Interplay of geometric frustration, magnetic anisotropy and dimerisation in quantum magnets

Investigating magnetic phenomena and materials where quantum mechanical effects play a role in determining their ground state properties is just one of the fascinating areas which falls under the field of quantum magnetism, where the complex interplay between geometric constraints, competing interactions, and quantum fluctuations can lead to the emergence of unconventional magnetic states. In particular, a phenomenon often arises whereby exchange constants are unable to be simultaneously satisfied - this is known as frustration. Frustrated magnetism is a subset of quantum magnetism which focuses on such systems, exhibiting an infinite number of competing states at low energies. This can result in the suppression of long-range magnetic order and the emergence of curious phases where spins remain disordered even at very low temperatures. A compelling topic which presents a plethora of interesting results, not only does it allow for theoretical challenges, forcing the continual development of new analytical and computational tools to tackle these systems, it also deepens our understanding of quantum many-body physics and has potential implications for the development of innovative technologies with novel functionalities. It is an active area of research and shall be explored in detail through two materials Cu₂OSO₄ and CuSeO₃, copper compounds which both possess a high level of degeneracy, complex geometry, anisotropy, and finally similarities to the kagome lattice and dimerisation respectively.

This thesis presents a thorough theoretical investigation of frustrated magnetism in these two novel materials, focusing on unraveling the underlying mechanisms that lead to the experimental results that have been published thus far and exploring the phase diagrams that emerge. Employing analytical and numerical techniques, we investigate the intricate interplay between geometric constraints and competing interactions. By elucidating the underlying mechanisms and making predictions for future experiments, this work contributes to the understanding of quantum magnetism and more specifically frustration, paving the way for future experimental realisations and potential technological applications in the field of condensed matter physics.