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The emergence of complex behavior out of simple elementary building blocks is a typical property of condensed matter systems. While the individual constituents may be well-studied, strongly interacting many-particle systems can give rise to novel collective behavior that can not be understood by considering the individual properties alone. Effective models are a powerful tool to handle this complexity: Instead of aiming at a full description a complex many-particle system on the high-energy scale, an effective model covers only those degrees of freedom which are essential for the low-energy physics. While the high-energy degrees of freedom are integrated out, they influence the low-energy degrees of freedom due to a renormalization of the effective coupling constants. In particular, the concept of the quasi-particle allows for the description of a strongly-interacting many-particle excitations in terms of a simple objects with similar degrees of freedom as a dispersive elementary particle, which gives rise to phenomena like quasi-particle bound states or quasi-particle decay. This thesis aims at the application and methodological improvement of a systematic and well-controlled framework to derive effective low-energy models, denoted as Continuous Unitary Transformations (CUT). In this method, a Hamiltonian is mapped continuously to an effective basis, in which the low-energy degrees of freedom can be interpreted as quasi-particles. Mathematically, the transformation is parametrized by a flow parameter and is represented as a differential equation, denoted as flow equation, while the direction of the transformation is controlled by the generator scheme. As foundation of our studies, we use the sCUT method, in which the types of possible interaction terms are fixed by a truncation scheme. In a common project, we established a new flavor of CUT, called epCUT. It allows us to derive the effective Hamiltonian in a perturbation series. In contrast to the already existent pCUT method, epCUT can handle system with a non-equidistant spectrum as well. Moreover, we discovered the deepCUT method, the non-perturbative twin of epCUT. While it bears large similarities to sCUT, it replaces the cumbersome definition of an appropriate truncation scheme by the order of the flow equation system. Compared to sCUT, deepCUT offers a larger robustness while the ambiguities of the truncation scheme are eliminated. My contribution comprises the computational, parallelized construction of the flow equation system as well. In another project, we investigated the breakdown of the conventional, particle-sorting generator schemes in system with strongly overlapping quasi-particle sub-spaces and identified the emergence of a spectrum unbounded from below due to truncation errors as origin of the divergence. As a testing ground, we used a system of two coupled bosonic degrees of freedom. To overcome these problems, we developed a family of three novel variational generator schemes, denoted as scalar, vectorial and tensorial optimization. After this, we investigated the dimerized, two-dimensional S=1/2 Heisenberg model with an emphasis on the quantum phase transition between a magnetically disordered and a magnetically ordered phase using sCUT. Parametrizing the starting point by a variational parameter, we were able to describe the spontaneous breaking of the SU(2) spin symmetry by CUT for the first time. We were able to calculate the ground state energy and the dispersion of triplons, and magnons, respectively, in both phases. However, we were not able to provide quantitative results for the spontaneous magnetization. Furthermore, we found a way to derive an optimal starting point for the integration of the flow equations that is independent on the particularities of the model and does not require a parametrization by a variational parameter. As a further application, we analyzed the S=1 Heisenberg chain by means of deepCUT. To this end, we mapped the system to an extended S=1/2 Heisenberg ladder with the help of a variational parameter. Using the variational generator schemes developed before, we were able to decouple the low-energy spectrum and to calculate spectral densities. In this investigation, we found an indication for a S=0 bound state. Furthermore, we were able to find some signs of spontaneous quasi-particle decay, but a quantitatively correct description is pending., Das Ganze ist mehr als die Summe seiner Teile - so ließe sich das Grundproblem der Physik kondensierter Materie in aller Kürze zusammenfassen. Auch wenn das Verhalten aller Grundbausteine im Detail bekannt ist, so können sich durch starke