Download Characterization of RScO3 , LuFe2 O4 and M72

Characterization of RScO3, LuFe2O4
and M72Fe30 based molecules by
x-ray spectroscopic techniques
Dissertation
zur Erlangung des Grades eines
Doktors der Naturwissenschaften (Dr. rer. nat.)
dem Fachbereich Physik der Universität Osnabrück
vorgelegt von
Christine Derks, Dipl. Phys.
Osnabrück im Dezember 2012
ii
Supervisor, first reviewer: apl. Prof. Prof. h.c. Dr.
Dr. h.c. Manfred Neumann
Second reviewer:
Prof. Dr. Joachim Wollschläger
Universität Osnabrück
Fachbereich Physik
AG Elektronenspektroskopie
Barbara Str. 7
D-49069 Osnabrück
iii
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”Wie konnte uns das Alles nur passieren!”
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Table of Contents
Introduction
1 Experimental Methods and Theory
1.1 Basics of X-ray Spectroscopy . . . . . . . . . . . . . . . . . . . .
1.1.1 X-ray Photoelectron Spectroscopy (XPS) . . . . . . . . .
1.1.2 Effects in Electron Spectroscopy . . . . . . . . . . . . . .
1.1.2.1 Exchange Splitting . . . . . . . . . . . . . . . .
1.1.2.2 Spin-orbit Coupling . . . . . . . . . . . . . . .
1.1.2.3 Satellites . . . . . . . . . . . . . . . . . . . . .
1.1.2.4 Multiplet Splitting . . . . . . . . . . . . . . . .
1.1.2.5 Auger Electrons . . . . . . . . . . . . . . . . .
1.1.3 X-ray Absorption Spectroscopy (XAS) . . . . . . . . . .
1.1.4 X-ray Emission Spectroscopy (XES) . . . . . . . . . . . .
1.1.4.1 Resonant X-ray Emission Spectroscopy (RXES)
1.1.5 X-ray Magnetic Circular Dichroism (XMCD) . . . . . . .
1.2 Principles of Multiplet Theory . . . . . . . . . . . . . . . . . . .
1.2.1 Single-particle Approximation . . . . . . . . . . . . . . .
1.2.2 Multiplet Effects . . . . . . . . . . . . . . . . . . . . . .
1.2.2.1 Atomic Multiplet Theory . . . . . . . . . . . .
1.2.2.2 Ligand-field Multiplet Theory . . . . . . . . . .
1.2.2.3 Charge-transfer Multiplet Theory . . . . . . . .
1.3 Experimental Details . . . . . . . . . . . . . . . . . . . . . . . .
1.3.1 The Photoelectron Spectrometer PHI 5600ci . . . . . . .
1.3.2 The Advanced Light Source (ALS) . . . . . . . . . . . .
1.3.2.1 Beamline 8.0.2 at the ALS . . . . . . . . . . . .
1.3.2.2 Beamline 4.0.2 at the ALS . . . . . . . . . . . .
1.3.3 The Swiss Light Source (SLS) . . . . . . . . . . . . . . .
1.3.3.1 TBT-XMCD Endstation at the SLS . . . . . .
1.3.4 Bessy II . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3.4.1 Russian German Dipole Beamline . . . . . . . .
1.3.5 European Synchrotron Radiation Facility (ESRF) . . . .
1.3.5.1 ID12 Circular Polarisation Beamline . . . . . .
1.3.6 Superconducting Quantum Interference Device - SQUID
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Table of Contents
2 RScO3
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Basic Properties and Preparation of RScO3 (R=Pr, Nd, Sm, Eu, Gd,
Tb and Dy) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 Core Level XPS of Rare-Earth, Scandium and Oxygen . . . . . . . . .
2.3.1 XPS of Scandium and Oxygen . . . . . . . . . . . . . . . . . . .
2.3.2 XPS of the Rare-Earth . . . . . . . . . . . . . . . . . . . . . . .
2.3.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4 XAS and XES/RIXS of R, Sc and O . . . . . . . . . . . . . . . . . . .
2.4.1 R M4,5 -Edges XAS and R 4f → 3d XES . . . . . . . . . . . . .
2.4.2 Sc L2,3 -Edges XAS and Sc 3d → 2p XES . . . . . . . . . . . . .
2.4.3 O K-Edge XAS and O 2p → 1s XES . . . . . . . . . . . . . . .
2.4.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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3 LuFe2 O4
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . .
3.2 Basic Properties of LuFe2 O4 . . . . . . . . . . . . .
3.3 Preparation of LuFe2 O4 . . . . . . . . . . . . . . .
3.4 XMCD of Iron L2,3 -edges in LuFe2 O4 . . . . . . . .
3.5 XAS and XMCD of Iron K-edge in LuFe2 O4 . . . .
3.6 XAS and XMCD of Lutetium L2,3 -edges in LuFe2 O4
3.7 SQUID and XMCD Hysteresis . . . . . . . . . . . .
3.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . .
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4 Iron-Based Magnetic Polyoxometalates
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Core Level XPS of Iron, Oxygen, Molybdenum and Wolfram . . . .
4.2.1 Specific Experimental Details . . . . . . . . . . . . . . . . .
4.2.2 Iron Core Levels . . . . . . . . . . . . . . . . . . . . . . . .
4.2.3 Oxygen Core Levels . . . . . . . . . . . . . . . . . . . . . . .
4.2.4 Wolfram and Molybdenum Core Levels . . . . . . . . . . . .
4.2.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3 XAS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.1 Specific Experimental and Theoretical Details . . . . . . . .
4.3.2 Iron L2,3 -edges . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.2.1 Mo72 Fe30 acetate and W72 Fe30 sulfate at the ALS .
4.3.2.2 Mo72 Fe30 acetate and Mo72 Fe30 sulfate at the Bessy
4.3.3 Oxygen K-edge . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4 Magnetic Measurements on W72 Fe30 sulfate . . . . . . . . . . . . .
4.4.1 Specific Experimental and Theoretical details . . . . . . . .
4.4.2 SQUID . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
viii
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49
Table of Contents
4.4.3
4.4.4
XMCD at the Iron L2,3 -edges of W72 Fe30 sulfate . . . . . . . . . 80
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
5 Conclusion
83
Fazit
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Danksagung
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References
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List of Publications
101
ix
x
List of Figures
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
1.10
1.11
Schematic representation of XPS and UPS processes .
Principle of XPS . . . . . . . . . . . . . . . . . . . .
Energy level diagram for an XPS experiment . . . . .
Principle of the Auger electron emission . . . . . . .
Schematic representation of XAS . . . . . . . . . . .
Schematic representation of XES . . . . . . . . . . .
Schematic representation of REXS . . . . . . . . . .
Schematic representation of XMCD . . . . . . . . . .
Scheme of the XPS spectrometer . . . . . . . . . . .
Scheme of the ALS . . . . . . . . . . . . . . . . . . .
Scheme of the ALS beamline . . . . . . . . . . . . . .
2.1
Orthorhombic RScO3 crystal structure; there is an octahedron tilting
about [001]p , [110]p and [111]p respectively. . . . . . . . . . . . . . . . .
O 1s XPS spectra of RScO3 (R=Pr, Nd, Sm, Eu, Gd, Tb and Dy) . . .
Sc 2p XPS spectra of RScO3 (R=Pr, Nd, Sm, Eu, Gd, Tb and Dy)
(red); the reference Sc2 O3 (black) was taken from Chastain et al. [1] . .
Pr 3d XPS spectra of PrScO3 . . . . . . . . . . . . . . . . . . . . . . .
Nd 3d XPS spectra of NdScO3 (red); the reference Nd2 O3 (black) was
taken from Suzuki et al. [2] . . . . . . . . . . . . . . . . . . . . . . . .
Sm 3d XPS spectra of SmScO3 . . . . . . . . . . . . . . . . . . . . . .
Eu 3d XPS spectra of EuScO3 . . . . . . . . . . . . . . . . . . . . . . .
Gd 3d XPS spectra of GdScO3 (red); the reference Gd2 O3 (black) was
taken from Lütkehoff [3] . . . . . . . . . . . . . . . . . . . . . . . . . .
Tb 3d XPS spectra of TbScO3 . . . . . . . . . . . . . . . . . . . . . . .
Dy 3d XPS spectra of DyScO3 . . . . . . . . . . . . . . . . . . . . . . .
XAS at the Pr M4,5 -edges of PrScO3 . . . . . . . . . . . . . . . . . . .
Pr 4f → 3d of PrScO3 . . . . . . . . . . . . . . . . . . . . . . . . . . .
XAS at the Nd M4,5 -edges of NdScO3 . . . . . . . . . . . . . . . . . . .
Nd 4f → 3d of NdScO3 . . . . . . . . . . . . . . . . . . . . . . . . . .
XAS at the Sm M4,5 -edges of SmScO3 taken from [4] . . . . . . . . . .
Sm 4f → 3d XES of SmScO3 taken from [4] . . . . . . . . . . . . . . .
XAS at the Eu M4,5 -edges of EuScO3 . . . . . . . . . . . . . . . . . . .
Eu 4f → 3d XES of EuScO3 . . . . . . . . . . . . . . . . . . . . . . .
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
2.10
2.11
2.12
2.13
2.14
2.15
2.16
2.17
2.18
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xi
List of Figures
2.19
2.20
2.21
2.22
2.23
2.24
2.25
2.26
2.27
2.28
2.29
2.30
2.31
2.32
2.33
2.34
2.35
2.36
3.1
3.2
3.3
3.4
3.5
3.6
xii
XAS at the Gd M4,5 -edges of GdScO3 taken from [4] . . . . . . . . . .
Gd 4f → 3d XES of GdScO3 taken from [4] . . . . . . . . . . . . . . .
XAS at the Tb M4,5 -edges of TbScO3 . . . . . . . . . . . . . . . . . . .
Tb 4f → 3d of TbScO3 . . . . . . . . . . . . . . . . . . . . . . . . . .
XAS at the Dy M4,5 -edges of DyScO3 taken from [4] . . . . . . . . . . .
Dy 4f → 3d of DyScO3 taken from [4] . . . . . . . . . . . . . . . . . .
XAS spectra taken at Sc L2,3 -edges of RScO3 (R=Pr, Nd, Sm, Eu, Gd,
Tb and Dy) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
XES spectra of the Sc L2,3 -edges of PrScO3 and EuScO3 with EExc =
419.3 eV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
XES spectra of the Sc L2,3 -edges of NdScO3 and TbScO3 with EExc =
403.7 eV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
XES spectra of the Sc L2,3 -edges of SmScO3 , GdScO3 and DyScO3 with
EExc = 420.2 eV taken from [4] . . . . . . . . . . . . . . . . . . . . . .
O K-edge XAS and O 2p → 1s XES of PrScO3 . . . . . . . . . . . . .
O K-edge XAS and O 2p → 1s XES of NdScO3 . . . . . . . . . . . . .
O K-edge XAS and O 2p → 1s XES of SmScO3 . . . . . . . . . . . . .
O K-edge XAS and O 2p → 1s XES of EuScO3 . . . . . . . . . . . . .
O K-edge XAS and O 2p → 1s XES of GdScO3 . . . . . . . . . . . . .
O K-edge XAS and O 2p → 1s XES of TbScO3 . . . . . . . . . . . . .
O K-edge XAS and O 2p → 1s XES of DyScO3 . . . . . . . . . . . . .
a) Tolerance factor (Goldschmidt factor) for RScO3 , b) Sc−O−Sc bond
angles of RScO3 , c) Distances between Sc and the two oxygen spectra,
d) Sc−O mean distance and experimental band gaps. All structural
parameters have been extracted from Liferovich et al. [5]. . . . . . . . .
40
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Multiferroic triangle . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Crystal structure of LuFe2 O4 with Lu (large dark-gray spheres), Fe
(small black spheres) and O (large white spheres). Taken from Subramanian et al. [6]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
LuFe2 O4 Fe L2,3 -edges XMCD performed at 150K (black), the belonging
dichroic signal is green (a). It is compared to multiplet calculations
considering different possible spin orderings (b and c). The data are
taken from Kuepper et al. [7]. . . . . . . . . . . . . . . . . . . . . . . .
XMCD measurement (dark green) and XAS measurement (light green)
of the Fe K-edge on LuFe2 O4 performed at 125K and 6T. . . . . . . . .
XMCD measurements of the Fe K-edge on LuFe2 O4 at different temperatures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
XMCD Pre-edge measurements (green) at the Fe K-edge of LuFe2 O4
compared to multiplet-calculation (black). . . . . . . . . . . . . . . . .
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57
List of Figures
3.7
XMCD (orange) and XAS (green) measurements on the Lu L2,3 -edges of
LuFe2 O4 . The temperature was 150K and the external applied magnetic
field had 9T. The k was parallel to the c-axis of the crystal. . . . . . . . 59
3.8
SQUID measurements (blue) compared to XMCD measurements (green),
both measurements are recorded at 150K. . . . . . . . . . . . . . . . . 61
4.1
XPS measurements of Fe 2p (left panel) and Fe 3s (right panel) of
W72 Fe30 sulfate (red) in comparison with Fe2+ to Fe3+ reference compounds (black). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.2
XPS measurements of Fe 2p of Mo72 Fe30 sulfate (left panel, red) and
Mo72 Fe30 acetate (right panel, red) in comparison with Fe2+ to Fe3+
reference compounds (black). . . . . . . . . . . . . . . . . . . . . . . . 66
4.3
XPS measurements of O 1s of W72 Fe30 sulfate (a), Mo72 Fe30 sulfate (b)
and Mo72 Fe30 acetate (c). . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.4
XPS measurement of W 4f of W72 Fe30 sulfate. . . . . . . . . . . . . . . 68
4.5
XPS measurement of Mo 3d of Mo72 Fe30 acetate (left) and Mo72 Fe30
sulfate (right). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.6
Fe L2,3 -edges XAS series of 1 (left) and 2 (right). The experimental
data are green and the black lines represent the corresponding simulated
spectra, which were obtained by superimposing corresponding fractions
of the simulated Fe3+ and Fe2+ spectra. . . . . . . . . . . . . . . . . . . 73
4.7
Fraction of Fe3+ versus the percentage x-ray photon flux for the XAS
series shown in figure 4.6. . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.8
First (left) and second (right) series of Fe L2,3 -edges of molecule 3. The
green lines represent the experimental data and the black lines represent
the corresponding simulated spectra that were obtained by superimposing corresponding fractions of simulated Fe2+ and Fe3+ spectra. . . . . 74
4.9
Series of Fe L2,3 -edges of molecule 1 in green and simulated spectra in
black. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
4.10 Fraction of Fe3+ versus the percentage x-ray photon flux for the XAS
series shown in figure 4.9 and 4.8. . . . . . . . . . . . . . . . . . . . . . 75
4.11 Top: O K edge XAS of 1 (left) and 3 (right). The spectra were taken
at a low photon flux and a fresh spot of the corresponding sample.
Bottom: Calculated unoccupied densities of states for Mo72 Fe30 acetate
(left) and W72 Fe30 sulfate (right). . . . . . . . . . . . . . . . . . . . . . 78
4.12 SQUID measurements of W72 Fe30 sulfate from -6T up to 6T at 2 (orange),5 (green) and 15K (black) . . . . . . . . . . . . . . . . . . . . . . 80
xiii
List of Figures
4.13 XMCD measurement of the Fe L2,3 -edges on W72 Fe30 sulfate. The experimental results are plotted on the top of the graph. The paddle in
the middle shows the experimental dichroic signal (green) compared to
CT multiplet simulations (black). In the panel on the bottom the experimental XAS signal (green) is compared to CT multiplet simulations
(black). The measurements were made at 6.5T and 0.7K. . . . . . . . . 82
xiv
List of Tables
2.1
2.2
2.3
Structural parameters of RScO3 taken from Liferovich et al. [5] . . . . 29
Measured inter peak separations (in eV ± 0.2 eV) in the Sc L2,3 XAS
spectra of Fig. 2.25. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
Band gaps of rare-earth scandates (in eV) as found in the present work
(the upper line) in comparison with previously reported values. Since
we applied the identical equivalent experimental conditions, the relative
error bars are ± 0.1-0.2 eV; the absolut error could be larger. . . . . . . 47
3.1
Slater integrals (in eV) used for the Fe2+ and Fe3+ charge-transfer multiplet simulations of the Fe K-edge XAS. . . . . . . . . . . . . . . . . . 58
4.1
Slater integrals (in eV) used for the Fe2+ and Fe3+ -charge-transfer multiplet simulations of the Fe L2,3 -edges XAS. The spin-orbit parameters
were not reduced, whereas the d-d and p-d integrals were reduced to
80% of the Hartree-Fock values for the subsequent simulation of the
spectra. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
Fraction of Fe3+ after x-ray radiation with different intensities. . . . . . 72
Fraction of Fe3+ after x-ray radiation at the Bessy . . . . . . . . . . . . 76
4.2
4.3
xv
xvi
List of Abbreviations
ALS
Advanced Light Source
BESSY Berliner Elektronen Speicherring
CT
Charge-Transfer
DOS
Density Of States
ESRF
European Synchrotron Radiation Facility
R
Rare-Earth
REXS
Resonant Elastic X-ray Scattering
RIXS
Resonant Inelastic X-ray Scattering
RXES
Resonant X-ray Emission Spectroscopy
SLS
Swiss Light Source
SXF
Soft X-ray Fluorescence
SXPS
Soft X-ray Photoelectron Spectroscopy
TEY
Total Electron Yield
TFY
Total Fluorescence Yield
UPS
Ultraviolet Photoeletron Spectroscopy
XAS
X-ray Absorption Spectroscopy
XES
X-ray Emission Spectroscopy
XMCD X-ray magnetic circular dichroism
XPS
X-ray Photoelectron Spectroscopy
xvii
xviii
Introduction
Over the last few decades computers and related electronic equipment have become
more and more powerful and faster. Simultaneously their basic submits, i.e. transistors
and hard discs (in particular the magnetic domain size) have shrunken dramatically.
As a consequence the CPU speed and the hard disc storage capability both gained
several magnitudes of order.
Nowadays engineers as well as researchers seek new advanced materials in order to
continue the miniaturization of electronic devices down to the nano- or molecular scale.
Among several others, two specific material classes appear to be of special interest for
potential future nanoelectric devices, namely: (i) (Transition) metal oxide based solid
state electronic devices and (ii) (Transition) metal oxide based molecular electronic
devices.
Both kind of materials are well promising candidates for a number of potential applications in novel (nano)electric devices since several electron quantum and correlation
effects dominate their intrinsic properties down to the atomic scale. Transition metal
based oxides and molecules display an enormous range of electronic transport phenomena, leading to a unique variety of electrical, magnetic and optical properties. This
includes fascinating collective ordering phenomena such as superconductivity, colossal
magneto resistance, or the simultaneous existence of more than one ferroic phase, e.g.
ferroelectricity and ferromagnetism. These exceptional electronic properties are dominated by the intricate interplay between the 3d electrons degrees of freedom (spin,
charge, and orbital), and their interaction with the 2p ligand states.
A detailed knowledge of the underlying electronic structure and the subsequent
electron correlation effects is of utmost importance for the interpretation and understanding of a transition metal based oxide or molecule as a functional part in a
potential new electronic device.
The detailed description of the electronic properties of transition metal based compounds is one of the challenges in nowadays state of the art condensed matter physics
and chemistry since the results of first principles band structure calculations are often inconsistent with experimental findings due to the mentioned 3d-3d and 3d-2p
electron correlation effects. However, from experimental point of view, x-ray spectroscopic techniques are extremely powerful tools for electronic structure investigations
of a compound in question.
Namely, X-ray Photoelectron Spectroscopy (XPS) and X-ray Emission Spectroscopy
(XES) are well established techniques in order to tackle the occupied densities of
states (valence band) as well as chemical valence states of transition metal ions, for
1
Introduction
instance. At the other side, X-ray Absorption Spectroscopy (XAS) at transition metal
L2,3 -edges allows to probe the local coordination (crystal field) of transition metal
ions in ionic compounds, and O K-edge spectroscopy gains information about the
unoccupied densities of states (conduction band), respectively. Furthermore, X-ray
Magnetic Circular Dichroism (XMCD) can be used for an element specific investigation
of the magnetic properties, including the possibility to separate the magnetic moments
into their spin and orbital contributions.
