outline ( mid 90’s to now)
DESCRIPTION
Initial goal: 70’s: Search for « macroscopic » quantum tunneling in magnetism Measurements on « narrow domain walls », ensemble of nanoparticles…. Nanomagnetism: From Classical to Quantum Nano-particles, atomic clusters, molecules, ions . _________. Outline ( Mid 90’s to now) - PowerPoint PPT PresentationTRANSCRIPT
Initial goal:70’s: Search for « macroscopic » quantum tunneling in magnetism
Measurements on « narrow domain walls », ensemble of nanoparticles…
Outline (Mid 90’s to now)
Single-particles measurements Classical dynamics, phonons bath… quantum effects ?...
Tunneling of ensembles of large spins molecules (Mn12-ac).Slow quantum dynamics and transition to classical dynamicsSome effects of the spin bath (tunneling and decoherence).
Case of a large molecule with spins ½ (V15)A gapped spin 1/2 molecule, phonons bath
Extension to Rare-Earth ions
Role of strong hyperfine coupling, electro-nuclear entanglement,From slow to fast quantum dynamics: towards a new type of spins qubits
Nanomagnetism: From Classical to QuantumNano-particles, atomic clusters, molecules, ions.
_________
Collaborations (Louis Néel lab)
S. Bertaina (Post-doc, LLN)
R. Giraud (LPN), I. Chiorescu (FSU),
E. Bonet (LLN), W. Wernsdorfer (LLN),
L. Thomas (IBM)
Other Collaborations
D. Mailly (LPN), A. Benoit (CRTBT)
S. Gambarelli (DRF-Grenoble), A. Stepanov (Marseille)
B. Malkin, M. Vanyunin (Kazan)
H. Pascard (Palaiseau), A.M. Tkachuk (St Petersbourg), H. Suzuki (Tsukuba),
D. Gatteschi (Florence), G. Cristou (FSU) , A. Müller (Bielefeld)
Tupitsyn, Stamp and Prokof’ev
Micro-SQUID magnetometry
particle
Josephson junctions
stray field
≈ 1 µmM - M
H ~ Hsw
I ~ Ic
M
Large dB/dt
• Fabricated by electron beam lithography(D. Mailly, LPM, Paris)
• Sensivity ~ 10-4 0, 10-18 emu, 102 B
Superconducting Normal
W. Wernsdorfer, K. Hasselbach, D. Mailly, B. Barbara, A. Benoit, L.Thomas, JMMM, 145, 33 (1995).
Particles from micrometers to 100 nanometers Obtained by: Lithography, Electro-deposition
Measurements: Micro-Squids
100 nm
50 nm x 1m
1m x 2 m
Small ellipse Large ellipseNanowire
-1
0
1
-40 -20 0 20 40M
/M
S
H(mT)
MULTI – DOMAIN: nucleation, pinning,
propagation and annihilation of domain
walls
-1
0
1
-100 0 100
M/M
S
H(mT)
SINGLE - DOMAINSingle Nucleation
Curling
2(dH/dt,T)
<Hsw(dH/dt,T)>counts
H
0
0.5
1
0°
30°
60°90°
120°
-150°
-120°-90°
-60°
-30°
hn
S < 1
S = 1.3
S = 1.6
S = 2
S = 3
S = 6
0
0.5
1
0°
30°
60°90°
120°
-150°
-120°-90°
-60°
-30°
hsw
S < 1
S = 1.4
S = 2.4
Evidence of the « curling mode » (nanowires)
Frei, Shtrikman, D. Treves et A. Aharoni, 1957
Evidence of the 2-D Stoner-Wohlfarth astroidPhil. Trans. R. Soc.,240, 599 (1948)
5 nm 0
50
100
150
200
250
0°
30°
60°90°
120°
210°
240°270°
300°
330°
oH
sw(m
T)
FeS, filled nanotubleN. Demoncy, H. Pascard, A. Loiseau
W. Wernsforfer, E. Bonet, B. Barbara,N. Demoncy, H. Pascard, A. Loiseau,
JAP, 81, 5543 (1997).
