Voyage dans le nanomonde des aimants
Wolfgang WernsdorferLaboratoire de
Magnétisme Louis NéelC.N.R.S. - Grenoble
S = 102 to 106 S = 1/2 to ≈ 30
10-910-610-3100103106
Magnets
1 nm1 mm1 mm1 m1 km1 Mm
nanoworld
Magnetic structures
S = 1020
1010
108 10
6 10
5 10
4 10
3 10
2 10 1
clusters atomsmolecularclustersnanoparticlesmicron
particlespermanentmagnets
macroscopic atomic
multi - domains
1 mm
single - domains
20 nm 3 nm
spins
1 nm
Magnetization reversal in magnetic structures
S = 1020
1010
108 10
6 10
5 10
4 10
3 10
2 10 1
clusters atomsmolecularclustersnanoparticlesmicron
particlespermanentmagnets
single - domains spins
macroscopic atomic
-1
0
1
-40 -20 0 20 40
M/M
S
µ0H(mT)
nucleation, propagation andannihilation of domain walls
-1
0
1
-1 0 1M/M
Sµ0H(T)
Fe8
1K0.1K
0.7K
quantum tunneling,interference, coherence
-1
0
1
-100 0 100
M/M
S
µ0H(mT)
uniform rotation,curling, etc.
multi - domains
Magnetization reversal in magnetic structures
S = 1020
1010
108 10
6 10
5 10
4 10
3 10
2 10 1
clusters atomsmolecularclustersnanoparticlesmicron
particlespermanentmagnets
single - domains spinsmulti - domains
macroscopic atomic
nucleation, propagation andannihilation of domain walls
quantum tunneling,interference, coherence
uniform rotation,curling, etc.
“Classical” magnetismMicromagnetics
Landau Lifshitz Gilbert equation
Quantum magnetismSchrödinger equationOperator formalism
Path intergralsab-initio calulations
etc.
Micro-SQUID magnetometry
• sensitivity : 10-4 Fo≈ 102 - 103 µB i.e. (2 nm)3 of Co
≈ 10-18 - 10-17 emu
• fabricated by electron beam lithography(D. Mailly, LPN, Marcoussis - Paris)
particle
Josephson junctions
stray field
≈ 1 µmB
A. Benoit, CRTBT, 1989
Cobalt cluster of 3 nmV. Dupuis, A. Perez, LPMCN, Lyon:
LASER vaporization and inert gas condensation sourceLow Energy Cluster Beam Deposition regime
HRTEL along a [110] directionfcc - structure, faceting
Ideal case: truncated octagedron with 1289 or 2406 atoms for diameters of 3.1 or 3.8 nm
blue: 1289-atoms truncated octahedrongrey: added atomes, total of 1388 atomes
Giant spin approximation
S ≈ 1000≈ 1000 atoms
z
M
H
!
"
#
ba -1
0
1
2
-45° 0° 45° 90° 135° 180°
E(!)
!
h = 0
h > 0
h = h0
B B
T = 0 K
E = K sin2q-m0MSH cos(q- j )
K = K1 +12m0MS
2(Nb -Na )
Uniform rotation of magnetization:Stoner - Wohlfarth model (1949)
• single domain magnetic particle• one degree of freedom: orientation q of magnetization M
• potential:
Stoner - Wohlfarth switching field
-1
0
1
-1.5 -1 -0.5 0 0.5 1 1.5
M
h
0°10°
30°45°
70°
90° 0
0.2
0.4
0.6
0.8
1
0°
30°
60°
90°
120°
210°
240°
270°
300°
330°
hs w
hsw = sin2/3! + cos2/3!( )
"3/2
Stoner - Wohlfarth astroid
easyaxis
hardaxis
Temperature dependence of the switching fields of a 3 nm Co cluster
=> in agreement with the Néel Brown theory
-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
µ0H
z (T
)
µ0Hy (T)
0.04 K
1 K
2 K
4 K
8 K
12 K
TB ! 14 K
∆t ≈ 1 s
PRL 86, 4676 (2001)
Single-moleculemagnets (SMM)
Mn12 S = 10
Fe8 S = 10
V15 S = 1/2
Ni12 S = 12
Giant spins
Mn84 S ≈ 6
Winpenny, 1999
Lis, 1980
Christou, 2004
Wiegart, 1984
Müller, 1993
Crystal of SMMs
Micro-SQUID array
B
crystal
50 µm
• crystal size > few µm• 10-12 to 10-17 emu• temperature 0.03 - 7 K• field < 1.4 T and < 20 T/s• rotation of field• transverse field• several SQUIDs at different positions
Giant spin approximation (Fe8)FeIII:
s = 5/2S = 10
Giant spin model
with S = 10, D = 0.27 K, E = 0.046K
Energy levels: Zeeman diagram
0 0.5 1 1.5 2 2.5 3-30
-20
-10
0
10
Energ
y (K
)
µ0Hz (T)
energ
y
magnetic field
!
