Magnetic techniques for molecular and nanometric

materialsDante Gatteschi &

Roberta Sessoli

February 2008

Diapositive disponibili:

ftp://lamm21.chim.unifi.it/pub/Corso_Gatteschi_Sessoli

Per ogni problema scrivere a: federico.totti@unifi.it

Molecular Magnetic Materials

(nano)

EPR(Gatteschi)

Magnetic Techniques(Sessoli)

Molecular magnetic materials

• simple paramagnets: step 1

• Interacting paramagnets: step 2

• Size effects: step 3

Bulk 3D magnets

The first molecular ferromagnet

Miller, Epstein et al. MolCrystLiqCryst 1985

The first room temperature molecular

magnet

Miller, Epstein et al. Science, 1991

Nitroxides

Tc= 0.6 K

N

NO.

CH3

CH3

CH3CH3

O.

TC= 1.5 K

N

NNO2

O

O

Fullerene

TC= 16 K Alemand et al. Science 1991

p-NC-Cp-NC-C66FF44-CNSSN-CNSSN••: : a monomeric S-based a monomeric S-based radicalradical

Single molecule magnets, SMM

The first single molecule magnet:Mn12-acetate

S4||z

top view

T. Lis Acta Cryst. 1980, B36, 2042.

MS=-10

MS= 10Easy axis of magnetization

lateral view z

Mn(AcO)2•4H2O + KMnO4 in 60% v/v AcOH/H2O

[Mn12O12(OAc)16(H2O)4]·2AcOH·4H2O

Ground stateS = 8*2 - 4*3/2 = 10Msaturation = 2.S = 20B

Barrier 60 K

The library of molecular magnets: single chain magnets

More complex structures

Three different organizations

• 2: embedded in amorphous silica

• 3: LB film• 4: SAM

• Bogani et al. Adv Mater in press

magnetmagnet paramagnetparamagnetsuper super paramagnetparamagnet

Reducing the size

Classical physicsQuantum mechanics????????????

Paramagnet

Inorganic radicalsO2, NO..

Organic radicalsTyrosyl, nitroxides

TM coordination compounds

RE coordinationcompounds

Outline of the EPR section

EPR in a nutshell:• The principle of the experiment • Basic EPR: the spin HamiltonianHF experiments:• Radicals and Biological systems• Clusters

Outline of the EPR section 2

Spin interactions:• The spin hamiltonian of pairs • SH parameters of pairsThe Mn12 testing ground:• Epr• Nmr

EPR Spectroscopy in a Nutshell

• It is like NMR but is limited to paramagnetic systems

• Invented by Zavoiski in Kazan in 1944

• It needs a magnetic field and electromagnetic radiation

• Unlike NMR the field is scanned and the frequency is fixed

.

General design of an EPR General design of an EPR spectrometerspectrometer

SourceSourceklystron (conventional)FIR lasers ( > 240 GHz)Gunn diodes (95-400 GHz)Carcinotron (very High power)

DetectorDetectorcrystal diodesbolometersSchottky diodes

Transmission lineTransmission linerectangular waveguides up to 150 GHz)corrugated waveguides.via space with refocusing devicesoversized waveguides

MagnetMagnetelectromagnets (up to 1.5 Tesla)superconductive magnets (up to 17 Tesla)resistive magnets (30 Tesla)hybrid magnets (45 Tesla)pulsed magnets (hundreds of Tesla)

Sample environmentSample environmentresonating structuretemperature controlmultiple irradiation

.•Most of the efforts for the development of EPR at high frequeny are aimed at the extention at millimeter and sub-millimeter waves of the general design of the conventional microwave bridge.• The main problem along this path is the availability and/or the design and realization of devices (magic Tees, circulator, phase shifter etc.) able to carry on the function of the low-frequency analogoue.

The microvave techniques are used in conventional EPR. The propagation of the radiation is made by using mono- modal metallic rectangular waveguides, metallic cavities and the other devices present in a typical microwave bridge.

The microwave techniques can be successfully extended up to 150 GHz ca. Above this frequency waveguides become eccessively lossy (typical figure of merit 12 dB/m at 250 GHz) and the rectangular or cylindric cavities eccessively small.

