Der Einsatz nanostrukturierter Magnetmaterialien als Speicherschichten in Festplatten stellt ein vielversprechendes Konzept zur weiteren Erhöhung der erreichbaren Speicherdichten im Vergleich zu den heute eingesetzten granularen Medien dar. Für die Realisierung dieses Konzeptes ist eine detaillierte Kenntnis der Struktureigenschaften und deren Einfluss auf das magnetische Verhalten der einzusetzenden Schichten erforderlich. Für die vorliegende Arbeit wurden drei verschiedene magnetische Materialien ausgewählt und insbesondere mit elektronenmikroskopischen Methoden in struktureller Hinsicht untersucht. Dazu zählen ferromagnetische (FePt)(100-x)Cu(x) -Schichten, ferromagnetische [Co/Pt]n -Multilagen sowie ferrimagnetische Fe(100-x)Tb(x) -Schichten. Der Schwerpunkt der Untersuchungen lag dabei auf der Korrelation zwischen strukturellen und magnetischen Eigenschaften sowie im Einfluss der Nanostrukturierung auf das magnetische Verhalten der Schichten. In dieser Hinsicht wurden Aspekte der durch die Struktur bedingten magnetischen Anisotropie in Form von magnetokristalliner und Grenzflächenanisotropie betrachtet. Zudem wurde das Kopplungsverhalten zwischen einzelnen Strukturelementen in nanostrukturierten Schichten untersucht. Aufbauend auf die Untersuchung der drei genannten Materialien wurden [Co/Pt]n und Fe(100-x)Tb(x) ausgewählt zum Aufbau eines Systems mit zwei magnetischen Komponenten: Fe(80)Tb(20) / [Co/Pt]10. Die Untersuchungen konzentrierten sich dabei auf die Morphologie der Grenzfläche zwischen den beiden Bestandteilen und deren Einfluss auf den Exchange Bias, der in diesem System vorliegt.

Gegenwärtige Bestrebungen materialwissenschaftlicher Forschung beschäftigen sich unter anderem mit der Überführung zweidimensionaler Elemente elektronischer, optischer, plasmonischer oder magnetischer Funktionalität in den dreidimensionalen (3D) Raum. Dieser Ansatz vermag mittels Krümmung und struktureller Topologie bereits vorhandene Eigenschaften abzuändern beziehungsweise neue Funktionalitäten bereitzustellen. Vor allem Vektoreigenschaften wie die Magnetisierung kondensierter Materie lassen sich aufgrund der Brechung der Inversionssymmetrie in gekrümmten Flächen stark beeinflussen. Neben der Entwicklung diverser Vorgänge zur Herstellung 3D magnetischer Gegenstände sind geeignete Untersuchungsmethoden wie beispielsweise tomografische Abbildungen der Magnetisierung von Nöten, die maßgeblich die physikalischen Eigenschaften bestimmen. Die vorliegende Dissertationsschrift befasst sich mit der Abbildung von magnetischen Domänen in 3D gekrümmten Dünnschichten beruhend auf dem Effekt des zirkularen magnetischen Röntgendichroismus (XMCD). Die in diesem Zusammenhang entwickelte magnetische Röntgentomografie (MXT) basierend auf weicher Röntgenmikroskopie stellt eine zu Elektronenholografie und Neutronentomografie komplementäre Methodik dar, welche großes Anwendungspotential in der elementspezifischen Untersuchung magnetischer gekrümmter Flächen mit örtlicher Auflösung im Nanometerbereich aufweist. Die Schwierigkeit der Interpretation von Abbildungen magnetischer Strukturen in gekrümmten Flächen rührt von der Dreidimensionalität und der Vektoreigenschaft der Magnetisierung her. Die hierzu notwendigen Kenntnisse sind anhand von zwei topologisch verschiedenen Flächen in Form hemisphärischer Kappen und hohler Zylinder erschlossen worden. Die praktische Anwendung von MXT ist abschließend anhand der Rekonstruktion magnetischer Domänen in aufgerollten Dünnschichten mit zylindrischer Form verdeutlicht. / One of the foci of modern materials sciences is set on expanding conventional two-dimensional electronic, photonic, plasmonic and magnetic devices into the third dimension. This approach provides means to modify conventional or to launch novel functionalities by tailoring curvature and three-dimensional (3D) shape. The degree of effect is particularly high for vector properties like the magnetization due to an emergent inversion symmetry breaking. Aside from capabilities to design and synthesize 3D magnetic architectures, proper characterization methods, such as magnetic tomographic imaging techniques, need to be developed