ICMSICMS--ICMR Winterschool ICMR Winterschool on Chemistry and Physics of Materialson Chemistry and Physics of Materialson Chemistry and Physics of Materials, on Chemistry and Physics of Materials,

November 6November 6--13, 2007, Bangalore13, 2007, Bangalore

Molecular Magnetic MaterialsMolecular Magnetic MaterialsP t II

Mi h l VERDAGUER d

Part II

Michel VERDAGUER andRodrigue LESCOUZEC, Valérie MARVAUD, Cyrille TRAIN, Christophe CARTIER

dit MOULIN, Françoise VILLAIN, Jacqueline VAISSERMANNLaboratory CIM2 CNRS UPMC Paris FranceLaboratory CIM2, CNRS, UPMC, Paris, France

Anne BLEUZEN Laboratory CI, ICMMO, Orsay, France

JNCASR, Bangalore 2 march, 2007

OutlineICMSICMS--ICMR Winterschool on Chemistry and Physics of Materials, Nov. 6ICMR Winterschool on Chemistry and Physics of Materials, Nov. 6--13, 2007, Bangalore13, 2007, Bangalore

1. IntroductionBrief history of molecular magnetism [1-6]

2. Mononuclear species (complexes)2.1. Prequisites : free ion terms, states, orbitals and ligand field. Point Group Symmetry2 2 Metal-ligand interaction to tune electronic structure2.2. Metal ligand interaction to tune electronic structure.2.3. Spin states, spin cross-over, devices [7]3. Magnetism of molecular assemblies in interaction. Polynuclear complexes3.1. Interaction between two electrons : phenomenological and orbital approaches

Localisation and delocalisation conditions, overlap, repulsion, exchangeHeisenberg Hamiltonian ;gHund and Mulliken, Heitler and London approaches

3.2. Interaction Models [1]Kahn ; comparison with Hoffmann (molecules)Comparison with Anderson, Goodenough-Kanamori (solids)

3.3. Case studies :Bi l l hi h i l l [1 5]Binuclear complexes, high spin moelcules [1,5]Ferrimagnetic chains [1,5]Molecule-based magnets ; devices [8]

4. Magnetism of molecules assemblies without interaction :Single-molecule, single-chain magnets [9]M l l "b tt " h f tMolecular, "bottom-up", approach of nanosystemsThe "Mn12" and "Fe8" moleculesLocal anisotropy ; magnetic quantum tunneling effect.

5. ProspectsMagnetism of a single molecule ; Information storage. Electronic quantum computing ;M l if i l i l [10]Multifunctional materials [10]

B f t tiBefore starting …

A warningabout exchangeabout exchange

with (de)localized electrons

Another mechanism for ferromagnetic couplingDelocalized Electrons : double exchangeDelocalized Electrons : double exchange

Delocalized ElectronsLocalized Electrons

NNNN b b

Delocalized Electrons

b b

Localized Electrons

NNNN

NNBr Ni BrNi

a

b

a

b

a

b

a

b

NN

"Polarisation"Ferromagnetism

Overlapantiferromagnetism

Ni(I) Ni(II) Ni(I) Ni(II)

Complex Ni(I)-Ni(II)mixed valency

FerromagnetismSF = 3/2

antiferromagnetismSF = 1/2

Delocalisation of electrons « polarises » : ferromagnetism

Single Molecule MagnetSingle Molecule Magnet

Magnetic moment remains oriented gafter withdrawing of the field(slow relaxation of the magnetisation …)

WITHOUTInteraction between the moleculesInteraction between the molecules

Phenomenon strictly molecular !

Top down3D

Fragments Threads

Dots

MetalsOxydes

• Nice Chemistry• New Physics• Q t / Cl i l Nanosystems • Single molecule magnets• Quantum / Classical• Quantum tunneling

Giant Molecular Clusters

• Applications (far …)• Recording0D, Molecules• Quantum computing

Bottom up

MMn4

Mn30Mn12 Mn84

1 10 100 1000N

Quantum worldMolecular (bottom-up) approach

Classical worldClassical (top-down) approach

I. Tasiopoulos, G. Christou, W. Wernsdorfer et al. Angew. Chem, 43, 2117, 2004

Nanomagnets throughg gMolecular Clusters

• No dispersion in size, in shape and in orientation

• Solubility• Biocompatibility

• Systems well characterised : structure,

ti t

p y

magnetic parameters• Control of parameters by

th isynthesis

Interest of magnetic gmolecular clusters

• Synthetic strategies to get large size molecules andSynthetic strategies to get large size molecules and supramolecular objects

• Creation of clusters analogues of biological systems• Exploration of mesoscopic region, where quantum and

classical effects are coexisting.Devel pment f materials f r the future• Development of materials for the future …

Magnetization : how objects behave in a magnetic field ?