EPR Spectroscopy in a Nutshell: Zeeman Term

In a system with S= 1/2, when the static magnetic field is parallel to z,

E(M)= MgμBH

a transition is observed when

gz BH= hν= ge BH0Similar expressions hold for x, and y.

The g values and their anisotropy depend on the chemical environment, therefore they provide structural information

Zeeman Splitting

-0.50

-0.25

0

0.25

0.50

0 2000 4000 6000 8000 10000

h=gBH

-1/2gBH

1/2 gBH

G

cm-1

Some Useful Relations1 GHz= 3.3561x10-2 cm-

1

Res. Freq. Band Res. Field (GHz) g=2.00

9 X 0.3234

35 Q 1.2578

95 W 3.1441

200 7.1876

300 10.7814

500 17.9690

Polycrystalline Powder EPR Spectra

The EPR spectra of polycrystalline powders or frozen solutions provide the gx, gy, and gz values directly provided that the linewidth is smaller than the anisotropy

Polycrystalline Powder Spectra

0.25 0.27 0.30 0.33 0.35

B (T)

g

g||

g

gz

gy

gx

isotropic

axial

rhombic

The Spin Hamiltonian

H = B B.g.S+S.D.S+ k Ik.Ak.S

Zeeman Fine Hyperfine

Interazione iperfine e Interazione iperfine e superiperfinesuperiperfineCu2+ S=1/2

63Cu I=3/2 69%

65Cu I=3/2 31%

1- Termine di contatto: Axx=Ayy=Azz=8/3(gegnBn)|n(0)|2

3- Pseudo- contatto :Interazione spin nucleare-momento orbitalico: è funzione dell’anisotropia di gTraccia non nulla, anisotropo

2- Termine dipolare:

anisotropo, traccia nulla (Axx+Ayy+Azz=0)

2nI+1 n=2, I=1

Informazioni sull’intorno di coordinazione

Il CuIl Cu2+ 2+ nei prioninei prioni

Determinazione dei diversi siti leganti e della stechiometria

Determinazione del numero di azoti leganti per uno dei siti coordinanti

Biochemistry 2003 42, 6794

1 eq.2 eq.3 eq. 4 eq.5 eq.6 eq.

Alta conc. Bassa conc.

5.3 eq. Cu2+

Cu2+ legato

pH=4.00

pH=7.40

Cu2+ libero

Affinità per il Cu2+ a pH>6

7 linee min. 3 N leganti

Q-band of 6

6 in solution. RT, X-band

The spin hamiltonian and the parameters

nucleii

NNCuCuCuCuBsp HH ii

2

10

65656363

1 IASIASIASSgB

g ACu/MHz

AN/MHz

QN/MHz

Euler angle/°

x 2.0405 95 36.3 1.28 = 35

y 2.0405 95 50.5 -0.70 = 14

z 2.1860 632 37.5 -0.58 = 0

High Frequency EPR: Why?

• increased resolution• simpler spectra• orientation effects• spectra from integer spin systems

with large zero field splitting• sign of the zero field splitting• different time scale

Enhanced Resolution

• The g tensor anisotropy of tyrosyl radicals present for instance in Photosystem II is completely resolved at high frequency. This provides important structural information, like their main orientation in the membranes.

Tyrosyl Radicals

• They are present in RNR and in Photosystem II

• RNR: ribonucleotide reductase catalyzes the reduction of ribonucleotide to deoxyribonucleotides

EPR of Tyrosyl rad. of S. typhymurium

250 GHz 9.45 GHz

O

H

HH

H

H H

COOHRHN

H

gx=2.0090

gy=2.0044

gz=2.0022

Tyrosyl Radical

The g values are sensitive to the environment

O

H

HH

H

H H

COOHRHN

H

x

y

gx is the most sensitive, because of the interaction of the non-bonding oxygen orbitalsUn et al. JACS 1999, 121, 5743