This thesis deals with a detailed electronic structure study of three particularly interesting transition metal based compounds of both above mentioned material classes,
which exhibit fascinating properties from fundamental as well as from potential applicative point of view. The materials investigated in depth within this thesis are
the rare earth scandates RScO3 (R=Pr, Nd, Sm, Eu, Gd, Tb and Dy) the potential
multiferroic and “ferroelectric” layered ferrite LuFe2 O4 , and magnetically frustrated
molecules with Mo72 Fe30 and W72 Fe30 cores. For all three kinds of compound various complementary x-ray spectroscopic techniques have been applied, and the results
are compared with other experimental probes as well as with different theoretical approaches, namely ab initio electronic structure calculations and full (charge transfer)
multiplet simulations.
An advanced understanding of the underlying electronic and magnetic structure is
developed and discussed for each of the above mentioned kind of compounds.
This thesis is structured as following:
• Chapter 1 introduces in the details and features of the employed experimental
techniques. This part is meant to give a rather complete but descriptive introduction to any reader which is not familiarized with this kind of measurements.
The cited references account for the state of the art development in this field and
can serve as important further literature. Additionally the basics of multiplet
theory are presented and in the end the used experimental facilities are shown.
• In Chapter 2 the electronic structure of rare-earth scandates of type RScO3
(R=Pr, Nd, Sm, Eu, Gd, Tb and Dy) is investigated in deep detail. These
compounds are well promising candidates in order to replace SiO2 as a high-k
gate dielectric on future metal-oxide-semiconductor field effect transistors (MOSFETs). Within this thesis a complete electronic structure investigation of a series
of seven RScO3 (R=Pr, Nd, Sm, Eu, Gd, Tb and Dy) has been performed. XPS,
XES and XAS have been used, and the experimental results are compared with
ab initio band structure calculations.
• An example of magneto electric coupling is presented in Chapter 3. The layered oxide LuFe2 O4 exhibits ferroelectric and ferrimagnetic properties due to its
crystalline structure. A large response of the dielectric constant by applying
relatively small magnetic fields has been reported, opening a potential avenue
toward novel magneto electric devices. Here XMCD has been used as a probe
2
at the Fe L2,3 , Lu L2,3 and Fe K-edges in order to investigate the fine details
of the relationship between electronic structure and magnetic properties in this
compound. The results of the Fe L and Fe K-edges are compared to each other
and partly simulated by means of full multiplet calculations. XMCD at the
Lu L-edges is used to study the Lu 5d-induced magnetic moment. Finally this
magnetic structure study is completed by SQUID measurements.
• In the last part of this thesis the focus moves toward the second class of material
mentioned above. In Chapter 4 a complete picture of the electronic structure
of molecules with Mo72 Fe30 and W72 Fe30 cores is developed. From fundamental
point of view these molecules are hosting a highly symmetric array of 30 magnetic Fe ions, building up a frustrated magnetic system. This type of molecule
is furthermore an interesting prototype for potential applications in molecular spintronics and quantum computing. Within this thesis XPS, XAS, and
XMCD have been used as experimental techniques and compared to complementary SQUID measurements and theoretical results of the above mentioned
approaches. Furthermore, an x-ray induced Fe3+ to Fe2+ photoreduction process
has been investigated.
• Chapter 5 summarizes the main findings of this thesis.
3
4
1 Experimental Methods and Theory
In this chapter the experimental methods to analyse the samples and their theoretical
background are presented. The introduced methods are X-ray Phototelectron Spectroscopy (XPS 1.1.1), X-ray Absorption Spectroscopy (XAS 1.1.3), X-ray Emission
Spectroscopy (XES 1.1.4) with the specification of Resonant X-ray Emission Spectroscopy (RXES 1.1.4.1) as well as X-ray Magnetic Circular Dichroism (XMCD 1.1.5).
In section 1.2 the basic principles of multiplet calculations are presented. The setup
of the used experimental equipment is presented in this chapter’s last section (1.3).
1.1 Basics of X-ray Spectroscopy
The basic principle of photoelectron spectroscopy is the photoelectric effect which was
discovered in 1887 by H. Hertz [8]. He noticed that a metal plate discharges much faster
when irritated with light. The following year his assistant W. Hallwachs [9] found out
that the velocity of the discharge depends on the used material, the wavelength and
the intensity of the light. An explanation for this phenomena was given by A. Einstein
in 1905 when he published his quantum hypothesis for electromagnetic radiation [10].
This was the beginning of the theory’s development of photoelectron spectroscopy.
1.1.1 X-ray Photoelectron Spectroscopy (XPS)
The photoelectron spectroscopy is based on the photo effect described in section 1.1.
The basic configuration of photoelectron spectroscopy consists of a light source, a
sample and a detector. This basic configuration can be seen in figure 1.2. The x-ray
source sends radiation toward a sample. The sample’s electrons absorb this energy
and if it is large enough an electron will be animated to leave the atom. The kinetic
energy Ekin of this so called photoelectron will be detected and allows a conclusion
from the binding energy of the electron to the kind of the atom. The quantum light
hypothesis leads to equation 1.1.
Ekin = hν − Φsolid
(1.1)
In this case h is the Planck’s constant, ν the frequency of light and Φ describes
the work function which is the energy an electron has to overcome to leave the atom.
The equation 1.1 only works for electrons at the Fermi level. For electrons near the
5
1 Experimental Methods and Theory
Figure 1.1: Schematic representation of XPS and UPS processes
nucleus and with higher binding energy the equation 1.1 needs to be expanded with
the effective binding energy EB,eff . That leads to the equation 1.2
Ekin = hν − EB,eff − Φsolid
(1.2)
One is interested in EB,eff , the effective binding energy of the emitted electron, so
the equation 1.2 will be transformed to equation 1.3.
EB,eff = hν − Ekin − Φsolid
(1.3)
In figure 1.3 the following used symbols are shown, so it will be much easier to
understand the next explanations by looking at the figure. There are two different
cases. The first one is that the spectrometer limits the kinetic energy and the second
is that the solid limits. The first case is the one which will be employed throughout
this thesis, so it will be described in detail. The explanations are for a conductive
sample, which are connected to the spectrometer. So the Fermi levels of sample and
spectrometer are equal.
0
The detected kinetic energy of the emitted electron is Ekin
and depends on Ekin due
to the following equations:
∆Φ = Φsolid − Φspectrometer
6
(1.4)
1.1 Basics of X-ray Spectroscopy
electron energy analyzer
X-ray source
X-rays
electron counter
(detector)
photoelectron
sample
Figure 1.2: Principle of XPS
0
Ekin
=
=
=
0
=⇒ Ekin =
Ekin + ∆Φ
Ekin + (Φsolid − Φspectrometer )
(hν − EB,eff − Φsolid ) + (Φsolid − Φspectrometer )
hν − EB,eff − Φspectrometer
Here Φspectrometer is the work function of the spectrometer and is well known in
contrast to the work function of the solid (Φsolid ). That makes it possible to calculate
the effective binding energy of the electron.
The binding energy of an electron depends on the number of protons and electrons
of an atom. Fortunately the binding energy of an electron is like a fingerprint, so it is
possible to calculate from which element and shell the electron comes. The valency of
an atom leads to a chemical energy shift so that the valency can also be determined.
There are several different methods based on the photoemission principle. When
the excitation energy hν is smaller than 100 eV the method is called Ultraviolet Photoelectron Spectroscopy (UPS), when hν is between 100 eV and 1000 eV it is Soft
X-ray Photoelectron (SXPS). In this work X-ray Photoelectron Spectroscopy (XPS)
with hν > 1000 eV is used. The used excitation energies in this work are 1486.6 eV
(Al Kα ) and 1253.6 eV (Mg Kα ). For more details see section 1.3.1.
The penetration depth of these photons in a solid sample is in the order of 110 micrometers, although XPS is a surface sensitive method because the electron
7
1 Experimental Methods and Theory
emission depth is around 10 Å. Due to the small mean free path XPS measurements
have to be in ultra-high vacuum (UHV) otherwise the photoelectrons could not reach
the analyzer and the surface would be polluted. Further information about the used
UHV techniques and the analyser are given in section 1.3.1. XPS is one of the x-ray
spectroscopic methods which gives the total density of states (tDOS).
Figure 1.3: Energy level diagram for an XPS experiment
1.1.2 Effects in Electron Spectroscopy
The principles of electron spectroscopy are described in section 1.1.1. But during an
experiment there are several effects which one has to bear in mind to come to the
correct conclusions. In the following section typical effects in electron spectroscopy
and their origin are described.
1.1.2.1 Exchange Splitting
Two atoms bond by interaction of their valence electrons. This bonding leads to a
change in the electric environment of the atoms and changes the electric potential. Due
to this change the binding energy of the electrons including the core level electrons
8
1.1 Basics of X-ray Spectroscopy
change. This changed binding energy can be measured and information about the
chemical bonding of the atoms can be achieved. To get information about the kind
of binding reference measurements from known materials are used. It is very difficult
to determine the so called chemical shift theoretically, because there are too many
interacting factors. It is mainly influenced by the kind of binding and the neighboring
atoms. An example for the chemical shift of Fe 2p is shown at the PhD Thesis of
Küpper [11] in section 2.3.2.3.
One theoretical possibility to describe the chemical shift is the chargepotential model.
In this model the effective binding energy EB,eff depends on the potentials created by
the valence electrons of the observed atom and the environmental electrons. EB,eff is
described in equation 1.5.
EB,eff = EB,atom + ∆(Echem + EMad )
∆EMad =
P
B6=A
qB
RAB
(1.5)
is the so called Madelung term, which describes the influence
of the surrounding atoms in the bulk. ∆Echem = KqA is the chemical shift which
is connected to the potentials of the valence electrons of the observed atom. The
interaction between the valence and the core electrons is here called K and the shift
relative to a reference state is denoted by qA . Thus the overall chemical shift can be
represented by:
EB,eff = EB, atom + KqA +
X qB
.
R
AB
B6=A
(1.6)
1.1.2.2 Spin-orbit Coupling
There are several quantum numbers to describe electronic levels of an electron. First
there is the quantum number n [n=1,2,...]. n declares the shell the electron is placed
on. The electron spin s [s= 12 , − 12 ] and the angular momentum l[l=0,1,2,...,n-1]. The
total angular momentum j (j > 0) is the sum of the spin s and the angular momentum
l. The interaction between spin and orbital angular momentum is called Spin-orbit
coupling and so each core level line is a doublet in the XPS-spectra for l > 0, because
j = l + s or j = l − s. Instead of l = 0, 1, 2, 3 one often uses s,p,d,f. The official
nomenclature is nlj . For example a level with n = 2, l = 1 and s = 21 leads to
j = 1 + 12 = 32 and is called 2p 3 . The relative intensity of the two peaks of a doublet
2
is given by:
Ij=l+s
l+1
=
Ij=l−s
l
(1.7)
9
1 Experimental Methods and Theory
1.1.2.3 Satellites
During a perfect photoemission process a photoelectron leaves the atom so fast, that
the remaining electrons do not have time to readjust. But during a real experiment
it is possible that the photoelectron interacts with the exited state (N-1 electron) of
an atom, that leads to additional lines in the spectra, called satellites. There are two
different types of satellites. On the one hand the extrinsic satellites which come from
inter-atomic excitations and on the other hand the intrinsic satellites are the result of
intra-atomic relaxations. During a photoemission process it is possible that a second
electron will be excited. If it stays bound to the atom but on a higher level it is called
shake up satellite, and if the electron leaves the atom it is called shake off satellite.
This shake off electron has a lower kinetic energy than for a direct excitation because
of the higher binding energy in an (N-1) electron system. Transition metal oxides
have an extra satellite due to charge-transfer. In this case an electron from the ligand
2p level will be transfered to the metal 3d shell: 3dn L −→ 3dn+1 L−1 . The required
energy is given in 1.8
∆ = E(3dn+1 L−1 ) − E(3dn L)
(1.8)
1.1.2.4 Multiplet Splitting
A core-level electron which will be released from a system with unpaired electrons in
the valence level keeps information about the spins of the electrons which have left
the system. The 3s level is currently the only system, in which one can interpret the
information because other systems have too many additional interactions. By the 3s
core-level the unpaired electron left in this shell interacts with the spin of the electrons
in the valence band levels. They couple parallel or anti parallel. The binding energy
of the photoelectron depends on the coupling. This causes a splitting of the core
level line and the exchange splitting (∆Es ) can be written according to the van Vleck
theorem [12]:
∆Es =
S+1 2
G (3s, 3d)
2l + 1
(1.9)
G2 (3s, 3d) is the Slater exchange integral and l the orbital quantum number (l=2).
The binding energy of the state with (S + 12 ) is lower than the binding energy corresponding to (S − 12 ). This leads to a doublet in the spectrum and to the intensity
ratio of the two peaks is given by:
IS+ 1
2
IS− 1
2
=
S+1
S
(1.10)
In 1970 Fadley et al. found that the van Vleck theorem does not work in all cases.
The ratio of the intensity (equation 1.10) was about two times smaller than expected
10
1.1 Basics of X-ray Spectroscopy
[13, 14]. Bagus et al. [15] associated this to intra atomic near-degeneracy correlation
effects. Today the treatment of the 3s multiplet splitting is based upon full multiplet
calculations [16].
For l 6= 0 the multiplet splitting is more complex because an additional spin-orbit
splitting occurs in the spectra.
1.1.2.5 Auger Electrons
An emitted photoelectron leaves a hole in the atom, this hole will be refilled with
an electron of a higher energy shell. The excess energy of the filling electron can be
transmitted to an electron which uses this energy to leave the atom. This electron will
be detected with a low kinetic and a high binding energy. This is a secondary process
and the detected electrons are called Auger electrons. To identify the origin of the
Auger electron the ABC form is used. A stands for the shell the photoelectron was
actuated from, B for the shell the refilling electron comes from and C for the shell the
Auger electron comes from. For example an photoelectron is excited from the K-shell
(1s level) an electron of the L1 (2s) level recombines with th hole in the K shell and
the resulting photon excites an electron of the L2,3 (2p1/2 or 2p3/2 ) level. The Auger
electron is then called KL1 L23 .
Figure 1.4: Principle of the Auger electron emission
11
1 Experimental Methods and Theory
1.1.3 X-ray Absorption Spectroscopy (XAS)
Figure 1.5: Schematic representation of XAS
X-ray Absorption Spectroscopy (XAS) is a method to determine the unoccupied
states of an atom. For this purpose a core electron is excited to an unoccupied state
above the Fermi level. The energy which is needed for this excitation can be disposaled
by an x-ray source, which emits different energies. It is important that one can change
the excitation energy (Eexc ) because one needs the exact energy difference between the
core level and the unoccupied states. With different excitation energies one can reache
different unoccupied states. The energy of the core level is called initial state Einitial
and the energy of the unoccupied state above the Fermi level is called final state Efinal .
The energy difference 1.11 between this both states is the energy which is needed to
excite an electron.
Eexc = hν = Efinal − Einitial
(1.11)
Due to the dipole selection rules there are only special transitions allowed. The
angular momentum quantum number l has to be changed by one (∆l = ±1). The
spin s has to be fixed (∆s = 0) and the z-component of the orbital momentum m can
be equal or changed by one (∆m = 0, ±1).
The first method to detect an XAS-signal is to measure the intensity of the transmitted
light. Because if one excites a transition, a photon is absorbed and the intensity of
the light is reduced. Unfortunately this method can only be employed for very thin
samples. The alternative and often used method is to measure the total electron
12
1.1 Basics of X-ray Spectroscopy
yield (TEY). This is the drain current to the sample to refill the empty core level.
The total electron yield is proportional to the XAS-signal. The measurement of the
TEY is suitable for conductive samples. If the sample is an insulator the intensity of
radiant recombination called partial- or total fluorescence yield (PFY or TFY) should
be measured.
1.1.4 X-ray Emission Spectroscopy (XES)
Figure 1.6: Schematic representation of XES
X-ray emission spectroscopy based on the recombination which is shown in figure
1.6. X-rays excite a core electron and the resulting hole will be refilled with an electron
from the valence band. Naturally the system prefers a state of minimum energy. The
excess energie will be released by a photon. The energy of the emitted photon can be
explained by equation 1.12.
Eem = Einitial − Efinal
(1.12)
Eem is the energy of the emitted light, Efinal is the binding energy of the electron in
the valence band and Einitial is the effective binding energy of the hole. To determine
the intensity of the emitted light a CCD camera is often used. There are dipole
selection rules: ∆l = ±1 and ∆j = ±1; 0. Electrical quadrupole transitions and
magnetic dipole selection rules are negligible. With XES one detects the partial density
of states (pDOS), because a special excitation energy excite only one specific element.
Therefore this method is element specific. The occupied states will be measured
13
1 Experimental Methods and Theory
because the recombining electrons come from occupied states. It is also a bulk-sensitive
method due to the mean free path of the photons which is much bigger than the mean
free path of the electrons by XPS or XAS. XES is a very good technique to determine
the occupied states of the valence band. XES is a so called photon in - photon out
spectroscopy.
1.1.4.1 Resonant X-ray Emission Spectroscopy (RXES)
Figure 1.7: Schematic representation of REXS
Resonant X-ray Emission Spectroscopy (RXES) is the generic term for two similar
spectroscopy methods. The so called Resonant Elastic X-ray Scattering (REXS) and
the Resonant Inelastic X-ray Scattering(RIXS). In the first case the excited electron
recombines in the initial state. In the second case an electron from any occupied state
above the core hole recombines into this core hole. This leads to characteristic loss
features. An great advantage of this method is that the charging of the sample has no
influence on the emitted photon in contrast to the emitted electrons by XPS.
1.1.5 X-ray Magnetic Circular Dichroism (XMCD)
X-ray Magnetic Circular Dichroism (XMCD) is a method to get magnetic information
of a sample. With the sum rules invented by Thole and Carra et al. [17, 18] one
can determine the element specific spin and orbital momentum of a sample. These
equations were modified by Chen et al. [19]. XMCD is element specific and the signal
can be separated into spin and orbital moments. The x-ray magnetic circular dichroism
14
8
Basics of x-ray spectroscopy
1.1 Basics of X-ray Spectroscopy
sample because the excited electron remains localized on the excited atom.
XES is a so called photon in − photon out spectroscopy.
theory was first approved by Schütz et al. [20]. Today this technique became an often
magnetic
dichroism (XMCD)
used method2.4
for theX-ray
characterization
of circular
magnetic materials.
An absorption
spectrum is measured with left and with right circularly polarized
By means of x-ray magnetic circular dichroism (XMCD) one can analyze the
light. During
this
spins
to be aligned
magnetic field
magnetic measurements
moments element the
specific
and have
also separated
into their in
spina and
orbital
moments.
wasx-ray
first verified
in 1987
by Schütz
et al. [8].
the
parallel to the
light.
To getItan
magnetic
circular
dichroism
theInspectra
have to
following
decade
it became an because
often usedof
method
for the characterization
of of electrons
be subtracted.
There
is a difference,
the preferential
excitation
magnetic materials. The XMCD is the difference between spectra measured
with different
spin directions with respect to the helicity of the light and the magnetic
with left and right circularly polarized x-rays. For this effect the spins have
field.
to be aligned in a magnetic field. Dependent on the light helicity one spin
direction is preferentially excited into the unoccupied 3d states.
3d states
sz = -
1
2
EF
L2 absorption of
left circular pol. x-rays
L2 absorption of
right circular pol. x-rays
2p3/2
­­ ¯¯
2p1/2
o
­
o
¯
Figure 1.8: Schematic representation of XMCD
Figure 2.3: Schematic representation of the XMCD process in the one electron picture [9].
The XMCD In
process
is the
schematically
in figure
1.8.The
The
excitation
to the
figure 2.3
XMCD processpresented
is schematically
presented.
d-band
is
3d band is taken as an example. The d-band is split into spin up and spin down bands.
First the absorption of circularly polarized x-ray photons leads to a spin polarization
of the photoelectrons due to the spin orbit coupling (j=l±s). In the second step the
d valence band acts as a spin detector. At the L3 edge (j=l+s) left hand circularly
polarized x-rays mainly probe the unoccupied spin up d states with respect to the
direction of the magnetization. The effect reverses at the L2 edge due to the opposite
sign of the spin orbit coupling (j=l-s).
