curve T, (P).Because the NMR frequency shifts vanish in pro-portion to 1 —T/T, near T„ the termination pointof Tv (P) has not been established, i.e., it may beon the T, (P) line or within the B phase. Some in-dication for the absence of a critical point is provid-ed by the observation that hk/X does not start todecrease when T, (P) is approached along Tt,(P).We also wish to point out the thermal hysteresis as-sociated with the vortex-core transition, as illustrat-ed in Fig. 1; this proves the first-order nature of theobserved phase change.In our recent hydrodynamic measurements,where we used an ac gyroscope, two regimes with0'I, 5 2 3T (mK)FIG. 2. Observed transitions on the phase diagram ofrotating 'He-B: open circles, H = 284 G (NMR experi-ment); closed circles, H =0; crosses, H = 40 G (gyro-scope experiment). Regions I, II, and III are discussed inthe text.25distinct critical velocities were found at P=29.3bars. A careful study of the maximum persistableangular momentum L, as a function of tempera-ture, pressure, and magnetic field has now beenmade. Our experiments at a low ( ( 2 G) externalfield and at 0=40 6 reveal a phase boundaryTG(P) running in the (P, T) plane as shown in Fig.2. Tz (P) also has a weak dependence on H.The discontinuous change observed in the criticalvelocity across the transition at TG is illustrated inFig. 3; data on L are shown from five different ex-periments. The sense of rotation always alternatedbetween two successive measurements of L. Aftereach preparative rotation O~, the persistent angularmomentum was measured with the cryostat at rest.According to our data, applying an H = 40 0 fielddecreases the v, = 7 rnm/s critical velocity in regionI (see Fig. 2) by only 10%. Unexpectedly, astronger effect was observed in region II: v, in-creases from 5-7 mm/s at H = 0 to 12—l5 mm/s at40 G under all pressures.An equally striking feature of the transition at T6is the large latent heat, QG= (0 —II ) p, J s/mol. rad, comparable to Qs„= 1.5 iu, J/mol, the la-tent heat of the 8 A transition under the meltingpressure. QG was estimated from warm-up curveslike those in Fig. 4. A latent heat was observedonly in the presence of a persistent superflowv, =R (Qv —0,).The identification of the changes at TG with thevortex-core transition requires the presence ofremanent vorticity, which is a concept well estab-lished in He u. 7 In our experiments, the remanent585VOLUME 53, NUMBER 6 PHYSICAL REVIEW LETTERS 6 AUGUST 1984T/Tc0.75 0.70 0.65 0.60I t 1IaAP =120 rad/& rtp =060 rod/s~ ~~~ ~~D 07CL~ ~~0~0N~0O00H=40 gauss~~+gO0~0~~gO 00 g300t +—-0.8C'Uo 09OO~ ~~0!time~05 min— 0.68—0.64FIG. 4. Warmup curves of the gyroscope at two differ-ferent values of O~; in this experiment P = 18.0 bars andM=40 6, Under these conditions 0,=0.35 rad/s. Thelatent heat is clearly seen as a plateau in the warmupcurves. The change in the gyroscope's resonant period,from that observed at T„ increases towards lower tem-peratures because the amount of normal fluid in thetorus decreases; we used this effect as our thermometricparameter (Ref, 4 ).~~1 — + $++ 0 Cl 0-Oloa O P I0.2 0.3 0.4p, /p0.5 0.6FIG. 3. The persistent angular momentum I. as afunction of reduced temperature T/T, (upper scale) andthe fraction of superfluid, p, /p, in the cell. P = 23.0 bars,and the preparation angular velocities were (open circles)0~=0.40 rad/s, and (closed circles and crosses) 0.86rad/s. The transition in v, is seen in all cases as anabrupt change in L. Arrows indicate the points at whicha latent heat was observed.vorticity curlv„of the order of v, /d, arises duringthe creation of superflow; vortices then becomepinned to the d=20-p, m-diam powder particles.This leads to the estimate nG = m3u, /td for thedensity of vortex lines in the torus. The equilibri-um vortex density ny in our NMR cell of opengeometry is 3 to 4 orders of magnitude less; this ex-plains why Q~ was not observed.If