![Page 1: 3 He NMR in Aerogel Yu. Bunkov H. Godfrin E. Collin A.S. Chen D. Cousins R. Harakaly S. Triqueneaux J. Sauls J. Parpia W. Halperin Yu. Mukharskiy V. Dmitriev](https://reader035.vdocuments.us/reader035/viewer/2022070412/56649ecf5503460f94bdc2ba/html5/thumbnails/1.jpg)
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
![Page 2: 3 He NMR in Aerogel Yu. Bunkov H. Godfrin E. Collin A.S. Chen D. Cousins R. Harakaly S. Triqueneaux J. Sauls J. Parpia W. Halperin Yu. Mukharskiy V. Dmitriev](https://reader035.vdocuments.us/reader035/viewer/2022070412/56649ecf5503460f94bdc2ba/html5/thumbnails/2.jpg)
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
![Page 3: 3 He NMR in Aerogel Yu. Bunkov H. Godfrin E. Collin A.S. Chen D. Cousins R. Harakaly S. Triqueneaux J. Sauls J. Parpia W. Halperin Yu. Mukharskiy V. Dmitriev](https://reader035.vdocuments.us/reader035/viewer/2022070412/56649ecf5503460f94bdc2ba/html5/thumbnails/3.jpg)
Experimental setup
vibrating wire
NMR coils
magnetic field
Stycast cells
Ag sinters
B // Cell
Pt powderAerogel
![Page 4: 3 He NMR in Aerogel Yu. Bunkov H. Godfrin E. Collin A.S. Chen D. Cousins R. Harakaly S. Triqueneaux J. Sauls J. Parpia W. Halperin Yu. Mukharskiy V. Dmitriev](https://reader035.vdocuments.us/reader035/viewer/2022070412/56649ecf5503460f94bdc2ba/html5/thumbnails/4.jpg)
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
![Page 5: 3 He NMR in Aerogel Yu. Bunkov H. Godfrin E. Collin A.S. Chen D. Cousins R. Harakaly S. Triqueneaux J. Sauls J. Parpia W. Halperin Yu. Mukharskiy V. Dmitriev](https://reader035.vdocuments.us/reader035/viewer/2022070412/56649ecf5503460f94bdc2ba/html5/thumbnails/5.jpg)
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!
![Page 6: 3 He NMR in Aerogel Yu. Bunkov H. Godfrin E. Collin A.S. Chen D. Cousins R. Harakaly S. Triqueneaux J. Sauls J. Parpia W. Halperin Yu. Mukharskiy V. Dmitriev](https://reader035.vdocuments.us/reader035/viewer/2022070412/56649ecf5503460f94bdc2ba/html5/thumbnails/6.jpg)
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
![Page 7: 3 He NMR in Aerogel Yu. Bunkov H. Godfrin E. Collin A.S. Chen D. Cousins R. Harakaly S. Triqueneaux J. Sauls J. Parpia W. Halperin Yu. Mukharskiy V. Dmitriev](https://reader035.vdocuments.us/reader035/viewer/2022070412/56649ecf5503460f94bdc2ba/html5/thumbnails/7.jpg)
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
![Page 8: 3 He NMR in Aerogel Yu. Bunkov H. Godfrin E. Collin A.S. Chen D. Cousins R. Harakaly S. Triqueneaux J. Sauls J. Parpia W. Halperin Yu. Mukharskiy V. Dmitriev](https://reader035.vdocuments.us/reader035/viewer/2022070412/56649ecf5503460f94bdc2ba/html5/thumbnails/8.jpg)
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
![Page 9: 3 He NMR in Aerogel Yu. Bunkov H. Godfrin E. Collin A.S. Chen D. Cousins R. Harakaly S. Triqueneaux J. Sauls J. Parpia W. Halperin Yu. Mukharskiy V. Dmitriev](https://reader035.vdocuments.us/reader035/viewer/2022070412/56649ecf5503460f94bdc2ba/html5/thumbnails/9.jpg)
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
![Page 10: 3 He NMR in Aerogel Yu. Bunkov H. Godfrin E. Collin A.S. Chen D. Cousins R. Harakaly S. Triqueneaux J. Sauls J. Parpia W. Halperin Yu. Mukharskiy V. Dmitriev](https://reader035.vdocuments.us/reader035/viewer/2022070412/56649ecf5503460f94bdc2ba/html5/thumbnails/10.jpg)
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
![Page 11: 3 He NMR in Aerogel Yu. Bunkov H. Godfrin E. Collin A.S. Chen D. Cousins R. Harakaly S. Triqueneaux J. Sauls J. Parpia W. Halperin Yu. Mukharskiy V. Dmitriev](https://reader035.vdocuments.us/reader035/viewer/2022070412/56649ecf5503460f94bdc2ba/html5/thumbnails/11.jpg)
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.)
