In the practice of solid state chemistry, structural phase transitions are fairly common events. Nonetheless, their understanding, in terms of both: A rationalization of the observed changes in symmetry pattern and; An understanding of the mechanisms allowing for a particular transformation, are outstanding problems. The thermodynamic classification of phase transitions distinguishes between first and second order transitions, on the basis of the discontinuous behavior of quantities related to first or second derivatives of the free energy, respectively. Small atomic displacements are typically associated with second order phase transitions, and latent heat changes amount to a few calories per gram only. Additionally, the symmetries of the phases surrounding the transition are typically in the relation of a group and a subgroup. Reconstructive phase transitions, on the contrary, involve breaking of (large) parts of the bond scaffolding of the initial structure, and exhibit drastic changes at the transition point, with large latent heat and hysteresis effects. The corresponding atomic displacements can be in the order of the lattice parameters, and no group-subgroup is found, between the symmetry of the phases. These type of transitions have generally a strong first-order character. Landau theory accounts for continuous, second-order phase transitions. As a phenomenological theory, it does not establish the existence of a phase transition, which remains an experimental fact. It only bridges microscopic characteristics, like space-group symmetries and structural changes, or phonon softening effects, with measurable macroscopic quantities. Therein, distortions are carried by an order parameter, which fully specifies the form of the analytical variational free energy. The latter is continuous and derivable with respect to temperature, pressure and atomic displacement, at the transition point. First order, non-continuous phase transitions are still within the scope of Landau theory in the mentioned special case of the existence of a group-to-(isotropic) subgroup relationship. In the majority of cases, however, and for the most interesting phase transitions (for basic and applied research), such a relationship is missing, making the choice of an order parameter less straightforward. Most of the allotropic transformations of the elements, many intermetallic systems, and numerous insulating systems belongs to this class. This class also includes most interesting and fundamental electronic effects, like metallization in perovskites or spinel oxides for example. This very simple fact of a missing symmetry condition has helped reinforcing the opinion of first-order phase transitions being a world apart, and possibly contributed to discouraging a firm theory to develop, able to account for their transformation mechanisms and the change of physical properties across phase transition. The thermodynamic distinction between first and second order phase transitions is too narrow, as, in case of first order phase transitions, it embraces both weakly discontinuous transition and reconstructive ones, where bonds are being strongly modified. Especially, a mean to qualify the distance between two structures (geometric, with respect to symmetry, a.s.o.), is missing. Clearly, a group-subgroup relationship may, and typically does imply shortest shifting distances, as a tiny atomic displacement can already do for a symmetry lowering. Naively, missing such a relation means no constraints, and apparently no means to conclude at a connection of two structures in general, let alone a full mechanistic analysis. First order phase transitions proceed by nucleation and subsequent growth of the new phase from the initial one. Different from (second-order) continuous phase transitions, they do imply coexistence of the transforming motifs. The discontinuity in some order parameter between the two phases is driven by lowering of the free energy as the new phase forms. However, close to the transition, the original phase remains metastable, and a fluctuation is needed to cause the formation of the new phase to set in. Such a process responds to thermal changes, and depending on the height of the nucleation barrier, its rate may be slower or faster. In the former case, large deviations from equilibrium may be required to achieve transformation to the stable phase, which means that large hysteresis effects will be observed in the course of transformation. The intent of this work consists in giving a face to the intermediate configurations appearing in first order phase transitions, in solid-solid reconstructive processes. Apart of a mechanistic elucidation, consisting in answering the question “Which atomic displacements bring structural motif A into structural motif B ?”, another purpose of this work is a rather pedagogical one, that is, showing that first-order phase transitions can be understood in detail, not only in principle but in fact. The core of the examples illustrated in this work is concerned with phase transformations where pressure represents the thermodynamic controlling parameter. Pressure is extensively used in chemical synthesis, as a mean to achieve novel properties, optical or mechanical just to mention a few. Additionally, reports on novel high-pressure polymorphs are regularly appearing. In this sense, pressure is a relevant parameter for approaching fundamental questions in solid state chemistry.

