a lecture proposed by spp molekular magnetismus...

How How molecules molecules go go magnetic magnetic ……

Michel Michel VerdaguerVerdaguer, Françoise , Françoise VillainVillain,,Ruxandra GheorgheRuxandra Gheorghe, Fabrice , Fabrice PointillartPointillart

Université Pierre et Marie Curie, Paris

A lecture A lecture proposed proposed byby

SPP SPP Molekular Magnetismus Molekular Magnetismus (DFG)(DFG)

Why experimentsexperiments ?

because …

- experiment arises curiosity- experiment is speaking …- experiment is demonstrating …- experiment can be beautiful !

Bad Durkheim, SPP Molecular Magnetismus (DFG) 6-9 may 2007

Why experiments in magnetismmagnetism ?

because …

- it is an important phenomenon …- it arises curiosity …- it needs to be demystified and explained- and experiments are beautiful !

Why experiments in molecular magnetismmolecular magnetism ?

because …

- our live relies on it and nobody knows …- it is badly known or unknown … - it can be explained simply …- and experiments are beautiful !

Goals ?

1) Citizen awareness 2) Attract good students to our discipline

3) Here : convincing you that such experiments are possible to realize during Science Festivals ..

LECTURELECTURE

Bad Durkheim, SPP Molecular Magnetismus (DFG) 6-9 may 2007

((abridged abridged ……))

Comments Comments about a possible about a possible ……

Publicity CampaignPublicity Campaign, , BarcelonaBarcelona, 2004 , 2004

or not ?

This is NOT

the question

Everything is magnetic Everything is magnetic

…… How ? How ?

Pierre CuriePierre CurieLectures NotesLectures Notes

Fonds documentaire ESPCIFonds documentaire ESPCI

Everything is magnetic Everything is magnetic ……

…… How ? How ?

Everything is magnetic Everything is magnetic ……

…… How ? How ?

Pierre CuriePierre CurieAnnales de ChimieAnnales de Chimie

77ème série, V, 1895, 289ème série, V, 1895, 289(Thèse de P. Curie)(Thèse de P. Curie)


Diamagnetic

Paramagnetic

Magnet

macroscopicworld

atomic ormolecular

world

« wonder »world

quantummacro

Cais do Sodre Metro Station Lisboa, Antonio Dacosta

Everyday lifeis full of useful magnets

which traditionally take the formof three-dimensional solids,

oxides, metals and alloys

Magnets in our world

We are in a real world, at our size

Courtesy Prof. Frank James, the RI

M. FaradayM. Faraday

A pioneering experimentby M. Faraday

« Faraday lines of forces » about magnetic flux

macroscopic world

Courtesy Prof. Peter Day, the RI ; See also :The Philosopher’s Tree,The Institute of Physics Publishing, Bristol, 19999

N

S

N

S

« Lines of field »

A magnet creates a magnetic field

What is a magnet ? What is NOT a magnet ?

macro

Magnetization

Applied magneticField H

Magnet

macroMagnetization : How behave objectsin a magnetic field ?

Magnetization M(how do they become « magnetized »?)Remnant Magnetization

CoerciveField

« hard »

Tout Tout est magnétique est magnétique

…… Comment ? Comment ?

Pierre CuriePierre CurieAnnales de ChimieAnnales de Chimie

77ème série, V, 1895, 289ème série, V, 1895, 289(Thèse de P. Curie)(Thèse de P. Curie)



which traditionally take the formof three-dimensional solids,

oxides, metals and alloys

macro

Curie Temperature

The magnetic moments order at Curie temperature

… Paramagnetic solid :thermal agitation (kT) largerthan 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 OrderTemperature

or CurieTemperature

Magnetic ordering : Curie Temperature …

… a demonstrator

from macroscopic to atomic world

S

Nmany sets of

« domains »≡ ≡ ≡

many sets of≡

atomic magneticmoments

looking closer to smaller and smaller magnets

N

S

macro

Domains

How magnets behave ?

