3 he nmr in aerogel yu. bunkov h. godfrin e. collin a.s. chen d. cousins r. harakaly s. triqueneaux...
TRANSCRIPT
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 ?