Spectroscopic Investigations of Magnetic Anisotropy in Molecular...

93
Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnets ECMM workshop on Magnetic Anisotropy Karlsruhe, 11th12th October 2013 Prof. Dr. Joris van Slageren Institut für Physikalische Chemie Dr. ShangDa Jiang 1. Physikalisches Institut Universität Stuttgart Germany

Transcript of Spectroscopic Investigations of Magnetic Anisotropy in Molecular...

Page 1: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnets

ECMM workshop on Magnetic AnisotropyKarlsruhe, 11th‐12th October 2013

Prof. Dr. Joris van SlagerenInstitut für Physikalische Chemie

Dr. Shang‐Da Jiang1. Physikalisches Institut

Universität StuttgartGermany

Page 2: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Contents1. Introduction

1.1 Magnetic Anisotropy

1.2 Magnetic Anisotropy in Transition Metal Clusters

1.3 Magnetic Anisotropy in f‐Elements

2. Single‐crystal SQUID measurements

2.1 Motivation

2.2 Magnetic susceptibility tensor

2.3 Determination

3. High‐frequency EPR spectroscopy

3.1 Theoretical background and Experimental Considerations

3.2 Examples

3.3 Frequency Domain EPR

24. Inelastic Neutron Scattering

4.1 Theoretical background and Experimental Considerations

4.2 Examples

5. Electronic Absorption and Luminescence

5.1 Electronic Absorption (f elements)

5.2 Luminescence (f elements)

5.3 Magnetic circular dichroism (transition metal clusters, f elements).

Page 3: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

ContentsLiterature

A. Abragam/B. Bleany – Electron Paramagnetic Resonance of Transition Ions, 1970

N.M. Atherton – Principles of Electron Spin Resonance, 1993.

R. Boča – Theoretical Foundations of Molecular Magnetism, 1999

R. Carlin – Magnetochemistry, 1986

C. Görller‐Wallrand, K. Binnemans in Handbook on the Physics and Chemistry of Rare Earths, Vol. 23, http://dx.doi.org/10.1016/S0168‐1273(96)23006‐5

O. Kahn – Molecular Magnetism, 1993

F.E. Mabbs/D.J. Machin – Magnetism and Transition Metal Complexes, Chapman and Hall, London, 1973

K.R. Lea, M.J.M. Leask, W.P. Wolf, J. Phys. Chem. Solids, 23, 1381 (1962)

H. Lueken – Magnetochemie, 1999

H. Lueken – Course of lectures on magnetism of lanthanide ions under varying ligand and magnetic fields, http://obelix.physik.uni‐bielefeld.de/~schnack/molmag/material/Lueken‐kurslan_report.pdf 2008

D.J. Newman/Ng (Ed.) – Crystal Field Handbook

A.J. Orchard – Magnetochemistry, 2003

3

Page 4: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

1. Introduction2. Single Crystal Magnetometry3. High‐Frequency EPR Spectroscopy4. Inelastic Neutron Scattering5. Electronic Absorption and Luminescence

Page 5: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Ch. 1. Introduction5

Magnetic anisotropy. The highly simplified, hand‐waving explanation

• Magnetic anisotropy means that the magnetic properties (of the molecule) have an orientationaldependence.

• This means that the response to an external magnetic field depends on the direction in the molecule along which the field is applied, e.g., g‐value anisotropy, hard/easy axes of magnetization.

• Susceptibility becomes anisotropic. M = χ H

• This also means that the magnetic moment of the molecule prefers (lower potential energy) to lie along a certain direction, e.g., double well picture in transition metals.

Easy axis

Hard plane-90 0 90 180 270

Angle between easy axis and magnetic moment

Ener

gy (a

rb. u

.)

ΔE = |D|S2

Section 1.1 Magnetic anisotropy

0 00 00 0

xx

yy

zz

χ

Page 6: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Ch. 1. Introduction6

Magnetic anisotropy. The highly simplified, hand‐waving explanation

• Electrons experience the following interactions:

• attraction to the nucleus (Coulomb)

• repulsion by other electrons

• spin‐orbit coupling

• crystal field (Coulomb)

• magnetic field (Zeeman) 

• The main difference between 3d transition metals and f‐elements is that the crystal field and exchange interactions are much weaker in the latter, while spin‐orbit coupling can be much stronger.

Lueken99, Lueken08

Section 1.1 Magnetic anisotropy

Page 7: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Ch. 1. Introduction7

A highly simplified, hand‐waving explanation.

• Most free ions have an orbital angular momentum (except d5 high‐spin).

• In most complexes, the orbital angular momentum appears to have disappeared.(quenching of the orbital moment).

• This is due to the crystal field splitting of the d‐orbitals ("t2g‐eg").

Lueken99, Atkins‐PC

Section 1.2 Magnetic anisotropy in Transition Metal Clusters

Page 8: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Ch. 1. Introduction8

Quenching of the orbital moment.

• Orbital angular momentum is generally picturedas a circular motion of electrons around the nucleus.

• The (classical) orbital angular momentum is

• Translated into quantum mechanics, we can picture orbital angular momentum as being due to a circular motion of the electron through degenerate orbitals, that are related by a rotation.

• For example:

• dxz / dxy (x axis)

• dxy / dx2‐y2 (z axis) 

• px / py (z axis).

Mabbs/Machin

Section 1.2 Magnetic anisotropy in Transition Metal Clusters

l r p

x

z

x

y

dxz dxy

related by 90o rotn. about x axisx

y

x

y

dx2-y2 dxy

related by 45o rotn. about z axis

x

y

x

y

px py

related by 90o rotn. about z axis

Page 9: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Ch. 1. Introduction9

Quenching of the orbital moment.

• In transition metal complexes, the degeneracy of the d‐orbitals is lifted by the interaction with the ligands (crystal/ligand field splitting).

• As a result, the circular motion is no longer possible and the orbital angular momentum disappears.

• For Oh and Td complexes, only in certain cases an orbital angular momentum is retained

• Importantly, in lower symmetry, fewer orbitals are degenerate:

Mabbs/Machin

Section 1.2 Magnetic anisotropy in Transition Metal Clusters

x

z

x

y

dxz dxy

related by 90o rotn. about x axisx

y

x

y

dx2-y2 dxy

related by 45o rotn. about z axis

x

y

x

y

px py

related by 90o rotn. about z axis

NoE

YesT

NoA

orbital contribution?ground state type

Page 10: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Ch. 1. Introduction10

g‐Value anisotropy.

• Spin orbit coupling reintroduces orbital angular momentum (2nd order perturbation).

• Quantitative formula:

• = x, y, or z; m is the excited d‐orbital.

• For dxy ‐ dx2‐y2 mixing induced by lz:

• > 0 for d1 gz = g|| < ge.

• Anisotropy must correspond topoint group symmetry.

Mabbs/Machin; Atherton

Section 1.2 Magnetic anisotropy in Transition Metal Clusters

0

ˆ ˆ0 02 ; 2e e

m m

m l l mg g g g

E E

E Λ

2 2 2 2

2 2 82zz e exy x y xy x y

i ig g gE E E E

Page 11: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Ch. 1. Introduction11

Types of anisotropy.