Observation of 3D Stoner-Wohlfarth astroidand origin of the magnetic anisotropy
Josephson junctions
Co clusters (3 nm)
Interface anisotropy
M. Jamet et al, J. Magn.Magn.Mat. 237, 293-301 (2001); PRL, 86, 10 (2001) 281.
clusters
Co (20 nm) and BaFeO (10 nm)
Shape anistropy + Surface anisotropy
E. Bonet, W. Wernsdorfer, B. Barbara, A. Benoit, D. Mailly, A. Thiaville, PRL, 83, 20, 4188 (1999).
Temperature dependence of the switching fields of a 3nm Co cluster
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
-0.3 -0.2 -0.1 0 0.1 0.2 0.3
0H
z (
T)
0Hy (T)
0.04 K
1 K2 K
4 K8 K
12 K
TB 14 K ∆t ≈ 1 s
Effect of a transverse field close to the anisotropy field: Telegraph noise
-200
-100
0
100
200
-400 -300 -200 -100 0 100 200 300 400
oH
x(m
T)
oHy(mT)
Hy = const.
0 10 20 30 40 50 60 70t(s)
0.2 K
0.25 K
0.3 K
µoHy = 430.7 mT
106 spins
- W. Wernsdorfer, E. Bonet, K. Hasselbach, A. Benoit, B. Barbara, N. Demoncy, A. Loiseau, H. Pascard, D. Mailly, Phys. R.ev. Lett., 78, 1791 (1997) - B. Barbara et al, Proc. Mat. Res. Symp. 475, 265 (1997); Lecture Notes in Physics (2001) http://www.springer.de
Single phonons shots
Reversal
up, down, up…
2
H sw
p(H)
0
0.4
0.8
1.2
-45° 0° 45° 90° 135°
E( )
h > 0
T ° 0 K
²E kT
activation thermique
Néel-Brown model
M ~ (Min- Meq)e-t/eq
t
0e-E0(1-H/H0)3/2/kT
HMP ~ H0 [1 – (kT/E0)
2/3.(ln(/ 0vH))2/3]H(t)~ (2H0/3)(kT/E0)2/3.(ln(0T/ vH))
-1/3
- J. Kurkijärvi, PRB 6, 832 (1972)- L. Gunther and B. Barbara, PRB 49, 3926 (1994)
H
M
Hsw
Two types of measurements
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
-300 -200 -100 0 100 200 300
Flux()
H(mT)
A
AB
B
0
20
40
60
80
100
no
mb
re
HSW
2
Switching field Measurements of
the 20 nm Co particle
One switch
20nm Co particle embeeded in Carbone
-W. Wernsdorfer, E. Bonet, K. Hasselbach, A. Benoit, B. Barbara, N. Demoncy, A. Loiseau, H. Pascard, D. Mailly, Phys. Rev. Lett., 78, 1791 (1997).- B. Barbara, W. Wernsdorfer, E. Bonet, K. Hasselbach, D. Mailly, A. Benoit, M.P. Pileni, Proc. Mat. Res. Symp. 475, 265 (1997).
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
-300 -200 -100 0 100 200 300
Flux()
H(mT)
A
AB
B
0
0.2
0.4
0.6
0.8
1
0.1 1 10
T = 4 K
P(t)
t(s)
141.953 mT= 6.1 s
141.922 mT= 33.8 s
141.983 mT= 1.7 s
142
142.2
142.4
142.6
142.8
143
0 5 10 15 20[Tln(105T/(v 1/2 ))] 2/3
0.14K
2K
0.9K
1.5K
3K
H
sw
(mT
)
5K
4K
Most probable switching field Exponential relaxation and Arrhenius law
E0 ≈ 2.2 10 5 K ≈ (20 nm)3
0 ~ 4 10-9 s
D. MaillyN. Demoncy, A. Loiseau, H. Pascard
Hysteresis measurements of ferromagnetic nanoparticles made by the micro-Squid technique (last decade)Obtained by: Lithography, Electro-deposition, Arc discharge, LECBD
100 nm50 nm x 1m1m x 2 m
-1
0
1
-40 -20 0 20 40
M/M
S
H(mT)
-1
0
1
-100 0 100
M/M
S
H(mT)
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
-300 -200 -100 0 100 200 300
Flux()
H(mT)
A
AB
B
20 nm
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
-150 -100 -50 0 50 100 150
Flux()
H(mT)
Hw
0
0.2
0.4
0.6
0.8
1
0.01 0.1 1 10
T = 0.13 K
P(t)
t(s)
64.22 mT= 5.4 s
= 0.64
64.34 mT= 1.0 s
= 0.67
64.09 mT= 21.8 s
= 0.6
0
0.2
0.4
0.6
0.8
1
0.01 0.1 1 10
T = 6 K
P(t)
t(s)
62.38 mT= 0.97 s
= 1.69
62.51 mT= 0.24 s
= 1.67 62.25 mT= 8.6 s
= 1.62
62.12 mT= 40.7 s
= 1.32
Waiting time measurements
Non-exponential single particle relaxation:
Low T: < 1 Nucleation-creep Propagation (surface)
High T: > 1 Nucleation-coalescence
Macroscopic Quantum Tunneling of 105 B ?
