or not ? This is NOT the question Everything is magnetic … How ?

or not ?

This is NOT

the question

Everything is magnetic Everything is magnetic

… … How ?How ?

macroscopicworld

atomic ormolecular

world

« wonder »world

meter … nano meter …

mole … molecule …

1 / 1 000 000 000 = 10-9 10-9

110+23

macroscopicworld

atomic ormolecular

world

« wonder »world

Lewis Carroll, Through the looking-glass, Penguin Books, London, 1998 Illustrations by John Tenniel

macroscopicworld

atomic ormolecular

world

« wonder »world

quantummacro

N

S

macroscopic world« traditional, classical » magnets

macro

A pioneering experimentby M. Faraday

« Farady lines of forces » about magnetic flux N

S

macroscopic world

macro

Courtesy Prof. Peter Day, the RI ; See also : The Philosopher’s Tree,The Institute of Physics Publishing, Bristol,

1999)

Courtesy Prof. Frank James, the RI

M. Faraday’s magnetic laboratory

Courtesy Prof. Frank James, the RI

M. Faraday in his laboratory

Courtesy Prof. Frank James, the RI

macroscopic world« traditional » magnets

N

S

N

S

attractionN

S

N

S

macro

macroscopic world« traditional » magnets

N

S

repulsion

N

S N

S

N

Smacro

macroscopic worldlooking closer to the magnetic domains

S

Nmany sets of

domains

many sets of

atomic magneticmoments

macro quantum

S = 1020 10 10 10 8 10 6 10 5 10 4 10 3 10 2 10 1

permanentmagnets

micronparticles

nanoparticles clustersmolecularclusters

individualspins

Physics : Macroscopic Mesoscopic Nanoscopic

-101

-40-2002040

M/MS

μ0 ( )H mT

multi - domainnucleation, propagation and annihilation of domain walls

-101

-1000 100M/MS

μ0 ( )H mT

single - domainuniform rotation

curling

-101

-1 0 1

M/MS

μ0 ( )H T

Fe81K 0.1K0.7K

magnetic momentquantum tunneling,

quantizationquantum interference

Wolfgang Wernsdorfer, Grenoble

macro quantum

Lewis Carroll, Alice’s Adventures in Wonderland, Penguin Books, London, 1998 Illustrations by John Tenniel

“No ! no ! The adventures first” said the Gryphon in an impatient tone : “explanations take such a dreadful time.”

Everyday life is full of useful magnets

which traditionally take the form of three-dimensional solids,

oxides, metals and alloys

macro

MagnetsDomains

Curie Temperature

The magnetic moments order at Curie temperature

… Paramagnetic solid : thermal agitation (kT) larger than the interaction (J) between molecules

Solid, Magnetically Orderedthermal agitation (kT) weaker than the interaction (J) between molecules

A set of molecules / atoms :

kT << J kT >> J

TC

kT ≈ J

Magnetic Order Temperature

or Curie Temperature

Magnetic Order : ferro-, antiferro- and ferri-magnetism

+ =

Ferromagnetism :Magnetic moments are identical and parallel

+ = 0

Antiferromagnetism :Magnetic moments are identicaland anti parallel

+ =

Ferrimagnetism (Néel) :Magnetic moments are differentand anti parallel

-1

-0.5

0

0.5

1

-1 -0.5 0 0.5 1

0 min1 min5 min20 min30 min70 min100 min3 h4 h12 h

M/Ms

μ0 ( )H T

4 K

50A

irradiation with white light

Magnetization of nanoparticles of Prussian Blue analogues,

(A. Bleuzen, W. Werndorfer)

MicroSQUID, 4 K

-1

-0.5

0

0.5

1

-1 -0.5 0 0.5 1

0 min1 min5 min20 min30 min70 min100 min3 h4 h12 h

M/Ms

μ0 ( )H T

4 K

50A

irradiation with white light

Magnetization of nanoparticles of Prussian Blue analogues,

(A. Bleuzen, W. Werndorfer)

MicroSQUID, 4 KRemnant magnetization

CoerciveField

Fernande Olivier, Loving Picasso, H.N. Abrams Publishers, New York, 2001, p.139

« He seemed to give off a radiance,an inner fire,

and I couln’t resist this magnetism

How magnetism How magnetism comes to molecules ?comes to molecules ?