to obtain a thorough understanding of the system’s response under external stimuli. The main objective of this thesis is to develop a visualization technique that provides nanometer spatial resolution to image the peculiarities of the magnetic domain patterns on extended 3D curved surfaces. The proposed and realized concept of magnetic soft X-ray tomography (MXT), based on the X-ray magnetic circular dichroism (XMCD) effect with soft X-ray microscopies, has the potential to become a powerful tool to investigate element specifically an entirely new class of 3D magnetic objects with virtually any shape and magnetization. Imaging curved surfaces meets the challenge of three-dimensionality and requires a profound understanding of the recorded XMCD contrast. These experiences are gained by visualizing magnetic domain patterns on two distinct 3D curved surfaces, namely magnetic cap structures and rolled-up magnetic nanomembranes with cylindrical shape. The capability of MXT is demonstrated by reconstructing the magnetic domain patterns on 3D curved surfaces resembling hollow cylindrical objects.

The concept of percolated perpendicular media (PPM) for magnetic data storage is expected to surpass the areal storage density of 1 Tbit in -², which is regarded as the fundamental limit of conventional granular CoCrPt:oxide based recording media. PPM consist of a continuous ferromagnetic thin film with densely distributed defects acting as pinning sites for magnetic domain walls. In this study, practical realizations of PPM were fabricated by the deposition of [Co/Pt]8 multilayers with perpendicular magnetic anisotropy onto nanoperforated templates with various perforation diameters and periods. The structural defects given by the templates serve as pinning sites for the magnetic domain walls within the [Co/Pt]8 multilayers. Magnetometry at both the integral and the local level was employed to investigate the influence of the template on the magnetization reversal and the domain wall pinning. It was found, that magnetic domains can be pinned at the ultimate limit, between three adjacent pinning sites. The coercivity and the depinning field, which both are a measure for the strength of the magnetic domain wall pinning, were found to increase with increasing perforation diameter. The size of magnetic domains within the magnetic film appeared not to depend solely on the diameter of the nanoperforations or on the period of the template, but on the ration between diameter and period. By means of micromagnetic simulations it was found, that the presence of ferromagnetic material within the pinning site given supports the pinning of magnetic domain walls, compared to a pinning site that is solely given by a hole in the magnetic thin film. Investigation of the evolution of the magnetization in magnetic fields smaller than the coercive field revealed, that the energy barrier against thermally induced magnetization reversal is sufficiently large to provide long-term (> 10 years) stability of an arbitrary magnetization state. This could also be qualitatively supported by micromagnetic simulations. Static read/write tests with conventional hard disk recording heads revealed the possibility of imprinting bit patterns into the PPM under study. The minimum bit pitch that could be read back thereby depended on the period of the nanoperforated template.

Die vorliegende Promotionsarbeit “Density functional study of the electronic and magnetic properties of selected transition metal complexes” beschäftigt sich mit dem Zusammenhang zwischen strukturellen Merkmalen sowie elektronischen und magnetischen Eigenschaften von Einzelmolekül-Magneten. Im Wesentlichen konnte dabei gezeigt werden, dass die magnetischen Eigenschaften sowohl von strukturellen Merkmalen als auch von den elektronischen Eigenschaften bestimmt werden. Des Weiteren ergab sich, dass verschiedene Kenngrößen der magnetischen Eigenschaften (im speziellen der magnetische Grundzustand S sowie die magnetische Anisotropie D) miteinander korreliert sind. Dies ist im Besonderen für eine mögliche Anwendung von Einzelmolekül-Magneten im Bereich der Datenspeicherung von Bedeutung.