the latent heat is, indeed, due to a change inthe condensation free energy F„„d of the vortexcore, we obtain QG = F„„dnGvrAO, which leads tothe core radius 8 0 = 30$, where g = 10 nm is thecoherence length. This value of Ro is still compati-ble with the estimate R q = 10( from NMR experi-ments. It is possible that n& is enhanced by thecomplicated geometry of the powder.As in He[I, pinned vorticity acts as a nucleationcenter for the growth of vortex rings when theFeynman critical velocity, uF= (lt/m3d)ln(d/80)=7 mm/s, is reached. Our measured critical ve-locities are of the order of vF. However, the differ-ence of v, in regions I and II shows that the processof vortex creation is more complicated. In regions Iand III the onset of the persistent supercurrent wassharp at 0 = Q„whereas in region II, especially ina magnetic field, the processs was smoothed. Thisindicates that the creation of vortices depends ontheir core structure. For example, pinning shouldbe different for the observed two types of vorticesand it should depend on the external magnetic field.The growth rate of vortex rings of critical size isessentially determined by vibrations, as has beenfound for He Ir. It may be that the 40% decrease inthe gyroscope's vibration intensity at 0= 40 6, incomparison with H=0, explains the puzzling in-crease of v, in region II with field, observed at eachpressure; we did not investigate, however, this ef-fect in detail.The observed clear, albeit small, differencesbetween the Tz and TG curves may be partly due todifferent calibrations of the thermometers at lowtemperatures. However, near T, the influence ofthe magnetic field on the core structures becomesimportant. It is worth noting from Fig. 2 that theT& data, corresponding to relatively low magneticfields, do not approach the T, curve. We could notfind any evidence of additional transition lines em-erging from the Tv or ?'& curves. For example,gyroscopic experiments at P = 12.0 bars and H =0and NMR data at P = 15.5 bars and 0= 284 6 do586VOLUME 53, NUMBER 6 PHYSICAL REVIEW LETTERS 6 AUGUS~ 1984not reveal any sign. s of tran. sition lines. Further,NMR experiments done at 17.1 bars and 284 G andgyroscopic measurements at I5.0 and 23.0 bars atH = 0 show that, at each pressure, the A. vs T curvesin regions I and III can be joined smoothly acrossregion II and that v, is the same in regions I and III.Therefore, the structures present in regions I andIII are similar as far as ) and v, are concerned.At H = 0 and near T, there thus exists only onetype of vortex. This is consistent with the recenttheoretical result of Salomaa and Volovik. Theyfound that there are five types of axially symmetricsingly quantized vortices, which differ in their corestructure. Numerical calculations show that atH = 0 and in the Ginzburg-Landau regime near T,only one of them is stable. This vortex, to be iden-tified with that observed experimentally in regions Iand III, has a core occupied by 3-phase liquid,responsible for the susceptibility anisotropy, and byferromagnetic P-phase liquid, with spontaneousmagnetization. However, the detailed mechanismsleading to the vortex-core transition at T& and thestructure of the vortex in region II have not yetbeen unambiguously identified.In summary, we note that the transitions at Tzand TG show similar features: The jump in theNMR frequency shift and the discontinuity in v,are both rotation induced but the transition tem-peratures are independent of 0, ; the similarity ofthe T„and TG curves in the (P, T) plane is obvious.We are thus dealing with the same vortex-care tran-sition in both cases. If this conclusion is correct,our data provide some clues about the vortex gen-eraiion process in He-8.We wish to thank P. Kumar, J. Kurkijarvi, M. M.Salomaa, J. A. Sauls, and E. V. Thuneberg for dis-cussions. Our work was supported by the Academyof Finland, the Wihuri Foundation, and the U. S.National