• In transition metals we have three kinds:

1. Zero‐field splitting: We can express the D tensor in terms of Λ.

2. g‐anisotropy:

• Relation between ZFS and g value anisotropy (this relation does not always hold).

3. Anisotropic, antisymmetric exchange interactions Mabbs/Machin; Atherton; Abragam/Bleaney

Section 1.2 Magnetic anisotropy in Transition Metal Clusters

2 2

0

ˆ ˆ0 0;

m m

m l l mD

E E

D Λ

0

ˆ ˆ0 02 ; 2e e

m m

m l l mg g g g

E E

E Λ

2 2

( )4

x yz

x y

g gD g

E g g

0 00 00 0

xx

yy

zz

gg

g

g

3 12 2

0 00 00 0

, | |

xx

yy

zz

zz xx yy

DD

D

D D E D D

D

Page 12: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Ch. 1. Introduction12

Zero‐Field Splitting in Transition Metal Clusters.

• The cluster zero‐field splitting is a linear combination of:

• single‐ion zero‐field splittings,

• dipolar spin‐spin interaction (usually a minor contribution)

• In addition anisotropic  and antisymmetric exchange interactions lead to energy splittings in zero field.

Bencini/Gatteschi

Section 1.2 Magnetic anisotropy in Transition Metal Clusters

siS i i ij ij

i i jd d

D D D

Factors of Importance

1. Magnitude and sign of projection coefficients di.

2. Orientation of single ion zero‐field splitting.

3. Magnitude and sign of single ion zero‐field splitting.

Page 13: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Ch. 1. Introduction13

Zero‐Field Splitting in Transition Metal Clusters.

1. Magnitude and sign of projection coefficients di.

• Projection coefficients di < 1.

• For each pairwise coupling D decreases.

• In the end the energy barrier is only linearly dependent on the spin of the ground state:

For S = n x Si   Waldmann, IC,2007; Sessoli, ICA, 2008: "Waldmann's dire prediction" (Hill, DT, 2009)

Section 1.2 Magnetic anisotropy in Transition Metal Clusters

(2 1)(2 1)

i ii

S SdS S

SI 2

max1

2 1/2 1/

Ni

SIi

SE D SS

Page 14: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Ch. 1. Introduction14

Zero‐Field Splitting in Transition Metal Clusters.

• Example: Mn19: S = 83/2 but very small D. Why?

2. Orientation of single ion zero‐field splitting.

Section 1.2 Magnetic anisotropy in Transition Metal Clusters

[Mn6O4Br4(Me2dbm)6]Aromí, JACS, 99S = 12D = 0.009 cm‐1

[Mn6O2(sao)6(O2CPh)2(EtOH)4]Milios, JACS, 07S = 12D = ‐0.43 cm‐1

siS i i

id D D Ako, Powell, ACIE, 2006

Page 15: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Ch. 1. Introduction15

Energy scales in Transition Metals.

• Example Mn3+, d4 HS

Section 1.2 Magnetic anisotropy in Transition Metal Clusters

5D

3H, 3P

3F, 3G

1I, 3D, 1G 

1D, 1S

1D

1F

3P, 3F

1G

5E

5T2

Electron repulsion Ligand Field Oh

5B1g

5A1g

Ligand Field D4helongated

ms = 0

ms = ±1

ms = ±2

D

3D

Spin‐Orbit Coupling

E

ZFS

Page 16: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Ch. 1. Introduction16Section 1.3 Magnetic anisotropy in f‐Elements

Energy scale of interactions‐ Example Tb3+

7FJ01

2

3

4

5

6

electron repulsion spin‐orbit coupling crystal‐field splitting

describe ground doublet as effective spin 1/2 with very anisotropic g

Page 17: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Ch. 1. Introduction17Section 1.3 Magnetic anisotropy in f‐Elements

Dieke Diagram

• Because f‐electrons are little influenced by metal‐ligand bonding, a general scheme of energy levels in lanthanides can be constructed (Dieke diagram).

• To a first approximation, the energy difference between multiplets that differ in J only is due to spin‐orbit coupling.

• The energy difference between groups of multiplets that differ in L and or S is due to electron repulsion.

• Originally  obtained by analysis of the optical (absorption/luminescence) spectra of Ln3+:LaCl3and Ln3+:LaF3.

• The thickness of the lines indicates the crystal field splitting.

Page 18: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Ch. 1. Introduction18Section 1.3 Magnetic anisotropy in f‐Elements

Susceptibility of free ions

• The susceptibilities of lanthanide compounds at room temperature are often very close to the free ion values.

• Exceptions are Sm3+, Eu3+(low lying excited J‐multiplets).

Page 19: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Ch. 1. Introduction19Section 1.3 Magnetic anisotropy in f‐Elements

Crystal field splitting

• Going from a free ion to a compound, the symmetry around the f‐element ion is lowered, leading to splitting of the states.

• Group theory can be exploited to predict the way in which the terms split (symmetry aspect). 

• The magnitude of the splitting can be obtained from crystal field theory (purely Coulombic interaction of point dipoles) or ligand field theory (taking into account σ‐bonding) (energy aspect).

mJ

Page 20: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Ch. 1. Introduction20Section 1.3 Magnetic anisotropy in f‐Elements

Crystal field splitting: Stevens operator equivalents

• We can write the electrostatic potential created by the ligands as an expansion in terms of spherical harmonics.

• The resulting operators act on each f‐electron separately, hence for each state |J MJ>, the corresponding wavefunction must be determined. This is rather complicated.

• In order to reproduce the splittings, we can replace the coordinates in the spherical harmonics by angular momentum operator components, which have simple properties.

•• To take into account the noncommutation between the angular momentum operators, we have 

to form symmetrized products, e.g.

• We end up with a Hamiltonian of the form 

• The parameters Bkq are taken as free parameters

Lueken; Boča

ˆ ˆ ˆ, , , ( 1)x y zx J y J z J r J J

12

ˆ ˆ ˆ ˆx y y xxy J J J J

2 4 6

2 2 4 4 6 62 4 6

ˆ ˆˆ q q q q q qLF

q q qH B O B O B O

d‐electrons

f‐electrons

Page 21: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Ch. 1. Introduction21Section 1.3 Magnetic anisotropy in f‐Elements

Crystal field splitting: Stevens operator equivalents

• A table of common Stevens operator equivalents and the related spherical harmonics

• The properties of the angular momentum operators.

Lueken; Abragam, Bleany.

2 22 0 2

0 22

22 2 2 212 2 22

4 2 2 424 0 4 2 2

0 44

44 4 4 414 4 24

5 3 ˆ ˆ3 116

15 ˆ ˆ ˆ32

9 35 30 3 ˆ ˆ ˆ35 25 30 1 6 1 3 1256

315 ˆ ˆ ˆ512

z

z z

z rY O J J Jr

x iyY O J J

rz z r rY O J J J J J J J J

rx iy

Y O J Jr

ˆ ˆ ˆx yJ J iJ

shift operators

2J J

J J

+ J J

J J

ˆ | ( 1) | ˆ | | ˆ | ( 1) - ( 1) | 1 ˆ | ( 1) - ( 1) | 1

z J

J J

J J

J m J J J m

J J m m J m

J J m J J m m J m

J J m J J m m J m

J

Page 22: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Ch. 1. Introduction22Section 1.3 Magnetic anisotropy in f‐Elements

Crystal field splitting: Symmetry

• Furthermore, the CF Hamiltonian must have the same symmetry as the complexed ion.