-10
8 -10
8
-10 -5 0 5 10
Ener
gy
quantum number M
H = 0
Tunneling probability at an avoided level crossingLandau-Zener model (1932)
L. Landau, Phys. Z. Sowjetunion 2, 46 (1932); C. Zener, Proc. R. Soc. London, Ser. A 137, 696, (1932); E.C.G.Stückelberg, Helv. Phys. Acta 5, 369 (1932); S. Miyashita, J. Phys. Soc. Jpn. 64, 3207 (1995); V.V. Dobrovitskiand A.K. Zvezdin, Euro. Phys. Lett. 38, 377 (1997); L. Gunther, Euro. Phys. Lett. 39, 1 (1997); G.Rose andP.C.E. Stamp, Low Temp. Phys. 113, 1153 (1999); M. Leuenberger and D. Loss, Phys. Rev. B 61, 12200 (2000);M. Thorwart, M. Grifoni, and P. Hänggi, Phys. Rev. Lett. 85, 860 (2000); …
-1
-0.5
0
0.5
1
-1 -0.5 0 0.5 1
v=140 mT/sv=70 mT/sv=14 mT/sv=2.8 mT/s
M/M
S
µ 0H(T)
40 mK
-1 -0.5 0 0.5 1-40
-30
-20
-10
0
Energ
y (K
)
µ0Hz (T)
-10
-9
-8
-7
10
9
8
7
Application ofLandau-Zener
tunneling
Fe8
! = "D Sz
2 + E Sx2"Sy
2( ) + gµB
r S
r H
with S = 10, D = 0.27 K, E = 0.046KA.-L. Barra et al. EPL (1996)
S = 10
Temperature dependenceSpin Hamiltonian:
! = "D Sz
2 + E Sx2"Sy
2( ) + gµB
r S
r H
(2S + 1) energy states: M = -S, -S+1, …, S
Anisotropy barrierΔE
ΔEAnisotropy
constantSpin
≈ D S2
-10 -5 0 5 10
Ener
gy
quantum number M
thermally assisted tunneling
Spin-phonon coupling : DM = ±1, ±2
Spin ground states of Mn based SMMs
0
5
10
15
20
25
1 10 100
S
number of Mn-ions
2 3 4 5 7 20 30 50
Mn12Mn4
Mn25
Mn84
Mn70Mn30
Mn18
Mn2
Mn9
Anisotropy barriers of Mn based SMMs
0
10
20
30
40
50
60
70
1 10 100
!E
(K)
number of Mn-ions
2 3 4 5 7 20 30 50
Mn12
Mn4
Mn25
Mn84
Mn70
Mn30
Mn18
Mn2
Mn9
Quantum computing in molecular magnetsMichael N. Leuenberger & Daniel Loss
NATURE, 410, 791 (2001)• implementation of Grover's algorithm• storage unit of a dynamic random access memory
device.• fast electron spin resonance pulses can be used to
decode and read out stored numbers of up to 105
with access times as short as 0.1 nanoseconds.