Iron filled carbon nanotubes (FeCNT) can be described as carbon nanotubes which contain an iron nanowire of several micrometers length and a diameter of approximately 10-100 nm. The carbon shells protect the iron core from oxidation and mechanical damage thus enabling a wide range of applications that require a long-term stability. The magnetic properties of the enclosed nanowire are in part determined by its small size and elongated shape. Magnetic force microscopy (MFM) measurements show that the iron wire exhibits a single domain behavior. Due to the large shape anisotropy it is magnetized along the long wire axis in the remanent state. Two magnetic monopoles of opposing polarity are located at the wire extremities. Depending on the structure and geometry of the individual nanowire, switching fields in the range of 100-400 mT can be found when the external field is applied along the FeCNT’s easy axis. Cantilever magnetometry shows that the switching can be attributed to a thermally assisted magnetization reversal mechanism with the nucleation and propagation of a domain wall. The defined magnetic properties of individual FeCNT combined with their mechanical strength make them ideal candidates for an application as high resolution high stability MFM probes. The fabrication of such probes can be achieved with the help of a micromanipulation setup in a scanning electron microscope. FeCNT MFM probes achieve a sub 25 nm lateral magnetic resolution. MFM measurements with FeCNT MFM probes in external fields show that the magnetization of these probes is exceptionally stable compared to conventional coated MFM probes. This greatly simplifies the data evaluation of such applied field MFM measurements. The emphasis of this work was put on the calibration of FeCNT probes to enable straightforward quantitative MFM measurements. The defined shape of the magnetically active iron nanowire allows an application of a point monopole description. Microscale parallel current carrying lines that produce a defined magnetic field are used as calibration structures to determine the effective magnetic moment of different MFM probes. The line geometry is varied in order to produce multiple magnetic field decay lengths and investigate the influence on the effective probe moment. The results show that while the effective magnetic monopole moment of a conventional MFM probe increases with an increasing sample stray field decay length, the effective moment of a FeCNT MFM probe remains constant. This enables a MFM probe calibration that stays valid for a large variety of magnetic samples. Furthermore, the fitted monopole moment of a FeCNT probe (in the order of 10E-9 Am) is consistent with the moment calculated from the nanowire geometry and the saturation magnetization of iron.

To fully understand how the brain works, it is necessary to relate the brain’s function to its anatomy. Cortical anatomy is subject-specific. It is character- ized by the thickness and number of intracortical layers, which differ from one cortical area to the next. Each cortical area fulfills a certain function. With magnetic res- onance imaging (MRI) it is possible to study structure and function in-vivo within the same subject. The resolution of ultra-high field MRI at 7T allows to resolve intracortical anatomy. This opens the possibility to relate cortical function of a sub- ject to its corresponding individual structural area, which is one of the main goals of neuroimaging. To parcellate the cortex based on its intracortical structure in-vivo, firstly, im- ages have to be quantitative and homogeneous so that they can be processed fully- automatically. Moreover, the resolution has to be high enough to resolve intracortical layers. Therefore, the in-vivo MR images acquired for this work are quantitative T1 maps at 0.5 mm isotropic resolution. Secondly, computational tools are needed to analyze the cortex observer-independ- ently. The most recent tools designed for this task are presented in this thesis. They comprise the segmentation of the cortex, and the construction of a novel equi-volume coordinate system of cortical depth. The equi-volume model is not restricted to in- vivo data, but is used on ultra-high resolution post-mortem data from MRI as well. It could also be used on 3D volumes reconstructed from 2D histological stains. An equi-volume coordinate system yields firstly