• Hence, with increasing symmetry, more terms must be zero by symmetry

• For example in D4d symmetry, the crystal field Hamiltonian reads:

• A Table of nonzero CF parameters in different symmetries, ± means parameters with both +q and –q are nonzero.

0 0 0 0 0 02 2 4 4 6 6

ˆ ˆ ˆˆCFH B O B O B O

H. Lueken; Newman/Ng; C. Görller‐Wallrand

k |q|  D2h  D3h D4h D∞h D2d D4d C2v C3v C4v  C∞v C2h C3h C4h C2 S4 C12 0  +  + + + + + + + +  + + + + + + +2 1      ±2 2  +  +   ± ± ±4 0  +  + + + + + + + +  + + + + + + +4 1      ±4 2  +  +   ± ± ±4 3    +   ±4 4  +  + + + +  ± ± ± ± ±6 0  +  + + + + + + + +  + + + + + + +6 1      ±6 2  +  +   ± ± ±6 3    +   ±6 4  +  + + + +  ± ± ± ± ±6 5      ±6 6  +  + + +   ± ± ± ± 

Page 23: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Ch. 1. Introduction23Section 1.3 Magnetic anisotropy in f‐Elements

Crystal field splitting: Kramers Theorem

• Whatever the symmetry, for an odd number of electrons, all microstates are doubly degenerate, in the absence of a magnetic field.

• This is known as Kramers' theorem, and ions with half integer angular momentum ground states are called Kramers ions.

• This degeneracy has major implications for spin dynamics, in that quantum tunnelling cannot be induced by the crystal field.

H. Lueken; Abragam/Bleaney

Page 24: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Ch. 1. Introduction24Section 1.3 Magnetic anisotropy in f‐Elements

Crystal field splitting: Crystal quantum number

• A crystal field interaction term BkqÔkq will mix mJ states only if mJ –mJ' = q.

• We can define a new quantum number, the crystal quantum number μ to designate a group ofstates satisfyingmJ = μ (mod q), i.e. mJ = μ + n q (n = integer).

• For even numbers of electrons: For odd numbers of electrons:

• For odd numbers of electrons, there is a one‐to‐one correspondence with the irreduciblerepresentations that the states belong to.

• For even numbers of electrons, the groups of states can contain states belonging to two different irreducible representations, which can be distinguished using 0+, 0– and 1+, 1–.

• ±μ states are degenerate

Wybourne; Goerller‐Wallrand

Page 25: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Ch. 1. Introduction25Section 1.3 Magnetic anisotropy in f‐Elements

Crystal field splitting: Crystal field ground states

• The shape of the electron distribution is different for the different CF states.

• Hence by choosing the ligands, one can influence the CF state energies.

• Hence different ground states can be obtained.

• The ground state and the energy splittings can be influenced by judicious choice of the ligands

• Note that the mJ states are the eigenstates only in C∞v, D∞h and D4d symmetries.

J. Sievers, Z. Phys. B, 45, 289 (1982), J.D. Rinehart, Chem. Sci., 2, 2078 (2011); Lueken

Page 26: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Ch. 1. Introduction26Section 1.3 Magnetic anisotropy in f‐Elements

Magnetic and spectroscopic measurements

• The magnetic susceptibility is the thermal average of the contributions due to the occupied microstates.

• Luminescence spectroscopy allows direct determination of the splitting of the ground Russell‐Saunders multiplet.

• Absorption/MCD spectroscopy allows determination of CF splittings of excited states:beyond Russell‐Saunders coupling.(intermediate coupling: CF and SOC at same level)

• Far infrared/inelastic neutron scattering allows investigation of intramultiplet excitations.

300K

Page 27: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

1. Introduction2. Single Crystal Magnetometry3. High‐Frequency EPR Spectroscopy4. Inelastic Neutron Scattering5. Electronic Absorption and Luminescence

Page 28: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Ch. 2. Single Crystal Magnetometry28

Contents

2.1 Motivation

2.2 Magnetic susceptibility tensor

2.3 Determination

(0)  Large enough crystal

(1) Faceindex

(2) Define the experimental space

(3) Transformation matrix

(4) Mount the crystal

(5) Three orthogonal rotations

(6) Fitting the tensor elements

(7) Symmetry and equivalent considerations

(8) Diagnalization

(9) Express in abc space

(10) ground state determination

Page 29: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Ch. 2. Single Crystal Magnetometry29Section 2.1 Motivation

• Determination of the molecular principal axes• magneto-relations• Possibility of ground state determination / /

ˆ2effJ z z zg g J J J

R. Sessoli,et al, Angew Chem Int Ed 2012, 164, 1238;

0 2 4 6 8 10 12 14 160

20

40

60

80

mT along easy mT along media mT along hard

m-1 along easy

linear fit

T / K

mT

/ em

u m

ol-1K

0.00

0.05

0.10

0.15

0.20

0.25

m

-1 / mol em

u-1

S.‐D. Jiang, X.‐Y. Wang,unpublished;

Page 30: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Ch. 2. Single Crystal Magnetometry30Section 2.2 magnetic susceptibility tensor

• Molecular tensor relation:

• In the paramagnetic limit, crystal behavior is the sum of all the molecules’ one in the unit cell, so is  tensor;

• In the paramagnetic limit, the molecular tensor can be fully determined only when the molecule symmetry is not lower than the crystal symmetry:

(a) Only one symmetrically independent molecule in the unit cell;(b1) The molecules are related by inversion center (P-1 space group) or(b2) The molecule is at highest symmetry position;

Neumann’s Principle:the symmetry elements of any physical property of a crystal must include all the symmetry elements of the point group of the crystal

†qp

mij

qp

mij AA pq

† q

qp

mij

qp

q

mij

Cryij AA pq

Page 31: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Ch. 2. Single Crystal Magnetometry31Section 2.3 Determination

(0) large enough single crystal• The background of the rotator provided by Quantum Design MPMS‐XL SQUID 

is around 10‐4 emu;• The crystal should be larger than 0.5 mg;(1) Face index

Page 32: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Ch. 2. Single Crystal Magnetometry32Section 2.3 Determination

(2) Define the experimental space• b as X axis;• (001) is XY plane;• Z follows right hand rule;

(3) Transformation matrix• Derive the abc unit vector into the same length!• High school geometry game• Complicated!