In the practice of solid state chemistry, structural phase transitions are fairly common events. Nonetheless, their understanding, in terms of both: A rationalization of the observed changes in symmetry pattern and; An understanding of the mechanisms allowing for a particular transformation, are outstanding problems. The thermodynamic classification of phase transitions distinguishes between first and second order transitions, on the basis of the discontinuous behavior of quantities related to first or second derivatives of the free energy, respectively. Small atomic displacements are typically associated with second order phase transitions, and latent heat changes amount to a few calories per gram only. Additionally, the symmetries of the phases surrounding the transition are typically in the relation of a group and a subgroup. Reconstructive phase transitions, on the contrary, involve breaking of (large) parts of the bond scaffolding of the initial structure, and exhibit drastic changes at the transition point, with large latent heat and hysteresis effects. The corresponding atomic displacements can be in the order of the lattice parameters, and no group-subgroup is found, between the symmetry of the phases. These type of transitions have generally a strong first-order character. Landau theory accounts for continuous, second-order phase transitions. As a phenomenological theory, it does not establish the existence of a phase transition, which remains an experimental fact. It only bridges microscopic characteristics, like space-group symmetries and structural changes, or phonon softening effects, with measurable macroscopic quantities. Therein, distortions are carried by an order parameter, which fully specifies the form of the analytical variational free energy. The latter is continuous and derivable with respect to temperature, pressure and atomic displacement, at the transition point. First order, non-continuous phase transitions are still within the scope of Landau theory in the mentioned special case of the existence of a group-to-(isotropic) subgroup relationship. In the majority of cases, however, and for the most interesting phase transitions (for basic and applied research), such a relationship is missing, making the choice of an order parameter less straightforward. Most of the allotropic transformations of the elements, many intermetallic systems, and numerous insulating systems belongs to this class. This class also includes most interesting and fundamental electronic effects, like metallization in perovskites or spinel oxides for example. This very simple fact of a missing symmetry condition has helped reinforcing the opinion of first-order phase transitions being a world apart, and possibly contributed to discouraging a firm theory to develop, able to account for their transformation mechanisms and the change of physical properties across phase transition. The thermodynamic distinction between first and second order phase transitions is too narrow, as, in case of first order phase transitions, it embraces both weakly discontinuous transition and reconstructive ones, where bonds are being strongly modified. Especially, a mean to qualify the distance between two structures (geometric, with respect to symmetry, a.s.o.), is missing. Clearly, a group-subgroup relationship may, and typically does imply shortest shifting distances, as a tiny atomic displacement can already do for a symmetry lowering. Naively, missing such a relation means no constraints, and apparently no means to conclude at a connection of two structures in general, let alone a full mechanistic analysis. First order phase transitions proceed by nucleation and subsequent growth of the new phase from the initial one. Different from (second-order) continuous phase transitions, they do imply coexistence of the transforming motifs. The discontinuity in some order parameter between the two phases is driven by lowering of the free energy as the new phase forms. However, close to the transition, the original phase remains metastable, and a fluctuation is needed to cause the formation of the new phase to set in. Such a process responds to thermal changes, and depending on the height of the nucleation barrier, its rate may be slower or faster. In the former case, large deviations from equilibrium may be required to achieve transformation to the stable phase, which means that large hysteresis effects will be observed in the course of transformation. The intent of this work consists in giving a face to the intermediate configurations appearing in first order phase transitions, in solid-solid reconstructive processes. Apart of a mechanistic elucidation, consisting in answering the question “Which atomic displacements bring structural motif A into structural motif B ?”, another purpose of this work is a rather pedagogical one, that is, showing that first-order phase transitions can be understood in detail, not only in principle but in fact. The core of the examples illustrated in this work is concerned with phase transformations where pressure represents the thermodynamic controlling parameter. Pressure is extensively used in chemical synthesis, as a mean to achieve novel properties, optical or mechanical just to mention a few. Additionally, reports on novel high-pressure polymorphs are regularly appearing. In this sense, pressure is a relevant parameter for approaching fundamental questions in solid state chemistry.

