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In a crystalline ordered magnet, coherent excitations called spin waves, or magnons, propagate in the material forming band structures in an analogous way to electrons. Spin waves can possess non trivial topology associated with novel response functions of fundamental and potential technological interest. In particular, topologically protected surface states of magnons offer a new path towards coherent spin transport for spintronics applications. One of the central issues in this area is to establish the conditions under which band topology can arise in magnons and explore its variety. In this work we harness the full power of symmetry as applied to magnetism, to facilitate the discovery of new topological magnon models and materials. We show how to efficiently identify such systems by adapting the electronic topological quantum chemistry scheme to magnons, using constraints imposed by time reversal and crystalline symmetries to determine possible gapped and nodal topology in magnon models. Further, we explore enhanced symmetries beyond this paradigm, which are nevertheless natural for magnons: the spin-space groups. Exploring spin-space symmetry, which has wholly or partially decoupled magnetic and lattice degrees of freedom, reveals a proliferation of nodal points, lines, and planes beyond the standard crystalline symmetries. Linear spin wave theory is one of the most valuable techniques to study magnons, however, it can fail in different scenarios. Because of its importance to the community, we explore cases where it contains spurious symmetries which can potentially hide important physics in the spectra, like topology. We provide therefore a simple way to identify and resolve such cases within the linear theory. Finally, a pressing issue in magnons is the experimental detection and manipulation of topological surface states. Even more, the characterisation of generic 2D magnetism is an open problem. We contribute to this by devising an experimental setup based on quasi-particle interference which potentially could solve this long-lasting challenge. / Kohärente Anregungen, wie Spinwellen, auch Magnonen genannt, formen Bandstrukturen in kristallin geordneten Materialien. Diese Magnonen können eine nicht triviale Topologie aufwei- sen, welche neuartige Antwortfunktionen erzeugen können. Sie sind daher von technologischem Interesse. Insbesondere die topologisch geschützten Oberflächenzustände der Magnonen ermöglichen eine Realisierung von kohärentem Spin Transport und erlauben eine potentielle Anwendung in der Spintronik. Zentraler Punkt der aktuellen Forschung sind Bedingungen, unter denen eine nicht triviale Magnon-Bandtopologie entstehen kann und welche Möglichkeiten diese eröffnen. In dieser Arbeit untersuchen wir diese neuartigen topologischen Phasen für verschiedene Mo- delle unter Nutzung verschiedener Symmetrien. Die Erweiterung des elektronischen “topological quantum chemistry” Ansatzes für Magnonen erlaubt eine effiziente Identifikation dieser topologischen Eigenschaften. Der Ansatz basiert auf verschiedenen Einschränkungen, welche von der Zeitumkehr und kristallinen Symmetrien induziert werden. Darüber hinaus untersuchen wir die Anwendung von weiteren Symmetrien, welche relevant für Magnonen sind: die Spin-Raumgruppen. Die Erforschung der Spin-Raum-Symmetrie, welche magnetische Freiheitsgrade und Gittersyme- trien ganz oder teilweise entkoppelt, führt zur Ausbreitung von Knotenpunkten, Linien und Ebenen jenseits der standardmäßigen Kristallsymmetrien. Die lineare Spinwellentheorie ist eine der erfolgreichsten Methoden zur Untersuchung von Magnonen, kann jedoch unter verschiedenen Umständen versagen, da künstliche Symmetrien essenzielle Physik, wie beispielsweise topologische Eigenschaften, verbergen. Ansätze, die im Rahmen dieser Dissertation erarbeitet worden sind, helfen dabei, solche Fälle zu identifizieren und zu verstehen. Aktuelle Experimente zur Manipulation topologischer Oberflächenzustände von Magnonen, sowie die allgemeine Untersuchung von Magnetismus in zwei Dimensionen, fehlen. Daher präsentieren wir einen möglichen experimentellen Aufbau, basierend auf Quasi-Teilchen-Interferenz, welcher einen möglichen Ausweg aufzeigt.

Spontaneous Raman spectroscopy (SR) is a versatile method for analysis and visualization of ferroelectric crystal structures, including domain walls. Nevertheless, the necessary acquisition time makes SR impractical for in situ analysis and large scale imaging. In this work, we introduce broadband coherent anti-Stokes Raman spectroscopy (B-CARS) as a high-speed alternative to conventional Raman techniques and demonstrate its benefits for ferroelectric domain wall analysis. Using the example of poled lithium niobate, we compare the spectral output of both techniques in terms of domain wall signatures and imaging capabilities. We extract the Raman-like resonant part of the coherent anti-Stokes signal via a Kramers–Kronigbased phase retrieval algorithm and compare the raw and phase-retrieved signals to SR characteristics. Finally, we propose a mechanism for the observed domain wall signal strength that resembles a Cerenkov-like behavior, in close analogy to domain wall signatures obtained by secondharmonic generation imaging.We, thus, lay here the foundations for future investigations on other poled ferroelectric crystals using B-CARS.

Two-dimensional (2D) membranes are emerging candidates for osmotic energy conversion. However, the trade-off between ion selectivity and conductivity remains the key bottleneck. Here we demonstrate a fully crystalline imine-based 2D polymer (2DPI) membrane capable of combining excellent ionic conductivity and high selectivity for osmotic energy conversion. The 2DPI can preferentially transport cations with Na+ selectivity coefficient of 0.98 (Na+/Cl− selectivity ratio ~84) and K+ selectivity coefficient of 0.93 (K+/Cl− ratio ~29). Moreover, the nanometer-scale thickness (~70 nm) generates a substantially high ionic flux, contributing to a record power density of up to ~53 W m−2, which is superior to most of nanoporous 2D membranes (0.8~35 W m−2). Density functional theory unveils that the oxygen and imine nitrogen can both function as the active sites depending on the ionization state of hydroxyl groups, and the enhanced interaction of Na+ versus K+ with 2DPI plays a significant role in directing the ion selectivity.

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