X-ray absorption spectroscopy can be used for the XMCD technique. For 2p → 3d
transitions in XAS the magnetic moments can be calculated by using the so called
XMCD sum rules, which are shown in equation 1.13. They are devised by Thole and
Carra et al. [17, 18] and modified by Chen et al. [19] as mentioned before.
15
1 Experimental Methods and Theory
R
(µ+ − µ− )dω
morb = − RL3 +L2
(10 − n3d )
3 L3 +L2 (µ+ + µ− )dω
R
R
6 L3 (µ+ − µ− )dω − 4 L3 +L2 (µ+ − µ− )dω
R
mspin = −
(µ+ + µ− )dω
L3 +L2
7 hTz i
×(10 − n3d ) 1 +
2 hSz i
4
(1.13)
(1.14)
morb is the orbital magnetic moment and mspin is the spin magnetic moment in
units of µB /atom. The indices L3 and L2 refer to the integrals of the L3 and L2 peaks.
(µ+ − µ− ) is the XMCD spectrum and (µ+ + µ− ) is the sum of the XAS spectra
excited with left and right polarized light. n3d is the number of 3d electrons in the
corresponding ion. hTz i is the ground state expectation value of the magnetic dipole
term originating from the expectation value of the magnetic dipole operator and hSz i
7hTz i
<< 1 and can
is the corresponding spin operator. Usually for bulk cubic crystals 2hS
zi
be neglected.
There are some simplifications made during the invention of the sum rules. It is
considered that the 2p → 3d transitions take place between free atoms. Secondly the
L3 and L2 -edges should have a complete energetic separation for the purpose of getting
exact results for the integrals. Problems occur for less than half filled 3d transition
metals. Hence the sum rules can be used for the late and intermediate 3d transition
metal ions.
Teramura et al. [21] found a deviation from the XMCD spin sum rule, due to the
Coulomb interaction between electrons, which mixes the so called L3 and L2 regions
with each other. In this paper [21] a list of the deviations for various ionic states for
the elements Ni, Co, Fe and Mn is presented, which may serve as a correction factor
in the estimation of expectation values of magnetic quantities from XMCD data. The
correction factor for iron is used in this thesis.
For 2p → 5d transitions in XAS the magnetic moments can be calculated by using
slightly different XMCD sum rules, which are shown in equation 1.15. They are
although devised by Thole and Carra et al. [17, 18], but the here presented version
with its necessary adjustments for 2p → 5d transitions were taken from Chaboy et al.
[22].
morb
mspin
R
2 L3 +L2 (µ+ − µ− )dω
(10 − n5d )
= R
(µ+ + µ− )dω
L3 +L2
R
R
3( L3 (µ+ − µ− )dω − 2 L2 (µ+ − µ− )dω)
R
=
2( L3 +L2 (µ+ + µ− )dω)
×(10 − n5d ) −
16
7 hTz i
2
(1.15)
(1.16)
1.2 Principles of Multiplet Theory
For the calculations at the lutetium
L-edge the following assumptions were
R made acR
3
cording to Chaboy et al. [22]: (i) L3 +L2 (µ+ + µ− )dω is approximated by 2 L3 +L2 (µ+ +
µ− )dω ; (ii) hTz i is assumed to be negligible in the spin sum rules; (iii) estimates of
both morb and mspin moments have been derived by considering n5d =0.
1.2 Principles of Multiplet Theory
In this work some x-ray absorption measurements and x-ray magnetic circular dichroism measurements are compared to so called multiplet calculations. In this section the
basic principles are shown, starting with a theoretical description of x-ray absorption.
1.2.1 Single-particle Approximation
X-ray absorption is, as mentioned before in section 1.1.3, an excitation of a core
electron to an unoccupied state. The resulting x-ray absorption spectrum can be
described with the so called Fermi Golden rule (equation 1.17).
IXAS ∝ |hΦf |ê · r| Φi i|2 δEf −Ei −~ω
(1.17)
One gets the absorption intensity IXAS by coupling the initial state (Φi ) and the
final state (Φf ) with a dipole matrix element (ê · r). The conservation of the energy
is given by the delta function (δ).
Now the assumptions which lead to the single-particle approximation will be mentioned. First the final state can be described as initial state plus an excited continuum
electron () minus a core electron (c); Φf = cΦi . The second assumption is that all
electrons which are not actively involved in the transition are removed from the matrix
element. As a result only the excited core electron stays in the initial state (Φi ) and
only the continuum electron remains in the final state (Φf ). The delta function will
be replaced by the density of states (ρ). This results in equation 1.18 from Muller et
al. [23].
IXAS ∝ |h |ê · r| ci|2 ρ
(1.18)
Due to the matrix element (ê · r) the density of states have an orbital moment that
differs by 1 from the core state (∆L = ±1) and the spin is conserved (∆S = 0).
For x-ray excitation the quadrupole transitions are some hundred times weaker than
the dipole transitions, so they are usually neglected. The density functional theorem
(DFT) is well-suited to describe for example the 1s x-ray absorption (K-edge) [24],
but there is to mention that the simulation of the iron K-pre-edge of the XMCD
measurement of LuFe2 O4 in chapter 3 is not possible with this theory. At the iron
K-pre-edge the quadrupole transitions are very important and can not be neglected.
17
1 Experimental Methods and Theory
1.2.2 Multiplet Effects
The single-particle approximation does not work for x-ray absorption measurements
which include 2p→3d transitions, because in this case the p core wave function overlaps
with the d valence wave function. The results are so called multiplet effects. The
multiplet theory of ionic transition metal (TM) compounds is based also on the Fermi
Golden rule, but the core hole and free electron of equation 1.18 are, in equation 1.19,
replaced by a 2p core hole (2p) and a 3d electron. For the calculations from the valence
electrons only the 3d electrons are taken into account, see equation 1.20.
2
IXAS ∝ Φi 2p3d |ê · r| Φi δEf −Ei −~ω
(1.19)
2
IXAS ∝ 2p3dN +1 |ê · r| 3dN δEf −Ei −~ω
(1.20)
1.2.2.1 Atomic Multiplet Theory
The atomic multiplet (AM) theory was founded inter alia by Cowan [25] and Weissbluth [26]. They were faced with the problem of calculating the electronic states of
a solid measured with x-ray spectroscopies. So on the one hand they had extended
valence states and on the other hand a localized core hole. Over the last three decades
it was found out that a complete localized approach, based on the atomic multiplet
theory is suited for calculating core-level spectroscopy measurements. The basic assumptions for the analysis of x-ray absorption will be shown in this section.
The basic equation to describe an N-electron atom in the atomic multiplet theory
is the Schrödinger equation for free atoms, without any influence of the surrounding
atoms. That leads to the Hamiltonian in 1.21.
H=
P
p2i
2m
X p2
X −Ze2 X e2 X
i
+
+
+
ζ(ri )li · si
2m
ri
r
pairs ij
N
N
N
is the kinetic energy of N electrons,
P N−Ze2
describes the Coulomb attraction of the nucleus
ri
N
P e2
= Hee is the electron-electron repulsion and
rij
pairs
P
N
(1.21)
with the atomic number Z,
ζ(ri )li · si = Hls is the spin-orbit coupling of each electron.
The average of a certain state will be defined as Hav , due to the kinetic energy and
the interaction with the nucleus which are the same for all electrons in a certain atomic
configuration. Hls and Hee still have to be solved. Hee is problematic to solve, the
solution was a central field approximation by separating the spherical average of the
electron-electron interaction hHee i from the non spherical part. The modified electron0
electron Hamiltonian Hee
(equation 1.22) is the result of the difference between Hee
18
1.2 Principles of Multiplet Theory
and hHee i. This leads to a simplified Hamiltonian in equation 1.23. So there are only
0
and Hls left to be solved.
the two interactions Hee
*
+
X e2
X e2
0
Hee = Hee − hHee i =
−
(1.22)
r
r
pairs ij
pairs ij
0
+ Hls
H = Hav + Hee
(1.23)
An calculated example of Ti4+ can be found in the thesis of Taubitz [27] in section
“Atomic multiplet theory”.
1.2.2.2 Ligand-field Multiplet Theory
A weakness of the atomic multiplet theory is that the influence of surrounding atoms is
not considered. For this reason the ligand-field multiplet (LFM) theory, or also called
crystal field multiplet theory, extends the atomic multiplet theory by adding a crystal
field (equation 1.24). This extension was developed by Thole and co-workers for core
level spectroscopy [28].
HLFM = H + HCF
(1.24)
H is already know from equation 1.21 and HCF is the crystal field, which consists of
the electronic charge e times a potential Φ(r) that describes the surroundings (1.25).
HCF = −eΦ(r)
(1.25)
The potential Φ(r) can be explained as series expansion of spherical harmonics YLM
(equation 1.26), they can be seen as disruption to the atomic energy states.
Φ(r) =
∞ X
L
X
f L ALM YLM (ψ, φ)
(1.26)
L=0 M =−L
The matrix element of Φ(r) will be determined regarding the atomic 3d orbitals.
The resulting matrix elements h3d |Φ(r)| 3di will be splitted into a radial part and a
spherical part. In this case the radial part gives the strength of the crystal field. The
spherical part of the matrix element will be written in YLM symmetry. For 3d electrons
the crystal field potential is reduced to:
Φ(r) = A00 Y00 +
2
X
M =−2
2
r A2M Y2M +
4
X
r4 A4M Y4M
(1.27)
M =−4
The crystal field is usually defined by the three parameters X400 , X420 and X220 .
Butler [29] defined this notation by indices {ijk}, due to the symmetry properties of
electron orbitals. In optical spectroscopy the crystal field is described by Dq, Ds and
19
1 Experimental Methods and Theory
Dt. There is a possibility to compare the different parameters, but it is not possible
to determine the real crystal field splitting only by absorption measurements. A good
overview about the crystal field theory can be found by Moffit and Ballhausen [30].
One often used crystal field is the cubic ligand-field, it has also the strongest effect on
the symmetry. It is described in detail in the textbooks of Sugano et al. [31], Butler
[29] and Fontaine [32]. In principle ligand-field multiplet calculations can be compared
to experiments and they show quite good results [33, 34]. The soft x-ray edges have
a high resolution, due to the long lifetime of the core states. That makes the spectra
sensitive to details of the electronic structure, like valence, symmetry, spin state and
crystal-field values [35, 36].
1.2.2.3 Charge-transfer Multiplet Theory
Finally one has to take into account the different itinerant electronic features. This
will be done by the charge-transfer multiplet theory. It is close to the ligand field
multiplet theory but it uses more than one configuration. For example to the 3dn
ground state a 3dn+1 L configuration is added, and a 3dn L2 configuration and so on.
Mostly two configurations are enough to explain an x-ray absorption spectrum, but
in special cases, like higher valence states, more configurations can be useful. The
charge-transfer effect adds a second dipole transition, second initial, and second final
states:
2
IXAS,2 ∝ 3dn+1 L |p| 2p5 3dn+2 L (1.28)
HINIT,2 = 3dn+1 L |HLF M | 3dn+1 L
(1.29)
HFINAL,2 = 2p5 3dn+2 L |HLF M | 2p5 3dn+2 L
(1.30)
The two initial states and two final states are coupled by monopole transitions, like
hybridization.
MI1,I2 = 3dn |HM IX | 3dn+1 L
(1.31)
MF1,F2 = 2p5 3dn+1 |HM IX | 2p5 3dn+2 L
(1.32)
P
+
The mixing Hamiltonian is defined as HM IX = ν V (Γ)(a+
dν aν +aν adν ). V (Γ) is the
+
hybridization strength and aν,dν are electron creation operators. The x-ray absorption
spectrum can be calculated by solving the above given equations. The analysis of the
effects of charge-transfer shows that the charge-transfer influences the spectral shape
by contracting the multiplet structure and by small satellites. These observations are
comparable to experimental results from Okada, Kotani and van der Laan [37–41]. Hu
20
1.3 Experimental Details
et al. [42, 43] found out that for many systems charge-transfer multiplet calculations
fit much better than ligand-field multiplet calculations.
More detailed information about multiplet calculations can be found at the paper
of deGroot [44] and the book of deGroot and Kotani [45].
1.3 Experimental Details
1.3.1 The Photoelectron Spectrometer PHI 5600ci
For the XPS measurements a PHI 5600ci multitechnique spectrometer produced by
the Perkin Elmer Cooperation [46] was used. A schematic construction of this system
is shown in figure 1.9.
Al/Mn anodes
monochromator
ion gun
electron gun
hemisferical
analyzer
electronic lens
X−rays
multi−channel detector
mono X−rays
sample
Al X−ray anode
Figure 1.9: Scheme of the XPS spectrometer
A preparation chamber is attached to the PHI 5600ci. This chamber is produced
by the fine mechanical workshop of the department of physics. The preparation chamber afford to file or cleave the sample in vacuum with the integrated diamond file
or the pincer. As described in section 1.1.1 XPS is a very surface sensitive method.
Unfortunately the samples contaminate very fast if kept in atmosphere. This contamination adulterates the measurements and due to that it is very important to have the
possibility to prepare the sample in vacuum.
Another or additional way to clean the surface is to sputter with an ion gun. There
is an argon ion gun in the main chamber. The argon ions are accelerated with a
maximum voltage up to 4.5 kV. When they hit the sample surface the contamination
21
1 Experimental Methods and Theory
will be excluded. Not every material is suitable for sputtering because the ions can
destroy the structure and stoichiometry of the sample. Especially oxides are difficult
to clean by sputtering but this method is appropriate for metals and alloys.
The PHI 5600ci is provided with two x-ray sources. On the one hand there is a
dual Mg/Al x-ray anode and on the other hand a monochromatized Al anode. The
radiation energies are 1253.6 eV for the Mg Kα with a half-width of 0.7 eV and
1486.6 eV for the Al Kα . The half-width by the dual anode for Al Kα is 0.85 eV and
for the monochromatized 0.3 eV. The monochomatized Al anode is used in most cases.
The small half-width of 0.3 eV will be achieved by a quartz crystal and based upon
the Bragg equation nλ = 2d · sin(θ).
For XPS measurements an ultra high vacuum (UHV) is necessary for two reasons.
First the mean free path of the photo electrons increases so they can reach the analyser without being scattered in the atmosphere. The second reason is that the UHV
keeps the surface of the sample clean during the measurements, because there are less
molecules to adsorb on the surface. The UHV is reached by a number of different
types of vacuum-pumps. First rotation pumps create a pressure in that turbo molecular pumps can work. They reach a pressure around 1 × 10−8 mbar. An ion getter
pump and a sublimation pump can then be used to achieve a pressure about 1 × 10−9
mbar.
To analyze the excited photoelectrons an 11 inch hemispherical analyser is used.
First the incoming electrons are focused by a lens system. Afterward their kinetic
energy is reduced to a certain pass energy Ep to ensure that the absolute resolution is
constant for the hole spectrum. The constant analyser transition (CAT) mode allows
only electrons with an energy Ep ± δE to pass the analyser, δE denotes the absolute
energy resolution. For a higher energy resolution of the recorded spectra the pass
energy has to be reduced, but that also leads to a smaller overall intensity of the XPS
signal.
By measuring insulating samples, like the rare-earth scandates investigated in this
thesis, local charges can occur at the surface. They lead to a movement of the spectra during the measurements because the resolved photoelectrons seem to get higher
binding energies due to the electric field between sample and analyser. To avoid this a
neutraliser, a low-energy electron gun, can be used to compensate the charging. The
accelerating potential can be chosen between 0 V and 10 V at a maximal current of
25 µA.
1.3.2 The Advanced Light Source (ALS)
The Advanced Light Source (ALS), Berkeley, California USA, is a research facility used
by scientists to explore the properties of materials, analyze samples for trace elements,
probe the structure of atoms and molecules as well as other targets. Exemplarily for
synchrotrons in general, the composition of the Synchrotron will be described in the
following passage.
22
1.3 Experimental Details
Figure 1.10: Scheme of the ALS
The ALS produces light, principally x-rays, with special qualities. In figure 1.10 a
simplified diagram of the ALS is shown, which will give a look at the most important
parts of the ALS. Number 1 shows the linear accelerator, or linac. It is the electromagnetic catapult that brings electrons from a standing start to relativistic velocity.
This velocity close to the speed of light. A linac long enough to accelerate electrons
to the energy needed by the ALS would not fit inside the building. Instead, a circular
booster synchrotron (number 2) is used, in which the electrons receive a boost from an
accelerating chamber each time they go around. In less than one second, the electrons
make 1,300,000 revolutions (and travel 98,000 kilometers) and reach 99.999994% of the
speed of light. Once the electrons reach their target energy in the booster synchrotron,
an injection system transfers them from the booster to the storage ring (number 3)
where they circulate for hours. The storage ring is roughly circular with 12 arc-shaped
sections (about 10 meters long) joined by 12 straight sections (about 6 meters long).
Hundreds of precision electromagnets focus and bend the electron beam as it circles
the storage ring more than a million times a second. Electrons curving through the
ring’s 12 arc sections emit fanlike beams of photons. Between these curves there are
straight sections where multi-magnet devices, called undulators and wigglers, shake
23
1 Experimental Methods and Theory
the electrons to form a narrow beam of light 100 million times brighter than conventional x-ray sources. The synchrotron light emitted by the electrons is directed to
beamlines through the round beam ports. The brightest synchrotron light at the ALS
comes from undulators (number 4) which contain over one hundred magnetic poles
lined up in rows above and below the electron beam. The magnets force the electrons
into a snake-like path, so that the light from all the curves adds together. As the
electrons travel in their circular orbit in the storage ring, they emit synchrotron light
in the ultraviolet and x-ray range of the spectrum. The beamlines (number 5) deliver
the light down an optical obstacle course from the storage ring to the experiment
stations. A detailed scheme of the beamline is shown in figure 1.11. Number 6 shows
the position of the end stations. The end stations used for this thesis are presented
below.
Figure 1.11: Scheme of the ALS beamline
This information is taken from the official homepage of the ALS, for further information see reference [47].
1.3.2.1 Beamline 8.0.2 at the ALS
The used endstation on beamline 8.0.1 at the Advanced Light Source (ALS) was the
soft x-ray fluorescence (SXF) endstation of the University of Knoxville, Texas. This
one was used to make the XAS and XES measurements on the rare-earth scandates,
which are presented in this work. The used detection modes were total fluorescence
yield (TFY) and total electron yield (TEY). The spot size was 100 µm horizontal
and 50 to 3000 µm vertical. The maximal size of the sample was up to 2 cm. The
measurements made on this endstation were made by a temperature around 293 K.
24
1.3 Experimental Details
1.3.2.2 Beamline 4.0.2 at the ALS
At the Beamline 4.0.2 the used endstation is the XMCD chamber (6T, 2K). This
endstation is from the University of California, Davis/Berkeley Lab, California. The
XMCD measurements on the Fe L-edge of LuFe2 O4 were made on this endstation.
The temperature was between 260 K and 280 K and at magnetic field of 6 T. The
spot size is 1 mm horizontal and 0.1 mm vertical. The maximal spot size is up to
5x5 mm. More details about this enstation can be found on the official homepage of
the ALS [47].
1.3.3 The Swiss Light Source (SLS)
The Swiss Light Source (SLS) at the Paul Scherrer Institute in Villingen, Switzerland
is a third-generation synchrotron light source. It was built to get a facility with high
brightness, a wide wavelength spectrum and very stable temperature conditions for the
primary electron beam and the secondary photon beams. It has an energy of 2.4 GeV
and is used for research in material science, biology and chemistry. The SLS has some
special features, like a very large spectrum of synchrotron light ranging from infrared
light to hard x-rays or the so called top-up injection which produces a constant beam
intensity for experiments. The here presented information is taken from the official
homepage of the Paul Scherrer Institute [48].
1.3.3.1 TBT-XMCD Endstation at the SLS
The XMCD experiments for the Fe L-edge of W72 Fe30 sulfate were performed at the
surface and interface microscopy (SIM) beamline [49]. The used endstation was the
TBT-XMCD endstation from the Institut de Physique et Chimie des Matériaux de
Strasbourg (IPCMS) [50]. This experimental setup is unique in Europe. The XMCD
experiments can be made by temperatures down to 300mK in a magnetic field up to
7T. For the investigated Fe L-edge XMCD measurements the magnetic field had 6.5T
and the temperature was 0.7K.
