3He NMR in Aerogel

Yu. BunkovH. GodfrinE. Collin

A.S. ChenD. CousinsR. HarakalyS. Triqueneaux

J. SaulsJ. ParpiaW. HalperinYu. Mukharskiy V. Dmitriev

Chamrousse, 17-22 December 2004

Phase diagram

“similar” 98 % samplesaverage geometric mfp la ~ 200 nmstructure correlation a

0

5

10

15

20

25

30

35

0 0.5 1 1.5 2 2.5 3

Gervais et al.Haard et al.Matsumoto et al.Our results

T (mK)

Our measures: NMR on three samples from N. Mulders

kF ~ 1 Å << la, one expects:no effect on Landau parameters

restriction of mean free path

“confined” Fermi liquid

“B-like” superfluid

?

supercooled“A-like”

?

plus:adsorbed disordered 2D solid

HISM and IISM modelsParameters l, a

zero field measure

P (

bar) la ~ 0 of the p-wave pairs

suppression of Tc

Experimental setup

vibrating wire

NMR coils

magnetic field

Stycast cells

Ag sinters

B // Cell

Pt powderAerogel

Magnetisation

M(P,T) = Cn nsolid(P) Msolid(T) + nliquid(P) Mliquid(T)

Msolid(T) = 1 / (T-W)

17.5 barlow fields, low powersintegrated NMR line

10-4

10-3

10-2

10-1

0.1 1 10 100 1000T (mK)

M (

a.u.

)

Tc,a

Tc,b

W effective ferromagnetic interaction

160

200

240

280

320

0 5 10 15 20 25 30P (bar)

Fermi liquid magnetisation

effectively: no change in the Landau parameters

BulkAerogel

TF**

(m

K)

New measures of TF**: 10 % smaller than in textbooks!

Solid contribution

2 10-3

3 10-3

4 10-3

5 10-36 10-37 10-38 10-39 10-310-2

1 10

5.20 bar

8.10 bar

12.1 bar

17.0 bar

21.0 bar

24.8 bar

29.5 bar

T (mK)40

M (

a.u

.)

1.5

2

2.5

3

3.5

0 5 10 15 20 25 30 35

P (bar)

0.070.080.090.1

0.2

0.3

0.4

0.5

0 5 10 15 20 25 30 35P (bar)

W (

mK

)S

olid

3H

e (

in %

of

liqu

id a

t 0

ba

r)

fit from Tc,b to the highest temperature

densification in the disordered solid

~ 1.5 layers

~ 3 layers

from BET surface

similar to fluorocarbon, Schuhl, Maegawa, Meisel, Chapellier, Phys. Rev. B 1987

Removing the 3He solid

2 10-3

4 10-3

6 10-3

8 10-3

10-2

1 10T (mK)

50

17.5 bar

M (

a.u.

)

0

0.08

0.16

0.24

0 20 40 60 80 100 120

Solid 3He (%)

W (

mK

)adding 4He removes the localised 3He atoms:allows to study the confined liquid properties alone

Transport properties

without solid 3Hespin diffusion D measurement (pulsed NMR, 34 mT)

-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

0 0.5 1 1.5 2 2.5 3 3.5 4

18.85 mK

33.00 mK

42.60 mK

05.05 mK

07.00 mK

10.05 mK

54.20 mK

70.20 mK

86.50 mK

90.00 mK

01.35 mK

A3

0.5 bar, Gz = 0.25 Gauss/cm

ln(H

/H0)

A = 2/3 D ( Gz)2

Spin diffusion

l = 130 nm for both fits HISM; consistent with other measuresless good at 30 bars… correlations of the aerogel structure ?

T (mK)

D

(cm

2 /s)

0.5 bar29.5 bar

specific heat Choi, Yawata, Haard, Davis, Gervais, Mulders, Sharma, Sauls, Halperin, PRL 2004thermal conductivity Fisher, Guénault, Hale, Pickett, JLTP 2001

from Sauls, Bunkov, Collin,Godfrin, Sharma,accepted inPhys. Rev B 2004

T-2

0 100

2 10-3

4 10-3

6 10-3

8 10-3

1 10-2

1.2 10-2

1 10 100T (mK)