ZYX

cba

18.1271.040.20093.11041.978.1

Page 33: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Ch. 2. Single Crystal Magnetometry33Section 2.3 Determination

(4) Mount the crystal• L shaped Cu-Be support: small background;• Fixed with Apiezon N-grease;

Rotation axis

b axis

This abc‐XYZ relation is not the one defined  before

Page 34: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Ch. 2. Single Crystal Magnetometry34Section 2.3 Determination

(5) Three orthogonal rotations

-90 0 90 180 2700

5

10

15

20

25

30x rotation = 90

m /

emu

mol

-1

/

1.7 K2.0 K2.3 K2.6 K3.1 K3.6 K4.1 K4.8 K5.5 K6.4 K7.4 K8.6 K10.0 K12 K13 K16 K

-90 0 90 180 2700

5

10

15

20

25

30

35

40

y rotation = 0

m /

emu

mol

-1

/

1.7 K2.0 K2.3 K2.6 K3.1 K3.6 K4.1 K4.8 K5.5 K6.4 K7.4 K8.6 K10.0 K12 K13 K16 K

-90 0 90 180 2700

5

10

15

z rotation = 90

m /

emu

mol

-1

/

1.7 K2.0 K2.3 K2.6 K3.1 K3.6 K4.1 K4.8 K5.5 K6.4 K7.4 K8.6 K10.0 K12 K13 K16 K

Page 35: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Ch. 2. Single Crystal Magnetometry35Section 2.3 Determination

(6) Fitting the tensor elements

cossinsincossin

cossinsincossin

0

zzzyzx

yzyyyx

xzxyxxT

HM

Surface fitting with two variables

Curve fitting with one variables (three functions parallelly)

Page 36: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Ch. 2. Single Crystal Magnetometry36Section 2.3 Determination

(7) Symmetry and equivalent considerations• Neuman’s principle: b of monoclinic system is always one of the principal axes• equivalent positions

-90 0 90 180 2700

5

10

15

20

25

m /

emu

mol

-1

Angle(for x and y, for z) /

x rotation y rotation z rotation fitting

T = 3 KH = 0.1 T

7019.1596.161.1096.122.143.161.1043.140.8

tensor in XYZ space

Page 37: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Ch. 2. Single Crystal Magnetometry37Section 2.3 Determination

(8) Diagonalization

7019.1596.161.1096.122.143.161.1043.140.8

82.096.0

54.23 {‐0.577552,‐0.108217,0.809149}

{‐0.104866,‐0.973128,‐0.204999}

{‐0.80959,0.20325,‐0.550684}

Fitting results

eigenvalues eigenvectors in XYZ

ZYX

cba

18.1271.040.20093.11041.978.1

{‐0.0164857,‐0.0593218,0.0664437}

{‐0.102119,0.00984252,‐0.0168336}

{0.0249881,‐0.0625164,‐0.0452197}

Eigenvectors in abc

Diagonalization

Page 38: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Ch. 2. Single Crystal Magnetometry38Section 2.3 Determination

(9) expressed in abc space

pseudo inversion

Page 39: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Ch. 2. Single Crystal Magnetometry39Section 2.3 Determination

(10) Ground state determination• Curie Law: Population is not changed a lot in the temperature range• The first excited state is high enough.

0 2 4 6 8 10 12 14 160

20

40

60

80

mT along easy mT along media mT along hard

m-1 along easy

linear fit

T / K

mT

/ em

u m

ol-1K

0.00

0.05

0.10

0.15

0.20

0.25

m

-1 / mol em

u-1

181 2 SSgT

/ /ˆ2eff

J z z zg g J J J

Page 40: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Magnetic Anisotropy40

Molecular Nanomagnets

Transition Metal Clusters f‐Elements

Field‐dependent:g‐value Anisotropy

Field‐independent:Zero‐Field Splitting

Field‐independent:Crystal‐Field Splitting

high‐frequencyelectron paramagnetic resonance

inelastic neutron scattering

electronic absorption,luminescence

Spectroscopic techniques

Ch. 1. Introduction

Page 41: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

1. Introduction2. Single Crystal Magnetometry3. High‐Frequency EPR Spectroscopy4. Inelastic Neutron Scattering5. Electronic Absorption and Luminescence

Page 42: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Ch. 3. High‐Frequency EPRSection 3.1 Theoretical Background and Experimental Considerations 42

Basics of EPR

• The Zeeman term describes the interaction of the spin with a magnetic field.

• In the absence of other interactions the field is chosen along the z‐axis.

• The electronic Zeeman term then has the form:

• Accordingly, the energies of the spin states depend on mS :

• g = 2.00235… for a free electron.

Zeeman ˆˆB zg BSΗ

B SE g BmNote: remember Ŝz |S ms I mI> = ms |S ms I mI>.

Ener

gy

Magnetic Field

12 BE g B

12 BE g B

Ener

gy

Magnetic Field

52 BE g B 32 BE g B 12 BE g B 12 BE g B 32 BE g B 52 BE g B

For S = 1/2 For S = 5/2

α

β

Page 43: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Ch. 3. High‐Frequency EPRSection 3.1 Theoretical Background and Experimental Considerations 43

Basics of EPR

• For S = 1/2, the energy difference between the two mS levels is:

• If the energy of the electromagnetic radiation matches the energy difference, radiation can be absorbed. The spin interacts with the magnetic field of the electromagnetic radiation.

• This is called the resonance condition:

• For technical reasons, in EPR conventionally the frequency is kept constant, while the field is swept.

• The EPR selection rule is therefore ΔS = 0, ΔmS = ±1 (perpendicular mode)

Bh g B

BE g B

S = ½

mS = ½

mS = -½

Page 44: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Ch. 3. High‐Frequency EPRSection 3.1 Theoretical Background and Experimental Considerations 44

Basics of EPR – Selection rules.

• Which transitions can be observed?

• Typically microwave magnetic field b1 external magnetic field B0.

• What about the Zeeman interaction of b1 with the spin?

• What is the action of Ŝx and Ŝy on the spin state |S ms I mI> ?

• It is useful to make combinations of Ŝx and Ŝy, called shift operators:

• The shift operators change the mS quantum number by ±1:

• The EPR selection rule is therefore ΔmS = ±1

• In addition ΔS = 0.

Zeeman1 ,

ˆˆB x yg b SΗ

ˆ ˆ ˆ ˆ ˆ ˆx y x yS S iS S S iS

- s s s sS | ( 1) - ( -1) | -1 S m S S m m S m

+ s sS | ( 1) - ( 1) | 1 s sS m S S m m S m

Page 45: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Ch. 3. High‐Frequency EPRSection 3.1 Theoretical Background and Experimental Considerations 45

Basics of EPR – High‐frequency EPR

• Conventional EPR uses 9 GHz radiation frequency.

• High‐frequency EPR with frequencies up to 1000 GHz possible.

• High‐frequency means high field, which gives increased g‐value resolution.

• This is usually not of interest in molecular magnetism

Photosystem I, light‐induced P700+•, A. Angerhofer inO.Y. Grinberg (Ed.), Very High Frequency EPR

B

E zyx

Field

9.74 GHz

108 GHz

217 GHz

325 GHz

437 GHz

Page 46: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Ch. 3. High‐Frequency EPRSection 3.1 Theoretical Background and Experimental Considerations 46

Zero‐Field Splittings: Axial ZFS

• Spin Hamiltonian

• The D parameter lifts the degeneracy of themS levels.

• For D < 0, themS = ±S levels are lowest in energy.

• For D > 0, themS = 0 ormS = ±½ are lowest in energy.

• D can be 0‐102 cm‐1.