… … the different faces the different faces of the electronof the electron

Origin of Magnetism … the electron *

I am an electron• rest mass me,

• charge e-, • magnetic moment µB

everything, tiny, elementaryquantum

* but do not forget nuclear magnetism !

Origin of Magnetism

e-

« Orbital » magnetic moment « Intrinsic » magnetic moment

due to the spin

quantum

µspin = gs x µB x s ≈ µB

s = ± 1/2

µorbital = gl x µB x l

µtotal = µorbital + µspin

µorbital

µspin

Origin of Magnetism

… in molecules

quantum

electrons * in atoms

in molecules

* forgetting the nuclear magnetism

(E'+eϕ ) ψ =[

12m

(p +ec

A )2 +eh2mc

σ•∇×A- p4

8m3c2 − eh2

8m2c2 ∇•∇ϕ − eh

4m2c2 σ•∇ϕ ×p ]ψ

Dirac Equation

http://www-history.mcs.st-and.ac.uk/history/PictDisplay/Dirac.html

19281905

Nobel Prize 1933The Principles of Quantum Mechanics, 1930

Lewis Carroll, Through the Looking-Glass, Penguin Books, London, 1998 Illustrations by John Tenniel

“When I use a word”, Humpty Dumpty said, … “it just means what I choose it to mean – neither more nor less “

“The question is”, said Alice, whether you can make words mean so different things”

“The question is”, said Humpty Dumpty, “which is to be master – that's all.”

Representations, Models, Representations, Models, Analogies …Analogies …

l = 0 1 2 3

x,y,zy,z,x

x

y zy

x

x y z

sp

d

angular representation

Electron : corpuscle and wave

Wave function or « orbital » n, l, ml

…

Vacant

Doubly occupied

Orbitals

EnergyDiagramme

Singly occupied

Electron : also an energy level

Singly occupied

CN N O•O

R

•

π*

O ONN C

π*

Nitrogen Monoxyde NO• Nitronylnitroxyde

Electron : also a spin !

Up

Down

Doubly occupied

« Paramagnetic »S = ± 1/2

« Diamagnetic »S = 0

Paul Klee, Théorie de l’art, Denoël, Paris

An Isolated Spin

Analogy :Analogy : Spin and Arrow

Spin in Maya World ?

Uxmal, Palacio del Gobernador, Mayab, Yucatan, July 2004

Molecules are most often regarded

as isolated, non magnetic, creatures

β

β

φ1 φ2

ψ1

ψ2

σg

σu

Dihydrogen

diamagneticSpin S = 0

the dioxygen that we continuously breathe

is a magnetic molecule

px py pz

OAE

O-O OB

paramagnetic, spin S =1

Two of its electrons have parallel magnetic moments that shapes aerobic life and allows our existence as human beings

orthogonal πmolecular orbitals

macro

when dioxygen is in an excited stateit can becomes a singlet (spin S=0)

and strange reactivity appearssometines useful (glow-worm …)

Paramagnetic O2

Luminol Light

More complex molecular frameworks called metal complexes built from transition metal and molecules are able to bear up to five or seven electrons with aligned magnetic moments (spins)