Solid-liquid interactionnormal state

Wid

th (

mT

)12 bar, 37 mTpure 3He

inhomogeneous width ~ bliquid

dense solid layer ~ bsolid

fast exchange: < b > = Mliquid bliquid + Msolid bsolid

< b > = Mliquid bliquid + Msolid bsolid

Mliquid + Msolid Mliquid + Msolid

Mliquid + Msolid Mliquid + Msolid

~ bLarmor

bsolid ~ 1/T2,solid > bliquid

similar toHammel, Richardson, PRL 1984

Solid-liquid interactionnormal state

fast exchange: < b > = Mliquid bliquid + Msolid bsolid

Mliquid + Msolid Mliquid + Msolid

2 10-3

4 10-3

6 10-38 10-3

10-2

1 10T (mK)

50 2 10-3

4 10-3

6 10-3

8 10-310-2

1 10T (mK)

50

Wid

th (

mT

)

17 bar, 37 mT, various amounts of 4He

M

(a.

u.)

0 100

2 10-3

4 10-3

6 10-3

8 10-3

1 10-2

1.2 10-2

5 10 15 20 25 30P (bar)

0 100

2 10-3

4 10-3

6 10-3

8 10-3

1 10-2

1.2 10-2

0 20 40 60 80 100% of solid left

Solid-liquid interactionnormal state

17 bar

Sol

id W

idth

(m

T)

Wid

th (

mT

)

stronglylocalisedatoms

Inh. width

fast exchange: < b > = Mliquid bliquid + Msolid bsolid

Mliquid + Msolid Mliquid + Msolid

37 mT

Line shapesnormal state

0 100

2 10-3

4 10-3

6 10-3

8 10-3

1 10-2

1.2 10-2

1 10 100T (mK)

W

idth

(m

T)

12 bar, pure 3He

17 bar, 4He

37 mT

Line shapesnormal state

0 100

2 10-3

4 10-3

6 10-3

8 10-3

1 10-2

1.2 10-2

1 10 100T (mK)

W

idth

(m

T)

12 bar, pure 3He

17 bar, 4He

-2.5

-2

-1.5

-1

-0.5

0

0.5

-0.015 -0.01 -0.005 0 0.005 0.01 0.015Field (mT)

Abs

orp

tion

(a.u

.)

4.1 mK, no 3He solid: Gaussian

37 mT

-2

-1

0

1

2

3

-0.015 -0.01 -0.005 0 0.005 0.01 0.015Field (mT)

Line shapesnormal state

0 100

2 10-3

4 10-3

6 10-3

8 10-3

1 10-2

1.2 10-2

1 10 100T (mK)

W

idth

(m

T)

12 bar, pure 3He

17 bar, 4HeAbs

orp

tion

(a.u

.)

100 mK, 3He solid: Gaussian

37 mT

-3

-2

-1

0

1

2

3

-0.03 -0.02 -0.01 0 0.01 0.02 0.03Field (mT)

Line shapesnormal state

0 100

2 10-3

4 10-3

6 10-3

8 10-3

1 10-2

1.2 10-2

1 10 100T (mK)

W

idth

(m

T)

12 bar, pure 3He

17 bar, 4HeAbs

orp

tion

(a.u

.)

4.1 mK, 3He solid: Lorentzian!

37 mT

Line shapesnormal state

from Lorentzian to Gaussian line shapes

37 mT

0.4

0.5

0.6

0.7

0.80.9

1

2

1 10 100

T (mK)

Sha

pe f

acto

r

12 bar, pure 3He

17 bar, 4He

Gaussian

summ of independent lines

Shape factor = Second Moment

Full Width Half Height

fast exchange…need a fastexchangemodel for the full line

Between Tc,b and Tc,a

0

5

10

15

20

25

30

35

0 0.5 1 1.5 2 2.5 3

Gervais et al.Haard et al.Matsumoto et al.Our results

T (mK)

“confined” Fermi liquid

“B-like” superfluid

?

supercooled“A-like”

?

zero field measureP

(ba

r)

Yuriy’s talk

Superfluid state

position of the peak shifts:well defined transition (~50 K)

-1 10-2

-8 10-3

-6 10-3

-4 10-3

-2 10-3

0 100

2 10-3

1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2T (mK)

Po

sitio

n (

mT

)25 bar, 37 mTPure 3He

Tc,a

Superfluid state

position of the peak shifts:well defined transition (~50 K)

A phase like supercooling

-1 10-2

-8 10-3

-6 10-3

-4 10-3

-2 10-3

0 100

2 10-3

1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2T (mK)