intracortical surfaces that follow anatomical layers all along the cortex, even within areas that are severely folded where previous models fail. MR intensities can be mapped onto these equi-volume surfaces to identify the location and size of some structural areas. Surfaces com- puted with previous coordinate systems are shown to cross into different anatomical layers, and therefore also show artefactual patterns. Secondly, with the coordinate system one can compute cortical traverses perpendicularly to the intracortical sur- faces. Sampling intensities along equi-volume traverses results in cortical profiles that reflect an anatomical layer pattern, which is specific to every structural area. It is shown that profiles constructed with previous coordinate systems of cortical depth disguise the anatomical layer pattern or even show a wrong pattern. In contrast to equi-volume profiles these profiles from previous models are not suited to analyze the cortex observer-independently, and hence can not be used for automatic delineations of cortical areas. Equi-volume profiles from four different structural areas are presented. These pro- files show area-specific shapes that are to a certain degree preserved across subjects. Finally, the profiles are used to classify primary areas observer-independently.:1 Introduction p. 1 2 Theoretical Background p. 5 2.1 Neuroanatomy of the human cerebral cortex . . . .p. 5 2.1.1 Macroscopical structure . . . . . . . . . . . .p. 5 2.1.2 Neurons: cell bodies and fibers . . . . . . . .p. 5 2.1.3 Cortical layers in cyto- and myeloarchitecture . . .p. 7 2.1.4 Microscopical structure: cortical areas and maps . .p. 11 2.2 Nuclear Magnetic Resonance . . . . . . . . . . . . . .p. 13 2.2.1 Proton spins in a static magnetic field B0 . . . . .p. 13 2.2.2 Excitation with B1 . . . . . . . . . . . . . . . . .p. 15 2.2.3 Relaxation times T1, T2 and T∗ 2 . . . . . . . . . .p. 16 2.2.4 The Bloch equations . . . . . . . . . . . . . . . . p. 17 2.3 Magnetic Resonance Imaging . . . . . . . . . . . . . .p. 20 2.3.1 Encoding of spatial location and k-space . . . . . .p. 20 2.3.2 Sequences and contrasts . . . . . . . . . . . . . . p. 22 2.3.3 Ultra-high resolution MRI . . . . . . . . . . . . . p. 24 2.3.4 Intracortical MRI: different contrasts and their sources p. 25 3 Image analysis with computed cortical laminae p. 29 3.1 Segmentation challenges of ultra-high resolution images p. 30 3.2 Reconstruction of cortical surfaces with the level set method p. 31 3.3 Myeloarchitectonic patterns on inflated hemispheres . . . . p. 33 3.4 Profiles revealing myeloarchitectonic laminar patterns . . .p. 36 3.5 Standard computational cortical layering models . . . . . . p. 38 3.6 Curvature bias of computed laminae and profiles . . . . . . p. 39 4 Materials and methods p. 41 4.1 Histology . . . . . p. 41 4.2 MR scanning . . . . p. 44 4.2.1 Ultra-high resolution post-mortem data p. 44 4.2.2 The MP2RAGE sequence . . . . . . . . p. 45 4.2.3 High-resolution in-vivo T1 maps . . . .p. 46 4.2.4 High-resolution in-vivo T∗ 2-weighted images p. 47 4.3 Image preprocessing and experiments . . . . . .p. 48 4.3.1 Fully-automatic tissue segmentation . . . . p. 48 4.3.2 Curvature Estimation . . . . . . . . . . . . p. 49 4.3.3 Preprocessing of post-mortem data . . . . . .p. 50 4.3.4 Experiments with occipital pole post-mortem data .p. 51 4.3.5 Preprocessing of in-vivo data . . . . . . . . . . p. 52 4.3.6 Evaluation experiments on in-vivo data . . . . . .p. 56 4.3.7 Application experiments on in-vivo data . . . . . p. 56 4.3.8 Software . . . . . . . . . . . . . . . . . . . . .p. 58 5 Computational cortical layering models p. 59 5.1 Implementation of standard models . .p. 60 5.1.1 The Laplace model . . . . . . . . .p. 60 5.1.2 The level set method . . . . . . . p. 61 5.1.3 The equidistant model . . . . . . .p. 62 5.2 The novel anatomically motivated equi-volume model p. 63 5.2.1 Bok’s equi-volume principle . . . . . .p. 63 5.2.2 Computational equi-volume layering . . p. 66 6 Validation of the novel equi-volume model p. 73 6.1 The equi-volume model versus previous models on post-mortem samples p. 73 6.1.1 Comparing computed surfaces and anatomical layers . . . . . . . . p. 73 6.1.2 Cortical profiles reflecting an anatomical layer . . . . . . . . .p. 79 6.2 The equi-volume model versus previous models on in-vivo data . . . .p. 82 6.2.1 Comparing computed surfaces