Domains

S = 1020

1010

108 10

6 10

5 10

4 10

3 10

2 10 1

clusters individualspins

molecularclustersnanoparticlesmicron

particlespermanentmagnets

Physics : Macroscopic Mesoscopic Nanoscopic

-1

0

1

-40 -20 0 20 40

M/M

S

µ0H(mT)

multi - domainnucleation, propagation andannihilation of domain walls

-1

0

1

-100 0 100

M/M

S

µ0H(mT)

single - domainuniform rotation

curling

-1

0

1

-1 0 1

M/M

S

µ0H(T)

Fe8

1K0.1K

0.7K

magnetic momentquantum tunneling,

quantizationquantum interference

Wolfgang Wernsdorfer, Grenoble

macro quantum


CompassesMagneticEarth

1600William Gilbert

De Magnete

Jan van der Straet (Giovanni Stradanus), Bruges, 1523 ; Florence, 1605Nova Reperta, vers 1620-1630 , 14 planches gravées par Jérôme Wierix at Adriaen Collaert,éditées par Philippe Galle

Calcul de la longitude, Burin 22 x 28 cm around 1600 Inv. n° 11786

Compasses, Jiangomen station, Beijing

The fascination ofmagnets on children

«« A A wonder wonder of of such such nature I nature I experience experience as a as a child child of 4 orof 4 or5 5 yearsyears, , when my father showed when my father showed me a me a compasscompass. . That thisThat thisneedle behaved needle behaved in in such such a a determined way did determined way did not not at at all fitall fitinto the into the nature of nature of events which could find events which could find a place in a place in thetheunconscious unconscious world of concepts (world of concepts (effects connected witheffects connected withdirect «direct « touchtouch »). I »). I can still remember can still remember –– or or at at least least believebelieveI I can remember can remember –– that that this experience this experience made a made a deep anddeep andlasting impression lasting impression upon upon meme..Something deeply hidden had Something deeply hidden had to to be behind thingsbe behind things.. » »

A. EinsteinA. EinsteinQuoted by Livingston, J. D. In Driving Force: The Natural Magic of Magnets. Cambridge, MA: Harvard University Press, 1996. ISBN: 0674216458.


macro

Toys

Everything is magnetic Everything is magnetic

…… thanks thanks to to electrons electrons ……

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

(E'+e! ) " = [1

2m (p +

e

cA )2 +

eh

2mc #•$ % A-

p4

8m3c

2 &

eh2

8m2c

2$•$! &

eh

4m2c

2#•$! % p ]"

Dirac Equation

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

19281905

Nobel Prize 1933The Principles of Quantum Mechanics, 1930

ReprRepreesentations, sentations, Mod Modeels,ls,

Analogies Analogies ……

About About what what are are we speaking we speaking ??

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

An isolated spin …

AnalogyAnalogy : : spin and arrow

Electron : corpuscle and wave

Wave functionΨ

Hokusai, the great wave in Kanagawa

Ψ+

Ψ−

l = 0 1 2 3

x,y,z

y,z,x

x

y zy

x

x y z

sp

d

angular representation

Electron : corpuscle and wave

Wave function or « orbital » Ψn, l, ml …

quantum

Vacant, empty

Orbitals

Doubly occupiedNO MORE than TWO !

Energy

Singly occupied

Electron : also an energy level

quantum

Energy Diagramme (« ladder »)

Principle 1 : fill from the bottom (aufbau)

!*

Nitrogen oxide NO•

C

N NO•O

R

•

!*

O ONN C

Nitronylnitroxyde

Electron : orbital and spin !

Singly occupied

Up

Down

« Paramagnetic »mS = ± 1/2

quantum

Electron : orbital and spin !

Doublyoccupied

S = 1/2 - 1/2 = 0 « Diamagnetic »

quantum

Principle 2 : no more than TWOelectrons per level (orbital)

with different spins !(Pauli’s exclusion principle)

DiamagneticSpin S = 0

quantum

Moleculesare most often regarded

as isolated, non magnetic, creatures

Dihydrogen

macro

N2 Diamagnetic

Pouring liquid dinitrogen

liquid dinitrogendoes NOT stick

diamagnetic

the dinitrogenis a diamagnetic molecule

px py pz

NAEN-N NB

diamagnetic, spin S = 0

All electrons are paired in bonds, very stable molecule

macro

when dioxygen is in its ground stateit is a triplet (spin S=1)

and its reactivity is weak

Paramagnetic O2

Liquid O2

liquid dioxygenliquid dioxygendoes does stickstick

OO22 is paramagneticis paramagnetic

the dioxygenthat 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

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

and strange reactivity appearssometines useful (glow-worm …)

Singlet dioxygenquantum

Luminol Light

macro

dioxygen singlet (spin S=0)

glow-worm …

Documents from Nassau and Alvarez

luminol

NH

NH

O

OHNH2

N

N

O

OHNH2

OO

quantum

More complex molecular frameworkscalled metal complexesbuilt from transition metal and moleculesare able to bear up to five or seven electronswith 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

Na Mg

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

Il sistema periodico … (Primo Levi)

È bello raccontare i guai passati …

E5 d orbitals

Partial Ocupancy

Paramagnetism

Conductivity

x2-y2 z2 yzxz xy

z

xy

Unpaired Electrons

Transition Elements

quantum

PuigcerdaPuigcerda, , CerdanyaCerdanya, , may may 31, 200631, 2006

ML

z

y

x

LL

L

L

L

Mononuclear complex ML6

E

Splitting of the energy levels

Electrons Electrons …… WANTED ! WANTED !

