Spin Dynamics of Superfluid 3He in Aerogel

Osamu Ishikawa

Osaka City University

Collaborator

H. Nakagawa, R. Kado,K. Obara,H. Yano,T. Hata

H. Yokogawa,M. Yokoyama

Outline of talk

• Aerogel properties and temporary phase diagram of superfluid 3He in 97.5 % porosity

• coexistence phenomena of A-like and B-like phases

• Spin Dynamics in A-like phase and B-like phase by pulsed NMR experiments

• Suppresion of Tc

Aerogel properties

Aerogel in cylindrical glass for NMR cell

aerogel is directly grown inside glass tube to avoid any space between glass and aerogel

NMR coils are wound on outside surface of glass

aerogel

empty

about 50 [m2/cc] estimated by the B.E.T surface measurements and ~1000 [m2/g] with aerogel mass

Surface to volume ratio

~ 6 [m2] surface area for aerogel in sample

Pre-coating of 4He film 2.5 layers of 4He film on silica strand in aerogel are controlled with large surface area in a heat exchanger in the sample cell of 660 [m2].

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.00 0.50 1.00 1.50 2.00 2.50 3.00

concentration of silica [%]

den

sity

[g/

cc]

97.5%porosity

Characteristic distance between strands by neutron scattering experiment

Evidence of weak periodicity in aerogel

silica beads with diameter of 8.4 nm• smooth surface of silica beads （ DS = 2.0 ）• Fractal dimension is 1.8

small-angle X-ray scattering

Temporary phase diagram of superfluid 3He

in 97.5 % porosity

0

1

2

3

0 1 2Temperature [mK]

A phaseB phase

Solid phase

Normal phase

A-like phaseB-like phase

NMR experiments showed two phases in superfluid 3He in aerogel; A-like phase and B-like phase.

(1) in A-like phase • an absorption spectrum being a narrow peak, shifted as a whole from the Larmor freq., showing a positive or negative shift depending on aerogels • the magnetization is the same as in normal state (2) in B-like phase • an absorption spectrum widely spread due to a “texture” depending on aerogels • the magnetization decreased as decreasing temperatures

0

40

80

120

0 1 2

1.969 mK

1.696 mK

1.646 mK

0.906 mK

1.444 mK

0.972 mK

1.140 mK

1.403 mK

0.549 mK

0.459 mK

0.738 mK

f - fLarmor

[kHz]

0

40

80

120

160

0 1 2

2.889 mK

1.787 mK

1.686 mK1.534 mK

1.444 mK1.241 mK1.171 mK0.947 mK0.916 mK0.783 mK0.551 mK0.471 mK

f - fLarmor

[kHz]

Coexisting signals on cooling from normal state

0

400

800

1200

1.4 1.5 1.6 1.7 1.8

coolingwarming

Temperature [mK]

TC

aero

TAB

aero

T*

Region A

Continuous phase conversion from A-like to B-like phase

0

0.4

0.8

1.2

1.4 1.5 1.6 1.7

A-like phaseB-like phaseTotal Magnetization

Temperature [mK]

3.2MPa

+4He film

Warming up from coexisting temperature (from Region A)

0

400

800

1200

1.4 1.5 1.6 1.7 1.8

coolingwarmingA-like Shift_warmingB-like Shift_warming

Temperature [mK]

TC

aero

A-like Shift

B-like Shift

0

50

100

150

200

0 0.5 1

1.815 mK

1.710 mK

1.685 mK

1.642 mK

1.594 mK

1.555 mK

1.520 mK

1.468 mK

f - fLarmor

[kHz]

0

0.1

0.2

0.3

0.4

0.5

1.4 1.5 1.6 1.7 1.8

A-like phaseB-like phase

0

400

800

1200

1.4 1.5 1.6 1.7 1.8

coolingwarming

Temperature [mK]

TC

aero

TAB

aero

T*

One peak signal in on cooling from normal state and on warming from below region A

Turn around experiment (1)

