This work focuses on characterising the chiral and topological nature of magnetic skyrmions in noncentrosymmetric helimagnets. In these materials, the skyrmion lattice phase appears as a long-range-ordered, close-packed lattice of nearly millimetre-level correlation length, while the size of a single skyrmion is 3-100 nm. This is a very challenging range of lengthscales (spanning 5 orders of magnitude from tens of nm to mm) for magnetic characterisation techniques. As a result, only three methods have been proven to be applicable for characterising certain aspects of the magnetic information: neutron diffraction, electron microscopy, and magnetic force microscopy. Nevertheless, none of them reveals the complete information about this fascinating magnetically ordered state. On the largest scale, the skyrmions form a three-dimensional lattice. The lateral structure and the depth profile are of importance for understanding the system. On the mesoscopic scale, the rigid skyrmion lattice can break up into domains, with the domain size about tens to hundreds of micrometers. The information of the domain shape, distribution, and the domain boundary is of great importance for a magnetic system. On the smallest scale, a single skyrmion has an extremely fine structure that is described by the topological winding number, helicity angle, and polarity. These pieces of information reveal the underlying physics of the system, and are currently the focus of spintronics applications. However, so far, there is no experimental technique that allows one to quantitatively study these fine structures. It has to be emphasised that the word 'quantitative' here means that no speculations have to be made and no theoretical modelling is required to assist the data interpretation -- what has been measured must be straightforward, and give a unique and unambiguous answer. Motivated by these questions, we developed soft x-ray scattering techniques that allow us to acquire much deeper microscopic information of the magnetic skyrmions -- reaching far beyond what has been possible so far. We will show that by using only one technique, all the information about the magnetic structure (spanning 5 orders of magnitude in length) can be accurately measured. The thesis is structured as follows: The key development is the Dichroism Extinction Rule, which is summarised in Chapter 6, and quintessentially summarises the thesis. In Chapter 1, the well-established theory for skyrmions is introduced, reconstructing the picture from single skyrmions to the skyrmion crystal. A few comments about the current characterisation techniques will be given. In Chapter 2, we will start with the largest lengthscale, the long-range-ordered skyrmion lattice phase. This is an intensely studied phase, mostly using neutron diffraction, and we will show that this piece of information can be equivalently (or actually even better) obtained using resonant x-ray diffraction. The theoretical foundation of this technique is also given. In Chapter 3, we will demonstrate imaging technique with which we were able to effectively map the skyrmion domains. The measurements also suggest a way to control the formation of skyrmion domains, which might be the key for enabling skyrmion-based device applications. Chapters 4 and 5 present the highlights of this work, in which we will show that using the dichroism extinction rule, the topological winding number and the skyrmion helicity angle can be unambiguously determined. In this sense, this technique is capable of accurately measuring the internal structure of single skyrmions.

The present thesis is devoted to theoretical studies of resonant X-ray scattering and propagation of strong X-ray pulses. In the first part of the thesis the nuclear dynamics of different molecules is studied using resonant X-ray Raman and resonant Auger scattering techniques. We show that the shortening of the scattering duration by the detuning results in a purification of the Raman spectra from overtones and soft vibrational modes. The simulations are in a good agreement with measurements, performed at the MAX-II and the Swiss Light Source with vibrational resolution. We explain why the scattering to the ground state nicely displays the vibrational structure of liquid acetone in contrast to excited final state. Theory of resonant X-ray scattering by liquids is developed. We show that, contrary to aqueous acetone, the environmental broadening in pure liquid acetone is twice smaller than the broadening by soft vibrational modes significantly populated at room temperature. Similar to acetone, the "elastic" band of X-ray Raman spectra of molecular oxygen is strongly affected by the Thomson scattering. The Raman spectrum demonstrates spatial quantum beats caused by two interfering wave packets with different momenta as the oxygen atoms separate. It is found that the vibrational scattering anisotropy caused by the interference of the "inelastic" Thomson and resonant scattering channels in O2. A new spin selection rule is established in inelastic X-ray Raman spectra of O2. It is shown that the breakdown of the symmetry selection rule based on the parity of the core hole, as the core hole and excited electron swap parity. Multimode calculations explain the two thresholds of formation of the resonant Auger spectra of the ethene molecule by the double-edge structure of absorption spectrum caused by the out-of- and in-plane modes. We predict the rotational Doppler effect and related broadening of X-ray photoelectron and resonant Auger spectra, which has the same magnitude as its counterpart-the translational Doppler effect. The second part of the thesis explores the interaction of the medium with strong X-ray free-electron laser (XFEL) fields. We perform simulations of nonlinear propagation of femtosecond XFEL pulses in atomic vapors by solving coupled Maxwell's and density matrix equations. We show that self-seeded stimulated X-ray Raman scattering strongly influences the temporal and spectral structure of the XFEL pulse. The generation of Stokes and four-wave mixing fields starts from the seed field created during pulse propagation due to the formation of extensive ringing pattern with long spectral tail. We demonstrate a compression into the attosecond region and a slowdown of the XFEL pulse up to two orders of magnitude. In the course of pulse propagation, the Auger yield is strongly suppressed due to the competitive channel of stimulated emission. We predict a strong X-ray fluorescence from the two-core-hole states of Ne created in the course of the two-photon X-ray absorption. / QC 20110426