1.3.4 Bessy II
Bessy II is a synchrotron of the Helmholtz Zentrum Berlin (HZB) [51]. It offers a large
variety of methods and experimental techniques involving a multitude of experimental
stations. Detailed information about the available endstations can be found on the
home page of the BESSY II [52].
1.3.4.1 Russian German Dipole Beamline
The Russian German Dipole Beamline (RGBL), has an energy range from 30 eV to
1500 eV. The used endstation was called Mustang. It was used for photoelectron
25
1 Experimental Methods and Theory
spectroscopy (XPS) and x-ray absorption spectroscopy (XAS) measurements. On this
endstations the XAS measurements for Mo72 Fe30 acetate and Mo72 Fe30 sulfate were
made at room temperature.
1.3.5 European Synchrotron Radiation Facility (ESRF)
The European Synchrotron Radiation Facility (ESRF) is an international x-ray light
source in Grenoble, France, supported by 19 countries. More information about the
ESRF can be found at the official homepage [53].
1.3.5.1 ID12 Circular Polarisation Beamline
The ID12 Polarisation-dependent X-ray Spectroscopy Beamline is a unique instrument
worldwide that offers users full control of the polarization state of the x-ray beam over
a wide energy range (2-15 keV) and is devoted to research at the ultimate limits of xray spectroscopy [54]. On this endstation the XMCD measurements on the Fe K-edge
and Lu L-edges were made. The endstation had an electromagnet to which enabled
magnetic fields up to 15T and an electromagnet which could offer a magnetic fields
up to 6T. The used temperatures varied from 125K up to 300K.
1.3.6 Superconducting Quantum Interference Device - SQUID
The here presented magnetometry measurements on LuFe2 O4 and W72 Fe30 sulfate
were performed at a Quantum Design MPMS at the University of Ulm, Germany.
The maximum field which was applicable had 7T. The temperature could be varied
from 1.9K up to 400K. The sensitivity was smaller than 10−8 emu.
26
2 RScO3
In this chapter the aim is to present a complete study about the RScO3 series including
PrScO3 , NdScO3 , SmScO3 , EuScO3 , GdScO3 , TbScO3 and DyScO3 . The first subsection describes the basic properties of the crystals. After this the x-ray photoelectron
(XPS) core levels will be shown. Afterward an x-ray absorption and x-ray emission
study will be presented. These measurements were used to determine band gaps and
opens up a discussion about the influence of structural parameters on the size of the
optical band gaps of these charge-transfer compounds. Some of the results of NdScO3 ,
SmScO3 , GdScO3 , TbScO3 and SmScO3 were already presented in my diploma thesis
[55] and the PhD thesis of M. Raekers [4]. Further some experimental results were
published by Raekers et al. [56] and Derks et al. [57]. The latest publication by
Postnikov et al. [58] is in print.
2.1 Introduction
Transition metal based perovskites exhibit a vast variety of unique physical characteristics, e.g., transport properties [59]. There were already a lot of investigations
on these materials in the nineties. Among the best known examples of such systems
during this time are cuprates, they show superconductivity at high-temperature [60].
Another group are manganites, they are well known because of the colossal magneto
resistance effect [61–63]. Cobaltes have a rich magnetic phase diagram and highspin to low-spin transitions [64]. More recently, superconducting iron pnictides [65]
and multiferroic perovskites like BiFeO3 [66] have attracted much attention. BiFeO3
shows ferromagnetic and ferroelectric ordering phenomena. On the other hand, dielectric and ferroelectric “d0 -perovskites” like BaTiO3 , LaTiO3 or SrTiO3 are subject
to intense research activities due to their remarkable dielectric properties and the
possibility to control the electrical polarization, which is a required pre-requisite for
constructing a ferroelectric memory (FeRAM) [67, 68]. The investigations during the
last thirty years changed the fundamental understanding of electron correlation effects.
Transition-metal oxides can be parted into two types of insulators. On the one hand
Mott-Hubbard insulators, their band gap is determined by the repulsive potential Udd
between the 3d electrons. On the other hand there are charge transfer insulators,
in which the energy energy gap (∆pd ) spans between the filled ligand p bands and
the unoccupied 3d conduction band states [69]. In this relation, there are two issues
of interest. First to get more information about the nature of correlation in mate-
27
2 RScO3
rial, by analyzing detailed trends in the band gap variation. The second intention
could be to use the detected trends for tailoring the optical band gap in wide-gap
oxidically insulators to desired values for possible applications. For example to use
it as a high-k gate dielectric [70, 71], or a transparent conducting oxide [72]. One of
these wide gap oxides are the scandates of type RScO3 (R = Pr, Nd, Sm, Eu, Gd,
Tb and Dy). They are particularly promising candidates for replacing SiO2 as gate
dielectric [73–76] in electrical devices. Moreover they can be used as a model system for applications in the terahertz regime [77]. Another purpose of applying these
scandium-based perovskites is the use as thin-film substrates. They belong to the best
available substrates for the epitaxial growth of high-quality thin films. So they can
be used for strain tailoring of ferroelectric, ferromagnetic, or multiferroic perovskite
thin films by choosing a suitable RScO3 [78–83]. Including a forecast of the band gap
reduction at the interface of DyScO3 and SrTiO3 [84]. The already known properties
of the RScO3 require a detailed description of the electronic structure to understand
the complex properties of RScO3 itself and its interaction to other materials. Up to
now there is only a limited knowledge about their electronic structure. Delugas et al.
[76] performed ab initio investigations on DyScO3 . Luckovsky et al. [74] published
some oxygen x-ray absorption spectra. Raekers et al. [56] investigated the electronic
structure of SmScO3 , GdScO3 , and DyScO3 . In the following chapter, the aim is to
extend the electronic structure studies on the RScO3 series onto further rare-earth
scandates, namely PrScO3 , NdScO3 , EuScO3 and TbScO3 .
2.2 Basic Properties and Preparation of RScO3
(R=Pr, Nd, Sm, Eu, Gd, Tb and Dy)
The RScO3 compounds crystallize in an orthorhombic
perovskite structure RMO3
p
(space group Pbnm (no. 62)) with a ≈ b ≈ 2ap , and c ≈ 2ap , and four formula units
per units per cell [5]. The lattice constances are shown in table 2.1. R represents a
trivalent rare earth metal and M a trivalent or mixed valent transition metal. [5]. The
lattice constances are shown in table 2.1 and a drawing of the crystal is presented in
figure 2.1. Uecker et al. [78] published the exact growing procedure. The perovskitetype melt congruently, so the crystals could be grown by the conventional Czochralski
technique with RF-heating (25 kW microwave generator) and automatic diameter
control. Flowing nitrogen or argon was used for the growth atmosphere. The pulling
rate was 0.5-1.5 mm h−1 and the rotation rate was 8-15 rpm. To achieve [110] R
scandate substrates, the R scandate crystals were grown along the [110] direction.
The here presented and investigated single crystals were grown by R. Uecker at the
Institute for Crystal Growth in Berlin.
28
2.2 Basic Properties and Preparation of RScO3 (R=Pr, Nd, Sm, Eu, Gd, Tb and Dy)
[001]
[111]
RE
[110]
ScO6
c
b
a
Figure 2.1: Orthorhombic RScO3 crystal structure; there is an octahedron
tilting about [001]p , [110]p and [111]p respectively.
PrScO3
NdScO3
SmScO3
EuScO3
GdScO3
TbScO3
DyScO3
a (Å)
5.6118(1)
5.5809(1)
5.5343(1)
5.5109(1)
5.4862(1)
5.4654(1)
5.4494(1)
b (Å)
5.7802(1)
5.7765(1)
5.7622(1)
5.7565(1)
5.7499(1)
5.7292(1)
5.7263(1)
c (Å)
8.0276(1)
8.0072(1)
7.9674(1)
7.9515(1)
7.9345(1)
7.9170(1)
7.9132(1)
Table 2.1: Structural parameters of RScO3 taken from Liferovich et al. [5]
29
2 RScO3
2.3 Core Level XPS of Rare-Earth, Scandium and
Oxygen
X-ray photoelectron spectroscopy (XPS) was used to investigate the rare-earth scandate single crystals. Information about the valence states of the compounds is given
by chemical shifts and the shape of the spectra. The measurements were performed
at the PHI 5600ci multitechnique spectrometer 1.3.1 at the University of Osnabrueck.
The crystals were cleaved in situ in a preparation chamber at a pressure of around
10−7 mbar. The main chamber had a pressure of around 10−9 mbar during the measurements. The temperature was 293K. The samples were neutralized by an electron
flood gun, so that the charging of the insulating samples could be avoided. The spectra were measured with a pass energy of 5.3 eV of the electron energy analyzer which
resulted in an overall spectral resolution of 80 meV.
2.3.1 XPS of Scandium and Oxygen
In figure 2.2 are the seven oxygen 1s spectra plotted. All seven XPS spectra have their
maximum at 530 eV, which is an indicator for O2− . The satellite at around 532 eV
results from OH-groups which can adsorb on oxygen defects on the surface. PrScO3 ,
TbScO3 and DyScO3 show a larger satellite so either the crystals have more defects
or the cleaved surface was not perfectly broken. PrScO3 , SmScO3 and DyScO3 show
a second, small but visible satellite at around 535 eV. This signal originates from a
carbonate (H2 CO3 ) contamination on the surface.
The 2p signals of the trivalent Sc atoms are shown in figure 2.3. The valence is
trivalent in all seven crystals. As a reference for Sc3+ the spectrum of Sc2 O3 is plotted
at the bottom of figure 2.3. The 2p3/2 main peak is located at 402 eV with a spin-orbit
splitting of around 4.5 eV. The 2p1/2 peak is visible around 406 eV. There are satellites
around 414 eV and 418 eV which result from an excitation in the valence band from
the oxygen 2p states to unoccupied scandium 3d states. O 2p and Sc 3d are hybridized.
This hybridization will be very useful in the following chapter to determine the band
gaps.
30
2.3 Core Level XPS of Rare-Earth, Scandium and Oxygen
Figure 2.2: O 1s XPS spectra of
RScO3 (R=Pr, Nd, Sm, Eu, Gd, Tb
and Dy)
Figure 2.3: Sc 2p XPS spectra of
RScO3 (R=Pr, Nd, Sm, Eu, Gd, Tb
and Dy) (red); the reference Sc2 O3
(black) was taken from Chastain et
al. [1]
31
2 RScO3
2.3.2 XPS of the Rare-Earth
The 3d core levels of the rare-earth ions are located at binding energies between 900 eV
and 1350 eV.
The praseodymium (Pr) 3d spectrum is shown in figure 2.4. The 3d5/2 peak is
located at around 933.2 eV and the Pr 3d3/2 peak at 953.5 eV. The location of the
peaks is an indicator for trivalent ions, because Pr4+ has higher binding energies [1].
The double peak structure of 3d5/2 and 3d3/2 could not be resolved. The spin-orbit
splitting is 20.3 eV. At this point it should be mentioned that the real spin-orbit
splitting has to take into account all satellites which belong to a certain energy level.
Sometimes this is hard to determine because of the small intensities of the satellites
and the large distances between them. So the here shown spin-orbit splittings belong
to the distances between the main peaks. Deviations are not excluded.
The second rare-earth ion in this row is neodymium (Nd). The Nd 3d core levels
are plotted on top of figure 2.5, in red. At the bottom of this graph an XPS measurement of Nd2 O3 , taken from Suzuki et al. [2], is shown (black). Both spectra have a
similar shape and the Nd 3d5/2 peak is located at 982.5 eV and the 3d3/2 at 1005 eV,
respectively. The spin-orbit splitting is 22.5 eV. Nd2 O3 is a reference for trivalent
neodymium, so it can be shown, that Nd ions in NdScO3 are trivalent. The shoulders
are typical for oxide bondings.
Figure 2.4: Pr 3d XPS spectra of
PrScO3
32
Figure 2.5: Nd 3d XPS spectra of
NdScO3 (red); the reference Nd2 O3
(black) was taken from Suzuki et al.
[2]
2.3 Core Level XPS of Rare-Earth, Scandium and Oxygen
The next spectrum discussed is the samarium (Sm) 3d core level spectrum. It is
shown in figure 2.6. The main 3d5/2 peak at 1083 eV indicates a trivalent state [1].
The Sm 3d3/2 peak is located at 1110 eV. The spin-orbit splitting of Sm 3d is 27 eV.
The small shoulders at both peaks and the small structures around the main peaks
are due to the complex multiplet splitting of the Sm 3d states.
Europium (Eu) 3d has two sharp peaks, they are shown in figure 2.7. The 3d5/2 is
located at 1135.6 eV and the 3d3/2 peak at 1165.5 eV, resulting in a spin-orbit splitting
of 29.9 eV. The position of the peaks is a good indicator for trivalent europium. Cho et
al. [85] showed, that the peaks emerge at lower binding energies for divalent europium.
Figure 2.6: Sm 3d XPS spectra of
SmScO3
Figure 2.7: Eu 3d XPS spectra of
EuScO3
Figure 2.8 contains two gadolinium (Gd) 3d XPS core level spectra, from GdScO3
(top, red) and Gd2 O3 (bottom, black). It is known, that the Gd in Gd2 O3 is trivalent
and it can be seen, that the spectrum is similar to the GdScO3 spectrum. The Gd 3d5/2
peak is located at around 1189 eV and the 3d3/2 at around 1221.5 eV. The positions
of the peak are also a clear indicator for Gd3+ . A satellite is located at 1199 eV.
The XPS spectrum of the terbium (Tb) 3d core levels is plotted in figure 2.9. The
main peak at 1241.8 eV belongs to the Tb 3d5/2 level. The Tb 3d3/2 is located at 1276
eV. This leads to a spin-orbit splitting of 34.2 eV for Tb 3d.
The last rare-earth 3d spectrum from dysprosium (red) is plotted in figure 2.10
together with the Dy 3d spectrum of Dy2 O3 (black), where Dy is trivalent. Both
spectra look similar regarding their shape and have the Dy 3d5/2 peak at a binding
energy of 1295.8 eV and the Dy 3d3/2 peak at 1334.7 eV. The spin-orbit splitting is
33
2 RScO3
Figure 2.8: Gd 3d XPS spectra of
GdScO3 (red); the reference Gd2 O3
(black) was taken from Lütkehoff [3]
Figure 2.9: Tb 3d XPS spectra of
TbScO3
about 39 eV. The intensity of the signal is rather low, because the excitation energy
of an Al Kα anode is 1486.6 eV and the excited electrons have a low kinetic energy
before they reach the analyser.
2.3.3 Conclusion
The photoelectron spectroscopy measurements of the rare-earth scandates showed
clear valence states for the ions in the investigated crystals. The oxygen is in all
seven crystals divalent (O2− ). The oxygen spectra make obvious that the crystals
have some defects, which lead to adsorptions of OH-groups and carbonates. The scandium spectra confirm the expected, trivalent state of scandium. The hybridization
between O 2p and Sc 3d states, which is known from Raekers et al. [56], can be
confirmed due to the satellites with 12 eV distances from the main peaks. Core-level
spectra from R 3d show that the spin-orbit splitting increases from 20.3 eV for Pr to
39 eV for Dy. Additionally all spectra confirm a trivalent state of the rare-earth ions.
34
2.3 Core Level XPS of Rare-Earth, Scandium and Oxygen
Figure 2.10: Dy 3d XPS spectra of DyScO3
35
2 RScO3
2.4 XAS and XES/RIXS of R, Sc and O
X-ray Absorption Spectroscopy (XAS) is a method to determine the element specific
density of unoccupied states above the Fermi level. X-ray Emission Spectroscopy
(XES) is used to examine the element specific density of occupied states below the
Fermi level. The XAS and XES measurements were performed at the Advanced Light
Source in Berkely, USA, at beamline 8.0.1. It is described in details in section 1.3.2. In
the last part of this section the band gaps of the rare-earth scandates are determined
by combining XAS and XES at the O K-edge. All rare earth emission spectra were
measured in second order of the spectrometer and therefore the spectra are at the half
energy value of the first order rare earth spectra. Measurements in second order for
the rare-earth ions were necessary because the first order energies were outside the
detection limit of the detector. All following x-ray absorption and emission spectra in
the chapter are detected in total fluorescence yield.
2.4.1 R M4,5 -Edges XAS and R 4f → 3d XES
The praseodymium M4,5 -edges XAS is dominated by two main peaks at the M5 -edge
at 932 eV and the M4 -edge at 952 eV. The splitting of 20 eV is due to the spin-orbit
splitting of Pr 3d. The spectrum is plotted in figure 2.11. The XES spectrum of
praseodymium is shown in figure 2.12. The spectrum was measured in the second
order with an excitation energy of 1000 eV. The two main peaks at around 465.6 eV
(M4 -edge) and 476.5 eV (M5 -edge) in second order are the equivalents to peaks at
931.2 eV and 953 eV in first order. There is a spin-orbit splitting of 22 eV.
The neodymium M4,5 -edges XAS (shown in figure 2.13) is dominated by two main
peaks at the M5 -edge at 982 eV and the M4 -edge at 1004 eV. The splitting is due
to the spin-orbit splitting of Nd 3d, and there are pre-peaks at around 977 eV and
999 eV. The XES spectrum of neodymium is plotted in figure 2.14. The spectrum
was measured in the second order with an excitation energy of 1016 eV. That way the
elastic peak, which is used for calibration, can be seen at 508 eV. The two main peaks
at around 486 eV and 497 eV are the energy pendants to 972 eV and 994 eV of the
first order. There is a spin-orbit splitting of 22 eV. The peak at around 495 eV is the
Sc 2s. If the measurements were detected in the first order of neodymium, the Sc 2s
would not be visible.
The Sm M4,5 -edges XAS is plotted in figure 2.15. The XAS spectrum consists of
two intense features at the M5 -edge at 1080.6 eV and the M4 -edge at 1104 eV due
to the spin-orbit splitting of Sm 3d states. The M5 -edge is splitted in a second peak
at 1078.6 eV and has a pre-peak at 1072.8 eV. The M4 -edge peak has a pre-peak
at 1098 eV. The excitation energies of the resonant x-ray emission measurements
are plotted in figure 2.16 close to the relevant spectrum. The first order oxygen K
emission at around 525 eV is present in each spectrum. The elastic peaks in the lower
three spectra are clearly visible at 552 eV, 541 eV and 538 eV in the corresponding
36
2.4 XAS and XES/RIXS of R, Sc and O
Figure 2.11: XAS at the Pr M4,5 -edges
of PrScO3
Figure 2.12: Pr 4f → 3d of PrScO3
spectrum. In the spectrum excited with 1076.5 eV there is only a small inelastic feature
at 537 eV. The resonantly excited inelastic part of the spectrum excited with 1082.5 eV
is more intense than the elastic peak in this spectrum. The resonant excitation at the
Sm M4 -edge results in a three peak structure centered at around 550 eV, with the
aforementioned elastic peak at 552 eV, and inelastic features at 550 eV and 549 eV,
respectively. The normal XES spectra at the top of figure 2.16 shows the mentioned
O Kα emission and just small inelastic peaks from the rare earth states at 537 eV
and 550 eV. In the resonant x-ray emission spectra no loss feature is observable that
would always appear in the same distance from the elastic peak. Therefore no small
excitation in the valence band region takes place. This is due to the large band gap
which suppresses such effects.
The x-ray absorption spectrum of Eu M4,5 -edges is plotted in figure 2.17. There are
two main peaks. The M5 peak is splitted in two and the peak positions are 1139.2 eV
and 1143 eV. There is a pre-peak at 1134.2 eV and a shoulder at 1145.8 eV. The
M4 peak is located at 1167.8 eV with a shoulder at 1171.4 eV. The x-ray emission
spectrum was measured in second order and is plotted in figure 2.18. It is dominated
by a peak at 577.7 eV which belongs to the Eu 3d3/2 state with an energy of 1155 eV.
The second peak at 563 eV is due to the Eu 3d5/2 -state which is in the first order at
1126 eV.