Region B

3.2 MPa with 4He film

0

400

800

1200

1.4 1.5 1.6 1.7 1.8

A-like by (D)

B-like by (D)

A-like by(C)

B-like by (C)

Temperature [mK]

TC

aero

T*

(A)

(D)

(C)

(B)

0

400

800

1200

1.4 1.5 1.6 1.7 1.8

A-like by (D)

B-like by (D)

A-like by(C)

B-like by (C)

Temperature [mK]

TC

aero

T*

(A)

(D)

(C)

(B)

0 1

1.657 mK

1.644 mK

1.617 mK

1.574 mK

1.551 mK

1.518 mK

1.439 mK

1.473 mK

f - fLarmor

[kHz]

Turn around experiment (2)

0

50

100

150

200

1.25 1.3 1.35 1.4 1.45

Cooling from NormalWarming from 1.273mK

0

30

60

-100 0 100 200 300

Cooling from Normal

1.298mK

0

30

60

-100 0 100 200 300

Cooling from 1.398mK

1.301mK

0

30

60

-100 0 100 200 300

Cooling from 1.363mK

1.304mK

0

30

60

-100 0 100 200 300

Cooling from 1.380mK

1.296mK

0

30

60

-100 0 100 200 300

Cooling from 1.354mK

1.304mK

Different spectra at 1.3 mK

with cooling

2.35 MPa with 4He film

0

90

180

-100 0 100 200 300

Cooling from 1.380mK

1.380mK

1.330mK

1.322mK

1.296mK

1.290mK

coexistence phenomena without 4He film

3He at 3.2MPa

0

200

400

1.2 1.4 1.6 1.8

coolingwarming

Temperature [mK]

TC

aero

TAB

aero

40 μK

0

200

400

0 1 2 3

coolingwarming

Temperature [mK]

TC

aero

TC

bulkT

AB

aero

Rapid spin exchange mechanism between liquid and solid covers coexisting phenomena

0

100

200

0 1 2 3

coolingwarming

Temperature [mK]

TC

aero TC

pure

0

20

40

60

1.1 1.2 1.3 1.4 1.5

coolingwarming

Temperature [mK]

TC

aero

TAB

aero

3He at 2.1MPa

Frequencies changed continuously with cooling liquid

This is an evidence of coexisting phases

Spin dynamics by pulsed NMR (A-like phase)

0

200

400

600

800

1.2 1.4 1.6

on coolingon warming

Temperature [mK]

f

[Hz]

2.4 MPa with 4He film

0

200

400

600

800

1.2 1.4 1.6

on coolingon warming

Temperature [mK]

-20

-10

0

10

20

30

40

50

0 50 100 150 200 250 300 350

F[Hz] 24bar

(1+cos β)/2

(1+3cos β)/4

f

[Hz]

Tipping angle [deg]

0

250

500

750

1000

1.5 1.8

coolingwarming

Temperature [mK]

f

[Hz]

3.2 MPa with 4He film

1.55 mK-40

-20

0

20

40

60

80

100

0 50 100 150 200 250 300 350

(1+cos β)/2

(1+3cos β)/4

[ ] 32 f Hz bar

Tipping angle [deg]

f

[Hz]

0

250

500

750

1000

1.5 1.8

coolingwarming

Temperature [mK]

Magnetization measurement

0

0.5

1

1.5

2

2.5

0 10 20 30 40 50 60

Temperature [mK]

Mag

net

izat

ion

[a.

u.]

pure 3He

Temperature [mK]

Mag

net

izat

ion

[a.

u.]

0.0

0.2

0.4

0.6

0.8

1.0

0 10 20 30 40 50 60 70 80

2.5 layers 4He film

0

0.5

1

1.5

2

2.5

0 10 20 30 40 50 60

Temperature [mK]

Mag

neti

zati

on [

a.u.

]

pure 3He

At 3.2 MPa, surface solid 3He shows Curie-Weiss magnetism on 2.5 layers of 4He film

0.0

0.2

0.4

0.6

0.8

1.0

0 10 20 30 40 50 60 70 80

Mag

net

izat

ion

[a.

u.]