Po

sitio

n (

mT

)25 bar, 37 mTPure 3He

Tc,a

first studied byBarker, Lee, Polukhina,Osheroff, Hrubesh, Poco, PRL 2000

Superfluid state

Consistent with other measures:same l as for spin diffusion

a = 0 nm a = 40 nm a = 44 nm

8 % solid 3He100 % solid 3He0 % solid 3He

Magnetisation

similar to Sprague, Haard, Kycia,Rand, Lee, Hamot, Halperin, PRL 1995, Barker, Lee, Polukhina, Osheroff, Hrubesh, Poco, PRL 2000

l = 130 nm P = 17 bar l = 130 nm

P = 29.5 bar

from Sauls, Bunkov, Collin,Godfrin, Sharma,accepted inPhys. Rev B 2004

0

0.4

0.8

1.2

1.6

2

-0.12 -0.08 -0.04 0 0.04Field (mT)

Superfluid stateFrequency shift

With 4He

1.2 mK

1.4 mK

1.5 mK

1.6 mK

1.8 mK

bLarmor17 bar, 37 mT

A

bsor

ptio

n (a

.u.)

1.94

1.95

1.96

1.97

1.98

1.99

-0.2 -0.1 0 0.1Field (mT)

Abs

orp

tion

(a.u

.)

0

5 109

1 1010

1.5 1010

0.6 0.7 0.8 0.9 1T/T

c,a

Superfluid state

B 2 2

B

Frequency shiftWith 4He

Edge = B,aero

F(A]Edge) + Larmor 2

2 Larmor

and take F(A]Edge) ~ 0.80 (similar to « flared-out »)

B

,Aer

o2 (H

z2 )

29.5 bar17.5 bar

19.5 bar Dmitriev, Fomin,JLTP 2004

(scaled for the Tc,a’s)

consistent withTc suppression

Superfluid stateFrequency shift

With 4He

Edge = B,aero

F(A]Edge) + Larmor 2

2 Larmor

and

29.5 bar17.5 bar

0

0.2

0.4

0.6

0.8

1

0.6 0.7 0.8 0.9 1

T/Tc,a

= B,aero < F(A) > + Larmor

2

2 Larmor

< F

(A

) >

/ F

(A

] Edg

e)

same texture forboth pressures…

Superfluid state

assumtions: • average position computed from fast exchange expression• edge shift taken from the interpolation of 17 bar and 29 bar

29.5 bar17.5 bar

0

0.2

0.4

0.6

0.8

1

0.6 0.7 0.8 0.9 1

T/Tc,a

< F

(A

) >

/ F

(A

] Edg

e)

24.5 bar, pure 3He

Frequency shiftWith 4He, compared to pure 3He

4He

again same texture with/without 4He…

-7 10-3

-6 10-3

-5 10-3

-4 10-3

-3 10-3

-2 10-3

-1 10-3

0 100

1 10-3

0.7 0.8 0.9 1T/T

c,a

Superfluid stateBut…

Pos

ition

(m

T f

or 3

7 m

T)

us: 17 bar

E2E3E4

Haard et al. 2001

Northwestern: 18 barB ┴ Cell

B // Cell

SAME Tc,a

if the same surface, then ….different textures…. Anisotropy?

bLarmor

-1.2 10-2

-1 10-2

-8 10-3

-6 10-3

-4 10-3

-2 10-3

0 100

0.2 0.4 0.6 0.8 1T/T

c,a

Superfluid stateLower and lower with the temperature

24.5 bar, 37 mT, pure 3He

Pos

ition

(m

T)

bLarmor

?0

0.2

0.4

0.6

0.8

1

0 0.5 1T/T

c,a<

F(A

)

> /

F(A

] E

dg

e)

Texture?

-1.2 10-2

-1 10-2

-8 10-3

-6 10-3

-4 10-3

-2 10-3

0 100

0.2 0.4 0.6 0.8 1T/T

c,a

Superfluid stateLower and lower with the temperature

24.5 bar, 37 mTpure 3He

Pos

ition

(m

T)

bLarmor

linear down

linear up

constant

Superfluid stateLower and lower with the temperature

24.5 bar, 37 mTpure 3He

-70

-60

-50

-40

-30

-20

-10

0

10

-0.06 -0.04 -0.02 0 0.02 0.04

Field (mT)

-25

-20

-15

-10

-5

0

5

-0.15 -0.1 -0.05 0 0.05 0.1

Field (mT)

17.5 bar, 37 mTwith 4He

A

bsor

ptio

n (a

.u.)