Resolution effect

P700+ radical cation of PSI

Tyrosyl Radical in Different Environments

N-ac-L-tyr L-tyr-HCl RNREC PSII YD PSII YZ

gx 2.0094 2.0067 2.00868 2.00740 2.00750

gy na 2.0045 2.00430 2.00425 2.00422

gz na 2.0023 2.00203 2.00205 2.00225

giso 2.0055 2.0045 2.00500 2.00466 2.00466

Brustolon et al. J Phys Chem A 1999, 103, 9636

Tyrosyl Radical in Different Species Tyrosyl radical

of RNR of different species

E.coli 2.0091

mouse 2.0076

herpes 2.0076

typhimurium 2.0089

JACS 120, 5080, 1998

Orientation Effects in membranes

Il tensore g nei metalli di transizione

L’anisotropia del fattore L’anisotropia del fattore gg

x2-y2 xy

xz yz

z2

662

22

8

2 2

zxy

Per un elettrone spaiato si ha:

gi=ge+

n

ng

ii

EE

gLnnLgΛ

g<ge dn n=1-4

g>ge dn n=6-9

g// = ge + 8 /(Edxy-Edx2-y

2)

g = ge + 2 /(Edyz- Edx2-y

2)

dx2-y

2

dz2

dxy

dxz,dyz

Es: Cu2+

elongato

dxy, dxz, dyz

dx2-y

2, dz2

d1, 2T2g

eg

t2g

Es: Ti3+

d2, 3T1g

Es: V3+

d3, 4A1g

Es: Cr3+

d5, 2T2g

Es: Fe3+

basso spin

d5, 6A1g

Es: Fe3+

alto spin

d6, 5T2g

Es: Fe2+

alto spin

Stati fondamentali in campo Stati fondamentali in campo ottaedrico -1ottaedrico -1

d9, 2Eg

Cu2+

Stati fondamentali Eg sono instabili rispetto alla distorsione Jahn-Teller e danno luogo a stati fondamentali orbitalmente non-degeneri

Stati fondamentali in campo Stati fondamentali in campo ottaedrico -2ottaedrico -2

d8, 3A2g

Es: Ni2+

Es: Co2+

d7, 4T2g

d4 , 5Eg

Mn3+

dx2-y

2

dz2

dxy

dxz,dyz

elong.

dz2

dx2-y

2

dxz,dyz

dxy

comp.

dz2

dx2-y

2

dxz,dy

z

dxy

comp.

dx2-y

2

dz2

dxy

dxz,dyz

elong.

Perturbative Approach

= ±/2S

n ng EE

gLnnLgΛ

g=

Valori di g per coordinazione pseudo-ottaedrica

Conf. elett. S Stato fond. gx gy gz

d1 1/2 2T2g ge-2/1 ge-2/2 ge-8/3

d2 1 3T1g ge-9/ ge-9/ ge

d3 3/2 4A2g ge-8/1 ge-8/2 ge-8/3

d4 2 5Eg comp. ge-6/1 ge-6/2 ge

elong. ge-2/1 ge-2/2 ge-8/3

d5 HS 5/2 6A1g ge ge ge

d6 2 5T2g ge+2/1 ge+2/2 ge+2/3

d7 3/2 4T2g Oh 2(5-)/3 2(5-)/3 2(5-)/3

elong. 0 0 2(3-)/3

comp. 4 4 2

d8 1 3A2g ge+8/1 ge+8/2 ge+8/3

d9 1/2 2Eg elong. ge+2/1 ge+2/2 ge+8/3

comp. ge+6/1 ge+6/2 ge

g values for some ions

Configurati

on

S GroundState

gxgy

gz

d1 1/2 T2ga -2/1 -2/2 -8/3

d3 3/2 A2gb -8/1 -8/2 -8/3

d4 2 Egc -2/1 -2/2 -8/3

d8 1 A2gd -8/1 -8/2 -8/3

d9 ½ Ege -2/1 -2/2 -8/3

Spin hamiltonian for an individual spin

H= B B.g1.S1+ S1.D1.S1+ j S1.A1j.Ij+..