Wechselwirkungen vieler Teilchen untereinander neuartige, kollektive Phänomene ergeben, die sich durch das Studium der einzelnen Bestandteile nur schwerlich verstehen. Einen Ausweg aus dieser Problematik bieten effektive Modelle: Anstatt ein komplexes System mit vielen Freiheitsgraden auf hohen Energieskalen vollständig zu beschreiben, bildet ein effektives Modell nur die Freiheitsgrade ab, die bei niedrigen Energien wichtig sind. Hochenergetische Freiheitsgrade werden aus dem effektiven Modell weggelassen, ihre indirekten Auswirkungen auf niedrige Energien aber durch modifizierte, effektive Wechselwirkungen berücksichtigt. Als besonders hilfreich hat sich in der Festkörperphysik das Modell des Quasiteilchens erwiesen: Eine Anregung eines Systems vieler, stark wechselwirkender Teilchen wird durch ein Objekt beschrieben, das sich wie ein einzelnes Elementarteilchen bewegen, Bindungen eingehen und zerfallen kann. Die vorliegende Arbeit widmet sich dem Einsatz und der Verbesserung eines Verfahrens zur systematischen, kontrollierten Ableitung effektiver Niederenergiemodelle: Die Methode der kontinuierlichen, unitären Transformationen (englisch: Continuous Unitary Transformations, CUT). Hierbei wird der Hamiltonoperator eines physikalischen Systems kontinuierlich durch Lösen einer Differentialgleichung, der Flussgleichung, in eine effektive Darstellung überführt, bei der die Niederenergiefreiheitsgrade als Quasiteilchen interpretiert werden können. Die Art der Transformation wird hierbei über das Generatorschema der CUT gesteuert. Als Näherung geht in der sCUT (selbstähnliche CUT, englisch: self-similar CUT), der hier als Grundlage dienenden Variante, das Trunkierungsschema ein. Als methodische Verbesserung wurde in einem gemeinsamen Projekt eine neue Variante der CUT, genannt (erweiterte perturbative CUT, englisch: enhanced perturbative CUT), etabliert, die eine Beschreibung des effektiven Hamiltonoperators des Systems als Reihe im Sinne einer Störungsrechnung bis zu einer vorgegebenen erlaubt. Dieser Ansatz ist allgemeiner als die bereits existierende pCUT Methode (perturbative CUT, englisch: perturbative CUT), da sich auch Systeme mit nicht äquidistantem Energiespektrum behandeln lassen. Darüber hinaus wurde mit deepCUT (direkt ausgewertete epCUT, englisch: directly evaluated epCUT) eine verwandte, nichtperturbative Methode entdeckt, die der sCUT ähnelt, aber das komplizierte Trunkierungsschema durch die Ordnung im Sinne einer epCUT-Rechnung ersetzt. Die deepCUT zeichnet sich hierbei gegenüber der sCUT durch eine höhere Robustheit und geringere Mehrdeutigkeit aus. Einen besonderen Anteil meiner Arbeit nahm hierbei die rechnergestützte, parallelisierte Implementierung des Aufstellens der Flussgleichungen. In einem weiteren Projekt wurde das Versagen der bisher üblichen teilchensortierenden Generatoren in Systemen mit stark überlappenden Quasiteilchenräumen untersucht und das Auftreten eines zu niedrigen Energien unbeschränkten Spektrums als Ursache festgestellt. Als Beispielsystem dienten hierbei zwei gekoppelte bosonische Freiheitsgrade. Daraufhin entwickelten wir eine Familie aus drei neuartigen Generatorschemata, die skalare, vektorielle und tensorielle Optimierung, die diese Probleme umgehen. Danach untersuchten wir das dimerisierte, zweidimensionale S=1/2 Heisenberg mit besonderem Schwerpunkt auf dem Quantenphasenübergang zwischen der magnetisch ungeordneten und der magnetisch geordneten Phase mittels sCUT. Durch Parametrisierung des Startpunktes mit einem Variationsparameter gelang uns erstmals die Beschreibung der spontanen Brechung der kontinuierlichen SU(2) Spinsymmetrie mittels CUT. Wir konnten die Grundzustandsenergie und die Disperisionsrelationen der Triplonen und Magnonen in beiden Phasen bestimmen, erhielten jedoch keine zufriedenstellenden Resultate für die spontane Magnetisierung. Ferner entwickelten wir in einem verwandten, eindimensionalen System ein Verfahren, um modellunabhängig und ohne Parametrisierung durch einen Variationsparameter einen optimalen Startzustand zu wählen. Als weitere Anwendung analysierten wir die S=1 Heisenbergkette mittels deepCUT. Hierzu bildeten wir das System unter Einführung eines Variationsparameters auf eine S=1/2 Heisenbergkette ab. Unter Verwendung der zuvor entwickelten variationellen Generatorschemata gelang uns trotz des starken Überlapps zwischen Zwei- und Dreiteilchenraum die Entkopplung des Niederenergiespektrums und die Berechnung spektraler Dichten. Wir fanden hierbei Anhaltspunkte für einen gebundenen S=0 Zustand. Weiterhin konnten wir wichtige Merkmale für den Zerfall eines Triplons in zwei Triplonen nachweisen; eine vollständige und quantitative Beschreibung steht jedoch noch noch aus.