H He

Li B N NeOC FBe

s Elements

d Elements : transition

p Elements 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

f Elements•

Ce

K

Rb

Fr

Cs

NaMg

Ca

Sr

Ba

Ra

Al P ClSi S Ar

AsGe

In Sb

Bi

Sn

Se Kr

Xe

RnAt

Br

Te

PoPb

I

Nd LuYbPr Sm TmErPm Eu HoDyTbGd

Th LrNoMdPa NpU Pu CmAm Bk FmEsCf

Ac

Sc

Y

La

44,956

88,906

138,91

21

39

57

Ti

Zr

Hf

47,867

91,224

178,49

22

40

72

V

Nb

Ta

50,942

92,906

180,95

23

41

73

Cr

Mo

W

51,996

95,94

183,84

24

42

74

Mn

Tc

Re

54,938

98,906

186,21

25

43

75

Fe

Ru

Os

55,845

101,07

190,23

26

44

76

Co

Rh

Ir

58,933

102,91

192,22

27

45

77

Ni

Pd

Pt

58,693

106,42

195,08

28

46

78

Cu

Ag

Au

63,546

107,87

196,97

29

47

79

Zn

Cd

Hg

65,39

112,41

200,59

30

48

80

VSc Cr Mn Fe ZnCuNiCoTi

Y

La

Zr Mo Ru Pd CdAgRhTcNb

Hf W Os HgAuIrReTa•

Ga

TlPt

E5 d orbitals

Partial OcupancyParamagnetismConductivity

x2-y2 z2 yzxz xy

z

xy

Unpaired Electrons

Transition Elements

quantum

ML

zy

x

LL

L

L

L

Mononuclear complex ML6

E

Splitting of the energy levels

How large is the splitting ?

∆oct

y

x

z

z2x2-y2

y

x

z

x

z

y

xy xz yz

t2g

eg

High spin

L = H2O[C2O4]2-

Low spin

L = CN-

?Weak Field Strong FieldIntermediate Field

TemperatureDependent

Spin Cross-Over

macro

The complexes of transition metal present often delicate and beautiful coloursdepending mostly on the splitting of the d orbitals

Colours in waterGeometry changes

Spin changes

h

story ofstory ofjumping electronsjumping electronsand moving spins … and moving spins …

two

blue

solutions

[CoII(H2O)6]2+

+ Methylene

Blue

KCN+

Methylene Blue

QuickTime™ et undécompresseur DV - PAL

sont requis pour visionner cette image.

one

yellow

solution

blue + blue=yellow !

[CoIII(CN)6]3-

+ Methylene

ReducedColorless

[FeII(H2O)6]2+

pale green

FeII(o-Phen)3]2+

bright red

S=0S=0

S=2S=2

Low spin, chiral, FeLow spin, chiral, FeIIII(bipyridine)(bipyridine)33]]2+2+

Playing with ligands, Playing with ligands, the chemist is ablethe chemist is ableto control to control the spin statethe spin state

Review byPhilipp Gütlich et al.Mainz UniversityAngewandte Chemie 1994

Spin Cross-Over

A Fe(II) « Chain » with spin cross-over

Fe

N

N N

R

N

N N

R

Fe

N

N N

R

Fe

N N

N N

N N

N N

N

N N

R

Fe

N

N N

R

Fe

N N

N N

N N

N N

Triazole substituted Ligand (R) ; insulated by counter-anionsMany groups : Leiden, Mainz, Kojima, O. Kahn, C. Jay, Y. Garcia, ICMC Bordeaux

4+

Curie LawCurie Law

MMT = ConstantT = Constant

MMT ≈ n (n+2) /8 …T ≈ n (n+2) /8 …

if n = 4, if n = 4, MMT ≈ 3 !T ≈ 3 !

Spin Cross-Over Bistability Domain

The system « remembers » its thermal past !

Room Temperature

TC TC

T / K

M / T cm3 mol-1

250 350300

O. Kahn, C. Jay and ICMC Bordeaux

Red White

33

00

macro

Hysteresis allows bistability of the system

and use in display, memories …

Spin and colour changes

Spin Cross-over Display Device

(1) (2) (3)

DisplayConnections

O. Kahn, J. Kröber, C. Jay Adv. Mater. 1992, 718

Kahn O., La Recherche, 1994, 163

Joule and PeltierElements

Compound inLow spin state(Thin Layer)

O. Kahn, C. Jay and ICMC Bordeaux

From the molecule to the material and to the device …

∆oct

E

(A) (B)

T / K

Blanc

Rouge

MT / cm3 mol-1

250 350300

TC TC

(C) (D)

(F)(E)

xy

z

From J.F. Letard, ICMC Bordeaux

Red

White

O. Kahn, Y. Garcia, Patent

May we go further and dream of molecular magnets 

i.e. low density, biocompatible

transparent or colourful

magnets ?