Easy axis
Barium ferrite Insulating ferri. nanoparticle (10 nm)
3D - astroid
W. Wernsdorfer, E. Bonet, K. Hasselbach, A. Benoit, D. Mailly, O. Kubo, H. Nakano, and B. Barbara, PRL, 79, 4014, (1997)
0
0.02
0.04
0.06
0.08
0 0.5 1 1.5 2 2.5 3
Hy=250mT
Hy=180mT
Hy=0mT
particle II
T(K)
odH/dt = 10 mT
(mT)
263
263.2
263.4
263.6
263.8
264
264.2
0 2 4 6 8 10[Tln(2*10 6T/(v 1/2 ))] 2/3
0.13K 0.3K
0.5K
H
sw
(mT
)1.3K
0.9K
= 79°
0.2K
0.13-0.3K
0.5K
1.3K
0.9KT = T*
0
50
100
150
200
250
300
50 50.1 50.2 50.3 50.4 50.5 50.6
cou
nts
µoHsw(mT)
2 K1.3 K
0.9 K
0.5 K
0.15 K
N = 2000
0.2
0.4
0.6
0.8
1
1.2
0° 15° 30° 45° 60° 75° 90°
Tc(
)/T
c(4
5°)
angle
Tc=0.31 K
Teff
T
Tc() 0Ha 1/4 cot 1/ 61 cot 2/3 1
E. Chudnovsky, PRB 54, 389 (1996)
Quantum description
W. Wernsdorfer, E. Bonet, K. Hasselbach, A. Benoit, D. Mailly, O. Kubo, H. Nakano, and B. Barbara, PRL, 79, 4014, (1997)
Hy=250 mT
Hy=180 mT
Hy= 0 mT
Bigger particle
Nanometer scale
NanoparticleCluster
20 nm3 nm1 nm 2 nm
Magnetic ProteinSingle Molecule
50S = 10 103 106
Single Molecule Magnets
The molecules are regularly arranged in the crystal
Tunneling of Magnetization in Mn12-ac, S=10
-1
-0,5
0
0,5
1
-3 -2 -1 0 1 2 3
1.5K
1.6K
1.9K
2.4K
M/M
S
BL (T)
Thomas et al Nature (1996); Friedman et al, PRL (1996). Barbara et al (ICM’94)
NATO ASI workshop QTM’94 Chichilianne and Grenoble (B.Barbara, L.Gunther, N.Garcia, A. Leggett).
…….
…. Slow quantum dynamics of molecule magnets spins ….
Resonances at Hn= nD/gB= 450.n mT
102
104
106
-2 -1 0
(s
ec)
H (T)
(sec
)
T(K)103
105
2 3
0 T0.44 T0.6 T0.88 T1.32 T1.76 T2.2 T2.64 T
Magnetic relaxation
Mn(IV)S=3/2
Mn(III)S=2
Total Spin =10
Mn12acetateMn12acetate
fig2
Magnetization of a single crystal of Mn12-ac
Tupitsyn and Barbara, review, Wiley-VCH (2001)
DH= 108 21
Barrier in zero field (symmetrical)H= - DSz
2 - BSz4 - E(S+
2 + S-2) - C(S+
4 + S-4)
spin down spin up
|S,S-2> |S,-S+2>
Ground state tunneling
|S,S-1> |S,-S+1>
|S,S> |S,-S>
SZ
En
erg
y
en
erg
y
magnetic field
²
| S, -m >
| S, m-n >
1 P
1 - P
| S, -m >
| S, m-n >
H // -M
New resonances at gBHn = nD (B=0)
Thermally activated tunneling
Landau-Zener transition at avoided level crossing
(single molecule)
Tunneling probability:
P=1 – exp[-(/ħ)2/c]
c = dH/dt
Coexistence of tunneling and hysteresis
From a single molecule to an ensemble of molecules at T ~0 : Both tunneling rate and decoherence increase
ener
gy
magnetic field
²
| S, -m >
| S, m-n >
1 P
1 - P
| S, -m >
| S, m-n >
LZ probability:PLZ = 1 – exp[-(/ħ)2/c] ~ 2/c
Spin-bath (Prokofiev and Stamp):
PSB ~ (2/0)e-││/0
.n(ED) >> PLZ
0= hyperfine energy = tunnel window
Large spins Mesoscopic tunneling (slow)
Nuclear spins Observation possible Strong decoherence.
H= - DSz2 - BSz
4 - E(S+2 + S-
2) - C(S+4 + S-
4) - gBSzHz