The diethyl ester of o-phenylenebis(oxamic acid) (opbaH2Et2) was treated with an excess of RNH2 in MeOH to cause the exclusive formation of the respective o-phenylenebis(N(R)-oxamides) (opboH4R2, R = Me 1, Et 2, nPr 3) in good yields. Treatment of 1–3 with half an equivalent of [Cu2(AcO)4(H2O)2] or one equivalent of [Ni(AcO)2(H2O)4] followed by the addition of four equivalents of [nBu4N]OH resulted in the formation of mononuclear bis(oxamidato) type complexes [nBu4N]2[M(opboR2)] (M = Ni, R = Me 4, Et 5, nPr 6; M = Cu, R = Me 7, Et 8, nPr 9). By addition of two equivalents of [Cu(pmdta)(NO3)2] to MeCN solutions of 7–9, novel trinuclear complexes [Cu3(opboR2)(L)2](NO3)2 (L = pmdta, R = Me 10, Et 11, nPr 12) could be obtained. Compounds 4–12 have been characterized by elemental analysis and NMR/IR spectroscopy. Furthermore, the solid state structures of 4–10 and 12 have been determined by single-crystal X-ray diffraction studies. By controlled cocrystallization, diamagnetically diluted 8 and 9 (1%) in the host lattice of 5 and 6 (99%) (8@5 and 9@6), respectively, in the form of single crystals have been made available, allowing single crystal ESR studies to extract all components of the g-factor and the tensors of onsite CuA and transferred NA hyperfine (HF) interaction. From these studies, the spin density distribution of the [Cu(opboEt2)]2− and [Cu(opbonPr2)]2− complex fragments of 8 and 9, respectively, could be determined. Additionally, as a single crystal ENDOR measurement of 8@5 revealed the individual HF tensors of the N donor atoms to be unequal, individual estimates of the spin densities on each N donor atom were made. The magnetic properties of 10–12 were studied by susceptibility measurements versus temperature to give J values varying from −96 cm−1 (10) over −104 cm−1 (11) to −132 cm−1 (12). These three trinuclear CuII-containing bis(oxamidato) type complexes exhibit J values which are comparable to and slightly larger in magnitude than those of related bis(oxamato) type complexes. In a summarizing discussion involving experimentally obtained ESR results (spin density distribution) of 8 and 9, the geometries of the terminal [Cu(pmdta)]2+ fragments of 12 determined by crystallographic studies, together with accompanying quantum chemical calculations, an approach is derived to explain these phenomena and to conclude if the spin density distribution of mononuclear bis(oxamato)/bis(oxamidato) type complexes could be a measure of the J couplings of corresponding trinuclear complexes. / Dieser Beitrag ist aufgrund einer (DFG-geförderten) Allianz- bzw. Nationallizenz frei zugänglich.