Science Foundation through Grant No.DMR-81-19542.'O.T. Ikkala, G. E. Volovik, P. J. Hakonen, Yu.M.Bunkov, S. T. Islander, and G. A. Kharadze, Pis'ma Zh.Eksp. Teor. Fiz. 35, 338 (1982) [JETP Lett. 35, 416(1982)].P. J. Hakonen, O. T, Ikkala, S. T. Islander, O. V.Lounasmaa, and G. E. Volovik, J. Low Temp. Phys. 53,425 (1983).3P. J. Hakonen, M. Krusius, M. M. Salomaa, J. T.Simola, Yu. M. Bunkov, V. P. Mineev, and G. E. Volo-vik, Phys. Rev. Lett. Sl, 1362 (1983).J. P. Pekola, J. T. Simola, K. K. Nummila, O. V.Lounasmaa, and R. E. Packard, Phys. Rev. Lett. 53, 70(1984).5P. J. Hakonen, O. T. Ikkala, S. T. Islan. der, T. K.Markkula, P. Roubeau, K. M. Saloheimo, D. I. Garibash-vili, and J. S. Tsakadze, Cryogenics 23, 243 (1983).6P. J. Hakonen, M, Krusius, G. Mamniashvili, andJ. T. Simola, to be published.D. D. Awschalom and K. W. Schwarz, Phys. Rev.Lett. 52, 49 (1984).sS. J. Putterman, Superfluid Hydrodynamics (North-Holland, Amsterdam, 1974), pp. 262-266.M. M. Salomaa and G. E. Volovik, Phys. Rev. Lett.51, 2040 (1983), and to be published.5S7

Phase Diagram of the First-Order Vortex-Core Transition in Superfluid 3He-B

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. & Hakonen, P. J. & Krusius, M. &
Lounasmaa, O. V. & Nummila, K. K. & Mamniashvili, G. & Packard,
R. E. & Volovik, G. E.
Title: Phase Diagram of the First-Order Vortex-Core Transition in Superfluid
3He-B
Year: 1984
Version: Final published version
Please cite the original version:
Pekola, Jukka & Simola, J. T. & Hakonen, P. J. & Krusius, M. & Lounasmaa, O. V. &
Nummila, K. K. & Mamniashvili, G. & Packard, R. E. & Volovik, G. E. 1984. Phase
Diagram of the First-Order Vortex-Core Transition in Superfluid 3He-B. Physical Review
Letters. Volume 53, Issue 6. P. 584-587. ISSN 0031-9007 (printed). DOI:
10.1103/physrevlett.53.584.
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 6 PHYSICAL REVIEW LETTERS 6 AUGUST 1984
Phase Diagram of the First-Order Vortex-Core Transition
in Superflnid 3He-B
J. P. Pekola, J. T. Simola, P. J. Hakonen, M. Krusius, 0. V. Lounasmaa, and K. K. Nummila
Low Temperature Laboratory, Helsinki University of Technology, SF 0215-0 Espoo 15, Finland
and
G. Mamniashvili
Institute ofPhysics, Georgian Academy ofSciences, 380077 Tbilisi,
Union ofSoviet Socr'alist Republics
and
R. E. Packard
Department ofPhysics, University of California, Berkeley, California 94720
and
G. E. Volovik
L Dlandau . .l.nstitute for Theoretical Physics, U. S.S.R. Academy of Sciences, 117334 Moscow,
Union ofSoviet Socialist Republics
(Ret:eived 13 3'une 1984)
The phase diagram of quantized vortices in 'He-B has been obtained with two techniques.
Our NMR measurements show that magnetization displays a pressure-dependent first-order
phase change at Tr(P). Our gyroscopic experiments reveal a transition curve To(P) which
marks an abrupt change in the critical velocity. Both curves show a weak magnetic field
dependence, run similarly in the (P, T) plane, and seem to mark the same vortex-core transi-
tion.
PACS numbers: 67.50.Fi
Earlier measurements' at P =29.3 bars and0= 284 6 revealed a discontinuity in the rotation-
induced NMR frequency shift at T& =0.6T, , identi-
fied as a first-order phase transition in the core
structure of quantized vortices. We have now ex-
tended these experiments to other pressures and
fields to establish the curve separating the two dif-
ferent types of vortices in the (P, T) plane. We
have also continued our gyroscopic experiments
and now can make a rather detailed report on the
phase transition, manifested by a discontinuous
change in the critical flow velocity v, and by a large
latent heat.
Our measurements were carried out in a rotating
nuclear demagnetization refrigerator. 5 The NMR
cel1 of open cylindrical geometry is 5 mm in diame-
ter and 30 mm long. The heart of the gyroscope ex-
periment4 is a torus, of radius 8 = 22 mm, packed
with 20-p, m plastic powder.