An indirect manifestationAn indirect manifestationof of the presence the presence ofofunpairedunpaired electrons electrons ::the colourthe colour

Complexes of transition metal ions often display beautiful coloursessentially to d levels splitting

Colours in waterGeometrical Changes

Spin Changes

hν

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

hνhν

quantum macro

hν hνhνhν

Complexes of transition metal ions often display beautiful coloursessentially to d levels splitting

Colours in waterGeometrical Changes

Spin Changes

∆S ≠ 0

quantum macro

Electrons Electrons …… WANTED ! WANTED !

A A direct direct manifestationmanifestationof of the presence the presence ofofunpairedunpaired electronselectrons ::the magnetismthe magnetismor interaction or interaction with with a a magnmagneetic fieldtic field

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

Energy

Curie LawCurie Law

χχMMT = ConstantT = ConstantPierre Curie, 1900 ParisPierre Curie, 1900 Paris

Curie BalanceCurie Balance

K4[Fe(II)(CN)6]

K3[Fe(III)(CN)6]

(NH4)2Fe(II)(SO4)2

Diamagnetic, spin 0

Paramagnetic, spin 1/2

Paramagnetic, spin 2

S=2S=2

S=0S=0

S=1/2S=1/2

Magnetization : how objects behave in a magnetic field ?

macro

Magnetization M(how they become « magnetized »)

Applied magnetic field H

magnet paramagnetic M = χ H, χ > 0

diamagnetic M = χ H, χ < 0

Playing with Playing with ligands, ligands, the chemist is the chemist is ableableto control to control the geometry the geometry and symmetryand symmetryof complexes of complexes ((colourcolour, , magnetismmagnetism))

Co(II)Cl2, 6H2O : from octahedral to tetrahedral

Heat

+ H2O

+ Cl-

- Cl-

quantummacro

2 Cl-

Co2+

Playing with Playing with ligands, ligands, the chemist is the chemist is ableableto control to control the the spin statespin state

Lisboa University, October 9, 2006

macro

Hysteresis allows bistability of the system

and use in display, memories …

Spin and colour changes

macro

quantumS=2S=2

[FeII(H2O)6]2+pale green

S=0S=0

FeII(o-phen)3]2+bright red

Low Low spin, chiral, spin, chiral, FeFeIIII((bipyridinebipyridine))33]]2+2+

ΛΛ ΔΔ

Playing with Playing with ligands, ligands, the chemist is the chemist is ableableto control to control the the spin statespin state

Lisboa University, October 9, 2006

Spin Cross-OverA 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+

Transition Cross-over Demonstrator by Jean-François LetardThe very samples presented were synthesized by students in Paris during practical worksCourtesy Prof. C. Roux, C. Train, A. Proust

Samplecoming from

Low T

Samplecoming from High T

Spin Cross-Over Bistability Domain

The system « remembers » its thermal past !

Room Temperature

TC TC

T / K

!MT / cm3 mol

-1

250 350300

O. Kahn, C. Jay and ICMC Bordeaux

RedWhite

33

00

Discussion sur la mati Discussion sur la matière vivante,ère vivante,10ème semaine internationale de synthèse, 1938, PUF, 1943, 219-22310ème semaine internationale de synthèse, 1938, PUF, 1943, 219-223

ThenThen, , mmemory emory ??

«« It is It is an essential an essential character character of living of living being that thebeing that thesensation sensation leaves leaves traces.traces.There is nothing There is nothing comparable in comparable in material material worldworldIt is It is a real a real joke joke to to name name «« memorymemory » » the hysteresisthe hysteresisphenomenonphenomenon. » . » ……

Paul Langevin,Paul Langevin,

O. Kahn, C. Jay and ICMC Bordeaux

From the molecule to the material and to the device …

O. Kahn, Y. Garcia, Patent

May we go furtherand dream of molecular magnets

i.e. low density, biocompatible

transparentor colourful magnets ?

Do Do the chemiststhe chemistsknow howknow howto to align the align the spinsspinsof of electronselectronsin in moleculesmolecules,,parallel parallel or or antiparallel antiparallel ??