Electronic Zeeman

Electron-electron interaction (zero field splitting)

Electron-nucleus interaction

Zero field splitting

H= D[S1z2-S1(S1+1)/3]+ E(S1x

2-S1y2)

0E/D1/3

diagonal

Couples states differing in M by ±2

-1.0

-0.5

0

0.5

1.0

1.5

-1.0 -0.5 0 0.5 1.0

axialaxial axial

Completely rhombic

Completely rhombic

Origin of the zero field splitting

For organic radicals: electron-electron dipolar interaction

For transition metal and rare earth ions: spin-orbit interaction

Ligand field approximation

= ±/2S

n ng EE

gLnnLgΛ

D1=2

A simpler treatmentD=(/2)[gz-(gx+gy)/2]; E=(/4)[gx-gy]

For tetragonally elongated Ni(II):

gx= gy= 2.25; gz= 2.24; =-315 cm-1

D= 1.57 cm-1

3A2

3A1

3E

Higher order termsHigher order terms, which have their origin in higher order perturbations, are most coveniently described by Stevens operator equivalents:

H=n k Bnk On

k operator

parameter

n=0,±2,±4,..±2S; k=0,1…n

Advantages of the Stevens Operators

• They fully exploit the symmetry: easy calculations

• The number of the terms to be included are defined by symmetry

• For a C4 quantization axis only the k= 0 and k= 4 terms must be included

• For C2, k=0,2,4

• The Onk operators couple states differing in

M by ±k

Some examples of operators

k=2 O20=3Sz

2-S(S+1)

O22=(S+

2+S-2)

k=4 O40 =35Sz

4-30S(S+1)Sz2+25Sz

2-6S(S+1)+3S2(S+1)2

O42={(7Sz

2-S(S+1)-5)(S+2+S-

2)}S/2

O43={Sz(S+

3+S-3)}S/2

O44=(S+

4+S-4)/2 {A,B}S=(AB+BA)/2

D=3B20;E=B2

2

Fine StructureWhen the Zeeman term is dominant each line is split into 2S equally spaced lines (fine structure)

For an axial anisotropy the resonance fields are given by:

H(M-M+1)=(g/ge)[H0+D’(M/2)(3cos2-1)]

D’= D/(geB)

Nel limite di gBH>>D e anisotropia uniassiale

H//

2S linee separate da H=2D/gB

H

2S linee separate daH=D/gB

H(MM+1)=(ge/g)[H0+(2M+1)/D’/2]

D’=(3cos2-1)D/(geB)

(M=-3)=9D-3gB H

(M=-2)=4D-2gB H

(M=-1)=1D-1gB H

etc

E(-3,-2)=5D-gB H

E(-2,-1)=3D-gB H

E(-1,-0)=1D-gB H

campi di risonanza:

HR(-3,-2)=(5D-h)/gB

HR(-2,-1)=(3D-h)/gB

HR(-1,-0)=(1D-h)/gB

H//

H

T

2D/gB

D/gB

Per T tutti i livelli sono equipopolati e l’intensità delle righe è proporzionale alla probabilità di transizione

Resonance fields for S states

H(MM+1)=(ge/g)[H0+(2M+1)/D’/2];

D’=(3cos2-1)D/(geB)

H//

H

2D/gB

D/gB

kBT<<gB

H

D < 0

HF-EPR Provides the Sign of DNegative D:±S lie

lowestEasy axis type anisotropy

At low T only the -S-S+1 transition is observed

Quantitative LF Approach

Bencini,A.; Ciofini,I.; Uytterhoeven, M.G. Inorg. Chim. Acta 1998, 274, 90

The energies of the LF levels are calculated using a full matrix diagonalization approach. The SH parameters, in principle to any order, are obtained by best fit of the calculated energies.

Both classic crystal field and Angular Overlap parametrization can be used

Ask him the program!