The diethyl ester of o-phenylenebis(oxamic acid) (opbaH2Et2) was treated with an excess of RNH2 in MeOH to cause the exclusive formation of the respective o-phenylenebis(N(R)-oxamides) (opboH4R2, R = Me 1, Et 2, nPr 3) in good yields. Treatment of 1–3 with half an equivalent of [Cu2(AcO)4(H2O)2] or one equivalent of [Ni(AcO)2(H2O)4] followed by the addition of four equivalents of [nBu4N]OH resulted in the formation of mononuclear bis(oxamidato) type complexes [nBu4N]2[M(opboR2)] (M = Ni, R = Me 4, Et 5, nPr 6; M = Cu, R = Me 7, Et 8, nPr 9). By addition of two equivalents of [Cu(pmdta)(NO3)2] to MeCN solutions of 7–9, novel trinuclear complexes [Cu3(opboR2)(L)2](NO3)2 (L = pmdta, R = Me 10, Et 11, nPr 12) could be obtained. Compounds 4–12 have been characterized by elemental analysis and NMR/IR spectroscopy. Furthermore, the solid state structures of 4–10 and 12 have been determined by single-crystal X-ray diffraction studies. By controlled cocrystallization, diamagnetically diluted 8 and 9 (1%) in the host lattice of 5 and 6 (99%) (8@5 and 9@6), respectively, in the form of single crystals have been made available, allowing single crystal ESR studies to extract all components of the g-factor and the tensors of onsite CuA and transferred NA hyperfine (HF) interaction. From these studies, the spin density distribution of the [Cu(opboEt2)]2− and [Cu(opbonPr2)]2− complex fragments of 8 and 9, respectively, could be determined. Additionally, as a single crystal ENDOR measurement of 8@5 revealed the individual HF tensors of the N donor atoms to be unequal, individual estimates of the spin densities on each N donor atom were made. The magnetic properties of 10–12 were studied by susceptibility measurements versus temperature to give J values varying from −96 cm−1 (10) over −104 cm−1 (11) to −132 cm−1 (12). These three trinuclear CuII-containing bis(oxamidato) type complexes exhibit J values which are comparable to and slightly larger in magnitude than those of related bis(oxamato) type complexes. In a summarizing discussion involving experimentally obtained ESR results (spin density distribution) of 8 and 9, the geometries of the terminal [Cu(pmdta)]2+ fragments of 12 determined by crystallographic studies, together with accompanying quantum chemical calculations, an approach is derived to explain these phenomena and to conclude if the spin density distribution of mononuclear bis(oxamato)/bis(oxamidato) type complexes could be a measure of the J couplings of corresponding trinuclear complexes. / Dieser Beitrag ist aufgrund einer (DFG-geförderten) Allianz- bzw. Nationallizenz frei zugänglich.

Understanding the connection of the atomic structure and the physical properties of materials remains one of the elementary questions of condensed-matter physics. One research line in this quest started with the discovery of quasicrystals by Shechtman et al. in 1982. It soon became clear that these materials with their 5-, 8-, 10- or 12-fold rotational symmetries, which are forbidden according to classical crystallography, can be described in terms of mathematical models for nonperiodic tilings of a plane proposed by Penrose and Ammann in the 1970s. Due to the missing translational symmetry of quasicrystals, till today only finite, relatively small systems or periodic approximants have been investigated by means of numerical calculations and theoretical results have mainly been obtained for one-dimensional systems. In this thesis we study d-dimensional quasiperiodic models, so-called labyrinth tilings, with separable Hamiltonians in the tight-binding approach. This method paves the way to study higher-dimensional, quantum mechanical solutions, which can be directly derived from the one-dimensional results. This allows the investigation of very large systems in two and three dimensions with up to 10^10 sites. In particular, we contemplate the class of metallic-mean sequences. Based on this model we focus on the electronic properties of quasicrystals with a special interest on the connection of the spectral and dynamical properties of the Hamiltonian. Hence, we investigate the characteristics of the eigenstates and wave functions and compare these with the wave-packet dynamics in the labyrinth tilings by numerical calculations and by a renormalization group approach in connection with perturbation theory. It