Origami-driven Dzyaloshinskii-Moriya interaction in centrosymmetric two-dimensional magnets

Origami-inspired approaches have presented exciting possibilities for engineering and manipulating two-dimensional (2D) materials in three-dimensional space. By introducing curvature through folding and bending, curved 2D materials offer unique opportunities to explore exotic magnetic phenomena that are absent in their planar counterparts. Here we demonstrate the existence of origami-driven Dzyaloshinskii-Moriya interaction (DMI) in centrosymmetric 2D magnets by means of symmetry analysis and noncollinear spin-polarized density functional theory. By taking $\mathrm{Cr}{\mathrm{I}}_{3}$ as an example, we show the decisive effect of spin-orbit interaction on the DMI of folded structures, which corresponds to the three-site Fert-L\'evy model. Furthermore, the geometry-governed anisotropy and the DMI contribute to the magnetic energy, resulting in chiral domain walls as the ground state. Our results present a general method for creating topological spin textures in centrosymmetric 2D magnets, providing insights into the formation of magnetochirality in origami 2D magnets, which will be beneficial to both the fundamental study of curvilinear magnetism and the application of chiral spin textures in spintronic devices.