This thesis is a detailed study of the magnetic, structural and orbital order parameters of the candidate multiferroic material LuFe2O4. Multiferroic oxides with a strong magnetoelectric coupling are of high interest for potential information technology applications, but they are rare because the traditional mechanism of ferroelectricity is incompatible with magnetism. Consequently, much attention is focused on various unconventional mechanisms of ferroelectricity. Of these, ferroelectricity originating from charge ordering (CO) is particularly intriguing because it potentially combines large electric polarizations with strong magneto-electric coupling. However, examples of oxides where this mechanism occurs are exceedingly rare and none is really well understood. LuFe2O4 is often cited as the prototypical example of CO-based ferroelectricity. In this material, the order of Fe valences has been proposed to render the triangular Fe/O bilayers polar by making one of the two layers rich in Fe2+ and the other rich in Fe3+, allowing for a possible ferroelectric stacking of the individual bilayers. Because of this new mechanism for ferroelectricity, and also because of the high transition temperatures of charge order and ferro magnetism LuFe2O4 has recently attracted increasing attention. Although these polar bilayers are generally accepted in the literature for LuFe2O4, direct proof is lacking. An assumption-free experimental determination of whether or not the CO in the Fe/O bilayers is polar would be crucial, given the dependence of the proposed mechanism of ferroelectricity from CO in LuFe2O4 on polar bilayers. This thesis starts with a detailed characterization of the macroscopic magnetic properties, where growing ferrimagnetic contributions observed in magnetization could be ascribed to increasing oxygen off-stoichiometry. The main focus is on samples exhibiting a sharp magnetic transition to long-range spin order accompanied by a low temperature phase transition into a phase with glassy magnetic dynamics. It is proposed that this magnetic behavior best approximates the intrinsic defectfree behavior of LuFe2O4. The spin structures of the long-range ordered phases could be refined properly by neutron diffraction as antiferromagnetic (AFM) and ferrimagnetic (fM) spin alignments. The two solutions exhibit a simple geometrical relation, where all spins in half of the bilayers change their sign. Furthermore, it is demonstrated that at the Néel Temperature and H=0 competing AFM and fM spin structures, which correspond respectively to ferro and antiferro stacking of equivalently ordered bilayers, are nearly degenerate. The observation of diffuse magnetic scattering in neutron diffraction far above the Néel Temperature indicates the random stacking of still individually ferrimagnetic ordered bilayers. The first crystal structural refinement, taking into account the superstructure due to the CO in LuFe2O4, was performed on these stoichiometric samples with the help of a monoclinic unit-cell and the C2/m symmetry. By clearly identifying the positions of Fe2+ and Fe3+ valences in this structure with the Bond Valence Sum (BVS) analysis, a completely new and unexpected CO pattern with charged Fe/O bilayers emerges. This new CO arrangement with charged, and consequently nonpolar, bilayers is in strong contrast to all previously suggested CO configurations with polar bilayers. The implications of this result on “ferroelectricity from CO” in LuFe2O4 are discussed, addressing the possibility of polarizing the charged bilayers by an external electric or magnetic field, which could not be verified for our samples. In summary, a possible ferroelectric behavior of LuFe2O4 from CO is very unlikely. This is discussed in the light of the so far published work, where some doubt about the “ferroelectricity from CO” scenario is already present. It is worth emphasizing that although the AFM-fM meta-magnetism has not been reported previously and may not be resolvable in the majority of LuFe2O4 samples; our results have strong implications for the general nature of magnetism in this material.Additionally, x-ray magnetic circular dichroism (XMCD) measurements are presented which could link the novel CO configuration with the previously determined spin order, further corroborating both the new CO pattern established by x-ray diffraction and the spin structures refined by neutron diffraction. Finally, the relevance of the strict spin-charge coupling to the CO transition is addressed and the possibility of an orbital ordered state in the low temperature phase is discussed.