turns out that many properties show a qualitatively similar behavior in different dimensions or are even independent of the dimension as e.g. the scaling behavior of the participation numbers and the mean square displacement of a wave packet. Further, we show that the structure of the labyrinth tilings and their transport properties are connected and obtain that certain moments of the spectral dimensions are related to the wave-packet dynamics. Besides this also the photonic properties are studied for one-dimensional quasiperiodic multilayer systems for oblique incidence of light, and we show that the characteristics of the transmission bands are related to the quasiperiodic structure. / Eine der elementaren Fragen der Physik kondensierter Materie beschäftigt sich mit dem Zusammenhang zwischen der atomaren Struktur und den physikalischen Eigenschaften von Materialien. Eine Forschungslinie in diesem Kontext begann mit der Entdeckung der Quasikristalle durch Shechtman et al. 1982. Es stellte sich bald heraus, dass diese Materialien mit ihren laut der klassischen Kristallographie verbotenen 5-, 8-, 10- oder 12-zähligen Rotationssymmetrien durch mathematische Modelle für die aperiodische Pflasterung der Ebene beschrieben werden können, die durch Penrose und Ammann in den 1970er Jahren vorgeschlagen wurden. Aufgrund der fehlenden Translationssymmetrie in Quasikristallen sind bis heute nur endliche, relativ kleine Systeme oder periodische Approximanten durch numerische Berechnungen untersucht worden und theoretische Ergebnisse wurden hauptsächlich für eindimensionale Systeme gewonnen. In dieser Arbeit werden d-dimensionale quasiperiodische Modelle, sogenannte Labyrinth-Pflasterungen, mit separablem Hamilton-Operator im Modell starker Bindung betrachtet. Diese Methode erlaubt es, quantenmechanische Lösungen in höheren Dimensionen direkt aus den eindimensionalen Ergebnissen abzuleiten und ermöglicht somit die Untersuchung von sehr großen Systemen in zwei und drei Dimensionen mit bis zu 10^10 Gitterpunkten. Insbesondere betrachten wir dabei quasiperiodische Folgen mit metallischem Schnitt. Basierend auf diesem Modell befassen wir uns im Speziellen mit den elektronischen Eigenschaften der Quasikristalle im Hinblick auf die Verbindung der spektralen und dynamischen Eigenschaften des Hamilton-Operators. Hierfür untersuchen wir die Eigenschaften der Eigenzustände und Wellenfunktionen und vergleichen diese mit der Dynamik von Wellenpaketen in den Labyrinth-Pflasterungen basierend auf numerischen Berechnungen und einem Renormierungsgruppen-Ansatz in Verbindung mit Störungstheorie. Dabei stellt sich heraus, dass viele Eigenschaften wie etwa das Skalenverhalten der Partizipationszahlen und der mittleren quadratischen Abweichung eines Wellenpakets für verschiedene Dimensionen ein qualitativ gleiches Verhalten zeigen oder sogar unabhängig von der Dimension sind. Zudem zeigen wir, dass die Struktur der Labyrinth-Pflasterungen und deren Transporteigenschaften sowie bestimmte Momente der spektralen Dimensionen und die Dynamik der Wellenpakete in Beziehung zueinander stehen. Darüber hinaus werden auch die photonischen Eigenschaften für eindimensionale quasiperiodische Mehrschichtsysteme für beliebige Einfallswinkel untersucht und der Verlauf der Transmissionsbänder mit der quasiperiodischen Struktur in Zusammenhang gebracht.

The molecular structure of the title compound, [Fe(C 5 H 5 )(C 15 H 12 N)], consists of a ferrocene moiety with an N-phenylpyrrole heterocycle bound to one cyclopentadienyl ring. The 1,3-disubstitution of the pyrrole results in an L- shaped arrangement of the molecule with plane intersections of 2.78 (17)° between the pyrrole and the N-bonded phenyl ring and of 8.17 (18)° between the pyrrole and the cyclopentadienyl ring. In the crystal, no remarkable intermolecular interactions are observed.

The molecular structure of the title compound, [Fe(C 5 H 5 )(C 15 H 12 N)], consists of a ferrocene moiety with an N-phenylpyrrole heterocycle bound to one cyclopentadienyl ring. The 1,3-disubstitution of the pyrrole results in an L- shaped arrangement of the molecule with plane intersections of 2.78 (17)° between the pyrrole and the N-bonded phenyl ring and of 8.17 (18)° between the pyrrole and the cyclopentadienyl ring. In the crystal, no remarkable intermolecular interactions are observed.