The main focus of this thesis is ab initio modeling of core level spectra with a high-level quantum chemical description both of the chemical interactions and of local atomic multiplet effects. In particular, the combination of calculations and synchrotron-based core-level spectroscopy aims at understanding the local structure of the electronic valence in transition metal complexes, and the details of the solvation mechanisms of electrolyte solutions, systems relevant for the dye-sensitized solar cell. Configurational sampling in solution is included through molecular dynamics simulations. Transition metal complexes are studied with x-ray absorption (XA) and resonant inelastic scattering (RIXS) spectroscopy, characterizing excited states with atomic site specificity. The theoretical multiconfigurational method, applying an active-space partitioning of the molecular orbitals (RASSCF), is used to assign the transitions observed in spectra of hydrated Ni2+ explicitly, including charge transfer and multiplet effects. Furthermore, the solvent-induced binding energy properties of the I- and I3- anions in aqueous, ethanol, and acetonitrile solutions are analyzed using photoelectron spectroscopy (XPS). The study shows that specific ion–solvent interactions are important for the core-level binding energy shifts in solution. The special case with I3- dissolved in water, where hydrogen bonding causes breaking of the molecular symmetry, is treated and proves that the geometry changes influence the photoelectron spectrum of aqueous I3- directly.

Owing to their versatile orbital character with both local and highly dispersive degrees of freedom, transition metal oxides span the range of ionic, covalent and metallic bonding. They exhibit a vast diversity of electronic phenomena such as high dielectric, piezoelectric, pyroelectric, ferroelectric, magnetic, multiferroic, catalytic, redox, and superconductive properties. The nature of these properties arises from sensitive details in the electronic structure, e.g. orbital mixing and orbital hybridization, due to non-stoichiometry, atomic displacements, broken symmetries etc., and their coupling with external perturbations. In the work presented here, these variations of the electronic structure of crystals due to structural and electronic defects have been investigated, exemplarily for the quasi-binary system SrO - SrTiO3 - TiO2. A number of binary and ternary structures have been studied, both experimentally as well as by means of electronic modeling. The applied methods comprise Resonant X-ray Scattering techniques like Diffraction Anomalous Fine Structure, Anisotropy of Anomalous Scattering and X-ray Absorption Fine Structure, and simultaneously extensive electronic calculations by means of Density Functional Theory and Finite Difference Method Near-Edge Structure to gain a thorough physical understanding of the underlying processes, interactions and dynamics. It is analyzed in detail how compositional variations, e.g. manifesting as oxygen vacancies or ordered stacking faults, alter the short-range order and affect the electronic structure, and how the severe changes in mechanical, optical, electrical as well as electrochemical properties evolve. Various symmetry-property relations have been concluded and interpreted on the basis of these modifications in electronic structure for the orbital structure in rutile TiO2, for distorted TiO6 octahedra and related switching mechanisms of the Ti valence, for elasticity and resistivity in strontium titanate, and for surface relaxations in Ruddlesden-Popper phases. Highlights of the thesis include in particular the methodical development regarding Resonant X-Ray Diffraction, such as the first use of partially forbidden reflections to get the complete phase information not only of the tensorial structure factor but of each individual atomic scattering tensor for a whole spectrum of energies, as well as the determination of orbital degrees of freedom and details of the partial local density of states from these tensors. On the material side, the most prominent results are the identification of the migration-induced field-stabilized polar phase and the exergonic redox behavior in SrTiO3 caused by defect migration and defect separation.

Owing to their versatile orbital character with both local and highly dispersive degrees of freedom, transition metal oxides span the range of ionic, covalent and metallic bonding. They exhibit a vast diversity of electronic phenomena such as high dielectric, piezoelectric, pyroelectric, ferroelectric, magnetic, multiferroic, catalytic, redox, and superconductive properties. The nature of these properties arises from sensitive details in the electronic structure, e.g. orbital mixing and orbital hybridization, due to non-stoichiometry, atomic displacements, broken symmetries etc., and their coupling with external perturbations. In the work presented here, these variations of the electronic structure of crystals due to structural and electronic defects have been investigated, exemplarily for the quasi-binary system SrO - SrTiO3 - TiO2. A number of binary and ternary structures have been studied, both experimentally as well as by means of electronic modeling. The applied methods comprise Resonant X-ray Scattering techniques like Diffraction Anomalous Fine Structure, Anisotropy of Anomalous Scattering and X-ray Absorption Fine Structure, and simultaneously extensive electronic calculations by means of Density Functional Theory and Finite Difference Method Near-Edge Structure to gain a thorough physical understanding of the underlying processes, interactions and dynamics. It is analyzed in detail how compositional variations, e.g. manifesting as oxygen vacancies or ordered stacking faults, alter the short-range order and affect the electronic structure, and how the severe changes in mechanical, optical, electrical as well as electrochemical properties evolve. Various symmetry-property relations have been concluded and interpreted on the basis of these modifications in electronic structure for the orbital structure in rutile TiO2, for distorted TiO6 octahedra and related switching mechanisms of the Ti valence, for elasticity and resistivity in strontium titanate, and for surface relaxations in Ruddlesden-Popper phases. Highlights of the thesis include in particular the methodical development regarding Resonant X-Ray Diffraction, such as the first use of partially forbidden reflections to get the complete phase information not only of the tensorial structure factor but of each individual atomic scattering tensor for a whole spectrum of energies, as well as the determination of orbital degrees of freedom and details of the partial local density of states from these tensors. On the material side, the most prominent results are the identification of the migration-induced field-stabilized polar phase and the exergonic redox behavior in SrTiO3 caused by defect migration and defect separation.