• For S = 1, energy gap between mS = 0 or mS = ±1 equals D.

zS = 1

mS = +1

mS = 0

mS = -1

mS = 0

mS = ±1

mS = ±1

mS = 0

D < 0 D > 0

2 2 2 2 2 21ZFS 2

ˆ ˆ ˆ ˆ ˆ ˆˆ ( ) ( )z x y zDS E S S DS E S S H

Page 47: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Ch. 3. High‐Frequency EPRSection 3.1 Theoretical Background and Experimental Considerations 47

Ene

rgy

Field

mS = 1

mS = -1

D

• Only ΔMS = ±1 allowed.

• At X‐band microwave quantum too small.

• At higher frequencies transitions can be observed.

• Large ZFS ions with integer spin are therefore traditionally called EPR silent

X Band W Band

Large Zero‐Field Splittings.

mS = 0

Page 48: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Ch. 3. High‐Frequency EPRSection 3.1 Theoretical Background and Experimental Considerations 48

High‐Field limit

S = 1, D = ‐1 cm‐1 = ‐30 GHz, ν = 150 GHz, T = 300 K

θ = 0: B0 || z θ = 90: B0 || z

Page 49: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Ch. 3. High‐Frequency EPRSection 3.1 Theoretical Background and Experimental Considerations 49

High‐Field limit

S = 1, D = ‐1 cm‐1 = ‐30 GHz, ν = 150 GHz, T = 300 K

Absorption First derivative

Forbidden transition

Page 50: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Ch. 3. High‐Frequency EPRSection 3.1 Theoretical Background and Experimental Considerations 50

High‐Field limit

• [Ni(5‐methylpyrazole)6](ClO4)2• S = 1, D = 0.72 cm‐1 = 21.6 GHz, T = 100 K

Collison, J. Chem. Soc., Faraday Trans., 1998, 3019

9.448 GHz

34.112 GHz

178.114 GHz

Page 51: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Ch. 3. High‐Frequency EPRSection 3.1 Theoretical Background and Experimental Considerations 51

High‐Field limit

• HFEPR allows the determination of the sign of D

At low temperature, and B0 // z:

• For D < 0 the low field line remains.

• For D > 0, the high field line remains.

0 1000 2000 3000 4000 5000

-400

-300

-200

-100

0

100

200

300

magnetic field [mT]

ener

gy [G

Hz]

B0//z, S = 3, D < 0 S = 3, D > 0

0 1000 2000 3000 4000 5000

-300

-200

-100

0

100

200

300

400

magnetic field [mT]

ener

gy [G

Hz]

Page 52: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Ch. 3. High‐Frequency EPRSection 3.1 Theoretical Background and Experimental Considerations 52

High‐Field limit

• For g mB H >> D and uniaxial anisotropy there are 2S resonance lines.

• The resonance fields are given by:

• B// = (ge/g//)[B0+(2MS‐1)D] B = (ge/g)[B0‐(2MS‐1)D/2]

• Spacing: 2D/gμB for B//z D/gμB for Bz

• Example: D negative

B//

B

2D/gB

kBT<<gBH D/gB

Page 53: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Ch. 3. High‐Frequency EPRSection 3.2 Examples 53

Example [Fe4(L)2(dpm)6]

• L = 2‐(bromomethyl)‐2‐(hydroxymethyl)‐1,3‐propanediol.

• Antiferromagnetic exchange coupling leads to S = 5 ground state. MS = −5, −4, …, 4, 5.

• Lines with large spacing at low fields, lines with small spacing at high field.

• That means that D < 0.

• From fit (black): D = −0.432 cm‐1,  B40 = 2 × 10‐5 cm‐1.

• B40 is a higher order ZFS term. HZFS = D Ŝz2 + B40Ô40.

[Accorsi, JACS, 2006]

Page 54: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Ch. 3. High‐Frequency EPR54

Example Ni(PPh3)2Cl2S = 1, D = +13.20 cm‐1 = 396 GHz, E = 1.85 cm‐1, g = 2.20 (isotropic), T = 4.5 K

J. Krzystek, Inorg. Chem., 41, 4478 (2002)

|+1> ‐ |‐1>

D=13.2 cm‐1

|0>

|+1> + |‐1>2E=3.7 cm‐1

Section 3.2 Examples

Page 55: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Ch. 3. High‐Frequency EPR55

Example Ni(PPh3)2Cl2S = 1, D = +13.20 cm‐1 = 396 GHz, E = 1.85 cm‐1, g = 2.20 (isotropic), T = 4.5 K

Rhombic anisotropy: x‐ and y‐axis different, θ and φ both important.

θ = 0, φ = 0: B0 || z θ = 90, φ = 90: B0 || y θ = 90, φ = 0: B0 || x

z

y

x

θ

φ J. Krzystek, Inorg. Chem., 41, 4478 (2002)

Section 3.2 Examples

Page 56: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Ch. 3. High‐Frequency EPR56

Example Ni(PPh3)2Cl2S = 1, D = +13.20 cm‐1 = 396 GHz, E = 1.85 cm‐1, g = 2.20 (isotropic), T = 4.5 K

Rhombic anisotropy: x‐ and y‐axis different, θ and φ both important.

yz‐plane xz‐plane xy‐plane

J. Krzystek, Inorg. Chem., 41, 4478 (2002)

Section 3.2 Examples

Page 57: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Ch. 3. High‐Frequency EPR57

Example Ni(PPh3)2Cl2• B not much larger than D: no high‐field simplification.

• Fictitious 2000 GHz spectrum goes up to 80 T.

Section 3.2 Examples

Page 58: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Ch. 3. High‐Frequency EPR58

Example Ni(PPh3)2Cl2• B not much larger than D: no high‐field simplification.

• Fictitious 2000 GHz spectrum goes up to 80 T.

Section 3.2 Examples

Page 59: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Ch. 3. High‐Frequency EPRSection 3.1 Theoretical Background and Experimental Considerations 59

Where can I do high‐frequency (ν > 95 GHz) EPR on molecular nanomagnets?

• France: LNCMI Grenoble (Barra)

• Germany: IFW Dresden (Kataev)

• Germany: HLD Dresden (Zvyagin)

• Germany: Uni Stuttgart (Van Slageren)

• Italy: CNR Pisa (Pardi)

• USA: HMFL Tallahassee (Hill, Krzystek, Ozarowski).

• Japan: Kobe (Nojiri)

Page 60: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Ch. 3. High‐Frequency EPR60Section 3.3 Frequency domain methods

Van Slageren, Top. Curr. Chem. 2012

Frequency Domain Magnetic ResonanceEPR: External field required FDMR: No field required

0

S = ½

mS = ½

mS = ‐½

mS

Page 61: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Ch. 3. High‐Frequency EPR61

Monochromatic sweepable sources vs interferometer (FTIR) based methods

Monochromatic sweepable sources

• synthesizer + multipliers or backward‐wave oscillators (+ multipliers)

+ high resolution, easier below 10 cm–1.

– limited range

Interferometer

• Mercury lamp or synchrotron

+ easy to obtain ultra broad band spectrum, easier at higher frequencies > 25 cm–1

– field/frequency not independent.

