Shape, strain and spin texture as a modern triad for magnetic materials.

Curvilinear magnetism has emerged as a powerful approach to create chiral and anisotropic responses at the nanoscale, using the effects of geometric curvature and topology. This concept complements traditional material screening when tailoring material properties for specific applications. Current research in curvilinear magnetism largely focuses on mean-field micromagnetics-a computational approach to predict magnetic microstructures. The roles of inhomogeneous strains and curvature-induced magnetoelectric coupling, mediated by spin textures, have gained attention only recently. In this Review, we discuss these novel phenomena and their relevance for designing 'metageometric' materials. Advances in geometrically engineered magnetic nanostructures could lead to exciting opportunities for energy-efficient, scalable nanoelectronic devices.