The work presented in this thesis encompasses the design, development, realization and testing of novel magnetoelectric thin film elements that do not rely on ferromagnets, but are based entirely on magnetoelectric antiferromagnets such as Cr2O3. Thin film spintronic elements, and in particular magnetoelectric transducers, are crucial building blocks of high efficiency data processing schemes that could complement conventional electronic data processing in the future. Recent developments in magnetoelectrics have revealed, that exchange biased systems are ill-suited to electric field induced switching of magnetization due to the strong coupling of their ferromagnetic layer to magnetic fields. Therefore, ferromagnet-free magnetoelectric elements are proposed here in an effort to mitigate the practical problems associated with existing exchange biased magnetoelectric elements. This goal is achieved by establishing an all-electric read-out method for the antiferromagnetic order parameter of thin films, which allows to omit the ferromagnet from conventional exchange biased magnetoelectric elements. The resulting ferromagnet-free magnetoelectric elements show greatly reduced writing thresholds, enabled operation at room temperature and do not require a pulsed magnetic field, all of which is in contrast to state-of-the-art exchange biased magnetoelectric systems. The novel all-electric read-out method of the magnetic field-invariant magnetization of antiferromagnets, so-called spinning-current anomalous Hall magnetometry, can be widely employed in other areas of thin film magnetism. Its high precision and its sensitivity to previously invisible phenomena make it a promising tool for various aspects of thin solid films. Based on this technique, a deep understanding could be generated as to what physical mechanisms drive the antiferromagnetic ordering in thin films of magnetoelectric antiferromagnets. As spinning-current anomalous Hall magnetometry is an integral probe of the magnetic properties in thin films, it offers no intrinsic scale sensitivity. In order to harness its great precision for scale related information, a statistical framework was developed, which links macroscopic measurements with microscopic properties such as the antiferromagnetic domain size.:TABLE OF CONTENTS Abbreviations 9 1 Introduction 11 1.1 Motivation 11 1.2 Objectives 12 1.3 Organization of the thesis 13 2 Background 15 2.1 History of magnetoelectric coupling 15 2.2 Long range magnetic ordering 16 2.2.1 Magnetic order parameter and field susceptibility 17 2.2.2 Magnetic proximity effect 19 2.2.3 Exchange bias 20 2.3 Phenomenology of magnetoelectric coupling 21 2.3.1 The linear magnetoelectric effect 21 2.3.2 Magnetoelectric pressure on the antiferromagnetic order parameter 22 2.3.3 Switching the antiferromagnetic order parameter 23 2.4 Realized magnetoelectric thin film elements 24 2.4.1 BiFeO3/CoFe system 24 2.4.2 Cr2O3/Co/Pt system 25 3 Experimental methods 27 3.1 Development of ferromagnet free magnetoelectric elements 28 3.1.1 The substrate 29 3.1.2 The Cr2O3 bulk and top surface 31 3.1.3 The V2O3 or Pt bottom electrodes 33 3.1.4 Epitaxial relationships 34 3.1.5 The Cr2O3 bottom interface 39 3.1.6 Twinning of Cr2O3 39 3.1.7 Hall crosses and patterning processes 43 3.2 Magnetotransport measurements 44 3.2.1 Hall effects 45 3.2.2 Anomalous Hall effect 46 3.2.3 Magnetoelectric writing 47 3.2.4 All electric read out 49 3.3 The experimental setup 50 3.3.1 Temperature control 50 3.3.2 Magnetic field control 51 4 Spinning-current anomalous Hall magnetometry 53 4.1 Characteristics of the technique 53 4.1.1 Operational principle 53 4.1.2 Advantages 55 4.1.3 Magnetic hysteresis loops and field-invariant magnetization 55 4.1.4 Measurement of field-invariant magnetization 56 4.1.5 Limitations 58 4.2 Application of