Magnetization M(how they become « magnetized »)

A li d i

magnet paramagnetic M = χ H, χ > 0

Applied magnetic field H

diamagnetic M = χ H χ < 0diamagnetic M = χ H, χ < 0

Magnetization« Soft » Magnet

Magnetization M

A li d i

Remnant Magnetization

CoerciveApplied magneticField H

Field

Magnetization« Hard »Magnet

Remnant Magnetization Magnetization M

A li d iCoercive

Applied magneticField H

Field

Mesoscopic PhysicsMacroscopic Nanoscopic

Clusters IndividualSpins

MolecularClusters

NanoparticlesMicronic Particles

PermanentMagnets

M p N p

S = 10 20 10 10 10 8 10 6 10 5 10 4 10 3 10 2 10 1

Multi - domains Unique Domain Magnetic MomentNucleation, propagation

and annihilation ofdomains’ walls

Unique DomainUniform Rotation

Curling

Magnetic MomentQuantum Tunneling Effect

QuantisationInterference Quantum

1 1 1Fe 8

1

0

M/M

S

0

M/M

S

0

M/M

S

1K 0.1K

0.7K

-1

-40 -20 0 20 40µ0H(mT)

-1

-100 0 100

M

µ0H(mT)

-1

-1 0 1

M

µ 0H(T)From W. Wernsdorfer, Grenoble

UnderstandingUnderstanding……

What is namedWhat is named Single Molecule Magnet ?

=

Hi h S iHigh SpinAnisotropic

High Spin Paramagnetic MoleculeHigh Spin Paramagnetic Molecule Paramagnetic

hphase

H

Single Molecule MagnetSingle Molecule Magnet

H

Single Molecule MagnetSingle Molecule Magnet

Below T < TBlocking

Slowrelaxation

f hof the magnetization

Towards information storage at the molecular level ?

[Mn[Mn1212OO1212(CH(CH33COO)COO)1616(H(H22O)O)44].2CH].2CH33COOH.4HCOOH.4H22OO

or : Mnor : Mn1212

M (IV)

Mn(III) S=2

S=3/2Mn(IV)

Ion Oxyde

S=3/2

Ion Oxyde

Carbone

S=10S =8x2 -4x3/2 =

From D.Gatteschi and R. Sessoli

Mn12 is a hard magnetg

Bi t bilit i

Remnant Magnetisation

10

20T=2.1K

µ B)

Bistability : in zero field the magnetisation can

Magnetisation

n /

µ B

0

10

ZATI

ON

(µ

gbe positive or negative depending of the story of theet

izat

io

-20

-10

MA

GN

ETI of the story of the

sample

C i Fi ld

Mag

ne

-3 -2 -1 0 1 2 3

20M

M A G N ETIC F IELD (T )

Coercive Field

Mn12 Magnetisation relaxes slowly at l t tlow temperature

25

τ=τ0exp(∆/kT)τ0 is much larger than a bulk

15 τ0=2x10-7s;∆/k=62 K

1 yog(τ

)

magnet.

The height of the b i i l t dLo

g τ

5

1 y

1 h

1 s

lo barrier is related to zfs, D, of the S = 10 ground

-52.5 5.0 7.5 10.0

gstate.

T(K)

Magnetic Circular Dichroïsm (MCD) Fe8Hysteresis in solution !y

MCD : Magnetic Circular Dichroïsm

Different absorption for light right or left circularly polarised underDifferent absorption for light, right or left circularly polarised, under applied magnetic field (Cotton Effect) D. Gatteschi et al.

UnderstandingUnderstanding……

ActingActing……

Ground State Energy LevelsE gy L

M=±8

H = 0M=±9

H = 0 M=±10

Energy Levels in a Magnetic FieldE gy L g F

S

M=S-S

M S

H≠0l i fi ld l l

M=-SH≠0At low temperature, a magnetic field populates only

the M = -S state

Going back to equilibrium :Th l i i i i lThermal activation :trivial

Axial symmetry

E(M) = DM2

H=0 M SM SH 0∆E=DS2

M=-SM=S

( E/k T)τ = τ0 exp(∆E/kBT)

T li ff t : !Towards equilibrium :

Tunneling effect : new !