The gadolinium x-ray absorption spectrum plotted in figure 2.19 has a sharp M5 edge peak at 1185 eV and two obvious shoulders at 1189.4 eV and 1192.9 eV. The
M4 -edge has two nearly equal tips on one peak at 1215 eV and 1216.8 eV. Next to
37
2 RScO3
Figure 2.13: XAS at the Nd M4,5 edges of NdScO3
Figure 2.14: Nd 4f → 3d of NdScO3
this spectrum, in figure 2.20, the x-ray emission spectra of the Gd M4,5 -edges are
plotted. The x-ray emission spectra were excited with various energies. To excite the
Gd M5 -edge in resonance the excitation energies 1181.51 eV and 1183.8 eV were used.
The complete inelastic emission structure of the Gd M5 -edge at 590 eV is visible in
the resonant emission spectrum excited with 1215.7 eV. In this spectrum the elastic
peak and the inelastic Gd M4 -edge emerge at 608 eV and 605 eV, respectively. In the
normal XES excited with 1263.5 eV the M5 - and the M4 -edges are located at 590 eV
and 605 eV, respectively. No energy loss features are present.
The Tb M4,5 -edges XAS of TbScO3 is shown in figure 2.21. There are, comparable
to the previous x-ray absorption spectra of the rare-earths, two peaks. The M5 -edge
is located at 1244.6 eV and the M4 -edge at 1276 eV. In figure 2.22 the XES spectrum
of terbium is plotted. The excitation energy was 1265 eV. Due to the measurement in
second order the peak at 632.5 eV is the elastic peak and is used for calibration. The
terbium peaks are located at 615.5 eV and 620.5 eV. In first order measurements this
would correspond to peaks at 1231 eV and 1241 eV. So there is a spin-orbit splitting
of 10 eV.
The M5 -edge of dysprosium has its maximum at 1290 eV with a pre-peak at
1293.5 eV and a shoulder around 1298.3 eV. The XAS M4 -edge is located at 1329.3 eV.
The spectrum is plotted in figure 2.23 next to the x-ray emission spectra, which is
shown in figure 2.24 and is also measured in second order. There are different excitation energies used. The values are connected to the spectra. The three lower spectra
excited resonantly at the M5 -edge comprise the elastic peak and a small shoulder to
38
2.4 XAS and XES/RIXS of R, Sc and O
Figure 2.15: XAS at the Sm M4,5 edges of SmScO3 taken from [4]
Figure 2.16: Sm 4f → 3d XES of
SmScO3 taken from [4]
lower photon energies which is due to inelastic features excited in resonance. The resonant emission spectrum excited at the M4 -edge at 1328.1 eV shows the weak inelastic
structure of the M5 -edge from 642 eV to 652 eV. The elastic peak and resonantly
excited inelastic features are present around 663 eV. The pure inelastic structure of
the Dy M4,5 -edges is visible in the normal emission spectra excited with 1363.6 eV.
No energy loss features are visible.
39
2 RScO3
Figure 2.17: XAS at the Eu M4,5 edges of EuScO3
Figure 2.18: Eu 4f → 3d XES of
EuScO3
Figure 2.19: XAS at the Gd M4,5 edges of GdScO3 taken from [4]
Figure 2.20: Gd 4f → 3d XES of
GdScO3 taken from [4]
40
2.4 XAS and XES/RIXS of R, Sc and O
Figure 2.21: XAS at the Tb M4,5 edges of TbScO3
Figure 2.22: Tb 4f → 3d of TbScO3
Figure 2.23: XAS at the Dy M4,5 edges of DyScO3 taken from [4]
Figure 2.24: Dy 4f → 3d of DyScO3
taken from [4]
41
2 RScO3
Figure 2.25: XAS spectra taken at Sc L2,3 -edges of RScO3 (R=Pr, Nd, Sm,
Eu, Gd, Tb and Dy)
2.4.2 Sc L2,3 -Edges XAS and Sc 3d → 2p XES
To get further information about the internal fields of the crystals, the x-ray absorption
measurements of the scandium L2,3 -edges of all seven investigated rare-earth scandates
are considered. The spectra are shown in figure 2.25. They show nearly the same peak
distances. The first two peaks belong to the 2p3/2 states or in another notation L3 edge. The third and fourth peak correspond to 2p1/2 states or the so called L2 -edge.
Higuchi et al. [86] wrote that the first peak of the double peak shows states of the t2g
sub band and the second peak, which is somewhat larger, results from the eg sub band.
The first peak is located at 401 eV, the second peak around 403 eV. The crystal-field
splitting (10Dq) amounts to 1.9-2 eV for all seven rare-earth scandates. The distance
between peak three and four is between 1.9 and 2 eV, with one exception. PrScO3
shows a distance of 1.8 eV. As a result the distances between peak one and three and
between two and four lay between 4.2 eV and 4.4 eV. This more than 4 eV splitting is
a result of the spin-orbit splitting of the Sc 2p core levels. The 2 eV splitting between
the first and second and third and fourth peak is caused by the crystal field of the
oxygen octahedral which surrounds the scandium atoms. The distances are equal for
all seven crystals, so it is clear that there is no local field splitting. Otherwise there
has to be a change in the peak positions and splittings in the absorption spectra of
different rare-earth ions.
42
2.4 XAS and XES/RIXS of R, Sc and O
a-b
c-d
a-c
b-d
PrScO3
1.9
1.8
4.3
4.2
NdScO3
2.0
1.9
4.3
4.2
SmScO3
2.0
1.9
4.4
4.3
EuScO3
1.9
1.9
4.2
4.2
GdScO3
2.0
2.0
4.4
4.4
TbScO3
1.9
2.0
4.2
4.3
DyScO3
1.9
2.0
4.3
4.4
Table 2.2: Measured inter peak separations (in eV ± 0.2 eV) in the Sc L2,3
XAS spectra of Fig. 2.25.
The occupied Sc 3d states were probed by XES. There were different excitation
energies used and that leads to quite different spectra. NdScO3 and TbScO3 were
excited with 403.7 eV and the probed occupied Sc 3d states can be seen in figure 2.27.
Due to the 3d0 configuration, the occupied Sc 3d states are nearly empty. But there
is a strong hybridization with O 2p states, that leads to a small signal. There are two
peaks, which have different intensities for NdScO3 and TbScO3 , but are located at the
same energies. The first peak is located at 392.3 eV and the second one is located at
394.3 eV. The peak at 394.3 eV refers to Sc 3d states. The different ratio of the two
peaks in both samples suggests an influence of the presence of the rare-earth. This
influence can originate from different distortions of the oxygen octahedral and from a
more complex hybridization of Sc 3d, O 2p and R 5d states. A complex hybridization
was already mentioned by Lucovsky et al. [87] and Liferovich et al. [5].
For PrScO3 and EuScO3 , the excitation energy was set to 419.3 eV (figure 2.26).
SmScO3 , GdScO3 and DyScO3 were excited by 420.2 eV and are plotted in figure 2.28.
The spectra comprise one common main feature at 394 eV. Also common is a shoulder
at 391 eV which is a result of the Sc 2p spin-orbit splitting. The different intensities
of the shoulder can not be explained this way, so there could be an influence by the
rare-earth atom. The different rare-earth ions could lead to different distortions of
the oxygen octahedral and to a more complex hybridization of Sc 3d, O 2p and R 5d
states. Such a complex hybridization was also mentioned by Lucovsky et al. [87] and
Liferovich et al. [5]. PrScO3 , EuScO3 and GdScO3 show additional peaks at 399 eV,
400.5 eV, 402 eV and 406.7 eV. A shoulder at 496 eV appears for SmScO3 , GdScO3
and DyScO3 .
43
2 RScO3
Figure 2.26: XES spectra of the Sc
L2,3 -edges of PrScO3 and EuScO3
with EExc = 419.3 eV
Figure 2.27: XES spectra of the Sc
L2,3 -edges of NdScO3 and TbScO3
with EExc = 403.7 eV
Figure 2.28: XES spectra of the Sc
L2,3 -edges of SmScO3 , GdScO3 and
DyScO3 with EExc = 420.2 eV taken
from [4]
44
2.4 XAS and XES/RIXS of R, Sc and O
Figure 2.29: O K-edge XAS and O 2p
→ 1s XES of PrScO3
Figure 2.30: O K-edge XAS and O 2p
→ 1s XES of NdScO3
2.4.3 O K-Edge XAS and O 2p → 1s XES
In this section the x-ray absorption and x-ray emission spectra of oxygen of the rareearth scandates are shown in figure 2.29, 2.30, 2.31, 2.32, 2.33, 2.34 and 2.35. The
two measurements of each single crystal are plotted in a common graph in order
to obtain and estimate the size of the band gap. The x-ray absorption spectra are
shifted by the binding energy of the O 1s XPS peak (530 eV), so that the results are
comparable with the band structure calculations already published by Raekers et al.
[56]. In that publication the measurements were compared with ab initio calculations
to determine the band gap of the investigated materials. Similar methods were already
published elsewhere. Dong et al. [88] used the onset of O K XAS and XES spectra
in order to determine the band gap of ZnO. Hüfner et al. [89] used the separation
between the Fermi level of photoelectron spectra and the maximum of the first peak
of bremsstrahlung isochromat spectroscopy (BIS). By using this methods it must be
taken into account that the final states are different. On the one hand there are partial
occupied, delocalised bands and on the other hand there are complete occupied bands.
The Fermi levels are pinned differently in both methods and thus they have to be
used very carefully. The advantages of XAS and XES compared with band structure
calculations are, that small densities of states at the edge of the band gap are taken
into account, the experiments are made under very similar conditions in a short time
45
2 RScO3
Figure 2.31: O K-edge XAS and O 2p
→ 1s XES of SmScO3
Figure 2.32: O K-edge XAS and O 2p
→ 1s XES of EuScO3
range, and the precise relative calibration of XAS and XES. A disadvantage is the
element-specific band gap, but due to the delocalization and hybridization of the O
2p electrons this method is applicable. The x-ray absorption spectra are shifted, as
mentioned before, by the binding energy of the O 1s XPS peak (530 eV) for easier
comparison with the measurements and calculations from Raekers et al. [56]. To
obtain experimental estimates for the sizes of the band gaps without the performance
of new calculations the theoretical highest occupied and lowest unoccupied state were
extrapolated by lines in the spectra of SmScO3 , GdScO3 and DyScO3 . The slopes of
the XAS and XES spectra were extrapolated to the abscissa in order to receive the
band gaps of the four further samples. The measurements show some states near the
band gap which result from defects, these resulting states which come from the sample
and not the system were ignored. By using the extrapolated lines in combination with
the measurements we got the band gaps listed in table 2.3. For the determination
of the band gaps states occurring in the band gap, caused by crystal defects, were
neglected.
The values for the band gaps obtained here are in a good agreement with band gaps
which were determined by different methods, like ellipsometry measurements [73, 74],
ultraviolet absorption results [90] and a combination of internal photoemission and
photoconductivity measurements [91]. This technique is a good means to determine
46
2.4 XAS and XES/RIXS of R, Sc and O
Figure 2.33: O K-edge XAS and O 2p
→ 1s XES of GdScO3
Figure 2.34: O K-edge XAS and O 2p
→ 1s XES of TbScO3
PrScO3
NdScO3
SmScO3
EuScO3
GdScO3
TbScO3
DyScO3
this work
5.7 eV
5.6 eV
5.6 eV
5.7 eV
5.8 eV
6.1 eV
5.9 eV
Cicerrella[90]
5.7 eV
5.5 eV
5.4 eV
5.2 eV
5.6 eV
5.3 eV
5.5-6.0 eV
6.5 eV
Lim et al. [73]
Afanasev et al. [91]
5.6 eV
Lucovsky et al. [74]
5.8 eV
5.7 eV
Table 2.3: Band gaps of rare-earth scandates (in eV) as found in the present
work (the upper line) in comparison with previously reported values. Since
we applied the identical equivalent experimental conditions, the relative
error bars are ± 0.1-0.2 eV; the absolut error could be larger.
47
2 RScO3
Figure 2.35: O K-edge XAS and O 2p
→ 1s XES of DyScO3
the band gap, especially when optical measurements are not possible for various reasons. The size of the band gaps changes in dependence of the involved rare-earth ions
and is formed by rare-earth 4f , 5d and scandium 3d states hybridized with oxygen 2p.
But surprisingly there is no linear dependence on the size of the rare-earth ions. To
find out which structural parameter could be responsible for this unexpected nonlinear
dependence, the band gaps together with various structural parameters were plotted
in figure 2.36.
The here discussed structural parameters were taken from Liferovich et al. [5].
The first checked value is the tolerance factor, the so called Goldschmidt factor. The
Goldschmidt factor is a measure for the degree of distortion of a crystal with perovskite
structure (ABO3 ). The ion radius of A, the rare-earth ion radius, is proportional to the
Goldschmidt factor. For decreasing the ion radius the Goldschmidt factor becomes
also decreases and thus is not suitable for describing the band gap behavior of the
rare-earth scandates. The next test was to check the dependence between the size
of the band gaps and the bonding angles between the scandium and the oxygen ions
distances (Sc-O1, Sc-O2), respectively. But also there no correlation was found. The
best accordance was found between the Sc-O mean bond length and the band gaps.
The larger the Sc-O mean bond length the smaller the band gap. To explain this
behavior, the electronic structure of the systems in question is reduced to that of
48
2.4 XAS and XES/RIXS of R, Sc and O
conventional, ionic perovskite-type oxides: the formal valencies are R3+ Sc3+ and O2− ,
with the Sc 3d and R 5d states forming the conduction band, and O 2p states the
valence band. At closer inspection it can be seen that the bonding is, typical for
many perovskites, partially covalent. That leads to a small admixture of O 2p in the
conduction band and an additional state of Sc 3d in the valence band. This could be
evidenced by first-principles calculations (see figure 3 in Raekers et al. [56]), and by
the present experiments.
In the following two aspects will be discussed. First the Sc 3d states are not partially
occupied, so that no Jahn-Teller effect comes about to induce the distortion of the
ScO6 octahedral. Secondly, the splitting between the R 4f valence band states and
unoccupied R 4f states admixed into the conduction band is much larger than the
band gap and do not contaminate the edges of the latter. The band gap is, therefore,
primarily influenced by the strength of the O 2p - Sc 3d interaction, which moves apart
the barycenters of the valence band and the conduction bands, from which, further
on, the (half-) width of each of these bands must be subtracted. As it seems, the band
widths are not markedly dependent on structure parameters of individual compounds,
whereas the band gaps (revealing, as it seems, the strength of O 2p - Sc 3d interaction)
inversely follow a non-trivial variation of the mean Sc-O distance, as R changes - see
figure 2.36 d). A remarkable observation is that the variations of bond length of ±0.4%
give rise to amplified band gap variations of ±4.2%! Obviously, the real trend is much
more complex, as the deformation of ScO6 octahedra is accompanied by non-negligible
variation of Sc-O-Sc bond lengths. However, the latter do not fall onto any noticeable
trend in the electronic structure. Also, no obvious correlation exists with the size of
the R ion.
2.4.4 Conclusion
The previous section contains a complete set of x-ray absorption an x-ray emission
measurements for RScO3 (R = Pr, Nd, Sm, Eu, Gd, Tb, Dy). The O K-edge (XAS)
and O 2p → 1s (XES) measurements were combined to determine the band gaps of
the crystals. A determination of the band gap by this combination is possible, due to
the delocalized and hybridized O 2p states. Finally a dependence between the band
gap and the Sc-O mean distance was discovered.
49
2 RScO3
Figure 2.36: a) Tolerance factor (Goldschmidt factor) for RScO3 , b)
Sc−O−Sc bond angles of RScO3 , c) Distances between Sc and the two
oxygen spectra, d) Sc−O mean distance and experimental band gaps. All
structural parameters have been extracted from Liferovich et al. [5].
50
3 LuFe2O4
In this chapter the magnetic ground state configuration of the magneto electric, ferroelectric compound LuFe2 O4 is determined by means of (high field) x-ray magnetic
circular dichroism (XMCD). Experimental data are compared with multiplet calculations, which are performed with the TT multiplet program [44] taking into account
charge transfer and the crystal field.
3.1 Introduction
Multiferroics are materials which exhibit more than one primary ferroic order parameter simultaneously. There are three basic primary ferroic order parameters, ferromagnetism, ferroelectricity and ferroelasticity. The way they can affect each other are
shown in a multiferroic triangle in figure 3.1.
Ferroelectricity
P
E
Ferroelasticity
Ferromagnetism
P
ε
M
ε
σ
N
M
S
H
Figure 3.1: Multiferroic triangle
One class of multiferroics are multiferroic transition metal oxides, they have gained
enormous attention during the last few years [66, 92–95]. Beside the group of per-
51
3 LuFe2 O4
ovskites and related compounds [93, 96, 97] the charge frustrated, layered compound
LuFe2 O4 has attracted vast of interest due to its fascinating ferroelectric and magneto
electric properties [6, 98, 99]. Especially the use of magneto electric coupling and
multiferroics in spintronics has led to these huge interest in ferro electric magnets.
The spinel LuFe2 O4 is a very promising candidate for such applications because of
its giant room temperature magneto dielectric response [6], which suggests a strong
coupling between spin moment and electric dipole [92]. The resulting giant magneto
capacitance is due to charge ordering of iron ions [100]. In ferroelectric crystals a
spontaneous polarization is arising from the arrangement of electric dipoles. First
principle calculations [101, 102] and electron density analysis [103] of ferroelectric materials have revealed that the covalent bond between the anions and cations, or the
hybridization of electrons on both ions, plays a key role in establishing the dipolar arrangement. However, for LuFe2 O4 an alternative model for electronic ferroelectricity
was hypothesized by Portengen et al. [104]. They sad that the electric dipole depends
on electron correlation, rather than on the covalence, that has been confirmed by Ikeda
et al. [105].
A complex two dimensional ferrimagnetism plays an important role for the multiferroic properties of LuFe2 O4 . Below 250 K a long range ferrimagnetic order sets in
[106]. The fact that the ferroelectricity is caused by correlated electrons from the iron
ions leads to unusual properties and unique capabilities of LuFe2 O4 . A large response
of the dielectric constant by applying small magnetic fields has been found, opening
a route for future devices [6]. Phase transitions from the charge ordered phase have
been very recently associated with a non linear current voltage behavior, and an electric field induced phase transition, which might be of interest for potential electric
pulse induced resistive switching applications [107, 108]. The large magneto electric
coupling has been attributed to an intricate interplay of charge and spin degrees of
freedom with the crystal lattice and external electrical and magnetic fields, to some
extent on a short range order [109–113]. However, there is still some confusion about
√
the
√ nature of spin-charge coupling in LuFe2 O4 . In particular a model proposing a 3 x
3 charge ordered (CO) ground state [100, 114] is challenged by simulations implying
that the electrical polarization in LuFe2 O4 is due to spin-charge coupling and a spin
frustrated magnetic ground state in a chain CO state [115, 116].On the other hand the
first model finds a ferromagnetic spin ground state where Fe2+ and 1/3 of Fe3+ make
up majority spin, and 2/3 of the Fe3+ make up minority spin, which is confirmed by
XMCD experiments performed at around 200K and fields up to 6T [7, 117]. However,
the discussion about the magnetic properties and the nature of the magnetoelectric
coupling in LuFe2 O4 goes on. E. g., Phan et al. found a complex magnetic phase diagram with not only a ferrimagnetic transition at 240K but also additional magnetic
transitions at 225K and 170K, and 55K [118]. Furthermore, it was not possible to fully
saturate the LuFe2 O4 crystal at low temperatures in the above mentioned XMCD experiments, since one needs high fields up to 16 Tesla in order to saturate LuFe2 O4 ,
which then shows widely open hysteresis loops [111]. Therefore, we want to go beyond
52
3.2 Basic Properties of LuFe2 O4
the research done so far and perform a systematic temperature dependent study of
the magnetic ground state of LuFe2 O4 with the possibility to perform experiments at
the Fe K edge and Lu L2,3 edges under high fields up to 18 T.