![Page 12: 3 He NMR in Aerogel Yu. Bunkov H. Godfrin E. Collin A.S. Chen D. Cousins R. Harakaly S. Triqueneaux J. Sauls J. Parpia W. Halperin Yu. Mukharskiy V. Dmitriev](https://reader035.vdocuments.us/reader035/viewer/2022070412/56649ecf5503460f94bdc2ba/html5/thumbnails/12.jpg)
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
![Page 13: 3 He NMR in Aerogel Yu. Bunkov H. Godfrin E. Collin A.S. Chen D. Cousins R. Harakaly S. Triqueneaux J. Sauls J. Parpia W. Halperin Yu. Mukharskiy V. Dmitriev](https://reader035.vdocuments.us/reader035/viewer/2022070412/56649ecf5503460f94bdc2ba/html5/thumbnails/13.jpg)
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
![Page 14: 3 He NMR in Aerogel Yu. Bunkov H. Godfrin E. Collin A.S. Chen D. Cousins R. Harakaly S. Triqueneaux J. Sauls J. Parpia W. Halperin Yu. Mukharskiy V. Dmitriev](https://reader035.vdocuments.us/reader035/viewer/2022070412/56649ecf5503460f94bdc2ba/html5/thumbnails/14.jpg)
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
![Page 15: 3 He NMR in Aerogel Yu. Bunkov H. Godfrin E. Collin A.S. Chen D. Cousins R. Harakaly S. Triqueneaux J. Sauls J. Parpia W. Halperin Yu. Mukharskiy V. Dmitriev](https://reader035.vdocuments.us/reader035/viewer/2022070412/56649ecf5503460f94bdc2ba/html5/thumbnails/15.jpg)
-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
![Page 16: 3 He NMR in Aerogel Yu. Bunkov H. Godfrin E. Collin A.S. Chen D. Cousins R. Harakaly S. Triqueneaux J. Sauls J. Parpia W. Halperin Yu. Mukharskiy V. Dmitriev](https://reader035.vdocuments.us/reader035/viewer/2022070412/56649ecf5503460f94bdc2ba/html5/thumbnails/16.jpg)
-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
![Page 17: 3 He NMR in Aerogel Yu. Bunkov H. Godfrin E. Collin A.S. Chen D. Cousins R. Harakaly S. Triqueneaux J. Sauls J. Parpia W. Halperin Yu. Mukharskiy V. Dmitriev](https://reader035.vdocuments.us/reader035/viewer/2022070412/56649ecf5503460f94bdc2ba/html5/thumbnails/17.jpg)
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
![Page 18: 3 He NMR in Aerogel Yu. Bunkov H. Godfrin E. Collin A.S. Chen D. Cousins R. Harakaly S. Triqueneaux J. Sauls J. Parpia W. Halperin Yu. Mukharskiy V. Dmitriev](https://reader035.vdocuments.us/reader035/viewer/2022070412/56649ecf5503460f94bdc2ba/html5/thumbnails/18.jpg)
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
![Page 19: 3 He NMR in Aerogel Yu. Bunkov H. Godfrin E. Collin A.S. Chen D. Cousins R. Harakaly S. Triqueneaux J. Sauls J. Parpia W. Halperin Yu. Mukharskiy V. Dmitriev](https://reader035.vdocuments.us/reader035/viewer/2022070412/56649ecf5503460f94bdc2ba/html5/thumbnails/19.jpg)
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