“EPR silent species”

• Ions with even numbers of unpaired electrons are EPR silent in a conventional X- or Q-band experiment due to large zero field splitting

• HF-EPR spectra of Mn(III), Fe(II), Ni(II), etc. become available

An example

-10

-5

0

5

10

15

0 0.5 1.0 1.5 2.0

H(T)

E (c

m-1)

Chromium(II) Manganese(III)

x2-y2

x2-y2z2

z2

Compressed Elongated

Jahn-Teller distortion

Chromium(II) Aquo Ion329 GHz

D=-2.20 cm-1; g= 1.98

Telser et al Inorg Chem 1998, 37, 5769

Manganese(III): SH Parameters

Compressed:

gz= 2.00; gx=1.97

D= 4.72 cm-1

B20= 3.854 cm-1

B40=-9.82 10-3 cm-1

B44=5.18 10-3 cm-1

Elongated:

gz= 1.96; gx=1.99

D= -4.83 cm-1

B20=-3.948 cm-1

B40=-6.70 10-5 cm-1

B44=1.86 10-3 cm-1

Dq=1600 cm-1

Vanadium(III) Alum

3T1g

3Ag

OhS6

Vanadium(III) EPR

D= 4.8581 cm-1;

gz=1.9500; gxy= 1.8656

Az= 0.0098, Axy= 0.0078 cm-

1

Tregenna-Piggott et al Inorg Chem 1999 38 5928

Gadolinium Contrast Agents

Contrast enhanced MRI is a very effective technique for detecting and characterizing lesions, for identifying patho-physiological abnormalities and for providing functional information.

Usually contrast agents are slowly relaxing paramagnets.

Gd3+ is widely used because of its large spin

Need for understanding the mechanism

Gadolinium Chelates

DOTAP

EOB-DTPA

Multifrequency Gd-DOTAP Spectra

9 GHz

94 GHz

249 GHz

Hpp= 400 G

Hpp= 25 G

Hpp= 9 G

The broadening effect is due to unresolved fine structure

At high frequency Zeeman energy is much larger than zfs and the lines sharpen

JACS 120, 1998m 5060

Gd-DOTAP in multilamellar aqueous dispersion

2

2

eff2

31gg

22zz

2yy

2xx

2 /DDD

R. S. Drago: Physical methods for chemists (Saunders, 1992)

J. S. Griffith: The theory of transition metal ions (Cambridge University Press, 1961)

J. R. Pilbrow: EPR of transition metal ions (Clarendon Press, 1990)

A. Abragam, B. Bleaney: EPR of transition ions (Dover, 1986)

J. A. Weil, J. E. Wertz, J. R. Bolton: Electron Paramagnetic Resonance (Wiley, 1994)

A. Bencini, D. Gatteschi: EPR of Exchange coupled systems (Springer Verlag, 1990)

A. Bencini, D. Gatteschi: Electron Paramagnetic Resonance Spectroscopy, in Inorganic Electronic Structure and Spectroscopy, E.I. Solomon, A.B.P.Lever, Vol. I Wiley 1999

Riferimenti bibliograficiRiferimenti bibliografici

Libri:

O. Kahn Molecular Magnetism VCH, Weinheim 1993.

Review:

A.-L. Barra, L.-C. Brunel, D. Gatteschi, L. Pardi, R. Sessoli, "High Frequency EPR Spectroscopy of Large Metal Ion Clusters. From Zero Field Splitting to Quantum Tunneling of the Magnetization" Acc. Chem. Res. 31, 460-466, 1998.

D. Gatteschi, R. Sessoli “Quantum tunneling of magnetization and related phenomena in molecular materials” Angew. Chem. Int. Ed. 42, 268-297, 2003.

D. Gatteschi, L. Pardi “High Frequency EPR Spectroscopy” in High Magnetic Fields, C. Berthier, L.P. Lévy, G. Martinez, Eds. Springer 2002.

J. van Slageren et al. “Frequency-domain magnetic resonance spectroscopy of moleuclar magnetic materials” Phys. Chem. Chem. Phys. 5, 3837-3843, 2003.

Riferimenti Riferimenti bibliograficibibliografici

Programmi di simulazioneProgrammi di simulazione

Alcuni esempi:

Sim (H. Weihe)http://sophus.kiku.dk/software/epr.html (Inorg. Chem 32, 1993, 1216)

Easyspin (S. Stoll) http://www.esr.ethz.ch

EPRNMR (J. A. Weil & M. J. Mombourquette) http://web.chem.queensu.ca/eprnmr/

3 - Convoluzione spettro (scelta di forme e larghezze di riga)

1 - Definizione del modello e dei parametri2 - Calcolo delle probabilità di transizione per diverse orientazioni e campi