Development of molecular Spin-Electronics
APS March Meeting 2004
La spintronique moléculaire en marche
Prédictions théoriques prometteuses
Rocha et al., Nat. Mat. 4, 335, 2005.
Magnétorésistance deNi(001)/tricene/Ni(001) enstructure de vanne de spin
DOS deNi(001)/tricene/Ni(001)
délocalisation desorbitales le long de la
molécule
Connexion électrique de molécules-aimants uniques
Collaboration T. Fournier, NANOFAB: plateforme de nanofabrication
Jonction par électromigration
Auto-assemblage par la chimie des ligandsObjectif du work package 3 du réseau QuEMolNa
Liang et al., Nature, 417, 725 (2002).
200 nm
Evaporation sous anglestructure verticale
Vaporisation sous vide
Gap nanométrique
Monocouches moléculaires
2 objectifs clés de nanofabrication
E. Bonet, NANOFAB
NanoworldQuantum world
1 10 100 1000N
Quantum world Classical world
Mn4Mn12 Mn84
Mn30
Mesoscopic Physics
A. J.Tasiopoulos, A. Vinslava, W. Wernsdorfer, K. A.Abboud, and G. Christou,Angew. Chem. Int. Ed., 43, 2117 (2004)
4 nm
http://www.elecmol.org/
Organizing Comitee: (Grenoble)
-Vincent Bouchiat (CRTBT, CNRS)-Benjamin Grévin (SPrAM,CEA)-Stephan Roche (SPSMS, CEA)-Guy Royal (LEOPR, UJF)
Collaborations (Physics)
V. Bouchiat, C. Paulsen, P. Gandi, A. Sulpice, A. Benoit, CRTBT, CNRS, GrenobleL. Sorace, A.-L. Barra, LCMI - CNRS, Grenoble
J. Villain, CEA, GrenobleD. Mailly, LPN, CNRS, Marcoussis
V. Mosser, Schlumberger Industries, MontrougeM. Jamet, C. Raufast, V. Dupuis, P. Mélinon, A. Perez, DPM, CNRS, Lyon
L. Thomas PhD 1996: Mn12-acF. Lionti PhD 1997: Mn12-ac, Fe17/19I. Chiorescu PhD 2000: Mn12-ac, V15R. Giraud PhD 2002: Ho3+
C. Thirion PhD 2003: nanoparticles, GHzR. Tiron PhD 2004: [Mn4]2K. Petukhov post-doc 2004-5: GHz
T. Ohm PhD 1998: Fe8V. Villar PhD 2001: Fe8 , chainesE. Lhotel PhD 2004: chaines
E. Bonet, W. Wernsdorfer, B. Barbara, LLN, CNRS, Grenoble
Collaborations (Chemistry)Group of G. Christou, Dept. of Chemistry, Florida
Group of R. Sessoli, D. Gatteschi, Univ. de Firenze, ItalieGroup of A. Cornia, Univ. de Modena, ItalieGroup of R.E.P. Winpenny, Univ. de Manchester, UKGroup of E. Brechin, Univ. de Manchester, UKGroup of T. Mallah, OrsayGroup of V. Marvaud, Univ. P. et M. Curie, ParisGroup of A. Müller, Univ. de Bielefeld, GermanyGroup of A. Powell, Univ. de Kahlsruhe, GermanyGroup of D. Hendrickson, Dept. of Chemistry, San DiegoGroup of E. Coronado, Univ. de Valence, SpainGroup of P. Rey et D. Luneau, CEA, Grenoble
Group of R. Clerac & C. Coulon, Univ. Bordeaux, PessacGroup of H. Miyasaka, Tokyo Metropolitan Uni.Group of M. Verdaguer, Univ. P. et M. Curie, ParisGroup of M. Julve, Univ. de Valence, Spain
• • •
Mn84
Christou, 2004
Winpenny, 2003
SMMs
SCMs