3.2 Basic Properties of LuFe2O4
The investigated single crystal LuFe2 O4 has a two-dimensional layered rhombohedral
(R3m) structure, with the lattice constants of a = 3.439Å and c = 25.258Å. It
is composed of the alternate stacking of the hexagonal FeO2.5 layer (W-layer) and
the hexagonal LuO1.5 (U-layer) along the c-axis [119]. The W layers comprise two
triangular nets of Fe ions, the resulting electric polarization is induced via a frustrated
charge ordering of Fe2+ and Fe3+ ions on the resulting honeycomb lattice below 330K
[105, 120, 121]. The color of the crystal is between black and purple. In figure 3.2
on the left side the layered arrangement of lutetium, iron and oxygen is shown. On
the right side the iron double layers are shown with a triangular interconnectivity.
The Fe-Fe distances within a layer are 3.44 Å and are longer than the Fe-Fe distance
between the layers which have a distance of 3.156Å. [6]
3.3 Preparation of LuFe2O4
The investigated LuFe2 O4 single crystal was made by D. Prabhakaran in cooperation
with the group of S. Blundell at the University of Oxford, Oxford, UK. The crystal
was grown by the conventional Czochralski technique.
3.4 XMCD of Iron L2,3-edges in LuFe2O4
The here presented measurements were made at beamline 4.0.2 at the advanced light
source (ALS) in Berkeley, USA. The XMCD measurements were performed at 150K
at 6T. The sample was cleaved at an ambient pressure of around 5x10−5 mbar and a
temperature of around 80K (so called nitrogen precooling) before being transferred into
the helium cryostat with a pressure around 5x10−8 mbar. The c-axis of the LuFe2 O4
single crystal was aligned parallel to the external applied magnetic field [7]. This
alignment is common for all presented XMCD measurements in this work. In figure
3.3 the Fe L2,3 -edges spectra, recorded with left and right circular polarized x-rays and
measured in TEY (black), are presented in the upper part of the graph. The belonging
dichroic signal is plotted in green (a). Two multiplet calculations considering different
possible spin orderings are plotted in the lower part of the graph for comparison (b
and c in orange). The Fe2+ and Fe3+ peak of the L3 -edge are located at 708 eV
and 709.5 eV, respectively. The best agreement between multiplet calculations and
experiment is achieved with 50% antiferromagnetic Fe3+ and 50% magnetic mixed
53
3 LuFe2 O4
Figure 3.2: Crystal structure of LuFe2 O4 with Lu (large dark-gray spheres),
Fe (small black spheres) and O (large white spheres). Taken from Subramanian et al. [6].
valent bulk, resulting in overall Fe3+ contribution of 75%. The Fe L2 -edge peaks are
located at 721 eV and 723 eV with a shoulder at 720 eV. The experimental dichroic
signal at the L2 -edge is very small, but the dichroism in the calculated L2 -edge can be
found also in the experiment. The L3 -edge shows a clear dichroism at the Fe2+ peak
and a smaller dichroism at the Fe3+ peak which is inverted. In figure 3.3, graph (b) is
calculated with the following spin ordering: Fe2+ (↑)+1/3*Fe3+ (↑)+2/3*Fe3+ (↓) and
(c) with: 2/3*Fe2+ (↑)+1/3*Fe2+ (o)+2/3*Fe3+ (↑)+1/3*Fe3+ (↓). The agreement at
the dichroism at the Fe3+ peak of the Fe L3 -edge with the calculated dichroism signal
in (b) is a clear indication of a majority spin at the Fe2+ sites, while 1/3 of the Fe3+
spin is in majority and 2/3 is in minority. This configuration gives a perfect agreement
with the experiment besides the shoulder at 707 eV which is over estimated by the
calculation. Such a configuration was found before in LuFe2 O4 by Mössbauer and
neutron diffraction [122, 123]. The calculation of the magnetic moment of LuFe2 O4
54
3.5 XAS and XMCD of Iron K-edge in LuFe2 O4
Figure 3.3: LuFe2 O4 Fe L2,3 -edges XMCD performed at 150K (black), the
belonging dichroic signal is green (a). It is compared to multiplet calculations considering different possible spin orderings (b and c). The data are
taken from Kuepper et al. [7].
with the sumrules applied on the XMCD measurement gives a result of 2.33µB /f.u. by
using the Teramura coefficient (presented in section 1.1.5). This is in a good agreement
with the results presented by Iida et al. [124]. A more detailed analysis of the XMCD
on iron L2,3 -edges can be found in Kuepper et al. [7].
3.5 XAS and XMCD of Iron K-edge in LuFe2O4
To investigate the magnetic ground state of the magnetoelectric and ferroelectric compound LuFe2 O4 some high field x-ray magnetic circular dichroism (XMCD) measurements were made. For a complete magnetic saturation a magnetic field of 15T at a
temperature of 10K is needed. These kind of measurements should be made at the high
field endstation at the ESRF on beamline ID12, which can create magnetic fields up to
18T. But after problems with the power supply, the second endstation with magnetic
fields up to 6T was used. So it was not possible to get into magnetic saturation, but
the here presented measurements were comparable to the XMCD measurements on
the Fe L2,3 -edges, performed at the SXF-endstation at the ALS (see 1.3.2.2) and presented in the previous section 3.4. Figure 3.5 shows iron K-edge spectra of LuFe2 O4
at different temperatures, aligned parallel to the crystal c-axis. The measurements
were made at an external magnetic field of 6T. The dichroic signal is plotted for 125K,
55
3 LuFe2 O4
Figure 3.4: XMCD measurement (dark green) and XAS measurement (light
green) of the Fe K-edge on LuFe2 O4 performed at 125K and 6T.
150K, 175K, 200K, 225K. 250K, 275K and 300K. The intensity of the signal increases
at lower temperatures, so in this case the maximal dichroic signal is visible at 6T
and 125K. Exemplarily the XMCD spectra for 6T at 125K and the corresponding
XAS spectrum are plotted in figure 3.4. The XMCD shows a rather sharp feature
between 7112 eV and 7114 eV. This area is called the pre-edge and stems from 1s →
3d transitions, it is followed by a small double peak with opposite sign located between
7115 eV and 7122 eV. From 7122 eV up to 7133 eV a rather broad feature appears
with a positive sign. In figure 3.6 the pre-edge of the dichroic signal is enhanced and
plotted in green. Now a small minimum is visible, followed by the main peak. In
addition a multiplet-calculation (black) is plotted. The multiplet calculation results
from a mixture of Fe3+ and Fe2+ calculations. It was considered that Fe3+ is five times
weighted and Fe2+ four time weighted, due to the different number of d-electrons. The
spin ordering of the iron ions in LuFe2 O4 was already determined by XMCD measurements and multiplet-calculations of the Fe L2,3 -edges [7]. The experiment allowed
the following calculated spin ordering: Fe2+ (↑)+1/3*Fe3+ (↑)+2/3*Fe3+ (↓). Also this
spin ordering was considered. The multiplet calculation is in a very good agreement
with the experiment. The first minimum and maximum are very good mapped by the
multiplet calculation. The second minimum and maximum over swing and the third
minimum is 2 eV shifted to smaller photon energies. It is not surprisingly that the
calculations are after the second minimum in a worse agreement with the experiment
because of the delocalized 1s → 2p dipole transitions at higher photon energies, which
56
3.5 XAS and XMCD of Iron K-edge in LuFe2 O4
Figure 3.5: XMCD measurements of
the Fe K-edge on LuFe2 O4 at different temperatures.
Figure 3.6: XMCD Pre-edge measurements (green) at the Fe K-edge
of LuFe2 O4 compared to multipletcalculation (black).
will not be reproduced by multiplet-calculations. The main-edge has to be calculated
by band structure calculations. These calculations are planed in the near future.
57
3 LuFe2 O4
Fe2+
1s2 3d6
initial
Fe2+
1s1 3d7
final
Fe3+
1s2 3d5
initial
Fe3+
1s1 3d6
final
F23d3d
10.966
11.680
9.634
10.189
F43d3d
6.815
7.258
6.028
6.370
Slater integrals
G32p3d
0.0584
0.0524
Spin-orbit coupling
LS3d
0.052
0.0672
0.058
0.075
Table 3.1: Slater integrals (in eV) used for the Fe2+ and Fe3+ charge-transfer
multiplet simulations of the Fe K-edge XAS.
58
3.6 XAS and XMCD of Lutetium L2,3 -edges in LuFe2 O4
3.6 XAS and XMCD of Lutetium L2,3-edges in
LuFe2O4
Figure 3.7: XMCD (orange) and XAS (green) measurements on the Lu L2,3 edges of LuFe2 O4 . The temperature was 150K and the external applied
magnetic field had 9T. The k was parallel to the c-axis of the crystal.
The lutetium L2,3 -edges was measured at the ID 12 beamline of the ESRF in Grenoble. The reason for this measurement was to elucidate if also the Lu ions carry a magnetic moment and in which orientation this moment is orientated with respect to the
magnetization of the iron ions. In figure 3.7 the XAS (green) and the XMCD signal
(orange) of the Lu L2,3 -edges are plotted. The measurements were made at 150K and
9T, so they are in the same temperature range and the same magnetic field range as
the previous shown Fe L2,3 -edges XMCD measurements and the Fe K-edge XMCD
measurements. The Lu L3 -edge and the Lu L2 -edge have a quite large distance, so the
energy axis (abscissa) is splitted. On the left side from 9220 eV up to 9300 eV the Lu
L3 -edge is shown. The XAS spectra is dominated by a sharp edge resulting in a main
peak at 9250 eV. This main peak is followed by a small shoulder/peak at 9260 eV and
two further peaks at 9270 eV and 9290 eV. The right part of the axis belongs to the Lu
L2 -edge and has an energy range from 10330 eV up to 10410 eV. The Lu L2 -edge signal
starts with higher intensities, due to an underground caused by the Lu L3 -edge. From
this background a sharp edge is rising at 10350 eV also resulting in the main peak at
10355 eV. The following smaller peaks resemble the peak structure of the Lu L3 -edge.
There is again a small shoulder like peak close to the main peak at 10365 eV and two
bigger peaks at 10380 eV 10395 eV. In the same graph the XMCD signal is shown
in orange. The measurements with different orientations of light and magnetic field
59
3 LuFe2 O4
are not shown, due to the very small differences in the absorption spectra of different
polarized light. The measurements were taken with all four possible combinations of
polarization of the light and magnetic field. The XMCD signal at the Lu L3 -edge
is dominated by a double peak with opposite sign, starting in negative direction. A
wavelike structure with four positive and four negative signals followed. Again the Lu
L2 -edge is very similar to the Lu L3 -edge apart from the first double peak with opposite direction, in this case the double peak starts with a positive signal. So it can be
concluded that the Lu ions carry a small magnetic moment, due to the clear dichroic
signal, although the size of the effect is very small. The orbital moment and the spin
moment for the Lu L2,3 -edges can be calculated by using the XMCD sum rules which
are explained in section 1.1.5. Therefore the integrals over the dichroicRsignal at the L3
and L2 -edge, respectively, are needed. The following values are used: L3 (µ+ − µ− )dω
R
R
= -0.001415, L2 (µ+ − µ− )dω = 0.018649 and L3 +L2 (µ+ + µ− )dω = 32.562. These
values result to an orbital moment of approximately morb = 0.011µB /f.u. and a spin
moment in range of mspin = −0.018µB /f.u.. These results are vulnerable to mistakes,
due to the small intensity of the used signal. But although it is difficult to extract
the magnetic moment quantitatively exact from the sum rules, the overall shape of
the XMCD signal allows to conclude that the moments of the Lu ions are aligned in
a similar way as those of the iron ions.
3.7 SQUID and XMCD Hysteresis
SQUID and XMCD are two methods to get information about the magnetization of
a material. Both methods were applied to the single crystal LuFe2 O4 and compared.
The SQUID measurement were performed at the University of Ulm, Germany by Dr.
Kuepper. The XMCD measurements on the iron K-edge as mentioned in section 3.5
at the ID12 beamline of the ESRF. Both presented measurements are shown in figure
3.8. They were made at around 150K. The magnetic field was changed from -6T to 6T
and vice versa. As result there is in both cases a hysteresis loop visible. The hysteresis
are in both cases normalized and the shape is absolutely equal. The XMCD hysteresis
is a result of the changing hight of the XMCD signal of the iron K-edge. There are
no sumrules available for this method so the analysis is absolutely qualitatively. The
perfect fit with the SQUID measurement is a proof that the magnetic behavior is really
good reproduced by XMCD K-edge measurements on iron. The SQUID measurements
yield a magnetic moment of 1.96µB per formula unit.
3.8 Conclusion
LuFe2 O4 was investigated by XAS/XMCD at the iron L-edges, iron K-edge and
lutetium L-edges, respectively. Supplemental SQUID measurements were made. The
60
3.8 Conclusion
Figure 3.8: SQUID measurements (blue) compared to XMCD measurements
(green), both measurements are recorded at 150K.
iron pre-edge of the iron K-edge measurements were simulated by multiplet-calculations,
which reproduce the localised quadrupole transitions. The changing in the intensity
of the XMCD signal at 150K at the iron K-edge in dependents from the strength of
the external magnetic field is in agreement with SQUID measurements at the same
temperature. So it can be ascertained, that XMCD at the iron K-edge is suitable to
get information about the element specific magnetization of a material. Additionally
the pre-edge was simulated by multiplet calculations. The XMCD measurements on
the lutetium L2,3 -edges show that the ions carry a moment, even though it is quite
small. The sum rules were used but the results were discussed on their plausibility.
61
62
4 Iron-Based Magnetic
Polyoxometalates
In the present chapter an experimental and theoretical study of three giant Keplerate
VI
VI
structural-type molecules of the type {(M)M5 }12 FeIII
30 (M=Mo , W ) is presented.
Besides x-ray photoelectron spectroscopy (XPS) and x-ray absorption spectroscopy
(XAS) measurements, DFT calculations and multiplet calculations are used to interpret the experimental results. Furthermore, a detailed study of the Fe3+ to Fe2+ photoreduction process, which is induced under soft x-ray radiation in these molecules, is
presented. In the last section x-ray magnetic circular dichroism (XMCD) and SQUID
magnetometry measurements of W72 Fe30 sulfate are presented. The molecules were
synthesized by the group of Prof. Achim Müller from the University of Bielefeld, Germany. The DFT calculations were performed by Prof. Andrei Postnikov from the
Paul Verlaine University in Metz, France. Parts of this chapter are already submitted
for published by Kuepper, Derks et al. [125].
4.1 Introduction
Polyoxometalates are an interesting class of inorganic compounds. One part of this
class are the giant Keplerate structural-type molecules. Three of these molecules will
be presented in the following chapter: Namely Mo72 Fe30 acetate, W72 Fe30 sulfate and
Mo72 Fe30 sulfate. The formulas and equal nomenclatures used in the following chapter
are shown here:
i)[M o72 F e30 O252 (CH3 COO)10 M o2 O7 (H2 O)H2 M o2 O8 (H2 O)3 (H2 O)91 ]•ca.100H2 O ≡
1 ≡ 1a • ca.100H2 O ≡ M o72 F e30 acetate
ii)N a6 (N H4 )20 [F eIII (H2 O)6 ]2 [(W IV )W5IV O21 (SO4 )12 F e(H2 O)30 (SO4 )13 (H2 O)34 ] ≡
2 ≡ N a6 (N H4 )20 [F eIII (H2 O)6 ]2 • 2a • ca.100H2 O ≡ W72 F e30 sulf ate
iii)N a9 K3 [K20 ⊂ M oV70I F eIII
3 0O252 (SO4 )24 (H2 O)75 ] • ca.140H2 O ≡
3 ≡ N a9 K3 3a • ca.140H2 O ≡ M o72 F e30 sulf ate
63
4 Iron-Based Magnetic Polyoxometalates
Further information about previous experimental and theoretical studies even in
the field of magnetic behaviour of Mo72 Fe30 acetate can be found in several articles
[126–131]. Information about W72 Fe30 sulfate are reported by Todea et al. [132] as
well as information about Mo72 Fe30 sulfate [133].
4.2 Core Level XPS of Iron, Oxygen, Molybdenum and
Wolfram
In this section the results of the x-ray photoelectron spectroscopic (XPS) studies of the
three molecules Mo72 Fe30 acetate, W72 Fe30 sulfate and Mo72 Fe30 sulfate are presented.
A special focus will be set on the different ligands according to their influence on the
iron, wolfram, molybdenum and oxygen ions during the x-ray measurements.
4.2.1 Specific Experimental Details
The following photoelectron spectra were recorded at the local PHI 5600ci MultiTechnique XPS-System. The total energy resolution of the used monocromated xray source is around 0.3-0.4 eV. The resolution of the electron energy analyser is
around 80 meV. The monochromatized Al Kα source was used with 250 W power
supply. To keep a stable charging of the samples the measured core level lines were
performed under the use of a low energy electron flood gun. The pressure was around
1*10−9 mbar. The investigated molecules are poly-crystalline powders and were fixed
with carbon tape on a sample holder. The measurements were performed at room
temperature.
4.2.2 Iron Core Levels
The formal valence state of the iron ions in Mo72 Fe30 acetate, W72 Fe30 sulfate and
Mo72 Fe30 sulfate is Fe3+ [126, 132, 133]. From earlier measurements on molecules it
is known that x-rays can change the valence state of ions in molecules. Hence profile
measurements were taken to get separated spectra over a long timescale.
In the left panel of figure 4.1 the first and the last Fe 2p spectrum of W72 Fe30 sulfate
of a 17 hours lasting measurement is shown. It is obvious that the spectra changed
during the measurement. The first spectrum plotted in red at the bottom of the
left panel of figure 4.1 looks close to the Fe3+ reference, LiFeO2 , which is plotted in
black at the bottom of the figure. The Fe 2p3/2 main peak is located at 711 eV and
the characteristic Fe2+ satellite around 715 eV is not visible. Nevertheless there is
to mention that the characteristic Fe3+ satellite around 719 eV is not visible as well.
The Fe 2p1/2 peak is at 725 eV and so the spin orbit splitting is 14 eV. The final
spectrum is shown in red at the top of the left panel of figure 4.1. It looks closer to
the reference for Fe2+ , FeO, which is plotted in black at the top of the graph. The
64
4.2 Core Level XPS of Iron, Oxygen, Molybdenum and Wolfram
Figure 4.1: XPS measurements of Fe 2p (left panel) and Fe 3s (right panel) of
W72 Fe30 sulfate (red) in comparison with Fe2+ to Fe3+ reference compounds
(black).
main Fe 2p3/2 peak now is located at 709.7 eV with a shoulder at 709 eV. In addition
the two satellites at 715 eV and 728.5 eV are typical for Fe2+ . Both spectra seem to
reflect a mixed Fe2+ , Fe3+ valence state during the measurement.
In the right panel of figure 4.1 the Fe 3s peak is measured, as shown before for
Fe 2p, in the beginning and after 17 hours. The first measurement is plotted in red
at the bottom of the graph and the last measurement also in red on the top of the
graph. The Fe3+ and Fe2+ references are plotted in black, as before, LiFeO2 (Fe3+ ) at
the bottom and FeO (Fe2+ ) at the top of the graph. In this case the shape differs less
than at the Fe 2p spectra. A clear interpretation of the valence state is not possible.
Next the two Fe 2p spectra of Mo72 Fe30 sulfate and Mo72 Fe30 acetate are discussed.
In the left panel of figure 4.2 the first and the last spectrum of a 19 hours lasting
measurement of Mo72 Fe30 sulfate is shown in red and in the right panel of figure 4.2
the first and the last measurement of a 4 hours lasting measurement of Mo72 Fe30
acetate is shown also in red. The references for the iron valence states 2+ and 3+
are plotted in black. For the first measurements in both cases the Fe 2p3/2 peaks
are around 711 eV and the Fe 2p1/2 peaks around 725 eV. That leads to a spin-orbit
splitting of 14 eV. At the last measurements which are plotted in red on the top of
the panels a chemical shift to lower binding energies and a shoulder around 709 eV
becomes obvious. So a reduction from Fe3+ to Fe2+ can be assumed.
On this first view the spectra look similar to each other and to the Fe 2p spectrum
of W72 Fe30 sulfate, but we have to take into account, that the measurements of the
65
4 Iron-Based Magnetic Polyoxometalates
Figure 4.2: XPS measurements of Fe 2p of Mo72 Fe30 sulfate (left panel, red)
and Mo72 Fe30 acetate (right panel, red) in comparison with Fe2+ to Fe3+
reference compounds (black).
molecules containing sulfate took nearly 4 to 5 times longer. So it was shown that the
changing of the ligand acetate to sulfate slows the reduction process down. But there
is no quantitative analysis possible by these XPS measurements. This will be done in
section 4.3.2, by using x-ray absorption spectra of iron in all three molecules.