An NMR result is illustrated in Fig. 1. The
rotation-induced frequency shift Au exhibits a
discontinuity at T&=0.6T, =1.6 mK. The jump in
hv is proportional to 0, the angular velocity of ro-
tation, while T& is independent of O. Such a
behavior rules out all textural tran. sitions in the
bulk liquid, leaving only a phase change inside the
vortex cores as an explanation. The latter is insen-
sitive to 0 because only at 0 & 10 rad/s does the
distance between vortices become small enough to
disturb the core structure, while the jump in 4v is
proportional to the density of vortices nz= (4m3/
h) A.
The influence of the vortex cores on the NMR
shifts, observed both in aixal, H Il 0, and in tilted
magnetic fields, are well accounted for by the extra
vortex terms, —', a) (f),;RkHk) and —', ate(A;Rk
x Hh), in the textural free energy. Here a is a mea-
sure of the small magnetic anisotropy energy in
bulk liquid, —a (n H), and R,k(n ) is a matrix
representing a rotation around the anisotropy axis n
by the angle cos '( ——,). Phenomenological con-
stants P and K, associated with the large magnetic
anisotropy and with the spontaneous magnetization.
in the vortex-core region, respectively, are mani-
fested by odd and even NMR shifts, in respect to H
and 0, .
Prominent discontinuities, 5X = (0.1—0.25) Q
s/rad and 15tr/H = —(0.002—0.02) 0 s/rad, were
observed during warmup at the vortex-core transi-
tion. . The magnitudes of these discontinuities scale
584 1984 The American Physical Society
VOLUME 53, NUMBER 6 PHYSICAL REVIEW LETTERS 6 AUGUsT 1984
pO
OOg
0.15—
OO
OO
o io
oi
O
O.
I
O
th
D
z)
0 20—
CL
0.0 5—
0.5 0,6 0.7 0.8
FIG. 1. The NMR frequency change hv (normalized
by the maximum frequency shift in 'He B) as -a function
of the reduced temperature. In this measurement, at
P = 29.3 bars, H = 284 G, and / ( 0, A) = 25', the cryo-
stat was continuously rotated at 0=1.4 rad/s during
cooldown (open circles) and warmup (closed circles).
The inset shows an example of the primary NMR absorp-
tion data at rest (left) and under rotation from which Av
iS Obtained. Thermal hySteresis near TI —0.6T, becomes
evident when the data points are compared with the solid
curve showing the measured equilibrium behavior.
with 0 but the transition temperature Tt is in-
dependent of Q.s The phase boundary Tt (P), de-
fined by the jump in hv, is shown in Fig. 2. Most
of our NMR measurements were carried out at0=284 G. Experiments were also made at 500 6
under P = 25.0 bars and an increase of about 1% in
Tv/T, was seen. At the lowest pressure, P =17.1
bars, the transition line was crossed twice, which in-
dicates that Tv (P) tends to curve towards higher
pressures when approaching the superfluid phase
transition curve T, (P).
Because the NMR frequency shifts vanish in pro-
portion to 1 —T/T, near T„ the termination point
of Tv (P) has not been established, i.e., it may be
on the T, (P) line or within the B phase. Some in-
dication for the absence of a critical point is provid-
ed by the observation that hk/X does not start to
decrease when T, (P) is approached along Tt,(P).
We also wish to point out the thermal hysteresis as-
sociated with the vortex-core transition, as illustrat-
ed in Fig. 1; this proves the first-order nature of the
observed phase change.
In our recent hydrodynamic measurements,
where we used an ac gyroscope, two regimes with
0
'I, 5 2 3
T (mK)
FIG. 2. Observed transitions on the phase diagram of
rotating 'He-B: open circles, H = 284 G (NMR experi-
ment); closed circles, H =0; crosses, H = 40 G (gyro-
scope experiment). Regions I, II, and III are discussed in
the text.
25
distinct critical velocities were found at P=29.3
bars. A careful study of the maximum persistable
angular momentum L, as a function of tempera-
ture, pressure, and magnetic field has now been
made. Our experiments at a low ( ( 2 G) external
field and at 0=40 6 reveal a phase boundary
TG(P) running in the (P, T) plane as shown in Fig.