and anatomical layers . . . . . . . . p. 82 6.2.2 Cortical profiles reflecting an anatomical layer . . . . . . . . .p. 85 6.3 Dependence of computed surfaces on cortical curvature . . . . .p. 87 6.3.1 Within a structural area . . . . . . . . . . . . . . . . . . p. 87 6.3.2 Artifactual patterns on inflated surfaces . . . . . . . . . .p. 87 7 Applying the equi-volume model: Analyzing cortical architecture in-vivo in different structural areas p. 91 7.1 Impact of resolution on cortical profiles . . . . . . . . . . . . . p. 91 7.2 Intersubject variability of cortical profiles . . . . . . . . . . . p. 94 7.3 Myeloarchitectonic patterns on inflated hemispheres . . . . . . .p. 95 7.3.1 Comparison of patterns with inflated labels . . . . . . . . . .p. 97 7.3.2 Patterns at different cortical depths . . . . . . . . . . . . .p. 97 7.4 Fully-automatic primary-area classification using cortical profiles p. 99 8 Discussion p. 105 8.1 The novel equi-volume model . . . . . . . . . . . . . . . . . . . . .p. 105 8.2 Analyzing cortical myeloarchitecture in-vivo with T1 maps . . . . . .p. 109 9 Conclusion and outlook p. 113 Bibliography p. 117 List of Figures p. 127

Ziel der vorliegenden Arbeit ist es, das Preisach-Modell bezüglich stochastischer äußerer Felder und temperaturbezogener Aspekte zu untersuchen. Das phänomenologische Preisach-Modell wird oft erfolgreich angewendet, um Systeme mit Hysterese zu beschreiben. Im ersten Teil der Arbeit wird die Antwort des Preisach-Modells auf stochastische äußere Felder untersucht. Hier liegt das Augenmerk hauptsächlich auf der Autokorrelation; sie dient dazu den Einfluss des hysteretischen Gedächtnisses zu quantifizieren. Mit analytischen Methoden wird gezeigt, dass sich ein Langzeitgedächtnis, sichtbar in der Autokorrelation der Systemantwort, entwickeln kann, selbst wenn das treibende Feld unkorreliert ist. Im Anschluss werden diese Resultate, m.H. von Simulationen, auf äußere Felder ausgeweitet, die selbst Korrelationen aufweisen können. Der zweite Teil der Arbeit befasst sich mit dem Einfluss einer endlichen Temperatur auf das Preisach-Modell. Es werden unterschiedliche Methoden besprochen, wie das Nichtgleichgewichtsmodell in seiner mikromagnetischen Interpretation mit Temperatur als Gleichgewichtseigenschaft verknüpft werden kann. Eine Formulierung wird genutzt, um die Magnetisierung von Nickelnanopartikeln in einer Fullerenmatrix zu simulieren und mit Experimenten zu vergleichen. Des Weiteren wird die Relaxationsdynamik des Gedächtnisses des Preisach-Modells bei endlichen Temperaturen untersucht. / The aim of this thesis is to investigate the Preisach model in regard to stochastically driving and temperature-related aspects. The Preisach model is a phenomenological model for systems with hysteresis which is often successfully applied. Hysteresis is a widespread phenomenon which is observed in nature and the key feature of certain technological applications. Further, it contributes to phenomena of interest in social science and economics as well. Prominent examples are the magnetization of ferromagnetic materials in an external magnetic field or the adsorption-desorption hysteresis observed in porous media. Hysteresis involves the development of a hysteresis memory, and multistability in the interrelations between external driving fields and system response. In the first part, we mainly investigate the response of Preisach hysteresis models driven by stochastic input processes with regard to autocorrelation functions to quantify the influence of the system’s memory. Using rigorous methods, it is shown that the development of a hysteresis memory is reflected in the possibility of long-time tails in the autocorrelation functions, even for uncorrelated driving fields. In the case of uncorrelated driving, these long-time tails in the autocorrelations of the system’s response are determined only by the tails of the involved densities. They will be observed if there are broad Preisach densities assigning a high weight to elementary loops of large width and narrow input densities such that rare extreme events of the input time series contribute significantly to the output for a long period of time. Afterwards, these results are extended by simulations to driving fields which themselves show correlations. It is shown that the autocorrelation of the output does not decay faster than the autocorrelation of