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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 ?