H=0 M=S M=-S

Mn12 is a Hard MagnetM

MsaturationMremnant

HH

HcoerciveHcoercive

St i th ti ti+ Steps in the magnetisation curve

Resonnant Tunneling Effect f H D/for H = nD/gµB

M=SM S

H = nD/gµB

M=-S

H = nD/gµB

Conditions to observe tunnelling effect

• Degenerated wave functions must superpose• A transversal field must couple the two wave p

functions • Coupling splits the two levels : “tunnel

splitting”• Tunnelling Effect Probability increases with

tunnel splitting”

From D. Gatteschi

MM

Tunneling EffectH

No resonnant Tunneling Effectgwith a magnetic field parallel to z

M = S

H ≠ nD/gµM = -S

H ≠ nD/gµB

MM

N t li ff tH No tunneling effect

Relaxation time of magnetization independent of temperature below 300 mKindependent of temperature below 300 mK

0.6

0.8a.

u.)

on

0 2

0.4

etiz

atio

n (a

agne

tizat

io

0.2

Mag

ne Ma

Change with temperature of l Frelaxation time τ in Fe8

Quantum l

8

12

QTunneling Effect4

8

/sec

)Lo

g τ

Thermal -4

0

ln (τ

/

Activation-12

-8

0 2 4 6

1/T (1/K)

τ(s ) Fe 8 w ith D

100

1000 Fe 8 standard

Fe 8 w ith 57 Fe

10

100

1

0.10 2 4 6 8 10

1/T (1/K )

Time to relax 1% of Msat

1/T (1 /K )

f satFe8

D > Fe8st > 57Fe8

Polarised Neutrons Diffraction Polarised Neutrons Diffraction Spin density Map in FeSpin density Map in FeSpin density Map in FeSpin density Map in Fe88

10µB

0µB

-8µBµB

Polarised Neutrons Diffraction Polarised Neutrons Diffraction Spin density Map in FeSpin density Map in FeSpin density Map in FeSpin density Map in Fe88

10µB

0µB

-8µBµB

Y. Pontillon et al. J. Am. Chem. Soc. 1999, 121, 5342.

10 99 88 77 66 55 44 33 22 11 010→99→88→77→66→55→44→33→22→11→0

Neutrons Inelastic scatteringNeutrons Inelastic scattering

UnderstandingUnderstanding……

Single molecule magnetsg gwithout interaction between the molecules !

High Spin Anisotropic MoleculesHigh Spin Anisotropic Molecules

zE Thermal

yx

E0

DS z2

Anisotropy Barrier

hermalActivation

SSz

S024 +2 +4

Anisotropy Barrier

Tunneling

Magnetisation reversal

- Sz +Sz0-2-4 +2 +4

Anisotropy Barrier

DSz2

DSz2 = 400K ?

D = 1KS = 20

For the chemistParameters to ControlParameters to Control

E0

DS 2

ThermalActivation

S = SpinD = Anisotropy

J = Exchange ConstantIntramolecular interaction

zJ’ = Intermolecular interactionSz

DS zAnisotropy Barrier

Tunneling

- Sz +Sz0-2-4 +2 +4

J’J

Remark : when DGS > 0GS

- Sz Sz+Sz0-2-4 +2 +4

D>0

z zz

DSz2

Sz=0Sz 0

In the ground state : f M 0 h lif MS = 0 at the lower energy

No more SMM behaviourD <0 is compulsoryDGS<0 is compulsory …

O i i f th b iOrigin of the barrier

• Isolated Ion Anisotropy Di

Dip l Int ti n• Dipolar Interaction• Anisotropic Exchange Di,j

D = ∑i ci Di + ∑ ci,j D i,j

Zero field splittingp g• Uniaxial Anisotropy D• Rhombic Anisotropy E (0 ≤ |E/D| ≤ 1/3)• Rhombic Anisotropy E (0 ≤ |E/D| ≤ 1/3)• Higher terms A, B

H = D [Sz2 -S(S+1)/3] + E[Sx

2-Sy2] + A Sz

4+ B (S+4+ S-

4)[ z ( ) ] [ x y ] z ( + - )

