Extended Kitaev magnetism in magnetic fields

Over the past years, the physics of Kitaev\'s spin-1/2 honeycomb model and its extensions have attracted enormous interest, fueled by a pursuit of the fundamental understanding as well as experimental realizations of quantum spin-liquid phases. A notorious achievement in this field has been the discovery that, when applied in specific directions, a magnetic field can induce a gapped topological spin liquid in the Kitaev quantum magnet ∝-RuCl3. In parallel, the search for other magnets with strong spin-orbit coupling has resulted in recent proposals of material candidates to host spin-1 and spin-3/2 analogs of the Kitaev interaction. Remarkably, all of these materials display nontrivial responses to magnetic fields, such as strongly anisotropic magnetization processes and novel field-induced states, due to the lack of spin-rotational symmetry. Given such a rich background, this dissertation aims at expanding the current knowledge of the effects of magnetic fields on extended Kitaev systems with three different contributions. First, we employ a combination of linear and nonlinear spin-wave theory to study the ordered field-induced phases of the nearestneighbor Heisenberg-Kitaev model, which is often regarded as a minimal model to describe Kitaev magnetism for different spin quantum numbers S. By developing a consistent 1/S expansion, we analyze the influence of the leading-order quantum fluctuations on physical observables and phase diagrams of the experimentally relevant cases of S = 1/2, 1 and 3/2. Second, we consider a more realistic spin model to describe the low-temperature elastic response of ∝-RuCl3 in an applied magnetic field and small uniaxial pressure. Our results suggest that anomalous features found in experiments are indicative of an intermediate-field quantum paramagnetic regime. Finally, we return to the Heisenberg-Kitaev model in a magnetic field, but by now applying the numerical technique of exact diagonalization for S = 1/2. Besides finding good agreement with our spin-wave calculations, we report possible evidence for a new quantum tricritical point. (AU)