A

bsor

ptio

n (a

.u.)

redistribution of the spectral weight

3peaks

3peaks

bLarmorbLarmor

1.2 mKT/Tc,a ~0.6

0.5 mKT/Tc,a ~0.25

Superfluid stateLower and lower with the temperature

0

0.2

0.4

0.6

0.8

1

0.2 0.4 0.6 0.8 1

T/Tc,a

24.5 bar, pure 3He

assumtions: • solid still described by Curie-Weiss law • fast exchange solid/liquid• B phase like superfluid

< F

(A

) >

/ F

(A

] Edg

e)

?

sudden reorientation of the texture n ┴ B state?

stable texture for B phase in Aerogel n ┴ B,Fomin, to be published

3He NMR in Aerogel

Lots of questions…

Additional slides

Between Tc,b and Tc,a

-0.5

0

0.5

1

1.5

2

2.5

-0.3 -0.2 -0.1 0 0.1Field (mT)

Abs

orp

tion

(a.u

.)

17.5 bar, no solid, 37 mT, 1.8 mK

-1

-0.5

0

0.5

1

1.5

2

2.5

-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2

Field (mT)

Abs

orp

tion

(a.u

.)

29.5 bar, no solid, 37 mT, 1.8 mK

7

7.2

7.4

7.6

7.8

8

8.2

8.4

8.6

-0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04

Field (mT)

Abs

orp

tion

(a.u

.)

29.5 bar, no solid, 37 mT, 2.2 mK

Satellite peaks

1,7 10-3

1,8 10-3

1,9 10-3

2 10-3

2,1 10-3

2,2 10-3

2,3 10-3

2,4 10-3

2,5 10-3

2 3 4 5 6

T (mK)

2 10-3

2.2 10-3

2.4 10-3

2.6 10-3

2.8 10-3

3 10-3

3.2 10-3

2 3 4 5

T (mK)

M (

a.u

.)

M (

a.u

.)

17 bar, 37 mT 29.5 bar, 37 mT

17 % 17 %

main NMR signal: 17 % reduction!which goes partially or totally to the measured satellite peaks

no 3He solid

21 % 3He solid left

8 % 3He solid left

pure 3He

Tc,b Tc,b

Tc,a Tc,a

0

0.05

0.1

0.15

0.2

0.4 0.5 0.6 0.7 0.8 0.9 1 1.1

T/Tc,b

Satellite peaks

0

0.05

0.1

0.15

0.2

0.25

0.4 0.5 0.6 0.7 0.8 0.9 1 1.1

T/Tc,b

Msa

t/Mn

29.5 bar, 37 mT

8 % 3He solid left

pure 3He

Msa

t/Mn

17.5 bar, 37 mT

no 3He solid left

73 % 3He solid left

similar, BUT different, on two « identical » samples…

similar sample studied in Bunkov et al., PRL 2000

0

5 109

1 1010

1.5 1010

2 1010

2.5 1010

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

T/Tc,b

Satellite peaks

B2

(Hz2 )

5.4 bar, 34 mT

sample E2

sample E4

fit to bulk-B phase, scaled by 0.6

F(A) ~ 0.6 topological defects ?Peak

= B F(A) + Larmor 2

2 Larmor

2 10-3

4 10-3

6 10-3

8 10-3

1 10-2

1.2 10-2

1.4 10-2

1 10T (mK)

Main NMR line

2 10-3

3 10-3

4 10-3

5 10-36 10-37 10-38 10-39 10-310-2

2 10-2

1 10T (mK)

W

idth

(m

T)

M

(a.

u.)

satellite(s)

Tc,bTc,b

?

8.3 bar, 37 mT

-1.4 101

-1.2 101

-1 101

-8 100

-6 100

-4 100

-2 100

0 100

2 100

-0.03 -0.02 -0.01 0 0.01 0.02 0.03Field (mT)

2 10-3

4 10-3

6 10-3

8 10-3

1 10-2

1.2 10-2

1.4 10-2

1 10T (mK)

Main NMR line

8.3 bar, 37 mT

W

idth

(m

T)

Tc,b

A

bsor

ptio

n (a

.u.)

1 mK, 2 mK, scaled to NMR line area

what is the state of the fluid/solid system between Tc,b and Tc,a ?