Diagonal Term Couples states differing

by ± 2 in M

Couples states differing

by ± 4 in M

Conditions to observe tunnelling effect

• Degenerated wave functions must superpose• A transversal field must couple the two wave p

functions • Coupling splits the two levels : “tunnel

splitting”• Tunnelling Effect Probability increases with

tunnel splitting”

From D. Gatteschi

Anisotropie Transversale et mélange Anisotropie Transversale et mélange d i Md i Mdes niveaux Mdes niveaux M

E/K

… « Single molecule magnets» Giant Molecular Clusters

Idée Mn4And many others

High spin + Anisotropy∆E = DSz

2 Mn12Fe8

SynthesisTheory

New

NewConcepts

y

Properties

NewMaterials

NewNewFunctions

A new comer : Mn6

Mn12,S=10,DSz2 ≈ 70K

Mn6,S=12, DSz2 ≈ 90K

R. TomsaP. Gouzerh

J.Milios et al. Angew, Chem. 2004,43, 210 ; E. Brechin et al., W. Wernsdorfer, J. Am. Chem. Soc. 2007, 129,8-9 & 2754-2755 & Chem Comm. 2007, 3476

Anisotropy A rational control is more difficult !A rational control is more difficult !

Two aspects :

- Structural- low symmetry of the clustery y- one anisotropy axis : Cnv, Dnh,…

- ElectronicElectronic- local anisotropy of the magnetic ions- exchange anisotropy

Single Chain MagnetsSingle Chain Magnets ……

Trinuclear speciesDouble

i h izig-zag chainsBis double

zig-zag chains

[{FeIII(L)(CN)4}2CoII(H2O)4] .4H2O

[{FeIII(L)(CN)4}2MII(H2O)4].4H2O [L = 2,2’-bipy and 1, 10-phen), M = Mn, Co, Cu, Zn]

[{FeIII(bpy)(CN)4}2MII(H2O)] .CH3CN . 1/2H2O [M = Mn, Co, Cu]

R. Lescouezec, PhD Thesis

Feasibility of « Molecular nanowires » ?

Anisotropic precursor

[F (III)(bi )(CN) ][Fe(III)(bipy)(CN)4]-

l lR. Lescouëzec, M. Julve, Valencia, Spain D. Gatteschi, W. WernsdorferAngewandte Chem. 2003, 142, 1483-6

2 [FeIII(bipy)(CN) ]- + [CoII(H O) ]2+2 [FeIII(bipy)(CN)4]- + [CoII(H2O)6]2+

Anisotropic precursor(Structure)

Anisotropic assembler(Electronic Structure)

FeIII, d5 CoII, d7

bas spinS = 1/2

haut spinS = 3/2

Chain [{FeIII(bipy)(CN)4 }2CoII(H2O)2•�4H2O]Chain [{Fe (bipy)(CN)4 }2Co (H2O)2 4H2O]nPerspective View

R. Lescouezec, M. Julve, F. Lloret (Valencia), Angewandte Chemie, march 2003

Magnetic Orbitals Orthogonality Ferromagnetism

{[FeIII(bpy)(CN)4]2CoII(H2O)2} ⋅ 6H2O

FF

F

AFN

N

N

N

FeCCN

NM

N

N

N

N

AF

F

AFC

CNN

MAF

Fx

y

[FeIII(AA)(CN)4]-

AA = bpy, phen, bpym

5 C II d7 hi h id5, low spin CoII, d7, high spin

Chain catena µ-[{FeIII(bipy)(CN)4 }2CoII(H2O)2•�4H2O]Chain catena µ [{Fe (bipy)(CN)4 }2Co (H2O)2 4H2O]n

Single crystal2.0

1000100

1010 1

Single crystal ac susceptibilityMeasurements

1.50.1(SQUID)

0 5

1.0

χ" / a. u.

0.0

0.5Slow relaxation of the magnetisation !