By implementing the rolled-up microfabrication method based on strain engineering, several systems are investigated within the contents of this thesis. The structural morphing of planar geometries into three-dimensional structures opens up many doors for the creation of unique material configurations and devices. An exploration into several novel microsystems, encompassing various scientific subjects, is made and methods for on-chip integration of these devices are presented. The roll-up of a metal and oxide allows for a cylindrical hollow-core structure with a cladding layer composed of a multilayer stack, plasmonic metamaterial. This structure can be used as a platform for a number of optical metamaterial devices. By guiding light radially through this structure, a theoretical investigation into the system makeup of a rolled-up hyperlens, is given. Using the same design, but rather propagating light parallel to the cylinder, a novel device known as a metamaterial optical fiber is defined. This fiber allows light to be guided classically and plasmonically within a single device. These fibers are developed experimentally and are integrated into preexisting on-chip structures and characterized. A system known as lab-in-a-tube is introduced. The idea of lab-in-a-tube combines various rolled-up components into a single all-encompassing biosensor that can be used to detect and monitor single bio-organisms. The first device specifically tailored to this system is developed, flexible split-wall microtube resonator sensors. A method for the capturing of embryonic mouse cells into on-chip optical resonators is introduced. The sensor can optically detect, via photoluminescence, living cells confined within the resonator through the compression and expansion of a nanogap built within its walls. The rolled-up fabrication method is not limited to the well-investigated systems based on the roll-up from semiconductor material or from a photoresist layer. A new approach, relying on the delamination of polymers, is presented. This offers never-before-realized microscale structures and configurations. This includes novel magnetic configurations and flexible fluidic sensors which can be designed for on-chip and roving detector applications.

The present thesis provides an extensive and original contribution to the investigation of magnetic nanoparticles regarding synthesis and structural characterization using advanced scattering methods in all length scales between the atomic and mesoscopic size range. Particular emphasis is on determination of the magnetic structure of single nanoparticles as well as preparation and characterization of higher dimensional assemblies thereof. The unique physical properties arising from the finite size of magnetic nanoparticles are pronounced for very small particle sizes. With the aim of preparing magnetic nanoparticles suitable for investigation of such properties, a micellar synthesis route for very small cobalt nanoparticles is explored. Cobalt nanoparticles with diameters of less than 3 nm are prepared and characterized, and routes for variation of the particle size are developed. The needs and limitations of primary characterization and handling of such small and oxidation-sensitive nanoparticles are highlighted and discussed in detail. Comprehensive structural and magnetic characterization is performed on iron oxide nanoparticles of 10 nm in diameter. Particle size and narrow size distribution are determined with high precision. Investigation of the long range and local atomic structure reveals a particle size dependent magnetite - maghemite structure type with lattice distortions induced at the particle surface. The spatial magnetization distribution within these nanoparticles is determined to be constant in the particle core with a decrease towards the particle surface, thus indicating a magnetic dead layer or spin canting close to the surface. Magnetically induced arrangements of such nanoparticles into higher dimensional assemblies are investigated in solution and by deposition of long range ordered mesocrystals. Both cases reveal a strong dependence of the found structures on the nanoparticle shape (spheres, cubes, and heavily truncated cubes). Nanospheres and nanocubes form closed packed mesocrystals and a short range ordered hard spheres interaction potential in dispersion. In addition, the arrangements of the cuboidal nanoparticles exhibit a strong tendency of face to face oriented attachment, which may result from van der Waals interaction of the cubic facets. Mesocrystals of aged nanocubes with higher degree of truncation reveal a structural transition between the structures of nanocubes and nanospheres.