SCAHM to Cr2O3(0001) thin films 59 4.2.1 Criticality and distribution of the antiferromagnetic phase transition 61 4.2.2 Evaluation of the magnetic proximity effect 64 4.3 SCAHM with thin metallic antiferromagnetic IrMn films 65 4.3.1 [Pt/Co]4/IrMn exchange bias system 65 4.3.2 Isolated antiferromagnetic IrMn thin films 67 5 Magnetoelectric performance 69 5.1 Magnetoelectric field cooling 69 5.2 The gate bias voltage 71 5.3 Isothermal binary magnetoelectric writing in Cr2O3 72 6 Order parameter selection in magnetoelectric antiferromagnets 77 6.1 Uncompensated magnetic moment 77 6.2 Extrinsic causes for broken sublattice equivalence 81 6.3 The V2O3 gate electrode 83 7 Measurement of microscopic properties with an integral probe 87 7.1 Interentity magnetic exchange coupling 87 7.2 Ensemble formalism for the entity size determination 90 7.3 Estimation of the entity sizes 94 7.4 Microscopic confirmation of the ensemble model 97 8 Summary and Outlook 101 8.1 Goal-related achievements 101 8.1.1 All-electric read-out of the AF order parameter 101 8.1.2 Electric field induced writing of the AF order parameter 102 8.2 Further achievements 103 8.2.1 Foreseen impact of SCAHM on thin film magnetism 103 8.2.2 Practical optimization routes of magnetoelectric Cr2O3 systems 104 8.2.3 Theoretical work 105 8.3 Future directions 105 8.3.1 Development of Cr2O3-based magnetoelectric systems 105 8.3.2 Applications of SCAHM 106 References 107 Erklärung 113 Acknowledgements 115 Curriculum Vitae 117 Scientific publications, contributions, patents 119

The work presented in this thesis encompasses the design, development, realization and testing of novel magnetoelectric thin film elements that do not rely on ferromagnets, but are based entirely on magnetoelectric antiferromagnets such as Cr2O3. Thin film spintronic elements, and in particular magnetoelectric transducers, are crucial building blocks of high efficiency data processing schemes that could complement conventional electronic data processing in the future. Recent developments in magnetoelectrics have revealed, that exchange biased systems are ill-suited to electric field induced switching of magnetization due to the strong coupling of their ferromagnetic layer to magnetic fields. Therefore, ferromagnet-free magnetoelectric elements are proposed here in an effort to mitigate the practical problems associated with existing exchange biased magnetoelectric elements. This goal is achieved by establishing an all-electric read-out method for the antiferromagnetic order parameter of thin films, which allows to omit the ferromagnet from conventional exchange biased magnetoelectric elements. The resulting ferromagnet-free magnetoelectric elements show greatly reduced writing thresholds, enabled operation at room temperature and do not require a pulsed magnetic field, all of which is in contrast to state-of-the-art exchange biased magnetoelectric systems. The novel all-electric read-out method of the magnetic field-invariant magnetization of antiferromagnets, so-called spinning-current anomalous Hall magnetometry, can be widely employed in other areas of thin film magnetism. Its high precision and its sensitivity to previously invisible phenomena make it a promising tool for various aspects of thin solid films. Based on this technique, a deep understanding could be generated as to what physical mechanisms drive the antiferromagnetic ordering in thin films of magnetoelectric antiferromagnets. As spinning-current anomalous Hall magnetometry is an integral probe of the magnetic properties in thin films, it offers no intrinsic scale sensitivity. In order to harness its great precision for scale related information, a statistical framework was developed, which links macroscopic measurements with microscopic properties such as the antiferromagnetic domain size.