![Page 20: 3 He NMR in Aerogel Yu. Bunkov H. Godfrin E. Collin A.S. Chen D. Cousins R. Harakaly S. Triqueneaux J. Sauls J. Parpia W. Halperin Yu. Mukharskiy V. Dmitriev](https://reader035.vdocuments.us/reader035/viewer/2022070412/56649ecf5503460f94bdc2ba/html5/thumbnails/20.jpg)
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
![Page 21: 3 He NMR in Aerogel Yu. Bunkov H. Godfrin E. Collin A.S. Chen D. Cousins R. Harakaly S. Triqueneaux J. Sauls J. Parpia W. Halperin Yu. Mukharskiy V. Dmitriev](https://reader035.vdocuments.us/reader035/viewer/2022070412/56649ecf5503460f94bdc2ba/html5/thumbnails/21.jpg)
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
![Page 22: 3 He NMR in Aerogel Yu. Bunkov H. Godfrin E. Collin A.S. Chen D. Cousins R. Harakaly S. Triqueneaux J. Sauls J. Parpia W. Halperin Yu. Mukharskiy V. Dmitriev](https://reader035.vdocuments.us/reader035/viewer/2022070412/56649ecf5503460f94bdc2ba/html5/thumbnails/22.jpg)
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
.)
![Page 23: 3 He NMR in Aerogel Yu. Bunkov H. Godfrin E. Collin A.S. Chen D. Cousins R. Harakaly S. Triqueneaux J. Sauls J. Parpia W. Halperin Yu. Mukharskiy V. Dmitriev](https://reader035.vdocuments.us/reader035/viewer/2022070412/56649ecf5503460f94bdc2ba/html5/thumbnails/23.jpg)
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
![Page 24: 3 He NMR in Aerogel Yu. Bunkov H. Godfrin E. Collin A.S. Chen D. Cousins R. Harakaly S. Triqueneaux J. Sauls J. Parpia W. Halperin Yu. Mukharskiy V. Dmitriev](https://reader035.vdocuments.us/reader035/viewer/2022070412/56649ecf5503460f94bdc2ba/html5/thumbnails/24.jpg)
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…
![Page 25: 3 He NMR in Aerogel Yu. Bunkov H. Godfrin E. Collin A.S. Chen D. Cousins R. Harakaly S. Triqueneaux J. Sauls J. Parpia W. Halperin Yu. Mukharskiy V. Dmitriev](https://reader035.vdocuments.us/reader035/viewer/2022070412/56649ecf5503460f94bdc2ba/html5/thumbnails/25.jpg)
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…
![Page 26: 3 He NMR in Aerogel Yu. Bunkov H. Godfrin E. Collin A.S. Chen D. Cousins R. Harakaly S. Triqueneaux J. Sauls J. Parpia W. Halperin Yu. Mukharskiy V. Dmitriev](https://reader035.vdocuments.us/reader035/viewer/2022070412/56649ecf5503460f94bdc2ba/html5/thumbnails/26.jpg)
-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
![Page 27: 3 He NMR in Aerogel Yu. Bunkov H. Godfrin E. Collin A.S. Chen D. Cousins R. Harakaly S. Triqueneaux J. Sauls J. Parpia W. Halperin Yu. Mukharskiy V. Dmitriev](https://reader035.vdocuments.us/reader035/viewer/2022070412/56649ecf5503460f94bdc2ba/html5/thumbnails/27.jpg)
-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?