Understanding Understanding ……

why the why the spins of spins of two neighbouring electronstwo neighbouring electrons(S = 1/2) (S = 1/2) become become ::

to get magnetic compounds to get magnetic compounds ……

antiparallel antiparallel ??

S=OS=O

or or parallel parallel ??

S=1S=1

SingletSinglet TripletTriplet

if S = 0Orthogonality

>0J = 2 k + 4ßS

if S≠0;|ßS|>>kOverlap

<0

H2Aufbau

ES

ETJ

Antiferro

O2Hund

ES

ET

J

Ferro

Tell it with flowers(find the orbital) isolated

Overlap (σ) Overlap (π)

OrthogonalityFlowers from the garden

of the Gulbenkian’s FoundationLisbon

Michelangelo, Sixtin Chapel, Rome

Exchange interactions can be very weak …

order of magnitude : cm-1 or Kelvins …

≈

order of magnitude : >> 150 kJ mol-1 …

« Chemical » bonds Robust !

Exchange interactions

Energy

Please, avoidPlease, avoidpairing electronspairing electronsinto into bonds bonds ……

macro

NO2 Dimerisation

Avoid Avoid ……

... to pair ... to pair the the «« magneticmagnetic »»

électronsélectrons

Interpretation(s)

Pairing of electrons, bondingDIA-magnetic !

N

O

O N

O

O N

O

ON

O

O

Orbital

Thermodynamics (Le Chatelier …)

2 NO2N2O4Equilibrium : + Heat

Brown colorless

12

A beautiful artefact

When some residual NO is present in the vessel :

NO2 + NO N2O3Reaction :

Brown

1

2Blue green

colorless

≈ 5 Å

Cu(II) Cu(II)

Orbital Interaction …

Ligand

A B

Which ligand ? Why not …• Cyanide, CN- ?

Ligand

Museo nacional dos azulejos, Lisboa

Cyanide Ligand

Friendly ligand : small, dissymetric, forms stable complexesWarning : dangerous, in acid medium gives HCN, lethal

C≡N-

Cr(III) Ni(II)

Dinuclear µ-cyano heterometallic complexes

NB : A dissymetric ligand helps to get stable heterometallic complexes …« Birds of the same feathers flock together » …

Polynuclear complex, synthetic strategy

Hexacyanometalate “Heart”Lewis Base

Mononuclear ComplexLewis Acid

Polynuclear Complex

3-

+ 6

2+ 9+

macro

Ferromagnetic …

ErosPaul KLEE

Nocturnal separation, 1922

Ferrimagnetic …

macro

C rC u6 S = 9/2

C rNi6 S = 15/2

C rMn6 S = 27/2

Hexagonal R -3 a = b = 15,27 Å; c = 78,56 Å a = b= 90°; g = 120°; V = 4831 Å3



… High Spin Heptanuclear Complexes

Marvaud et al., Chemistry, 2003, 9, 1677 and 1692

electrons electrons …… WANTED ! WANTED !

How to How to manipulatemanipulateelectrons electrons betweenbetween molecules molecules ??Towards magnetsThe saga of high TC Prussian Blues Analogues

1704 …

Diesbach, draper in Berlin …

… prepares a blue pigment « Prussian blue »

… said to be the first coordination compound

2004 : 300th anniversary !

Classical Coordination Chemistry… 3[Fe(CN)6]4-aq + 4Fe3+

aq {Fe4[Fe(CN)6]3}0•15H2O

Cyanotypes

Einstein a portrait, Cyanotypes by F. Villain, CIM2, UPMC

TC ∝ z |J|

z : number of magneticneighbours|J| : coupling constantbetween nearestneighbours

TC = 5.6 K

Magnetic Properties of Prussian Blue

Néel, 1948

Ferromagnetic Prussian blue analogues …

TC ∝ z |J|

TC >> 5.6 K

JFerro > 0

Orthogonality

TC ∝ z |J|

TC >> 5.6 K

JAntiferro < 0

Overlap …

Ferrimagnetic Prussian blue analogues …

TC / K

Z

200

Ti V Cr Mn Fe Co Ni Cu Zn

300

100

• ••[Cr(CN)6]

3-

(t2g)3

d3

• ••

• •

6 F

9 AF

MnII

d5

• ••

9 AF

(t2g)3

VII

d3

• ••

• 3 F

9 AF

CrII d4

• ••

• •

• • •

6 F

NiIId8

V4[Cr(CN)6]8/3.nH2ORoom Temperature TCOn a rational basis !