2. Tz (P) also has a weak dependence on H.
The discontinuous change observed in the critical
velocity across the transition at TG is illustrated in
Fig. 3; data on L are shown from five different ex-
periments. The sense of rotation always alternated
between two successive measurements of L. After
each preparative rotation O~, the persistent angular
momentum was measured with the cryostat at rest.
According to our data, applying an H = 40 0 field
decreases the v, = 7 rnm/s critical velocity in region
I (see Fig. 2) by only 10%. Unexpectedly, a
stronger effect was observed in region II: v, in-
creases from 5-7 mm/s at H = 0 to 12—l5 mm/s at
40 G under all pressures.
An equally striking feature of the transition at T6
is the large latent heat, QG= (0 —II ) p, J s/
mol. rad, comparable to Qs„= 1.5 iu, J/mol, the la-
tent heat of the 8 A transition under the melting
pressure. QG was estimated from warm-up curves
like those in Fig. 4. A latent heat was observed
only in the presence of a persistent superflow
v, =R (Qv —0,).
The identification of the changes at TG with the
vortex-core transition requires the presence of
remanent vorticity, which is a concept well estab-
lished in He u. 7 In our experiments, the remanent
585
VOLUME 53, NUMBER 6 PHYSICAL REVIEW LETTERS 6 AUGUST 1984
T/Tc
0.75 0.70 0.65 0.60
I t 1
I
a
AP =120 rad/& rtp =060 rod/s
~ ~
~
~ ~
~
D 07
CL
~ ~
~0
~
0
N
~
0
O
00
H=40 gauss
~
~
+
gO
0
~0
~
~gO 00 g3
0
0
t +
—
-0.8
C'
U
o 09
OO
~ ~
~0
!
time
~0
5 min
— 0.68
—0.64
FIG. 4. Warmup curves of the gyroscope at two differ-
ferent values of O~; in this experiment P = 18.0 bars and
M=40 6, Under these conditions 0,=0.35 rad/s. The
latent heat is clearly seen as a plateau in the warmup
curves. The change in the gyroscope's resonant period,
from that observed at T„ increases towards lower tem-
peratures because the amount of normal fluid in the
torus decreases; we used this effect as our thermometric
parameter (Ref, 4 ).
~
~
1 — + $++ 0 Cl 0-
Oloa O P I
0.2 0.3 0.4
p, /p
0.5 0.6
FIG. 3. The persistent angular momentum I. as a
function of reduced temperature T/T, (upper scale) and
the fraction of superfluid, p, /p, in the cell. P = 23.0 bars,
and the preparation angular velocities were (open circles)
0~=0.40 rad/s, and (closed circles and crosses) 0.86
rad/s. The transition in v, is seen in all cases as an
abrupt change in L. Arrows indicate the points at which
a latent heat was observed.
vorticity curlv„of the order of v, /d, arises during
the creation of superflow; vortices then become
pinned to the d=20-p, m-diam powder particles.
This leads to the estimate nG = m3u, /td for the
density of vortex lines in the torus. The equilibri-
um vortex density ny in our NMR cell of open
geometry is 3 to 4 orders of magnitude less; this ex-
plains why Q~ was not observed.
If the latent heat is, indeed, due to a change in
the condensation free energy F„„d of the vortex
core, we obtain QG = F„„dnGvrAO, which leads to
the core radius 8 0 = 30$, where g = 10 nm is the
coherence length. This value of Ro is still compati-
ble with the estimate R q = 10( from NMR experi-
ments. It is possible that n& is enhanced by the
complicated geometry of the powder.
As in He[I, pinned vorticity acts as a nucleation
center for the growth of vortex rings when the
Feynman critical velocity, uF= (lt/m3d)ln(d/80)
=7 mm/s, is reached. Our measured critical ve-
locities are of the order of vF. However, the differ-
ence of v, in regions I and II shows that the process
of vortex creation is more complicated. In regions I
and III the onset of the persistent supercurrent was
sharp at 0 = Q„whereas in region II, especially in
a magnetic field, the processs was smoothed. This
indicates that the creation of vortices depends on
their core structure. For example, pinning should
be different for the observed two types of vortices
and it should depend on the external magnetic field.
The growth rate of vortex rings of critical size is
essentially determined by vibrations, as has been
found for He Ir. It may be that the 40% decrease in
the gyroscope's vibration intensity at 0= 40 6, in
comparison with H=0, explains the puzzling in-
crease of v, in region II with field, observed at each
pressure; we did not investigate, however, this ef-
fect in detail.
