![]() ![]() ![]() This approach naturally brings the shape anisotropy to the system and leads to the formation of specific spin textures, for example, magnetic vortices and antivortices as well as provides control over the dynamics of the topologically nontrivial magnetic solitons. Until recently, in the case of magnetism, the influence of the geometry on the spin vector fields was addressed primarily by the design of the sample boundaries. Currently, much attention is paid to strongly correlated electronic systems, for example, ferromagnets and superconductors, as they provide a unique tool to manipulate the topology of coexisting vector and scalar fields, associated with geometries of conventional systems. The interplay between geometry and topology of the order parameter is one of the fundamental properties in soft and condensed matter physics, including cell membranes, nematic crystals, superfluids, semiconductors, ferromagnets, and superconductors. In addition, the perspective should stimulate the development and dissemination of research and development oriented techniques to facilitate rapid transitions from laboratory demonstrations to industry-ready prototypes and eventual products. Overall, the perspective is aimed at crossing the boundaries between the magnetism and superconductivity communities and drawing attention to the conceptual aspects of how extension of structures into the third dimension and curvilinear geometry can modify existing and aid launching novel functionalities. Highlighting the recent developments and current challenges in theory, fabrication, and characterization of curvilinear micro- and nanostructures, special attention is paid to perspective research directions entailing new physics and to their strong application potential. Here, the state of the art is summarized and prospects for future research in curvilinear solid-state systems exhibiting such fundamental cooperative phenomena as ferromagnetism, antiferromagnetism, and superconductivity are outlined. ![]() In recent studies, however, the impact of curvilinear geometry enters various disciplines, ranging from solid-state physics over soft-matter physics, chemistry, and biology to mathematics, giving rise to a plethora of emerging domains such as curvilinear nematics, curvilinear studies of cell biology, curvilinear semiconductors, superfluidity, optics, 2D van der Waals materials, plasmonics, magnetism, and superconductivity. Traditionally, the primary field, where curvature has been at the heart of research, is the theory of general relativity. ![]()
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