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