Section 3.3 Frequency domain methods

Van Slageren, Top. Curr. Chem. 2012; Schnegg, HZB Berlin

Mn12ac

Page 62: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Example 1. [MnIII6O2(Me2Bz)2(Et‐sao)6(EtOH)4] (ΔE = 84 K)

• S = 12. D = –0.43 cm‐1 from magnetisation. ΔE = 84 K (record).

• Powder pellet sample. 6 sharp magnetic resonance lines

• Oscillating baseline due to interference within pellet

• Single scan takes ca. 30 seconds

Section 3.3 Frequency domain methodsCh. 3. High‐Frequency EPR

62

Carretta, Van Slageren et al., PRL 2008, Pieper, Van Slageren et al. PRB 2010

4 6 8 10

10-2

10-1

100

Tran

smis

sion

Wavenumber (cm-1)

5K 10K 15K 20K 30K 40K

6 5 4 3 2 1

4 6 8 10

10-2

10-1

100

Tran

smis

sion

Wavenumber (cm-1)

5K 10K 15K 20K 30K 40K

6 5 4 3 2 1

300 GHz120 GHzd

Page 63: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Example 1. [MnIII6O2(Me2Bz)2(Et‐sao)6(EtOH)4] (ΔE = 84 K)

• Giant spin model (ground state only).

• H =DŜz2 + B4

0 Ô40

• D = ‐0.362 cm‐1

• B40 = ‐6.08 x 10‐6 cm‐1

Section 3.3 Frequency domain methodsCh. 3. High‐Frequency EPR

63

Carretta, Van Slageren et al., PRL 2008, Pieper, Van Slageren et al. PRB 2010

4.0 6.0 8.0 10.0

10-2

10-1

100

10-1

1000.50 0.75 1.00 1.25

5 K 10 K 15 K 20 K 30 K 40 K

Energy (meV)

Tran

smis

sion

10 K Expt. Fit

Tran

smis

sion

Wavenumber (cm-1)

-12 -8 -4 0 4 8 12

-60

-50

-40

-30

-20

-10

0

Ene

rgy

(cm

-1)

MS

6543

2

1

-12 -8 -4 0 4 8 12

-60

-50

-40

-30

-20

-10

0

Ene

rgy

(cm

-1)

MS

6543

2

1

Page 64: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Section 3.3 Frequency domain methodsCh. 3. High‐Frequency EPR

64

Example 1. [MnIII6O2(Me2Bz)2(Et‐sao)6(EtOH)4] (ΔE = 84 K)

• Comparison with HFEPR

• Single crystal.

• D = –0.360(5) cm–1

• B40 = –5.7(5)  10–6 cm–1

• 7 Frequencies x 7 T sweep....

Datta, Dalton Trans. 2009

Page 65: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Example 2. [Ni(PPh3)2Cl2]

• Read off D and E from single scan.

Section 3.3 Frequency domain methodsCh. 3. High‐Frequency EPR

65

Vongtragool, IC, 2003

0 5 10 15 20 25 300.1

1.0

0.7

Tran

smis

sion

Frequency (cm-1)

0.4

0.2

|+1> - |-1>

D=13.2 cm-1

|0>

|+1> + |-1>2E=3.7 cm-1

Page 66: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Example 3. (NBu4)+[Ln(Pc)2]–

• Bruker 113v FTIR, Ln = Ho.

Section 3.3 Frequency domain methodsCh. 3. High‐Frequency EPR

66

Marx, Dörfel, Moro, Waters, Van Slageren, unpublished

20 40 60 80 10010-2

10-1

100

Tran

smis

sion

Wavenumber / cm-1

6T 5T 4T 3T 2T 1T 0T

Divide by 6T, 10K spectrum

Divide by 0T, 5K spectrum

Page 67: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

1. Introduction2. Single Crystal Magnetometry3. High‐Frequency EPR Spectroscopy4. Inelastic Neutron Scattering5. Electronic Absorption and Luminescence

Page 68: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Introduction

• Neutrons can have energies in the same range as the microwave/THz electromagnetic radiation used in EPR.

• However, the neutron wavelength is much shorter, and can be of the order of bond distances.

• Some data on the neutron:

• Mass m = 1.674927351(74)×10−27 kg

• Magnetic moment μ = –1.04187563(25)×10−3 μB.

• Spin s = ½.

• De Broglie wavelength :

• For an energy of E = 25 cm–1 ≈ 3 meV, λ = 5 Å

• Rather than the wavelength, we can deal with the wave vector 

Section 4.1 Theoretical background and experimental considerationsCh. 4. Inelastic Neutron Scattering

68

9.044605 [Å]2 [meV]

h hp mE E

2k

Page 69: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Introduction

• Because the wavelength is much shorter than for photons of the same energy, we have to consider momentum conservation in addition to energy conservation.

• Energy conservation: the energy change of the neutron is taken up by the sample: ΔE = ħω = Ef – Ei.

• Momentum conservation: Δ

• Neutrons are detected  at different angles.

• Time of arrival corresponds to kinetic energy

• Plot of S(Q,ω).

• Selection rules ΔS = 0, ±1; ΔmS = 0, ±1

Section 4.1 Theoretical background and experimental considerationsCh. 4. Inelastic Neutron Scattering

69

ESample

Page 70: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Introduction

• Determining the nature of the excitaton from the Q‐dependence.

• Magnetic excitation:

• Phonons:

• Generally confine to low Q to focus on magnetic transitions

Section 4.1 Theoretical background and experimental considerationsCh. 4. Inelastic Neutron Scattering

70

Q

E

ΔS 0:

ΔS 1: → , → 0

→ , →

, , ∝1

1 ⁄

Q

I

I

Q

Page 71: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Example: Mn6

• Compare INS with FDMR

Section 4.1 Theoretical background and experimental considerationsCh. 4. Inelastic Neutron Scattering

71

-4 -2 0 2 4 6 8 10 120

1

2

3

4

5

6

T = 1.5 K T = 12.0 K T = 17.0 K

Inte

nsity

(a.u

.)

Energy loss (cm-1)

= 6.7 Å

4 6 8 10

10-2

10-1

100

Tran

smis

sion

Wavenumber (cm-1)

5K 10K 15K 20K 30K 40K

6 5 4 3 2 1

4 6 8 10

10-2

10-1

100

Tran

smis

sion

Wavenumber (cm-1)

5K 10K 15K 20K 30K 40K

6 5 4 3 2 1

Pieper, PRB, 2010

Page 72: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

FDMR vs HFEPR vs INS

Section 4.1 Theoretical background and experimental considerationsCh. 4. Inelastic Neutron Scattering

72

0 4 8 12 16 20 24 280.0

0.2

0.4

0.6

0.8

1.0

In

tens

ity d

eter

min

ed b

y B

oltz

man

n po

pula

tions

Temperature (K)

EPR INS

HF Cavity EPR HFEPR/FDMRS INS

Selection rules ∆MS = ±1, ∆S = 0 ∆MS = ±1, ∆S = 0 ∆MS = 0, ±1, ∆S = 0, ±1

Sample quantity Few mg 50 – 200 mg 1 g

Resolution 10-2 cm-1 10-2 cm-1 0.5 cm-1

Intensity

Page 73: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Example: Mn6

• Take advantage of the ΔS = 0, ±1 selection rule of INS

Section 4.1 Theoretical background and experimental considerationsCh. 4. Inelastic Neutron Scattering

73

-4 -2 0 2 4 6 8 10 120

1

2

3

4

5

6

T = 1.5 K T = 12.0 K T = 17.0 K

Inte

nsity

(a.u

.)