The diversity of applications in the Internet and the heterogeneity of today's networked platforms make the development of communication protocols complex and time-consuming. This work introduces mechanisms, models, and tools to reduce the complexity and engineering effort required for protocol development and evaluation. It makes the following three key contributions:1. Similarities in protocol mechanisms are extracted into modular building blocks to reduce the complexity of communication system development.2. We introduce a platform abstraction layer to gradually evolve protocol implementations across platforms avoiding frequent reimplementation.3. Automated instrumentation of models with system properties allows to accurately analyzing the time dependent behavior and power consumption of networked devices.

In Kapitel "Alternativer Mechanismus des Vorzeicheneffektes in SFS Josephson-Kontakten" betrachten wir ein einfaches Model des Multi-Domänen S/F/S Systems. Antiparallele Orientierung der Magnetisierung in den Domänen führt zu der räumlichen Modulation der Phasendifferenz. Wegen dieser Modulation kann der kritische Josephson Strom verschiedene Vorzeichen haben. In Kapitel "Ungerade Komponente der Triplet-Supraleitung in einer S/F Struktur mit rotierender Magnetisierung" analysieren wir ein S/F System mit rotierender Magnetisierung in dem Ferromagneten. Wir kalkulieren die weitreichende Triplet-Komponente der Supraleitung, die in den Ferromagneten auf lange Distanzen eindringt. In Kapitel "Kollektive Moden in Zwei-Band Supraleitern" haben wir gezeigt, dass diese Moden bei jeder Temperatur unter Tc existieren, wenn die Frequenz der Moden größer als unelastische Streuungsfrequenz und kleiner als die Energielücken ist.

Obwohl ultrahohe Magnetfelder jenseits von 100 T mittels spezieller Methoden experimentell nutzbar wurden, sind Magnetisierungsmessungen in diesen Feldern noch immer sehr kompliziert. Magnetfelder im Megagauß-Bereich lassen sich heute allein durch die semidestruktive Single-Turn-Coil (STC)-Methode und durch die vollständig destruktive Flußkompression erzeugen. In beiden Fällen sind die gepulsten Felder auf eine Dauer von wenigen Mikrosekunden und ein nutzbares Feldvolumen von wenigen Kubikzentimetern beschränkt. Dadurch bedingt sind nur solche Methoden für Magnetisierungsmessungen anwendbar, die sich an diese ungünstigen Randbedingungen anpassen lassen. Die Faraday-Rotation kann für optisch transparente Proben sinnvoll sein, jedoch ist die induktive Messung mittels kompensierter Pick-up-Spulen die einzige direkte Methode. Die vorliegende Arbeit beschreibt die Entwicklung und Anwendung eines solchen Meßsystems in einem STC-Feldgenerator. Im Hinblick auf das Meßsystem hat sich die sehr gute geometrische Kompensation der Pick-up-Spulen als wesentlich herausgestellt. Wichtig sind daneben aber auch eine hohe Bandbreite bzw. eine unverzerrte Sprungantwort. Als äußerst effektiv hat sich insbesondere die umfassende elektromagnetische Abschirmung des Meßsystems erwiesen, so daß die vom STC-Generator ausgehenden Störungen weitgehend unterdrückt werden. Besondere, für Magnetisierungsmessungen ungünstige Eigenschaften des STC-Systems, werden dargestellt und diskutiert. Magnetisierungsmessungen bei tiefen Temperaturen an den van Vleck-Paramagneten TmPO4 und TmPO4 ergaben Anomalien bei rund 30 T bzw. 50 T für ein Feld parallel zur tetragonalen Achse. Dieser Effekt resultiert aus einer Überkreuzung der beiden niedrigsten Energieniveaus in starken Magnetfeldern und führt zu einem scharfen Sprung in der Magnetisierung. Temperaturabhängige Messungen belegen den wesentlichen Einfluß des magnetokalorischen Effekts in kurzen gepulsten Feldern. Pulverproben der intermetallischen Verbindungen RMn2Ge2 (R = Gd, Tb, Dy, Ho, Er, Y) wurden bei Helium-Temperaturen in Feldern bis zu 150 T untersucht. Abhängig vom Selten-Erd-Ion wurden in allen Verbindungen ein oder mehrere feldinduzierte metamagnetische Phasenübergänge beobachtet. Sie können auf eine Änderung der magnetischen Struktur des Mn-Untersystems