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
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).
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
1. Introduction2. Single Crystal Magnetometry3. High‐Frequency EPR Spectroscopy4. Inelastic Neutron Scattering5. Electronic Absorption and Luminescence
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
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
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
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
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
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
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
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.
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
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
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
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
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.
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).
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
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
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
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 + + + + ± ± ± ±
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
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
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
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
1. Introduction2. Single Crystal Magnetometry3. High‐Frequency EPR Spectroscopy4. Inelastic Neutron Scattering5. Electronic Absorption and Luminescence
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
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;
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
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
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
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
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
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)
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
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
Ch. 2. Single Crystal Magnetometry38Section 2.3 Determination
(9) expressed in abc space
pseudo inversion
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
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
1. Introduction2. Single Crystal Magnetometry3. High‐Frequency EPR Spectroscopy4. Inelastic Neutron Scattering5. Electronic Absorption and Luminescence
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
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
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
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
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
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
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
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
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
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]
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
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]
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
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
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
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
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
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)
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
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
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
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
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
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
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
1. Introduction2. Single Crystal Magnetometry3. High‐Frequency EPR Spectroscopy4. Inelastic Neutron Scattering5. Electronic Absorption and Luminescence
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
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
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
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
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
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
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
1. Introduction2. Single Crystal Magnetometry3. High‐Frequency EPR Spectroscopy4. Inelastic Neutron Scattering5. Electronic Absorption and Luminescence
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+
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
Lanthanides
• Many lanthanides are strongly luminescent.
Section 5.2 LuminescenceCh. 5. Electronic Absorption and Luminescence
78
Natrajan, EUFEN2, COST CM 1006, Dublin 2013
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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