Energy loss (cm-1)

= 6.7 Å

0 4 8 12 16 200.0

0.5

1.0

1.5

2.0

Inte

nsity

(arb

.u.)

Energy loss (cm-1)

T = 6.0 K T = 18.0 K

= 5.0 Å

Pieper, PRB, 2010

Page 74: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Example: Mn6

• The Q dependence reveals the nature of the spin excitation

Section 4.1 Theoretical background and experimental considerationsCh. 4. Inelastic Neutron Scattering

74

0 4 8 12 16 200.0

0.5

1.0

1.5

2.0

Inte

nsity

(arb

.u.)

Energy loss (cm-1)

T = 6.0 K T = 18.0 K

= 5.0 Å

ΔS 0:

ΔS 1: → , → 0

→ , → Q

I

I

Q

Pieper, PRB, 2010

Page 75: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

1. Introduction2. Single Crystal Magnetometry3. High‐Frequency EPR Spectroscopy4. Inelastic Neutron Scattering5. Electronic Absorption and Luminescence

Page 76: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Lanthanides

• f‐Orbitals are buried deep within the electron cloud

• ff‐transitions are Laporte‐forbidden (u ↔ u)

• Hence, the extinction coefficients are very small (ε ~ 1 M–1 cm–1), cf. dd 102, CT 104.

• On the other hand, the absorption bands are very narrow, and split due to the CF splitting of the excited state.

Section 5.1 Electronic AbsorptionCh. 5. Electronic Absorption and Luminescence

76

Bünzli in Lanthanide Luminescence: Photophysical, Analytical and Biological Aspects, Springer Ser Fluoresc (2010), DOI 0.1007/4243_2010_3

Eu3+

Page 77: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Lanthanides

• Excitations can be electric dipole, magnetic dipole, or electric quadrupole

• In actinides, extinction coefficients are larger.

• Judd‐Ofelt theory describes the absorption intensityof ED transitions.

• Parameters Ω are phenomenological.

Section 5.1 Electronic AbsorptionCh. 5. Electronic Absorption and Luminescence

77

Bünzli in Lanthanide Luminescence: Photophysical, Analytical and Biological Aspects, Springer Ser Fluoresc (2010), DOI 0.1007/4243_2010_3Mills, Nature Chem. 2011 

Page 78: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Lanthanides

• Many lanthanides are strongly luminescent.

Section 5.2 LuminescenceCh. 5. Electronic Absorption and Luminescence

78

Natrajan, EUFEN2, COST CM 1006, Dublin 2013

Page 79: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Lanthanides

• The splitting of the luminescence band yields information on thecrystal field splitting of the ground state.

Section 5.2 LuminescenceCh. 5. Electronic Absorption and Luminescence

79

H.‐D. Amberger, many publications; Görller‐Wallrand, many publications; Boulon, ACIE, 2013

mJ

Page 80: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Magnetic Circular Dichroism

• The intensity of an absorption band due to an electronic transition between two states is proportional to the square of the electric dipole matrix element:

• In MCD, the difference in absorption between left‐ (σ‐)and right‐(σ+)‐circularly polarised light is measured:

• No MCD without field.

Applied magnetic field can:

• Lift magnetic degeneracies of the ground and excited states.

• Change the population of the levels via a new Boltzmann distribution.

• Mix the levels G and X with other electronic levels.

Section 5.3 Magnetic Circular DichroismCh. 5. Electronic Absorption and Luminescence

80

2I X G

12MCD

X

G

K

Page 81: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Magnetic Circular Dichroism

• This leads to three contributions to the MCD spectrum:

• the A‐term, due to Zeeman splitting of the ground and/or excited degenerate states,

• the B‐term, due to field‐induced mixing of states, 

• the C‐term, due to a change in the population of molecules over the Zeeman sublevels of a paramagnetic ground state.

• Δε is MCD extinction coefficient.

• E = hν.

• γ is bunch of constants including dielectric permittivity.

• μB is Bohr magneton.

• f(E) is lineshape function.

Ch. 5. Electronic Absorption and Luminescence81

01 0

( ) ( )BB

Cf EB A B f EE E k T

Section 5.3 Magnetic Circular Dichroism

Page 82: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Magnetic Circular Dichroism. Example 1 [Cr8F8Piv16]

• UV/Vis spectrum gives energies of excited states.

• Spin‐allowed transitions stronger than spin‐forbidden.

• Exchange coupling enhances intensity of spin‐forbidden transitions.

• Resolution typically not enough to resolve all transitions.

Ch. 5. Electronic Absorption and Luminescence82

30000 25000 20000 150000.0

0.2

0.4

Abso

rptio

n

Wavenumber (cm-1)Piligkos, Van Slageren, Dalton Trans. 2010

Section 5.3 Magnetic Circular Dichroism

Page 83: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Magnetic Circular Dichroism. Example 1 [Cr8F8Piv16]

• MCD signal can be both positive and negative.

• This often leads to much better resolution.

• Spin forbidden transitions are often pronounced.

Section 5.1 Theoretical background and experimental considerationsCh. 5. Electronic Absorption and Luminescence

83

Piligkos, Van Slageren, Dalton Trans. 2010

30000 25000 20000 15000

-5

0

5

corr

ecte

d M

CD

/ m

deg

30000 25000 20000 150000.0

0.2

0.4

Abso

rptio

n

Wavenumber (cm-1)

4T1 4T2 2T1 2E4T1 4T2 2T1 2E2T2

MCD

UV/Vis

Page 84: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Magnetic Circular Dichroism. Example 1 [Cr8F8Piv16]

• MCD splitting of absorption bands is related to ZFS.

• H = d Ŝz2 + e (Ŝx2‐Ŝy2).

• d = ‐0.364 cm‐1; e = 0.119 cm‐1.

• cf. d = ‐0.334 cm‐1 (strong exchange)

• cf. d = ‐0.24 cm‐1; e = 0.032 cm‐1 (microscopic, neglecting dipolar).

Ch. 5. Electronic Absorption and Luminescence84

Piligkos, Van Slageren, Dalton Trans. 2010; Bradley, Dalton Trans. 2008

30000 25000 20000 15000

-5

0

5

corr

ecte

d M

CD

/ m

deg

4T1 4T2 2T1 2E2T2

MCD

Section 5.3 Magnetic Circular Dichroism

Page 85: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Magnetic Circular Dichroism. Example 1 [Cr8F8Piv16]

• MCD intensity is related to the magnetization of the sample.

• It gives information about the magnetic properties of the cluster.

• MCD intensity vs. B or vs. B/T shows more than just a stepat the level crossing from S = 0 to S = 1.

• No MCD intensity is expected for the S = 0 state.

