<p>Ferrofluids are remarkable materials composed of magnetic nanoparticles dispersed in a carrier liquid. These suspensions exhibit fluid-like behavior in the absence of a magnetic field, but when exposed to a magnetic field, they can respond and deform into a variety of patterns. This responsive behavior of ferrofluids makes them an excellent material for applications such as drug delivery for targeted therapies and soft robots. In this thesis, we will focus on the interfacial dynamics of ferrofluids in Hele-Shaw cells. The three major objectives of this thesis are: understanding the pattern evolution, unraveling the underlying nonlinear dynamics, and ultimately achieving passive control of ferrofluid interfaces. First, we introduce a novel static magnetic field setup, under which a confined circular ferrofluid droplet will deform and spin steadily like a `gear’, driven by interfacial traveling waves. This study combines sharp-interface numerical simulations with weakly nonlinear theory to explain the wave propagation. Then, to better understand these interfacial traveling waves, we derive a long-wave equation for a ferrofluid thin film subject to an angled magnetic field. Interestingly, the long-wave equation derived, which is a new type of generalized Kuramoto--Sivashinsky equation (KSE), exhibits nonlinear periodic waves as dissipative solitons and reveals fascinating issues about linearly unstable but nonlinearly stable structures, such as transitions between different nonlinear periodic wave states. Next, inspired by the low-dimensional property of the KSE, we simplify the original 2D nonlocal droplet problem using the center manifold method, reducing the shape evolution to an amplitude equation (a single local ODE). We show that the formation of the rotating `gear’ arises from a Hopf bifurcation, which further inspires our work on time-dependent control. By introducing a slowly time-varying magnetic field, we propose strategies to effectively control a ferrofluid droplet's evolution into a targeted shape at a targeted time. The final chapter of this thesis concerns our ongoing research into the interfacial dynamics under the influence of a fast time-varying and rotating magnetic field, which induces a nonsymmetric viscous stress tensor in the ferrofluid, requiring the balance of the angular momentum equation. As a consequence, wave propagation on a ferrofluid interface can be now triggered by magnetic torque. A new thin-film long-wave equation is consistently derived taking magnetic torque into account.</p>

In this dissertation, we utilized a wide range of complementary synchrotron-based X-ray spectroscopic and scattering techniques, notably X-ray absorption spectroscopy (XAS), hard X-ray photoelectron spectroscopy (HAXPES), standing-wave X-ray photoelectron spectroscopy (SW-XPS), and X-ray resonant magnetic reflectometry (XRMR), to understand and control the phenomenon of emergent interfacial ferromagnetism in strongly-correlated oxide heterostructures. This field holds great promise for the development of next-generation spintronic devices. In the heterostructures we investigated, neither of the parent oxide layers exhibits inherent ferromagnetism. Yet, when these layers are combined in an epitaxial film stack, charge-transfer phenomena give rise to an emergent ferromagnetic state at the interface. Throughout my graduate studies, I focused on studying such charge-transfer phenomena as the driving force for stabilizing interfacial ferromagnetism. This dissertation is structured around two main projects. The first project delves into the intriguing possibility of tuning the emergent interfacial ferromagnetism. More specifically, we investigated the mechanisms for suppressing interfacial charge transfer to gain control over and manipulate this magnetic phenomenon. In our second project, we explored a different facet of interfacial ferromagnetism, focusing on the origins of the imbalance in the magnitudes of the magnetic moment between the top and bottom interfaces in the same layer. Our investigation aimed to uncover the possible causes of this imbalance, ultimately leading us to scrutinize the role of defect states in this magnetic asymmetry. In the first part of this dissertation, we investigated the thickness-dependent metal-insulator transition within LaNiO3 and how it impacts the electronic and magnetic states at the interface between LaNiO3 and CaMnO3. We present a direct observation of a reduced effective valence state in the interfacial Mn cations. This reduction is most pronounced in the metallic LaNiO3/CaMnO3 superlattice, where the above-critical LaNiO3 thickness of 6-unit cells triggers this phenomenon, facilitated by the charge transfer of the itinerant Ni 3d eg electrons into the interfacial CaMnO3 layer. In contrast, when we examine the insulating superlattice with a LaNiO3 thickness below the critical value (2-unit cells), we observe a homogeneous effective valence state of Mn throughout the CaMnO3 layers. This homogeneity is attributed to the suppression of charge transfer across the interface. The second part of this dissertation delves deeply into the complexities of interfacial magnetism within the CaMnO3/CaRuO3 superlattices. Our experimental investigation unveiled an unexpected asymmetry in the strength of magnetism at these interfaces. Our findings suggest that within the superlattice CaMnO3/CaRuO3, the lower interface (CaRuO3/CaMnO3) exhibits a weaker magnetic moment when compared to the upper interface (CaMnO3/CaRuO3). This observation, supported by XRMR and XAS experimental data, was further clarified by first-principles density functional theory (DFT) calculations. Our calculations suggest that the observed magnetic asymmetry may be linked to the presence of oxygen vacancies at the interfaces. Our study significantly contributes to our understanding of interfacial ferromagnetism, potentially paving the way for controlling and manipulating this emergent property. This may be achieved by utilizing engineered defect states, offering exciting prospects for applications in the field of spintronics devices. / Physics

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