the input process. Further, there is a possibility that long-term memory in the hysteretic response is more pronounced in the case of uncorrelated driving than in the case of correlated driving. The behavior of the output probability distribution at the saturation values is quite universal. It is not affected by the presence of correlations and allows conclusions whether the input density is much more narrow than the Preisach density or not. Moreover, the existence of effective Preisach densities is shown which define equivalence classes of systems of input and Preisach densities which lead to realizations of the same output variable. The asymptotic behavior of an effective Preisach density determines the asymptotic correlation decay of the system’s response in the case of uncorrelated driving. In the second part, temperature-related effects are considered. It is reviewed how the non-equilibrium Preisach model in its micromagnetic picture can be related to temperature within the framework of extended irreversible thermodynamics. The irreversible response of a ferromagnetic material, namely, Nickel nanoparticles in a fullerene matrix, is simulated. The model includes superparamagnetism where ferromagnetism breaks down at temperatures lower than the Curie temperature and the results are compared to experimental data. Furthermore, we adapt known results for the thermal relaxation of the system’s memory in the form of a front propagation in the Preisach plane derived basically from solving a master equation and by the use of a contradictory assumption. A closer look is taken at short time scales which dissolves the contradiction and shows that the known results apply, taking into account the fact that the dividing line propagation starts with an additional delay time depending on the front coordinates in the Preisach plane. Additionally, it is outlined how thermal relaxation behavior in the Preisach model of hysteresis can be studied using a Fokker-Planck equation. The latter is solved analytically in the non-hysteretic limit using eigenfunction methods. The results indicate a change in the relaxation behavior, especially on short time scales.

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.

In the vast realm of inorganic materials, the Cu2+-containing cuprates form one of the richest classes. Due to the combined effect of crystal-field, covalency and strong correlations, all undoped cuprates are magnetic insulators with well-localized spins S=1/2, whereas the charge and orbital degrees of freedom are frozen out. The combination of the spin-only nature of their magnetism with the unique structural diversity renders cuprates as excellent model systems. The experimental studies, boosted by the discovery of high-temperature superconductivity in doped La2CuO4, revealed a fascinating variety of magnetic behaviors observed in cuprates. A digest of prominent examples should include the spin-Peierls transition in CuGeO3, the Bose-Einstein condensation of magnons in BaCuSi2O6, and the quantum critical behavior of Li2ZrCuO4. The magnetism of cuprates originates from short-range (typically, well below 1 nm) exchange interactions between pairs of spins Si and Sj, localized on Cu atoms i and j. Especially in low-dimensional compounds, these interactions are strongly anisotropic: even for similar interatomic distances |Rij|, the respective magnetic couplings Jij can vary by several orders of magnitude. On the other hand, there is an empirical evidence for the isotropic nature of this interaction in the spin space: different components of Si are coupled equally strong. Thus, the magnetism of cuprates is mostly described by a Heisenberg model, comprised of Jij(Si*Sj) terms. Although the applicability of this approach to cuprates is settled, the model parameters Jij are specific to a certain material, or more precisely, to a particular arrangement of the constituent atoms, i.e. the crystal structure. Typically, among the infinite number of Jij terms, only several are physically relevant. These leading exchange couplings constitute the (minimal) microscopic magnetic model. Already at the early stages of real material studies, it became gradually evident that the assignment of model parameters is a highly nontrivial task. In general, the problem can be solved experimentally, using elaborate measurements, such as inelastic neutron scattering on