4.2.3 Oxygen Core Levels
The oxygen core levels of W72 Fe30 sulfate (a), Mo72 Fe30 sulfate (b) and Mo72 Fe30
acetate (c) can be seen in figure 4.3. The spectra at the bottom are always the first
measurements and the spectra at the top of the graph refer the last measurements. At
the beginning the O 1s peak of W72 Fe30 sulfate is located at 530.2 eV, for Mo72 Fe30
sulfate it is 530.4 eV and for Mo72 Fe30 acetate the O 1s is located at 530.6 eV. After
17 hours radiation the O 1s peak of W72 Fe30 sulfate is still at the same position. The
O 1s peak of Mo72 Fe30 sulfate is shifted after 19 hours radiation marginal to 530.4 eV.
A similar result has been found for Mo 3d and will be discussed within the chapter
4.2.4. Mo72 Fe30 acetate has a small shift to 530.2 eV after 4 hours of x-ray radiation.
So it can be assumed that the oxygen and its electronic configuration is influenced by
the x-ray radiation. This result is used in the next section 4.3.3 by discussing the O
K-edge spectrum of the molecules. There seem to be no radiation caused effects.
66
4.2 Core Level XPS of Iron, Oxygen, Molybdenum and Wolfram
Figure 4.3: XPS measurements of O 1s of W72 Fe30 sulfate (a), Mo72 Fe30 sulfate (b) and Mo72 Fe30 acetate (c).
4.2.4 Wolfram and Molybdenum Core Levels
The wolfram 4f core levels of W72 Fe30 can be seen in figure 4.4. The first measurement
is plotted at the bottom of the graph and the last spectrum on the top. The first
spectrum consist of a W 4f7/2 peak which is located at 36 eV and a W 4f5/2 peak
at 37.8 eV. Additional there are two shoulders at 34.1 eV and 35.3 eV. The shoulder
around 41.8 eV is the W 5d3/2 peak. The positions of the peaks are an indicator
for W6+ [134]. The spin orbit splitting is 1.8 eV. There seems to be no significant
amount of lower valences, otherwise there would be a triplet instead of a doublet. The
last spectrum, at the top of the graph, is taken after 17 hours. The W 4f7/2 peak is
located at 35.9 eV and the W 4f5/2 peak at 37.9 eV. The spin orbit splitting is 2 eV
and the W 5d3/2 peak is located at 41.9 eV. There are only marginal shifts of the peak
positions. So it seems that there is a stable W6+ valence state under the permanent
x-ray radiation.
The molybdenum 3d core levels are plotted in figure 4.5, Mo72 Fe30 acetate on the left
panel and Mo72 Fe30 sulfate on the right panel. The first taken spectra are, as usual,
plotted at the bottom of the graphs and the last spectra on the top. The Mo 3d5/2
and Mo 3d3/2 peak positions of Mo72 Fe30 acetate are equal for the first and the last
measurement at 232.6 eV and 235.8, respectively. For Mo72 Fe30 sulfate the Mo 3d3/2
peak is shifted a little bit from 235.6 eV to 235.5 eV and the Mo 3d3/2 peak is shifted
67
4 Iron-Based Magnetic Polyoxometalates
Figure 4.4: XPS measurement of W 4f of W72 Fe30 sulfate.
from 235.6 eV to 235.5 eV. In both cases the peak positions are typical for Mo6+ [46],
which was expected.
Mo72 Fe30 sulfate shows a small satellite around 240 eV. The O 1s peak of this
molecule shows also such a peak in the same distance. As the O 1s spectrum also the
Mo 3d spectrum of Mo72 Fe30 sulfate contains a small satellite located at 4.5 eV higher
binding energy than the main peak (240 eV in case of Mo 3d).
4.2.5 Conclusion
In conclusion it was shown that the three molecules change under x-ray radiation, but
there are differences in the affected ions. There was a change in the valence state of the
iron ions from 3+ to 2+. The amount of the reduction could not be denominated in
numbers, nevertheless differences at the reduction rate became obvious. At the three
investigated molecules it could be observed that the sulfate ligand reduces or at least
slows the reduction. The second result is that there seem to be no significant changes
in the valence states of oxygen, molybdenum or wolfram under x-ray irradiation.
68
4.2 Core Level XPS of Iron, Oxygen, Molybdenum and Wolfram
Figure 4.5: XPS measurement of Mo 3d of Mo72 Fe30 acetate (left) and
Mo72 Fe30 sulfate (right).
69
4 Iron-Based Magnetic Polyoxometalates
4.3 XAS
In the last section (4.2.2) the x-ray photoelectron measurements of iron in the molecules
1 to 3 were reported. It was not possible to give a quantitative estimation of the
amount of Fe2+ and Fe3+ in the sample after the samples were radiated by a certain
flux of x-rays. In the following section the order of the reduction process and a basic
approach about the underlying mechanism is given. The shown XAS measurements
and the multiplet calculations are already submitted for publication by Kuepper, Derks
et al. [125].
4.3.1 Specific Experimental and Theoretical Details
The here presented x-ray absorption measurements were performed at two different
beamlines. W72 Fe30 sulfate and Mo72 Fe30 acetate were measured at the Advanced
Light Source, beamline 8.0.1. The experiments were made at the x-ray fluorescence
end station from the University of Tennessee at Knoxville at room temperature. For
more detailed information see section 1.3.2.1. Mo72 Fe30 acetate and Mo72 Fe30 sulfate
were measured at the Russian-German Beamline at Bessy II. All spectra were recorded
at room temperature. Additional information can be found in section 1.3.4.1. All
absorption spectra were taken in total electron yield (TEY) mode.
The measured Fe L2,3 -edges x-ray absorption spectra were simulated within the
charge-transfer multiplet model using the TT-multiplet program [36, 45, 135]. After
the atomic energy levels of the initial (2pn 3dm ) and final (2pn−1 3dm+1 ) states were
calculated and reduced to 80% of their Hartree-Fock values (see table 4.1), an octahedral crystal field was considered. Finally, we considered charge transfer by introducing
3dm+1 L states and broadened the simulated spectra, considering lifetime broadening
and spectrometer resolution.
The first-principles density-functional calculations, performed by the SIESTA method
[136], were made by Prof. A. Postnikov. The SIESTA method uses norm-conserving
pseudo potentials in combination with numerical atom-centered strictly confined basis
functions. Exchange-correlation potential was taken after generalized gradient approximation (GGA) in the formulation of Perdew-Burke-Ernzerhof [137]. The molecules
(neutral Mo72 Fe30 acetate and 6-charged W72 Fe30 sulfate) were placed in a cubic simulation cell having a 36 Å edge, preventing an overlap of basis functions across the
cell boundary with the molecule’s spurious replicas. Basis functions were generated
by the split-norm technique, the standard technique in SIESTA. Typically, the quality
of the basis set was double-zeta with polarization orbitals‘(see [138]), except for the
’
Fe 3d status, which was of triple-zeta quality.
70
4.3 XAS
Fe2+
2p6 3d6
initial
Fe2+
2p5 3d7
final
Fe2+
Fe2+
Fe3+
2p6 3d7 L 2p5 3d8 L 2p6 3d5
initial
initial
final
Fe3+
2p5 3d6
final
Fe3+
Fe3+
2p6 3d6 L 2p5 3d7 L
initial
final
Slater integrals
F23d3d
10.966
11.779
9.762
10.623
12.043
12.818
10.966
11.779
F43d3d
6.815
7.327
6.018
6.560
7.535
8.023
6.815
7.327
F22p3d
6.793
6.143
7.446
6.793
G12p3d
5.004
4.467
5.566
5.004
G32p3d
2.844
2.538
3.166
2.844
8.200
8.202
8.199
8.200
Spin-orbit coupling
LS2p
LS3d
0.000
0.000
0.000
0.000
0.059
0.074
0.052
0.067
Table 4.1: Slater integrals (in eV) used for the Fe2+ and Fe3+ -charge-transfer
multiplet simulations of the Fe L2,3 -edges XAS. The spin-orbit parameters
were not reduced, whereas the d-d and p-d integrals were reduced to 80%
of the Hartree-Fock values for the subsequent simulation of the spectra.
4.3.2 Iron L2,3 -edges
There were two series of the molecules measured. The first one with the molecules 1
and 2 at the undulator based beamline 8.0.1 at the ALS and the second series of the
molecules 1 and 3 at the dipole Russian-German-Beamline at the Bessy II. Due to the
different kind of beamlines the two series are discussed seperately. A final conclusion is
made in the end of this chapter. All measurements were compared to spectra simulated
by the charge-transfer multiplet model using the TT-multiplet program [36, 45, 135].
So the following quantitative analysis stem from this simulations. The specifications
for these simulations are described above in section 4.3.1.
4.3.2.1 Mo72 Fe30 acetate and W72 Fe30 sulfate at the ALS
The now described Fe L2,3 -edges measurements are displayed in figure 4.6. The results
for Mo72 Fe30 acetate on the left side and for W72 Fe30 sulfate on the right side.
71
4 Iron-Based Magnetic Polyoxometalates
For the first measurement on molecule 1 the beamline photon flux was reduced to
12.5 % of its normal intensity and took, like all following measurements, 8 minutes.
For this scan there was, compared to multiplet calculations, a fraction of 90 % Fe3+ in
the sample. Due to technical reasons this is the only measurement with such a small
intensity, afterwards the lowest used intensity is 25 % intensity of the maximum flux.
On a fresh, second spot, there were four measurements made with 25 %, 50 %, 75 %
and 100 % intensity of the photon flux. The peaks at the L3 -edge around 707 eV
correspond to the Fe2+ and the peaks at 709 eV to the Fe3+ contribution. At the
L2 -edge the peak for Fe2+ is located at 720 eV and for Fe3+ at 722 eV. The reduction
from Fe3+ to Fe2+ is easy visible on the L3 -edge were the left peak corresponding to
Fe2+ increased and the right peak decreased. In numbers, the percentage quotation of
Fe3+ decreased from 80 % to 12.5 %. All values can be seen in table 4.2. For molecule
2 the reduction rate is slower. After the first cycle the Fe3+ percentage quotation is
85 % and after the fourth cycle, with full intensity, the Fe3+ fraction is still 37.5 %.
To get the percentage quotation independent from the beam current the intensity and
the beam current were combined to a new variable photon flux‘. The Fe3+ fraction is
’
plotted over the photon flux‘in figure 4.7. This plot makes obvious, that the reduction
’
processes have different timescales and different final values. Possible reasons for these
differences will be discussed after the results of molecule 1 and molecule 3 from the
Bessy II measurement were interpretated in the following section (4.3.2.2).
Sample
Spot
Scan
Intensity
Fe3+
total time
total flux
1
1
1
12.5%
90%
8 min
6.6 %
1
2
1
25%
80%
8 min
9.1 %
1
2
2
50%
35%
16 min
29.87 %
1
2
3
75%
30%
24 min
57.52 %
1
2
4
100%
12.5%
32 min
100 %
2
1
1
25%
85%
8 min
6.3 %
2
1
2
50%
67.5%
16 min
22.6 %
2
1
3
75%
47.5%
24 min
53.7 %
2
1
4
100%
37.5%
32 min
95.2 %
Table 4.2: Fraction of Fe3+ after x-ray radiation with different intensities.
72
4.3 XAS
Figure 4.6: Fe L2,3 -edges XAS series of 1 (left) and 2 (right). The experimental data are green and the black lines represent the corresponding simulated
spectra, which were obtained by superimposing corresponding fractions of
the simulated Fe3+ and Fe2+ spectra.
Figure 4.7: Fraction of Fe3+ versus the percentage x-ray photon flux for the
XAS series shown in figure 4.6.
73
4 Iron-Based Magnetic Polyoxometalates
4.3.2.2 Mo72 Fe30 acetate and Mo72 Fe30 sulfate at the Bessy
The molecules Mo72 Fe30 acetate and Mo72 Fe30 sulfate were measured at the dipole
Russian-German Beamline at the Bessy II. All spectra were taken with full intensity.
The spectra of sample 3 are plotted in figure 4.8. Each scan took 14 minutes and it is
obvious, that there is a reduction from Fe3+ to Fe2+ . To make the results comparable
(to the previous measurements of molecule 1 and 2) the Fe L2,3 -edges of molecule
1 is also measured and plotted in figure 4.9. Each scan took 14 minutes. Already
after three scans a Fe3+ percentage quotation of only 25 % is reached. To make the
reduction more obvious, the Fe3+ percentage quotation of the three series of the two
molecules are plotted over the photon flux ‘in figure 4.10 and additionally shown in
’
table 4.3. It can be seen, that the reduction from Fe3+ to Fe2+ happens faster in
the molecule 1. An even much faster Fe3+ to Fe2+ photoreduction process has been
observed for star shaped Fe4 single magnetic molecule [139], where the Fe3+ ions are
coordinated within an octahedral environment comprising four oxygen atoms and two
nitrogen ligands. This is a further indication that the reason for the photoreduction
process and especially the timescale of the photoreduction process depends from the
different coordination chemistry.
Figure 4.8: First (left) and second (right) series of Fe L2,3 -edges of molecule
3. The green lines represent the experimental data and the black lines
represent the corresponding simulated spectra that were obtained by superimposing corresponding fractions of simulated Fe2+ and Fe3+ spectra.
74
4.3 XAS
Figure 4.9: Series of Fe L2,3 -edges of
molecule 1 in green and simulated
spectra in black.
Figure 4.10: Fraction of Fe3+ versus
the percentage x-ray photon flux for
the XAS series shown in figure 4.9
and 4.8.
75
4 Iron-Based Magnetic Polyoxometalates
Sample
Spot
Scan
Intensity
Fe3+
total time
total flux
3
1
1
100%
85%
14 min
9.7 %
3
1
2
100%
65%
28 min
19.3 %
3
1
3
100%
60%
42 min
28.28 %
3
1
4
100%
55%
56 min
38.7 %
3
1
5
100%
52.5%
70 min
40.3 %
3
1
6
100%
50%
84 min
42.5 %
3
1
7
100%
50%
98 min
48 %
3
1
8
100%
47.5%
112 min
50.5 %
3
1
1
100%
75%
14 min
15.2 %
3
1
2
100%
55%
28 min
30.1 %
3
1
3
100%
52.5%
42 min
44.6 %
3
1
4
100%
47.5%
56 min
53.9 %
3
1
5
100%
45%
70 min
72.8 %
3
1
6
100%
42.5%
84 min
86.5 %
3
1
7
100%
40%
98 min
100 %
1
1
1
100%
60%
14 min
10.1 %
1
1
2
100%
37.5%
28 min
20.2 %
1
1
3
100%
25%
42 min
30.1 %
Table 4.3: Fraction of Fe3+ after x-ray radiation at the Bessy
76
4.3 XAS
4.3.3 Oxygen K-edge
In the following, the oxygen K-edge XAS of molecules 1 and 2 will be discussed in
comparison to the projected calculated DOS. These first-principles density-functional
calculations, performed by the SIESTA method [136], were made by Prof. A. Postnikov. For detailed information see section 4.3.1. On top of figure 4.11 the O K XAS
of Mo72 Fe30 acetate (left) and W72 Fe30 sulfate (right) are shown. They were taken at
a new spot with a low photon flux in order to get mainly information about the “original” electronic ground state. As it was already shown in the XPS section 4.2.3, the
oxygen ions are less influenced by potential soft x-ray induced modifications. There is
a strong hybridization between Fe 3d, Mo 4d or W 5d and the unoccupied O 2p states,
so the x-ray absorption spectra of the O K-edge represents the conduction band. For
comparison of the measurements and the calculated DOS, the spectra were shifted to
a common energy scale, with the Fermi energy set to zero.
Looking at the left side of figure 4.11, three main features stand out for Mo72 Fe30
acetate. The first one at 2 eV, the second at 4 eV and a less intense feature at 7 eV,
which depends on the O 2p/Mo 4d hybridization. There is a minimum intensity at
4.5 eV in the calculated DOS, which can not be recovered in the measurement. One
reason could be the missing core-hole potentials in the calculations.
The spectra of W72 Fe30 sulfate can be seen in the right panel of figure 4.11. The
dominating parts are the peaks at 2 eV and 3 eV as well as the broad feature from
7 to 11 eV. They are a consequence of the O 2p/W 5d hybridization. The calculated
DOS for the ions are shifted toward the Fermi level.
The hybridization between O 2p and Mo 5d or W 4d is much stronger, than that
between O 2p and Fe 3d, but there are still small features visible at 0.5 eV and 0.75 eV.
They are results from the Fe 3d t2g states. The Fe 3d eg states are overlapped by the
contributions of Mo 4d and W 5d, respectively. That way they are not visible in the
spectra.
4.3.4 Conclusion
It was observed that the photoreduction rate strongly depends on the ligand structure
surrounding the Fe ions, with negatively charged ligands leading to a dramatically
reduced photoreduction rate. This opens up the possibility of tailoring such polyoxometalates for x-ray spectroscopic studies and also for potential applications in the
field of x-ray induced photochemistry and catalysis.
77
4 Iron-Based Magnetic Polyoxometalates
Figure 4.11: Top: O K edge XAS of 1 (left) and 3 (right). The spectra were
taken at a low photon flux and a fresh spot of the corresponding sample.
Bottom: Calculated unoccupied densities of states for Mo72 Fe30 acetate
78
(left) and W72 Fe30 sulfate (right).
4.4 Magnetic Measurements on W72 Fe30 sulfate
4.4 Magnetic Measurements on W72Fe30 sulfate
Magnetic properties of materials become more and more important for future applications. W72 Fe30 sulfate is a molecule which shows a magnetic behavior. To get more
detailed information about the nature of the magnetic properties, SQUID magnetometry and XMCD measurements were performed, compared and shown in this section.
4.4.1 Specific Experimental and Theoretical details
The here presented SQUID magnetometry measurements were performed with a Quantum Design MPMS SQUID magnetometer in Ulm, Gemany (1.3.6), with a maximum
field of 5.5T and a temperature range from 2K to 15K.
The x-ray magnetic circular dicroism experiments were performed at the surface and
interface microscopy (SIM) beamline of the Swiss Light Source. The used endstation
was the 7T cryomagnetic TBT-XMCD endstation. For more detailed information
about the endstation see section 1.3.3. The temperature during the measurements
were around 0.7K. The W72 Fe30 sulfate powder sample was put on carbon tape before
connecting the sample holder to the cryostat coldfinger. The used record mode was
the total electron yield (TEY). To reduce the radiation damage process the maximum
flux of approximately 1012 photons per second at a photon energy around 700 eV, was
reduced to 1-2% of the maximum photon flux.
4.4.2 SQUID
Superconducting Quantum Interference Device measurements, so called SQUID - measurements, give information about the integral magnetization as a function of the
internal field and temperature. The measurements presented here are already submitted by Kuepper, Derks et al. [125]. W72 Fe30 sulfate was measured in a capsule with
27.1 mg powder of the sample. The molecular weight of W72 Fe30 sulfate is 25820 g/mol
and the sample comprised 6.321·1017 molecules. In figure 4.12 the magnetization per
molecule is plotted against the magnetic field B at 2 K, 5 K and 15 K. The largest
magnetic moment per molecule is µM = 58µb at 5.5 T and 2 K. There are no changes
in the magnetization by increasing the temperature to 5 K. At 15 K the magnetization is significant lower and is up to µM = 43µb at 5.5 T. A qualitatively similar
magnetization curve was obtained for Mo72 Fe30 acetate [126, 127]. For molecule 1 and
2 a nearest neighbor antiferromagnetic Fe-Fe interaction has been published recently
[132]. These SQUID data will be used as reference for the XMCD measurements,
which are presented in the following section.
