| Gaia: | <p>In his programmatic article <em>More Is Different</em> (1972), Nobel laureate P. W. Anderson captured the fundamental interest in quantum matter in a nutshell. The central motive in this field is <em>emergence</em>. In the inaugural volume of the homonymous journal, J. Goldstein defined this as “the arising of novel and coherent structures, patterns and properties during the process of self-organization in complex systems". Famously, the idea that the "the whole is greater than the sum of its parts" goes back to Aristotle's <em>metaphysics</em>, and it has served as a stimulating concept in 19th century biology, economics and philosophy.</p> <p>The study of emergence in condensed matter physics is unique in that the underlying <em>complex systems</em> are sufficiently "simple" to be modelled from first principles. Notably, the emergent phenomena discovered in this field, such as high-temperature superconductivity, giant magnetoresistance, and strong permanent magnetism have had an enormous impact on technology, and thus, society. Historically, there has been a distinction between materials with localized, strongly interacting (or <em>correlated</em>) electrons — and non-interacting, itinerant electronic states. In the last decade, several new states of matter have been discovered, which emerge not from correlations, but from peculiar symmetries (or <em>topology</em>) of itinerant electronic states. The term <em>quantum materials</em> has therefore become popular to subsume these two strands of condensed matter physics: Electronic correlations and topology.</p> <p>In this thesis, I report investigations of four quantum materials which each illustrate present key interests in the field: The mechanism of high temperature superconductivity, the search for materials that combine both electronic correlations and non-trivial topology and novel emergent phenomena that arise from the synergy of electronic correlations and a strong coupling of spin- and orbital degrees of freedom. The common factor and potential key to understanding these materials is <em>magnetism</em>. My experimental work is focused on neutron and x-ray scattering techniques, which are able to determine both <em>order</em> and <em>dynamics</em> of magnetic states at the atomic scale.</p> <p>I illustrate the full scope of these methods with experimental studies at neutron and synchrotron radiation facilities. This includes both diffraction and spectroscopy, of either single- or polycrystalline samples. My in-depth analysis of each dataset is aided by structural, magnetic and charge transport experiments. Thus, I provide a quantitative characterization of magnetic fluctuations in an iron-based superconductor and in two Dirac materials, and determine the magnetic order in a Dirac semimetal candidate and a complex oxide. As a whole, these results demonstrate the elegant complementarity of modern scattering techniques. Although such methods have a venerable history, they are presently developing at a rapid pace. Several results of this thesis have only been enabled by very recent instrumental advances.</p>
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