Understanding the connection of the atomic structure and the physical properties of materials remains one of the elementary questions of condensed-matter physics. One research line in this quest started with the discovery of quasicrystals by Shechtman et al. in 1982. It soon became clear that these materials with their 5-, 8-, 10- or 12-fold rotational symmetries, which are forbidden according to classical crystallography, can be described in terms of mathematical models for nonperiodic tilings of a plane proposed by Penrose and Ammann in the 1970s. Due to the missing translational symmetry of quasicrystals, till today only finite, relatively small systems or periodic approximants have been investigated by means of numerical calculations and theoretical results have mainly been obtained for one-dimensional systems. In this thesis we study d-dimensional quasiperiodic models, so-called labyrinth tilings, with separable Hamiltonians in the tight-binding approach. This method paves the way to study higher-dimensional, quantum mechanical solutions, which can be directly derived from the one-dimensional results. This allows the investigation of very large systems in two and three dimensions with up to 10^10 sites. In particular, we contemplate the class of metallic-mean sequences. Based on this model we focus on the electronic properties of quasicrystals with a special interest on the connection of the spectral and dynamical properties of the Hamiltonian. Hence, we investigate the characteristics of the eigenstates and wave functions and compare these with the wave-packet dynamics in the labyrinth tilings by numerical calculations and by a renormalization group approach in connection with perturbation theory. It turns out that many properties show a qualitatively similar behavior in different dimensions or are even independent of the dimension as e.g. the scaling behavior of the participation numbers and the mean square displacement of a wave packet. Further, we show that the structure of the labyrinth tilings and their transport properties are connected and obtain that certain moments of the spectral dimensions are related to the wave-packet dynamics. Besides this also the photonic properties are studied for one-dimensional quasiperiodic multilayer systems for oblique incidence of light, and we show that the characteristics of the transmission bands are related to the quasiperiodic structure. / Eine der elementaren Fragen der Physik kondensierter Materie beschäftigt sich mit dem Zusammenhang zwischen der atomaren Struktur und den physikalischen Eigenschaften von Materialien. Eine Forschungslinie in diesem Kontext begann mit der Entdeckung der Quasikristalle durch Shechtman et al. 1982. Es stellte sich bald heraus, dass diese Materialien mit ihren laut der klassischen Kristallographie verbotenen 5-, 8-, 10- oder 12-zähligen Rotationssymmetrien durch mathematische Modelle für die aperiodische Pflasterung der Ebene beschrieben werden können, die durch Penrose und Ammann in den 1970er Jahren vorgeschlagen wurden. Aufgrund der fehlenden Translationssymmetrie in Quasikristallen sind bis heute nur endliche, relativ kleine Systeme oder periodische Approximanten durch numerische Berechnungen untersucht worden und theoretische Ergebnisse wurden hauptsächlich für eindimensionale Systeme gewonnen. In dieser Arbeit werden d-dimensionale quasiperiodische Modelle, sogenannte Labyrinth-Pflasterungen, mit separablem Hamilton-Operator im Modell starker Bindung betrachtet. Diese Methode erlaubt es, quantenmechanische Lösungen in höheren Dimensionen direkt aus den eindimensionalen Ergebnissen abzuleiten und ermöglicht somit die Untersuchung von sehr großen Systemen in zwei und drei Dimensionen mit bis zu 10^10 Gitterpunkten. Insbesondere betrachten wir dabei quasiperiodische Folgen mit metallischem Schnitt. Basierend auf diesem Modell befassen wir uns im Speziellen mit den elektronischen Eigenschaften der Quasikristalle im Hinblick auf die Verbindung der spektralen und dynamischen Eigenschaften des Hamilton-Operators. Hierfür untersuchen wir die Eigenschaften der Eigenzustände und Wellenfunktionen und vergleichen diese mit der Dynamik von Wellenpaketen in den Labyrinth-Pflasterungen basierend auf numerischen Berechnungen und einem Renormierungsgruppen-Ansatz in Verbindung mit Störungstheorie. Dabei stellt sich heraus, dass viele Eigenschaften wie etwa das Skalenverhalten der Partizipationszahlen und der mittleren quadratischen Abweichung eines Wellenpakets für verschiedene Dimensionen ein qualitativ gleiches Verhalten zeigen oder sogar unabhängig von der Dimension sind. Zudem zeigen wir, dass die Struktur der Labyrinth-Pflasterungen und deren Transporteigenschaften sowie bestimmte Momente der spektralen Dimensionen und die Dynamik der Wellenpakete in Beziehung zueinander stehen. Darüber hinaus werden auch die photonischen Eigenschaften für eindimensionale quasiperiodische Mehrschichtsysteme für beliebige Einfallswinkel untersucht und der Verlauf der Transmissionsbänder mit der quasiperiodischen Struktur in Zusammenhang gebracht.