large single crystals, yielding the magnetic excitation spectrum. The measured dispersion is fitted using theoretical models, and in this way, the model parameters are refined. Despite excellent accuracy of this method, the measurements require high-quality samples and can be carried out only at special large-scale facilities. Therefore, less demanding (especially, regarding the sample requirements), yet reliable and accurate procedures are desirable. An alternative way to conjecture a magnetic model is the empirical approach, which typically relies on the Goodenough-Kanamori rules. This approach links the magnetic exchange couplings to the relevant structural parameters, such as bond angles. Despite the unbeatable performance of this approach, it is not universally applicable. Moreover, in certain cases the resulting tentative models are erroneous. The recent developments of computational facilities and techniques, especially for strongly correlated systems, turned density-functional theory (DFT) band structure calculations into an appealing alternative, complementary to the experiment. At present, the state-of-the-art computational methods yield accurate numerical estimates for the leading microscopic exchange couplings Jij (error bars typically do not exceed 10-15%). Although this computational approach is often regarded as ab initio, the actual procedure is not parameter-free. Moreover, the numerical results are dependent on the parameterization of the exchange and correlation potential, the type of the double-counting correction, the Hubbard repulsion U etc., thus an accurate choice of these crucial parameters is a prerequisite. In this work, the optimal parameters for cuprates are carefully evaluated based on extensive band structure calculations and subsequent model simulations. Considering the diversity of crystal structures, and consequently, magnetic behaviors, the evaluation of a microscopic model should be carried out in a systematic way. To this end, a multi-step computational approach is developed. The starting point of this procedure is a consideration of the experimental structural data, used as an input for DFT calculations. Next, a minimal DFT-based microscopic magnetic model is evaluated. This part of the study comprises band structure calculations, the analysis of the relevant bands, supercell calculations, and finally, the evaluation of a microscopic magnetic model. The ground state and the magnetic excitation spectrum of the evaluated model are analyzed using various simulation techniques, such as quantum Monte Carlo, exact diagonalization and density-matrix renormalization groups, while the choice of a particular technique is governed by the dimensionality of the model, and the presence or absence of magnetic frustration. To illustrate the performance of the approach and tune the free parameters, the computational scheme is applied to cuprates featuring rather simple, yet diverse magnetic behaviors: spin chains in CuSe2O5, [NO]Cu(NO3)3, and CaCu2(SeO3)2Cl2; quasi-two-dimensional lattices with dimer-like couplings in alpha-Cu2P2O7 and CdCu2(BO3)2, as well as the 3D magnetic model with pronounced 1D correlations in Cu6Si6O18*6H2O. Finally, the approach is applied to spin liquid candidates --- intricate materials featuring kagome-lattice arrangement of the constituent spins. Based on the DFT calculations, microscopic magnetic models are evaluated for herbertsmithite Cu3(Zn0.85Cu0.15)(OH)6Cl2, kapellasite Cu3Zn(OH)6Cl2 and haydeeite Cu3Mg(OH)6Cl2, as well as for volborthite Cu3[V2O7](OH)2*2H2O. The results of the DFT calculations and model simulations are compared to and challenged with the available experimental data. The advantages of the developed approach should be briefly discussed. First, it allows to distinguish between different microscopic models that yield similar macroscopic behavior. One of the most remarkable example is volborthite Cu3[V2O7](OH)2*2H2O, initially described as an anisotropic kagome lattice. The DFT calculations reveal that this compound features strongly coupled frustrated spin chains, thus a completely different type of magnetic frustration is realized. Second, the developed approach is capable of providing accurate estimates for the leading magnetic couplings, and consequently, reliably parameterize the microscopic Hamiltonian. Dioptase Cu6Si6O18*6H2O is an instructive example showing