Gadet et al., J.Am. Chem. Soc. 1992Mallah et al. Science 1993Ferlay et al. Nature, 1995

quantum

2[CrIII(CN)6]3-+3Vaq

2+ [V3[CrIII (CN6)]2]

0

A blue, transparent, low density magnet at room temperature

macro

DevicesBased on Room temperature Magnets

Prussian blue analogues

Permanent Magnet

Hot

CoupleSample ( MM)

Magnetic Switch… Or thermal probe …

Other device

Up to 2004 … magnetic analogues used as …

… devices and demonstratorsmacro

… another demonstrator

macro

PermanentMagnet

Sample ( MM)

Heater

… another demonstrator

macro

Single MoleculeMagnets

Chemists have managedto transform

isolated single moleculesinto magnets

=

What is named Single Molecule Magnet ?

High SpinAnisotropic

High Spin Paramagnetic Molecule

H

Single Molecule Magnet

H

Single Molecule Magnet

Towards information storage at the molecular level ?

if T < TBlocking

Single molecule magnetsz

y

x

E

- Sz

Sz

+Sz

0

DSz2

0-2-4 +2 +4

Anisotropy Barrier

Tunneling

Thermal

Activation

quantum

[Mn[Mn1212OO1212(CH(CH33COO)COO)1616(H(H22O)O)44].2CH].2CH33COOH.4HCOOH.4H2200

Mn(IV)

Mn(III)

Ion Oxyde

Carbone

S=10

or Mnor Mn1212

From D.Gatteschi and R. Sessoli

S=2

S=3/2

S =8x2 -4x3/2 =

Mn12 is a hard magnet

-3 -2 -1 0 1 2 3

-20

-10

0

10

20

T=2.1K

MA

GN

ET

IZA

TIO

N (µ

B)

MAGNETIC FIELD (T)

Bistability : inzero field themagnetisation canbe positive ornegativedepending of thestory of thesample

Coercive Field

RemnantMagnetisation

The dream …

Surface

Magnetic Tip H

≈ 10 nm

High Spin "down"

High Spin"down"

quantum macro

Surface

Magnetic Tip H

≈ 10 nm

High Spin "down"

High Spin"down"

macroquantum

… information storage at the molecular level !

Surface

Magnetic Tip H

≈ 10 nm

HSM «up»High Spin"down"

The dream …

Nanosciences …

… a challenge for chemists and friends …

Surface

H

≈ 10 nm

HSM «up»High Spin"down"

The possibilities The possibilities are are endless endless ……

as attractive but less recommended …

Another popular non scientific use

of the word « magnetism »

To To be demystified be demystified ……

An interaction An interaction through spacethrough space invisible, invisible, incomprincomprehensible ehensible ……

MagnMagneetism tism = = Magic Magic !!

Levitating top

EURASIA TRADING COMPANY 5, place Anatole France 44 000 - Nantes 45 € + 6,40 € de port

« This flask is equipped with magnets and induces in its centre an intense magneticfield which magnetizes the whole liquid.

Keep in the magnetic flask, tap or mineral water or any other drink, from 15mns toseveral hours, for an optimum magnetization.

Drink daily Magnetized Water : in preference, 1 cup when getting up, 1 or 2 in themorning and the afternoon and 1 cup at bedtime.

As a matter of fact, the body and tyhe blood are composed at 70 and 80% ofwater, hence magnetized water, more lively, more energetizing due to its magneticproperties, carries its energy into the whole organism.

Active research in hospitals, worldwide and mainly in China, havedemonstrated the beneficent effects of magnetized water.

Some specialists foresee that ..

Magnetism will play an important rôle in the world of tomorrow.

M. Noyori, Hanoi, october 2003

To daythe chemist is able

to synthesizeany molecule

at will

NEWMAGNETICOBJECTS

High spinMolcules

High TC MagnetsPhoto-Magnets

ChiralMagnets

Single Chain Magnets

BEAUTIFULOBJECTS

High spinMolcules


ChiralMagnets


NEW PROPERTIES

kId+

Id-≠

k

Unpolarised light γd(w)k.M

0

2

4

8 12 16 20 24Temperature /K

hν

0.0

0.5

1.0

1.5

2.0

3 4 5 6 7 8

!" / a. u.

T /

1000100

101

0.1

K

H

M

High spinMolcules


ChiralMagnets


Earth needs care ….

Science for peace … (Vincenzo Balzani)

Pablo PicassoChild with a dove, 1901oil on canvas, 73x54 cm

Private collectionon loan to National Gallery

Peace,PaixPace,PazPau, Friede