zurückgeführt werden. Die kritischen Felder für den Übergang zur ferromagnetischen Phase betragen zwischen 90 T und 118 T (YMn2Ge2: 55 T). Detaillierte Rechnungen werden im Rahmen eines erweiterten Molekularfeld-Modells durchgeführt. Although ultrahigh magnetic fields in excess of 100 T have become available by specialized techniques, magnetization measurements in these fields are still a challenging task. Nowadays, magnetic fields in the megagauss range can be produced only by the semidestructive single-turn coil (STC) technique and by the fully destructive flux compression. In both cases these pulsed fields are limited to microsecond pulse duration and a usable field volume of not more than a few cubic centimeters. As a result, only those methods can be used for magnetization measurements, which can be adapted to these difficult boundary conditions. The Faraday rotation can be suitable for optically transparent samples, but the only direct technique is the induction method based on compensated pick-up coils. The present work deals with the development of such a measurement system and its application to various materials in fields up to 150 T produced by the STC. Regarding the measurement system, geometrically very well compensated pick-up coils turned out to be absolutely necessary as well as a large bandwidth and an appropriate transient response. In particular a comprehensive electromagnetic shielding, which makes use of a wire metal, proved to be very effective in suppressing disturbances produced by the STC system. Besides, some inherent characteristics and limitations of the STC generator with respect to magnetization measurements are revealed and discussed. Magnetization measurements were performed on the van Vleck paramagnets TmPO4 and PrVO4, and anomalies were found at about 30 T and 50 T, respectively, at low temperatures for a field along the tetragonal axis. This effect is due to a crossing of the lowest energy levels in high magnetic fields and results in a sharp jump in magnetization. Temperature dependent measurements provide evidence that the magnetocaloric effect plays an essential role in short pulse fields produced by the STC. Powder samples of the intermetallic compounds RMn2Ge2 (R = Gd, Tb, Dy, Ho, Er, Y) have been investigated at liquid helium temperature up to 150 T. Depending on the rare-earth ion one or more field-induced metamagnetic phase transitions have been observed in all compounds, and they are found to be associated with a change in the magnetic structure of the Mn subsystem. The phase transitions to the ferromagnetic phase occur between 90 T and 118 T (YMn2Ge2: 55 T). Detailed calculations are performed using an extended molecular field model.

We have prepared multilayered compositionally modulated films by alternately depositing Co and Nb layers of 50 and 24 A nominal thickness, respectively. Two e -beam evaporation systems in ultra high vacuum were used. Magnetization and B-H loop measurements were done at 293 K. Ferromagnetic resonance was observed at 9.79 GHz using cavity techniques and as a function of frequency in the range 4–14 GHz using a planar microwave structure. The magnetization 4 πM =13 kG is found to be lower than the Co bulk value. The observed frequency dependence of the linewidth in the parallel orientation can be interpreted. Possible explanations for the reduction of 4π M are discussed.

We have prepared Ni-Ag multilayers and studied their magnetization (M) (68 - 293 K) and FMR properties (290 K). The Ag layer thickness (t Ag) was kept constant at 5 nm and that of Ni (t Ni) varied from 0.7 to 10 nm. At 4 K, M decreases slightly from the bulk value but remains much higher than that reported so far in other systems. We attribute this to the presence of Ag in the pores of thin layers of Ni and their mixing which leads to an increase in Ni moment. FMR results are shown to indicate to relatively high M for t < 3 nm where no anisotropy expected. The large increase in the line width in these cases also confirms the presence of magnetic inhomogeneities.