that the microscopic theoretical approach eliminates possible ambiguity and reliably yields the correct parameterization. Third, DFT calculations yield even better accuracy for the ratios of magnetic exchange couplings. This holds also for small interchain or interplane couplings that can be substantially smaller than the leading exchange. Hence, band structure calculations provide a unique possibility to address the interchain or interplane coupling regime, essential for the magnetic ground state, but hardly perceptible in the experiment due to the different energy scales. Finally, an important advantage specific to magnetically frustrated systems should be mentioned. Numerous theoretical and numerical studies evidence that low-dimensionality and frustration effects are typically entwined, and their disentanglement in the experiment is at best challenging. In contrast, the computational procedure allows to distinguish between these two effects, as demonstrated by studying the long-range magnetic ordering transition in quasi-1D spin chain systems. The computational approach presented in the thesis is a powerful tool that can be directly applied to numerous S=1/2 Heisenberg materials. Moreover, with minor modifications, it can be largely extended to other metallates with higher value of spin. Besides the excellent performance of the computational approach, its relevance should be underscored: for all the systems investigated in this work, the DFT-based studies not only reproduced the experimental data, but instead delivered new valuable information on the magnetic properties for each particular compound. Beyond any doubt, further computational studies will yield new surprising results for known as well as for new, yet unexplored compounds. Such "surprising" outcomes can involve the ferromagnetic nature of the couplings that were previously considered antiferromagnetic, unexpected long-range couplings, or the subtle balance of antiferromagnetic and ferromagnetic contributions that "switches off" the respective magnetic exchange. In this way, dozens of potentially interesting systems can acquire quantitative microscopic magnetic models. The results of this work evidence that elaborate experimental methods and the DFT-based modeling are of comparable reliability and complement each other. In this way, the advantageous combination of theory and experiment can largely advance the research in the field of low-dimensional quantum magnetism. For practical applications, the excellent predictive power of the computational approach can largely alleviate designing materials with specific properties.:List of Figures List of Tables List of Abbreviations 1. Introduction 2. Magnetism of cuprates 3. Experimental methods 4. DFT-based microscopic modeling 5. Simulations of a magnetic model 6. Model spin systems: challenging the computational approach 7. Kagome lattice compounds 8. Summary and outlook Appendix Bibliography List of publications Acknowledgments

Nanomaterials have the remarkable characteristic of displaying physical properties different from their bulk counterparts. An additional degree of complexity and functionality arises when oxide nanoparticles interact with metallic nanostructures. In this context the Raman spectra due to plasmonic enhancement of iron oxide nanocrystals are here reported showing the activation of spin-waves. Iron oxide nanoparticles on gold and silver tips are found to display a band around 1584 cm−1 attributed to a spin-wave magnon mode. This magnon mode is not observed for nanoparticles deposited on silicon (111) or on glass substrates. Metal–nanoparticle interaction and the strongly localized electromagnetic field contribute to the appearance of this mode. The localized excitation that generates this mode is confirmed by tip-enhanced Raman spectroscopy (TERS). The appearance of the spin-waves only when the TERS tip is in close proximity to a nanocrystal edge suggests that the coupling of a localized plasmon with spin-waves arises due to broken symmetry at the nanoparticle border and the additional electric field confinement. Beyond phonon confinement effects previously reported in similar systems, this work offers significant insights on the plasmon-assisted generation and detection of spin-waves optically induced. / Dieser Beitrag ist aufgrund einer (DFG-geförderten) Allianz- bzw. Nationallizenz frei zugänglich.