3 4 5 6 7 8T / Kχ‘‘ vs. T plots along the b axis R. Lescouezec, F. Lloret

Chain catena µ-[{FeIII(bipy)(CN)4 }2CoII(H2O)2•�4H2O]Chain catena µ [{Fe (bipy)(CN)4 }2Co (H2O)2 4H2O]n

Magnetisation on microSQUID (microcrystal)Magnetisation on microSQUID (microcrystal)

W. Wernsdorfer, LLN Grenoble

Coll. A. R. Lescouezec, M. Julve, F. Lloret P. Herson, Y. Dromzée

Slow relaxation of the magnetisation …

1Magnetization as a function f tim

0.6

0.8

M/M

s

1.5 K

1.6 K

2 6 K2.5 K 2.3 K

2.4 K

of time

0 2

0.4

M

1.7 K

1.8 K

1.9 K

2.8 K

2.7 K

2.6 K2.2 K

2.1 K

2.0 KThermally activated l i f h

0

0.2

0.01 0.1 1 10 100 1000t (s)

relaxation of the magnetization

t (s)

M vs. t plots along the b axis. ac: Ea= 142 K, τ0 = 6.10-11 s

W. Wernsdorfer, Grenoble

Scaling plot of the f ld1 2

1.60.04 K

0.6 K 0.8 K0.2 K

0.5 K

0.4 K

0.3 K 0.7 K 0.9 K

1.0 K 1.1 K1.2 K

1.3 K1.4 K

1.5 K

coercive fieldof the Fe2Co(bipy)

chain0.8

1.2

µ 0H n

(T) 1.6 K

1.7 K

1.8 K1.9 K2.0 K

2.2 K

Hn0 = 5.8 T

E0 = 54 K chain

0

0.4

0 1 2 3 4 5 6 7 8

2.6 K

2.4 K

2.8 K

E0 54 K

τ0 = 1.3 x 10 -8 s

0 1 2 3 4 5 6 7 8[Tln(c/v)] 1/2

0 04 1 0 K

1.2

1.6

(T)

0.04 - 1.0 K 1.1 K1.2 K

1.3 K1.4 K

1.5 K

1.6 K1.7 K

T* (K)

Tc = 1.0 KH 0 = 5 8 T

0.4

0.8µ 0H n

2.4 K

1.8 K1.9 K2.0 K

2.2 K

0.5

1

1.5

2 T* (K)

T (K)

Tc

Hn0 = 5.8 T

E0 = 54 Kτ0 = 1.3 x 10-8 s

00 1 2 3 4 5 6 7 8

[Tln(c/v)] 1/2

2.6 K

2.8 K0

0 0.5 1 1.5 2

T (K)

Low temperature relaxation at H = 1.5 T

11.6 K

0.51.5 K

1.4 K

1.3 K

0M/M

s

1.2 K1.1 K

1.0 K0.9 K

0.8 K0 7 K

-0.5

0.7 K0.6 - 0.04 K

-1

1.5 T

1 10 100 1000 10 4

t (s)

Devices ? To come …m

Two kinds :Two kinds :• Information storage at the molecular level

I l d R b A i iIsolated Robust AnisotropicMagnetic Molecular Dots on a Surface

• Electronic Quantum bitsQFine tuning of magnetic tunnelingTunneling : information change No Tunneling : storageNo Tunneling : storage

Control of the ground spin state• Nuclearity

• Exchange interaction J (F or AF)• Nature of the paramagnetic ions

Control of the anisotropy• Molecular (and Crystal) Structure

Control of the intermolecular interaction J ’• Electronic anisotropy (nature of the ions)

• Bulky ligands• Charged complexes and counterions

• Dilution in an diamagnetic matrix

Prospects (short term)• New chemical systems with larger ∆E

• Improved Instrumentation (microSQUID and nanoSQUID)

New chemical systems with larger ∆E

Prospects (long term)• Magnetic storage on ONE single molecule• Quantum computing

Next « device » ?Recording on one molecule !

Magnetic TipMagnetic TipHSM "up" HSM "down"

SurfaceSurface

Quantum Computing : principleQ m mp g p p

M = ± 8hν

M 10

M = ± 9hν

∆M = + 2(left polarized)

H 0

M = ± 10

H = 0See D. Loss et al., Nature, 2000

Quantum Computing : principlei h (E H ) dto mix the states (E, Hy) and …

1 0 10TunnelingH = 0

M 8 M 8

1 0

M = - 8 M = + 8

10

M = - 8 M = + 8 M = - 8 M = + 8

COMPUTING !

H ≠ 0No

10

10No

TunnelingM = - 8M = + 8

M = - 8M = + 8

0

M 8

STORAGE !

M + 8

Molecular information processing : Will it h ?Will it happen ?

Please, look atthe answer of

P. DayProceedings of the Royal Institution of Great BritainProceedings of the Royal Institution of Great Britain

Oxford, 1998, 85-106