Temperature [mK]

pure 3He

Mag

net

izat

ion

[a.

u.]

Temperature [mK]

with 2.5 layers 4He film

0

0.2

0.4

0.6

0.8

1

1.1 1.2 1.3 1.4 1.5 1.6

Tca

Tc

a = 1.50mK

T* = 1.45mK

T*

2.5 layers 4He films

At 2.4 MPa, Curie-Weiss behavior almost disappears

-20

-10

0

10

20

30

40

50

0 50 100 150 200 250 300 350

F[Hz] 24bar

(1+cos β)/2

(1+3cos β)/4

f

[Hz]

Tipping angle [deg]

-40

-20

0

20

40

60

80

100

0 50 100 150 200 250 300 350

(1+cos β)/2

(1+3cos β)/4

[ ] 32 f Hz bar

Tipping angle [deg]

Tipping angle dependent frequency shift is attributed to superfluidity

But they are different from those in bulk liquid

A rubust phaseA rubust phase proposed by I.A. Fomin explains FID frequencies

dμj =Δ3

ˆ d μ ˆ m j +iˆ n j( )+ˆ e μ ˆ l j +iˆ p j( )[ ]

Δf(β) =frbst

2

fL

1+cosβ8

pulsedNMR

=Δf(0)1+cosβ

2

f2 = fL2 +

12

frbst2 cwNMR

M.Miura and K.Nagai (Hiroshima univ.)

60

80

100

300

1.00 10.0 100

coolingwarming

TC

pure

TC

aero

TAB

aero

Temperature [mK]

Fu

ll W

idth

at H

alf

Max

imu

m

[Hz]

Spin dynamics by pulsed NMR (B-like phase)r H r

n θ

ω2=ωL2+ΩB

2sin2θθ=0 for bulkliquid

sin2θ=45

nearsurfaceparalleltor H

Flare out texturein cylindrical cell

Large peak at Larmor freq. And having a tail to higher freq. by cw NMR .

f [Hz]

[ a

.u.]

-400 0 400 800 1200

normal(1.54mK)

B-like phase(0.93mk)

2.35 MPaDifferent from flare out texture

Similar to absorption of bulk liquid confined inslab geometry where magnetic field parallel to surface r

H r n

θ

ω2=ωL2+ΩB

2sin2θθ≠0 for mainpart

V.V.Dmitriev et al., JETP Letters 76 312-317 (2002)

5.3 mm diameter5.6 mm height98 % aerogel

104˚

An evidence showing that B-like phase is B phase

Confirmation of the order parameter of B-like phase as that of B phase in bulk liquid

“n-vector”

Tipping angle [deg]

f

[kH

z]

-0.2

0

0.2

0.4

0.6

0.8

0 100 200 300 400

f [kHz]

T = 0.93mK

T = 0.655Tc

a

tw = 136μsec

P=2.4 MPa

nz

Sz−So

BS-mode

θ=θL

Suppression of Tc

0

0.4

0.8

0 1 2

TC

aero / TC

bulk_3He only

TC

aero / TC

bulk_4He coat

HSMIISM (R=5.6L , j=8)IISM (R=4.6L , j=8)IISM (R=4.6L , j=2)

98%_Porto&Parpia(1995)98%_Matsumoto(1997)

ξ0 / L

T cae

ro /

Tcpu

re

Inhomogeneous Impurity Scattering Model includes a length L as a parameter.L=16.0 μm for pure 3He, L=16.5 μm for 3He+ 4He with Radius R=4.6L.

Thuneberg et al.

Summary• Aerogel has average periodicity• Adding a small amount 4He helped us to observe c

oexisting phenomena by reducing solid contribution to NMR signal

• Boundaries between phases are probably pinned at inhomogeneous parts

• Tipping angle dependent frequency shifts were observed in A-like phase and in B-like phase.

• A-like phase seems to be a robust phase by Fomin• B-lile phase seems to be BW state as in bulk liqui

d