Topology, imaging, and emergent phenomena of spin textures.

Spin textures are magnetic configurations that vary smoothly in space, momentum, or time. This review explores the topology, geometry, dynamics, and imaging of these complex, often noncollinear configurations in magnetic and multiferroic systems, providing a framework for investigating the interplay between local spatial patterns and their global physical properties. A central theme is the role of Berry phases and quantum geometry, which provide a common framework linking topological textures, emergent electrodynamics, charge transport, and magnetically induced ferroelectricity. Spin textures can manifest as stable topological particles, coupling to electrons or magnons via emergent electromagnetic fields. Advanced real-space imaging techniques resolve the internal structure and dynamics of topological textures like magnetic skyrmions or multiferroic domains, enabling the direct observation of their nucleation, motion, and annihilation in both two and three dimensions. In multiferroic systems, spin textures can induce ferroelectricity, and nonlinear optical techniques, such as second-harmonic generation, can resolve the coexisting order parameters in such systems. Last, we examine emergent functionalities of spin textures and multiferroics, such as nonreciprocal transport, and provide an outlook on the technological potential of magnetic textures and their role in exploring the link between topology and magnetism.