79
4 Iron-Based Magnetic Polyoxometalates
Figure 4.12: SQUID measurements of W72 Fe30 sulfate from -6T up to 6T at
2 (orange),5 (green) and 15K (black)
4.4.3 XMCD at the Iron L2,3 -edges of W72 Fe30 sulfate
As shown in the previous section the radiation damage is quite small for W72 Fe30
sulfate, providing that some boundary conditions are considered. So the following
XMCD-spectra give information about the magnetic properties of iron in the not reduced molecule. In the first graph of figure 4.13 the Fe L2,3 -edges spectra, recorded
with right and left circular polarized light, is shown. The external applied field was
6.5 T and the sample temperature was 0.7 K. The resulting XMCD signal and its integral are also plotted. The XMCD measurement and the isotropic XAS measurement,
respectively, can be simulated by a combination of 85% Fe3+ and 15% Fe2+ . They are
shown in the second and third graph of figure 4.13. This corresponds to the Fe L-edges
measurement of W72 Fe30 sulfate on a fresh spot, which was shown before. So it can
be assumed that the reduction process was reduced to a minimum and the results can
be interpretated as results of a nearly unchanged sample. XMCD measurements will
be interpretated by using the sum rules [19]. In this case the magnetic spin moment
of W72 Fe30 sulfate is determined to µs = 51.5 µB /molecule. The orbital moment contribution is almost quenched. The here determined µs = 51.5 µB /molecule is smaller
than the µM of 58 µb at 5.5 T and 2 K as measured by SQUID magnetometry measurements shown before. One reason could be, that the spin sum rules underestimate
the moments for ionic systems due to core-hole Coulomb interactions [140, 141]. So
the spin sum rule correction factors for Fe2+ (1/0.685) and Fe2+ (1/0.875) as derived
by Teramura [140] have been used. Then the final value is 52 µB /molecule. This value
80
4.4 Magnetic Measurements on W72 Fe30 sulfate
is still smaller. There are four possible reasons for this dicrepance:
• Weak initial Fe3+ to Fe2+ photoreduction processes can not be entirely excluded.
• The sum rules correction factors were calculated for perfectly octahedral and homogeneous crystal fields, already small differences can lead to different correction
factors [141].
• At low temperatures, like in this case for 0.7 T, weak antiferromagnetic intermolecular interactions might be present.
• It was shown (4.3.3) that there might be some hybridized spin states because
of the element specific XMCD signal. These spin states may not be entirely
included.
4.4.4 Conclusion
The magnetic properties of the molecule W72 Fe30 sulfate were investigated by XMCD
and SQIUD. SQUID is a very well established method to determine magnetic moments and gives reliable data. But in contrast to XMCD it is not element specific.
So XMCD is a good extension. In this case the magnetic moment calculated from
XMCD measurements leads to little to small values. The possible reasons for this
discrepancy are presented above. The charge-transfer multiplet calculations were in
good agreement with the experiment
81
4 Iron-Based Magnetic Polyoxometalates
Figure 4.13: XMCD measurement of the Fe L2,3 -edges on W72 Fe30 sulfate.
The experimental results are plotted on the top of the graph. The paddle in
the middle shows the experimental dichroic signal (green) compared to CT
multiplet simulations (black). In the panel on the bottom the experimental
XAS signal (green) is compared to CT multiplet simulations (black). The
measurements were made at 6.5T and 0.7K.
82
5 Conclusion
The here presented work, gives an overview about three groups of materials, which
have in common, that they are materials with potential for possible future applications.
The presented materials are a series of rare-earth scandates, the muliferroic LuFe2 O4
and three iron-based magnetic polyoxometalates of the type {(M)M5 }FeIII
3 0 (M =
MoV I ,WV I ). They were examined by several different x-ray spectroscopic techniques
and multiplet calculations, respectively. The results are summarized below.
• RScO3 (R=Pr, Nd, Sm, Eu, Gd, Tb and Dy)
In chapter 2, a coherent picture of seven rare-earth scandates was conveyed.
In the first part core-level photoelectron spectroscopy results were shown, these
included the rare-earth R 3d (R=Pr, Nd, Sm, Eu, Gd, Tb and Dy), oxygen
O 1s and scandium Sc 2p spectra. They provided information of the valence
states of the ions in the crystal. The measurements confirmed the expected
valences of 3+ for the rare-earths and scandium, respectively and the valence 2for oxygen. To get more detailed information about the occupied and unoccupied
states x-ray absorption measurements (XAS) and x-ray emission measurements
(XES) were made. The M4,5 -edges (XAS) and the transition from R 4f → 3d
(XES) of the rare-earth were measured as well as the L2,3 -edges (XAS) and the
transition from Sc 3d → 2p (XES) of the scandium. The oxygen O K-edge
(XAS) and the transition from O 2p → 1s (XES) were measured and used to
determine the band gap of the rare-earth scandates. This was possible due to
the hybridization of the Sc 3d states and the O 2p states. So all electronic states
close to the Fermi level were represented by the XAS and XES spectra of the
oxygen. Hence a conclusion to the band gaps was possible. A comparison with
different crystallographic characteristics, determined a correlation between the
mean-distance of the scandium and oxygen ions and the size of the band gaps.
The results summarized here have already been published [56–58].
• LuFe2 O4
In chapter 3, LuFe2 O4 was investigated by x-ray absorption and x-ray magnetic
circular dichroism measurements at the iron L2,3 -edges, iron K-edge and lutetium
L2,3 -edges, respectively. Supplemental SQUID measurements were made. The
iron pre-edge of the iron K-edge measurement at a temperature of 150K was
simulated by multiplet calculations, which reproduce the localized quadrupole
transitions. The changing in the intensity of the XMCD signal at 150K at the
83
5 Conclusion
iron K-edge in dependents from the attached magnetic field is in perfect agreement with SQUID measurements, performed at the same temperature. So it can
be ascertained, that XMCD at the iron K-edge is suitable to get information
about the element specific magnetization of a material. The XMCD measurements on the lutetium L2,3 -edges show that the ions carry a moment, even though
it is quite small. The sum rules were used but the results have to be discussed
on their reliability.
• Iron-Based Magnetic Polyoxometalates
The last investigated group of materials were three iron-based magnetic polyVI
VI
oxometalates of type (M)M5 FeIII
30 (M=Mo W ) in chapter 4. The core levels
were measured by photoelectron spectroscopy (XPS). During the measurements
the spectra changed due to two different reasons. On the one hand the samples
were charged by the leaching of the photoelectrons. This charging effects could
be partially compensated in the here presented measurements by the use of an
electron flood gun. On the other hand the valence of the iron ions changed
due to the x-ray radiation and so the iron 2p spectra changed during the measurement. Depending on the ligand, it was observed that the change in the
spectra occurred at different time scales. A quantitative analysis of the time,
was not possible due to the charging effects, which could not be reduced completely. But the qualitative analysis could be made in connection with x-ray
absorption measurements (XAS). During the absorption measurements (XAS)
the sample had a stable state of charge. Furthermore, in the x-ray absorption
spectrum the difference between iron 3+ and iron 2+ can be clearly recognize,
due to an obvious changing in the peak positions for those two valence states.
By using multiplet calculations the ratio of iron 3+ to iron 2+ was determined.
Depending of the ligands of the molecule, the rate of conversion from iron 3+ to
iron 2+ is different. Furthermore an irradiance can be determined, in which the
results of the measurements were relatively close to the undamaged material.
So this low intensity was used for magnetic measurements by x-ray magnetic
circular dichroism (XMCD) and the results can be interpreted as results of an
almost unreduced molecule. The results of these measurements were compared
with SQUID measurements and a basic agreement was found. The results of the
XAS measurements, XMCD measurements, SQUID measurements and calculation, respectively are submitted for publication [125].
84
Fazit
Die hier vorgestellte Arbeit gibt einen Überblick über drei Gruppen von Materialien, die alle potenzielle Kandidaten für mögliche zukünftige Anwendungen sind. Die
vorgestellten Materialien sind eine Reihe von seltenen-erden Skandaten, das muliferroische LuFe2 O4 und drei auf Eisen basierenden magnetischen Polyoxometallaten vom
VI
VI
Typ {(M)M5 }FeIII
3 0 (M = Mo ,W ). Sie wurden mit mehreren verschiedenen rötgen
spektroskopischen Techniken und Multiplett-Rechnungen untersucht. Die Ergebnisse
sind nachstehend zusammengefasst.
• RScO3 (R=Pr, Nd, Sm, Eu, Gd, Tb und Dy)
In Kapitel 2 wurde ein zusammenhängendes Bild über sieben seltene-erd Skandate gezeichnet. Im ersten Teil wurden Ergebnisse der XPS Messungen gezeigt,
dazu gehören Spektren der selten-erd Elemente R 3d (R=Pr, Nd, Sm, Eu, Gd,
Tb und Dy), O 1s und Sc 2p. Sie liefern durch ihre Form und Peakpositionen, Informationen über die Valenzen der Ionen im Kristall. Die Messungen
bestätigten die zu erwartenden Valenz 3+ für die seltenen-Erden und Skandium,
sowie die Valenz 2- für Sauerstoff. Um detaillierte Informationen über die besetzten und unbesetzten elektronischen Zustände zu bekommen, wurden Röntgen
Absorptions- (XAS) und Röntgen Emissions-Messungen (XES) gemacht. Es
wurden die M4,5 -Kanten der seltenen-erd Elemente mit XAS und der Übergang
von R 4f →3d mit XES, sowie die L2,3 -Kanten (XAS) und der Übergang von
Sc 3d→2p (XES) von Skandium gemessen. Die Sauerstoff K-Kante (XAS) und
der Übergang von O 2p→1s (XES) wurden gemessen und verwendet, um die
Bandlücken der selten-erd Skandate zu bestimmen. Dies war, aufgrund der Hybridisierung der Sc 3d Zustände mit den O 2p Zuständen möglich. So können
alle elektronischen Zustände in der Nähe des Fermi-Niveaus durch XAS und XES
Spektren des Sauerstoffs abgebildet werden. Dies macht eine Bestimmung der
Bandlücken möglich. Ein Vergleich mit den verschiedensten kristallografischen
Eigenschaften zeigte eine Korrelation zwischen dem durschnittlichen Abstand
der Skandium und Sauerstoff Ionen und der Größe der Bandlücken. Die hier
zusammengefassten Ergebnisse sind in diesen Publikationen veröffentlicht [56–
58].
• LuFe2 O4
In Kapitel 3 wurde LuFe2 O4 an den Eisen L-Kanten, der Eisen K-Kante und
den Lutetium L-Kanten mit Röntgen Absorptionsmessungen und zirkularem,
85
Fazit
magnetischen Röntgendichroismus untersucht. Zusätzlich wurden SQUID Messungen gemacht. Die vordere Kante der Eisen K-Kanten Messungen wurden, bei
einer Temperatur von 150K, mit Multiplett Rechnungen simuliert, diese berücksichtigen die lokalisierten Quadrupolübergänge. Die Änderung der Intensität
des XMCD Signals an der Eisen-K-Kante stimmt bei 150K und unterschiedlich
angelegten externen Magnetfeldern perfekt mit den SQUID-Messungen überein.
So konnte gezeigt werden, dass XMCD an der Eisen-K-Kante geeignet ist, um
Informationen über die elementspezifische Magnetisierung eines Materials zu erhalten. Die Messungen an den XMCD Lutetium L2,3 -Kanten zeigen, dass die
Ionen ein magnetisches Moment haben, obwohl es sehr klein ist. Die Summen Regeln wurden angewendet, aber die Ergebnisse müssen, aufgrund der sehr
kleinen Messsignale, auf ihre Belastbarkeit überprüft werden.
• Eisenbasierte, magnetische Polyoxometallate
Als letzte Materialgruppe wurden im Kapitel 4 drei eisenbasierte, magnetische
VI
VI
Polyoxometalate des Typs (M)M5 FeIII
30 (M=Mo , W ) in Kapitel vier untersucht. Mit Photoelektronenspektroskopie (XPS) wurden die kernnahen Niveaus
gemessen. Die Spektren veränderten sich während der Messung, was zwei verschiedene Ursachen hatte. Auf der einen Seite wurden die Proben durch das
Herauslösen der Photoelektronen aufgeladen. Diese Aufladungseffekte konnten
aber teilweise durch die Benutzung einer Elektronenkanone kompensiert werden. Auf der anderen Seite wurde deutlich, dass bei den Eisen 2p Spektren eine
Veränderung eintrat, die sich durch die Änderung der Valenz des Eisens erklären
lassen konnte. Je nach Ligand konnte beobachtet werden, dass die Veränderung
mit unterschiedlichen Geschwindigkeiten auftrat. Eine quantitative Analyse zum
zeitlichen Ablauf konnte aber aufgrund der Aufladungseffekte nicht erfolgen. Die
qualitative Analyse konnte jedoch im Anschluss mit Hilfe von Röntgen Absorptionsmessungen (XAS) durchgeführt werden. Während der Absorption war ein
stabiler Ladungszustand der Probe gewährleistet. Des Weiteren lässt sich in
dem XAS-Spekrum deutlich der Unterschied zwischen Eisen 3+ und Eisen 2+
erkennen. Mit Hilfe von Multiplett-Rechnungen konnte das Verhältnis von Eisen
3+ zu Eisen 2+ bestimmt werden. Es konnte eine Tendenz der Geschwindigkeit
der Umwandlung von Eisen 3+ zu Eisen 2+, in Abhängigkeit vom Liganden,
erkannt werden. Außerdem konnte eine Bestrahlungsstärke bestimmt werden,
bei der die Messergebnisse relativ nah am unbeschädigten Material liegen. Diese
Erkenntnis wurde genutzt um magnetische Messungen mit Hilfe des zirkular
magnetischem Röntgendichroismus (XMCD) am nahezu unveränderten Molekül
zu machen. Die Ergebnisse dieser Messungen wurden mit SQUID Messungen
verglichen und eine grundsätzliche Übereinstimmung wurde gefunden.
86
Danksagung
Ich möchte mich zuerst für die finanzielle Unterstützung durch den Fachbereich Physik
der Universität Osnabrück bedanken. Außerdem wurde ich mit einem Abschlussstipendium des “Pools Frauenförderung ” durch die Zentralen Kommission für Gleichstellung gefördert.
Als nächstes gilt mein Dank Herrn apl. Prof. Prof. H.C. Dr. Dr. H.C. Manfred
Neumann. Seine wissenschftliche Erfahrung und seine persönliche Betreuung waren
eine große Hilfe und machten diese Arbeit erst möglich.
Dann habe ich auch Dr. Karsten Küpper für die wissenschaftliche und persönliche
Zusammenarbeit herzlich zu danken. Seine wissenschaftliche Hilfe und Unterstützung
haben mir bei der Erstellung dieser Arbeit sehr geholfen. Seine Anträge machten
die zahlreichen Synchrotronmessungen, die ein Kern dieser Arbeit sind erst möglich.
Vielen Dank für die Unterstützung in den letzten Wochen und Monaten vor Abgabe
dieser Arbeit!
Des weiteren gilt mein Dank Prof. Dr. Andrei Postnikov. Er hat einen wichtigen
Teil zu der Interpretation experimenteller Ergebnisse beigetragen. Seine Hilfsbereitschaft bei der Besprechung und dem Korrekturlesen von Papern soll hier besonders
hervor gehoben werden.
Ich möchte auch Prof. Dr. Frank de Groot von der Abteilung für Anorganische
Chemie und Katalyse an der Universität Utrecht danken. Er hat es uns, durch das zur
Verfügungstellen des TTmultiplet Programms, ermöglicht Multiplettrechugen selber
durchzuführen. Bei der Erstellung von neuen Inputfiles stand er uns immer mit Rat
und Tat zur Seite.
Ganz wichtig war für mich die Arbeitsgruppe Elektronenspektroskopie. Sie wird
häufig vergessen, trotzdem ist sie mir sehr wichtig und darum möchte ich den ehemaligen und aktuellen Mitgliedern von ganzem Herzen für die freundschaftliche Zusammenarbeit danken. Vielen Dank an: Dr. Michael Raekers, Dr. Manuel Prinz, Dr.
Christian Taubitz, Dipl. Phys. Stefan Bartkowski, Dipl. Phys. Miriam Baensch, M.
Sc. Olga Schuckmann, B. Sc. Andreas Meyering und M. Sc. Daniel Taubitz.
Als momentan (fast) letztes Arbeitsgruppenmitglied, möchte ich mich bei meiner
Kollegin und Freundin Anna Buling bedanken. Es war eine Freude mit ihr zu Arbeiten
und ich hoffe, dass uns das Schicksal noch einmal in ein gemeinsames Büro verschlägt.
Ein weiteres Dankeschön geht an Werner Dudas und seine magischen Hände bei
der Betreuung der ESCA. Marion von Landsberg war als Arbeitsgruppensekretärin
und Mensch ein Segen. Wenn an anderer Stelle häufiger die Worte “so einfach geht
das nicht” fielen. hat Marion es einfach ohne viel Aufhebens möglich gemacht. Dafür
87
Danksagung
meinen ganz herzlichen Dank!
Ein weiterer freundschaftlicher Kontakt ist über die Jahre zu Claudia Meyer entstanden. Ihr Engagement bei der Finanzierung meiner Arbeit war großartig. Auch an
dieser Stelle noch einmal herzlichen Dank.
Die letzten Monate habe ich auf dem Flur der AG Wollschläger verbracht. An
dieser Stelle ein herzliches Dankeschön an alle AG Mitglieder für die nette Aufnahme
in ihren unterhaltsamen Kreis, exemplarisch möchte ich Dipl. Phys. Henrik Wilkens
erwähnen, weil er so gerne in Danksagungen steht.
Zuletzt möchte ich mich bei meinen Eltern, meiner Schwester und meinem Freund
bedanken. Vielen Dank für Eure Geduld. Ich bin jetzt fertig!
88
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List of Publications
• K. Kuepper, C. Derks, C. Taubitz, M. Prinz, L. Joly and J.P. Kappler, A. Postnikov, W.L. Yang, T.V. Kuznetsova and P. Ziemann Electronic structure nd softX-ray-induced photoreduction studies of iron-based magnetic polyoxometalates of
VI
VI
type{(M)M5 }12 FeIII
30 (M=Mo , W ) submitted to Dalton Transactions
• A. Postnikov, C. Derks, K. Kuepper and M. Neumann Electronic Structure of
Rare-Earth Scandates from X-Ray Spectroscopy and First-Principles Calculations (2012) in print
• C. Derks, K. Kuepper, M. Raekers, and M. Neumann Band gap variation in
RScO 3 (R=Pr, Nd, Sm, Eu, Gd, Tb, and Dy): X-ray absorption and O K-edge
x-ray emission spectroscopies Physikal Review B 86 Issue:15, 155124 (2012)
• T.V. Kuznetsova, V.I. Grebennikov, H. Zhao, C. Derks, C. Taubitz, M. Neumann, C. Persson, M.V. Kuznetsov, I.V. Bodnar, R. W. Martin and M. V.
Yakushev A photoelectron spectroscopy study of the electronic structure evolution in CuInSe2 -related compounds at changing copper content, Applied Physics
Letters 101, 11, 11607 (2012)
• H.H. Pieper, C. Derks, M. H. Zoellner, R. Olbrich, L. Tröger, T. Schroeder,
M. Neumann and M. Reichling Morphology and nanostructure of CeO2 (111)
surfaces of single crystals and Si(111) supported ceria films, Physical chemistry
chemical physics : PCCP 14 Issue:44,155361-8 (2012)
• A. Gryzia, H. Predatsch,A. Brechling, V. Hoeke, E. Krickemeyer, C. Derks, M.
Neumann, T. Glaser and U. Heinzmann Preparation of monolayers of [Mn-III
Cr-6(III)](3+) single-molecule magnets on HOPG, mica and silicon surfaces and
characterization by means of non-contact AFM, Nanoscale Research Letters 6,
486 (2011)
• K. Kuepper, M. Raekers, C. Taubitz, M. Prinz, C. Derks, M. Neumann, A.V.
Postnikov, F.M.F. deGroot, C. Piamonteze, D. Prabakharan and S.J. Blundell
Charge order, enhanced orbital moment, and absence of magentic frustration in
layered multiferroic LuFe2 O4 , Physical Review B 80, 220409(R) (2009)
101
102
Erklärung
Hiermit erkläre ich an Eides Statt, die vorliegende Abhandlung selbständig und ohne
unerlaubte Hilfe verfasst, die benutzten Hilfsmittel vollständig angegeben und noch
keinen Promotionsversuch unternommen zu haben.
Christine Derks
Osnabrück, 15. Dezember. 2012