![Page 28: 3 He NMR in Aerogel Yu. Bunkov H. Godfrin E. Collin A.S. Chen D. Cousins R. Harakaly S. Triqueneaux J. Sauls J. Parpia W. Halperin Yu. Mukharskiy V. Dmitriev](https://reader035.vdocuments.us/reader035/viewer/2022070412/56649ecf5503460f94bdc2ba/html5/thumbnails/28.jpg)
-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
![Page 29: 3 He NMR in Aerogel Yu. Bunkov H. Godfrin E. Collin A.S. Chen D. Cousins R. Harakaly S. Triqueneaux J. Sauls J. Parpia W. Halperin Yu. Mukharskiy V. Dmitriev](https://reader035.vdocuments.us/reader035/viewer/2022070412/56649ecf5503460f94bdc2ba/html5/thumbnails/29.jpg)
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
![Page 30: 3 He NMR in Aerogel Yu. Bunkov H. Godfrin E. Collin A.S. Chen D. Cousins R. Harakaly S. Triqueneaux J. Sauls J. Parpia W. Halperin Yu. Mukharskiy V. Dmitriev](https://reader035.vdocuments.us/reader035/viewer/2022070412/56649ecf5503460f94bdc2ba/html5/thumbnails/30.jpg)
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
![Page 31: 3 He NMR in Aerogel Yu. Bunkov H. Godfrin E. Collin A.S. Chen D. Cousins R. Harakaly S. Triqueneaux J. Sauls J. Parpia W. Halperin Yu. Mukharskiy V. Dmitriev](https://reader035.vdocuments.us/reader035/viewer/2022070412/56649ecf5503460f94bdc2ba/html5/thumbnails/31.jpg)
3He NMR in Aerogel
Lots of questions…
![Page 32: 3 He NMR in Aerogel Yu. Bunkov H. Godfrin E. Collin A.S. Chen D. Cousins R. Harakaly S. Triqueneaux J. Sauls J. Parpia W. Halperin Yu. Mukharskiy V. Dmitriev](https://reader035.vdocuments.us/reader035/viewer/2022070412/56649ecf5503460f94bdc2ba/html5/thumbnails/32.jpg)
Additional slides
![Page 33: 3 He NMR in Aerogel Yu. Bunkov H. Godfrin E. Collin A.S. Chen D. Cousins R. Harakaly S. Triqueneaux J. Sauls J. Parpia W. Halperin Yu. Mukharskiy V. Dmitriev](https://reader035.vdocuments.us/reader035/viewer/2022070412/56649ecf5503460f94bdc2ba/html5/thumbnails/33.jpg)
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
![Page 34: 3 He NMR in Aerogel Yu. Bunkov H. Godfrin E. Collin A.S. Chen D. Cousins R. Harakaly S. Triqueneaux J. Sauls J. Parpia W. Halperin Yu. Mukharskiy V. Dmitriev](https://reader035.vdocuments.us/reader035/viewer/2022070412/56649ecf5503460f94bdc2ba/html5/thumbnails/34.jpg)
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
![Page 35: 3 He NMR in Aerogel Yu. Bunkov H. Godfrin E. Collin A.S. Chen D. Cousins R. Harakaly S. Triqueneaux J. Sauls J. Parpia W. Halperin Yu. Mukharskiy V. Dmitriev](https://reader035.vdocuments.us/reader035/viewer/2022070412/56649ecf5503460f94bdc2ba/html5/thumbnails/35.jpg)
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
![Page 36: 3 He NMR in Aerogel Yu. Bunkov H. Godfrin E. Collin A.S. Chen D. Cousins R. Harakaly S. Triqueneaux J. Sauls J. Parpia W. Halperin Yu. Mukharskiy V. Dmitriev](https://reader035.vdocuments.us/reader035/viewer/2022070412/56649ecf5503460f94bdc2ba/html5/thumbnails/36.jpg)
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
![Page 37: 3 He NMR in Aerogel Yu. Bunkov H. Godfrin E. Collin A.S. Chen D. Cousins R. Harakaly S. Triqueneaux J. Sauls J. Parpia W. Halperin Yu. Mukharskiy V. Dmitriev](https://reader035.vdocuments.us/reader035/viewer/2022070412/56649ecf5503460f94bdc2ba/html5/thumbnails/37.jpg)
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
![Page 38: 3 He NMR in Aerogel Yu. Bunkov H. Godfrin E. Collin A.S. Chen D. Cousins R. Harakaly S. Triqueneaux J. Sauls J. Parpia W. Halperin Yu. Mukharskiy V. Dmitriev](https://reader035.vdocuments.us/reader035/viewer/2022070412/56649ecf5503460f94bdc2ba/html5/thumbnails/38.jpg)
-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 ?