Understanding the excitations of quantum materials is essential for unraveling how their microscopic constituents interact. Among these, particle-hole excitations form a particularly important class, as they govern fundamental processes such as screening, dissipation, and transport. In metals, the continuum of electron-hole excitations is described by the Lindhard function. Although central to the theory of Fermi liquids, the corresponding Lindhard continuum has remained experimentally elusive. Here, we report its direct observation in the weakly correlated metal MgB$_{2}$ using ultra-soft resonant inelastic X-ray scattering (RIXS). We resolve a linearly dispersing excitation with velocity comparable to the Fermi velocity and find quantitative agreement with simulations of the non-interacting charge susceptibility. A detailed analysis and decomposition of the simulations reveal the intra-band origin of this low-energy excitation, confirming it as the Lindhard continuum. Our results establish ultra-soft RIXS as a momentum-resolved probe of the fermiology in metals and call for deeper investigations of continuum features in RIXS and related spectroscopy of other materials beyond MgB$_{2}$.

Magnetic topology and its associated emergent phenomena are central to realizing intriguing quantum states and spintronics functionalities. Designing spin textures to achieve strong and distinct electrical responses remains a significant challenge. Layered transition metal dichalcogenides offer a versatile platform for tailoring structural and magnetic properties, enabling access to a wide spectrum of topological magnetic states. Here, we report a domain-wall-driven, large, and tunable topological Hall effect (THE) in a non-centrosymmetric intercalated transition metal dichalcogenides series Fe$_x$TaS$_2$. By systematically varying the Fe intercalation level, we exert precise control over the magnetic ground states, allowing manipulation of the topological Hall effect. Real-space magnetic force microscopy (MFM) provides direct evidence of periodic magnetic stripe domain formation, confirming the microscopic origin of the observed topological transport phenomena. Our findings establish a promising way for tuning the topology of domains to generate substantial electromagnetic responses in layered magnetic materials.

Phonon-polaritons offer significant opportunities for low-loss, subdiffractional light guiding at the nanoscale. Despite extensive efforts to enhance control in polaritonic media, focused and spatially confined phonon-polariton waves have only been realized in in-plane-anisotropic crystals (e.g., MoO$_3$) and remain elusive in in-plane-isotropic materials (e.g., hexagonal boron nitride, hBN). In this study, we introduce a novel approach to launching phonon-polaritons by leveraging hBN subwavelength cavities at the Au/SiO$_2$ interface, enabling efficient coupling of cavities to the far-field component of mid-infrared light. Utilizing standard lithographic techniques, we fabricated subwavelength cavities of various shapes and sizes, demonstrating strong field enhancement, resonant mode localization, and generation of propagating phonon-polaritons with well-defined spatial structure. The cavity geometry governs wavefront curvature, spatial confinement, and polariton focusing, providing control over their propagation and achieving record-high in-plane confinement up to $\lambda/70$. Scattering-type scanning near-field optical microscopy reveals the real-space optical contrast of these cavity-launched modes, allowing for detailed characterization. We believe that our cavity-based approach to phonon-polariton focusing in isotropic media will pave the way for advanced nanophotonic applications.