The observed clear, albeit small, differences
between the Tz and TG curves may be partly due to
different calibrations of the thermometers at low
temperatures. However, near T, the influence of
the magnetic field on the core structures becomes
important. It is worth noting from Fig. 2 that the
T& data, corresponding to relatively low magnetic
fields, do not approach the T, curve. We could not
find any evidence of additional transition lines em-
erging from the Tv or ?'& curves. For example,
gyroscopic experiments at P = 12.0 bars and H =0
and NMR data at P = 15.5 bars and 0= 284 6 do
586
VOLUME 53, NUMBER 6 PHYSICAL REVIEW LETTERS 6 AUGUS~ 1984
not reveal any sign. s of tran. sition lines. Further,
NMR experiments done at 17.1 bars and 284 G and
gyroscopic measurements at I5.0 and 23.0 bars at
H = 0 show that, at each pressure, the A. vs T curves
in regions I and III can be joined smoothly across
region II and that v, is the same in regions I and III.
Therefore, the structures present in regions I and
III are similar as far as ) and v, are concerned.
At H = 0 and near T, there thus exists only one
type of vortex. This is consistent with the recent
theoretical result of Salomaa and Volovik. They
found that there are five types of axially symmetric
singly quantized vortices, which differ in their core
structure. Numerical calculations show that at
H = 0 and in the Ginzburg-Landau regime near T,
only one of them is stable. This vortex, to be iden-
tified with that observed experimentally in regions I
and III, has a core occupied by 3-phase liquid,
responsible for the susceptibility anisotropy, and by
ferromagnetic P-phase liquid, with spontaneous
magnetization. However, the detailed mechanisms
leading to the vortex-core transition at T& and the
structure of the vortex in region II have not yet
been unambiguously identified.
In summary, we note that the transitions at Tz
and TG show similar features: The jump in the
NMR frequency shift and the discontinuity in v,
are both rotation induced but the transition tem-
peratures are independent of 0, ; the similarity of
the T„and TG curves in the (P, T) plane is obvious.
We are thus dealing with the same vortex-care tran-
sition in both cases. If this conclusion is correct,
our data provide some clues about the vortex gen-
eraiion process in He-8.
We wish to thank P. Kumar, J. Kurkijarvi, M. M.
Salomaa, J. A. Sauls, and E. V. Thuneberg for dis-
cussions. Our work was supported by the Academy
of Finland, the Wihuri Foundation, and the U. S.
National Science Foundation through Grant No.
DMR-81-19542.
'O.T. Ikkala, G. E. Volovik, P. J. Hakonen, Yu.M.
Bunkov, S. T. Islander, and G. A. Kharadze, Pis'ma Zh.
Eksp. Teor. Fiz. 35, 338 (1982) [JETP Lett. 35, 416
(1982)].
P. J. Hakonen, O. T, Ikkala, S. T. Islander, O. V.
Lounasmaa, and G. E. Volovik, J. Low Temp. Phys. 53,
425 (1983).
3P. J. Hakonen, M. Krusius, M. M. Salomaa, J. T.
Simola, Yu. M. Bunkov, V. P. Mineev, and G. E. Volo-
vik, Phys. Rev. Lett. Sl, 1362 (1983).
J. P. Pekola, J. T. Simola, K. K. Nummila, O. V.
Lounasmaa, and R. E. Packard, Phys. Rev. Lett. 53, 70
(1984).
5P. J. Hakonen, O. T. Ikkala, S. T. Islan. der, T. K.
Markkula, P. Roubeau, K. M. Saloheimo, D. I. Garibash-
vili, and J. S. Tsakadze, Cryogenics 23, 243 (1983).
6P. J. Hakonen, M, Krusius, G. Mamniashvili, and
J. T. Simola, to be published.
D. D. Awschalom and K. W. Schwarz, Phys. Rev.
Lett. 52, 49 (1984).
sS. J. Putterman, Superfluid Hydrodynamics (North-
Holland, Amsterdam, 1974), pp. 262-266.
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51, 2040 (1983), and to be published.
5S7


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Phase Diagram of the First-Order Vortex-Core Transition in Superfluid 3He-B

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