Ch. 5. Electronic Absorption and Luminescence85

Piligkos, Van Slageren, Dalton Trans. 2010

-12 -8 -4 0 4 8 12-60

-40

-20

0

20

40

60

80Cr8F8Piv16 MCD in poly(dimethylsiloxane) mull = 415 nm

Rot

atio

n (m

deg)

B / T

1.6 K 3.0 K 5.2 K 10 K

0.0 0.5 1.0 1.5 2.0 2.5

-10

0

10

20

30

40

50

60

= 415 nm = 24096 cm-1

4A2 -> 4T1

Rot

atio

n (m

deg)

H/2kT

T = 1.6 K T = 2.8 K T = 5.0 K T = 10 K

0

2

4

S = 0S = 1

S = 2

E

M / B

B

Section 5.3 Magnetic Circular Dichroism

Page 86: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Magnetic Circular Dichroism. Example 1 [Cr8F8Piv16]

• MCD curves cannot be simulated by summingcontributions due to different spin states.

• Mixing between spin states occurs.

• Rhombic term (E) necessary.

• Spin Hamiltonian:

• MCD intensity

• .

Ch. 5. Electronic Absorption and Luminescence86

Piligkos, Van Slageren, Dalton Trans. 2010

0.0 0.5 1.0 1.5 2.0 2.5

-10

0

10

20

30

40

50

60

BB / 2kT

rota

tion

/ mde

g

experiment fit

0.0 0.5 1.0 1.5 2.0 2.5

-10

0

10

20

30

40

50

60experiment fit

BB / 2kT

rota

tion

/ mde

g

S = 3/2g = 1.98D = ‐0.58 cm‐1

E / D = 0.1J = ‐3.5 cm‐1

2 2 2ˆ ˆ ˆ ˆ ˆ2 i j i z i x y Bi j i i

J d S e S S

S S S g BH

Axial fit (E = 0)

Rhombic fit (E ≠ 0)

2

0 0

ˆ

ˆ sin d d4

ˆ

x x yzi

i y y xzii

z z xyi

l S M

N l S ME S

l S M

Section 5.3 Magnetic Circular Dichroism

Page 87: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Magnetic Circular Dichroism. Example 2 [Ln(Pc)2]–

• Anions in EtOH:MeOH glass. 

• Transitions based on ligand.

• MCD bands have derivative lineshapes: A‐term intensity.

• Lowest‐energy transition has opposite MCD sign for Tb3+ and Dy3+.

Section 5.1 Theoretical background and experimental considerationsCh. 5. Electronic Absorption and Luminescence

87

Krivokapic, Waters, Van Slageren, unpublished

10000 20000 30000 40000

-3000

0

3000

MC

D in

tens

ity (m

deg)

wavenumber (cm-1)

[DyPc2]-, 1.6 K, 7 T

[TbPc2]-, 1.6 K, 7 T

15000 20000 25000 30000 350000.0

0.2

0.4

0.6

0.8

1.0

Abs

orpt

ion

Wavenumber (cm-1)

UV/Vis MCD

N

N N

N

N

N

N N

Page 88: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Magnetic Circular Dichroism. Example 2 [Ln(Pc)2]0/–

• Hysteresis is observed for all complexes in spite of ligand based nature of transitions.

• For [DyPc2]0 no hysteresis is observed in powder magnetisation measurements.

Ch. 5. Electronic Absorption and Luminescence88

Krivokapic, Waters, Van Slageren, unpublished; Gonidec, JACS, 2010

0

-2

-1

0

1

2

-1 0 1

-400

-200

0

200

400 MCD on frozen solution magnetisation on powder

MC

D (m

deg)

Field (Tesla)

mag

netic

mom

ent (

10-2 e

mu)

-2 -1 0 1 2

-1000

-800

-600

-400

-200

0

200

400

600

800

1000

DyPc2-14599cm-1

T=1.6K

MC

D in

tens

ity (m

deg)

External Field (T)

hyst_685nm_fast_0.973 T/min

[DyPc2]‐ [DyPc2]0

Section 5.3 Magnetic Circular Dichroism

Page 89: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Magnetic Circular Dichroism. Example 3 [C(NH2)3]5[Ln(CO3)4] (1‐Ln) with Ln = Dy, Er

• Crystal field split ff transitions

Ch. 5. Electronic Absorption and Luminescence89

Rechkemmer, Van Slageren, unpublished

Section 5.3 Magnetic Circular Dichroism

Page 90: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

The fundamental difference between magnetization dynamics in single‐ion and polynuclear species

• In polynuclear TM clusters, Arrhenius behaviour overmany orders of magnitude; sharp transition to tunnelling

• In f‐elements generally curved Arrhenius plots. Different temperature regime.

• The reason is that  in single‐ion systems, there are many relaxation pathways with different field‐and temperature dependences (direct process, tunnelling, Raman, Orbach, multistep direct process).

• Hence a straight line in the Arrhenius plot is not necessarily expected

Ch. 6. Some words on relaxation of the magnetization90Section 6.1 Spin‐Lattice relaxation

[Mn3O(Me‐salox)3(2,4′‐bpy)3(ClO4)], Yang, Tsai, IC, 2008 [Dy(hfac)3(PyNO)]2, Yi, CEJ, 2012

Page 91: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

The fundamental difference between magnetization dynamics in single‐ion and polynuclear species

The first f‐element "single‐molecule magnets".

• Relaxation parameters

ΔE/kB (K) τ0 (s) ref

• Tb/– 331 6.3 x 10–8 Ishikawa,  J. Am. Chem. Soc., 125, 8694 – 8695 (2003)

• Dy/– 40.3 6.3 x 10–6 Ishikawa,  J. Am. Chem. Soc., 125, 8694 – 8695 (2003)

• Tb/0 590 1.5 x 10–9 Ishikawa,  Inorg. Chem, 43, 5498 – 5500 (2004)

• Dy/0 –

• Many substituted (terbium) double deckers known

• Strong correlation between ΔE and τ0.

Ch. 6. Some words on relaxation of the magnetization91Section 6.1 Spin‐Lattice relaxation

Michael Waters PhD Thesis University of Nottingham, 2013

Page 92: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Ch. 6. Some words on relaxation of the magnetization92Section 6.1 Spin‐Lattice relaxation

Basic Spin‐Lattice Relaxation Mechanisms in dilute systems

• assume dilute systems. 

• A further mechanism is quantum tunnelling

Direct Van Vleck Raman Orbach 2nd order Raman

(1st order Raman)

• Note that the figure was changed compared to literature. It seems to be more logical this wayBertini in Handbook of Electron Spin Resonance, Misra in Multifrequency Electron Paramagnetic Resonance

Orbach in Electron Paramagnetic Resonance, Geschwind (Ed.), 1972; Abragam and Bleaney

energy conservation in both steps

0

ħω

Page 93: Spectroscopic Investigations of Magnetic Anisotropy in Molecular Nanomagnetsobelix.physik.uni-bielefeld.de/~schnack/molmag/ecmm-2013/... · 2015-02-18 · Spectroscopic Investigations

Ch. 6. Some words on relaxation of the magnetization93Section 6.1 Spin‐Lattice relaxation

General formulas (not considering tunnelling)

• non‐Kramers ions:

• Kramers ions:

1

31 3 71 0

0 0

coth exp 12d Or RT R R R TkT kT

1

51 3 9 71 0 0

0 0

coth exp 12d Or R RT R R R T R TkT kT k

Abragam/Bleaney