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A superposition of spin helices can yield topological spin textures, such as skyrmion and hedgehog lattices. Based on the analogy with the moire in optics, we study the magnetic and topological properties of such superpositions in a comprehensive way by modulating the interference pattern continuously. We find that the control of the angles between the superposed helices and the net magnetization yields successive topological transitions associated with pair annihilation of hedgehogs and antihedgehogs. Accordingly, emergent electromagnetic fields, magnetic monopoles and antimonopoles, and Dirac strings arising from the noncoplanar spin textures show systematic evolution. In addition, we also show how the system undergoes the magnetic transitions with dimensional reduction from the three-dimensional hedgehog lattice to a two-dimensional skyrmion lattice or a one-dimensional conical state. The results indicate that the concept of spin moir{e} provides an efficient way of engineering the emergent electromagnetism and topological nature in magnets.
The skyrmion crystal (SkX) characterized by a multiple-q helical spin modulation has been reported as a unique topological state that competes with the single-q helimagnetic order in non-centrosymmetric materials. Here we report the discovery of a ri
Emergent electromagnetic induction based on electrodynamics of noncollinear spin states may enable dramatic miniaturization of inductor elements widely used in electric circuits, yet many issues are to be solved toward application. One such problem i
A moir{e} system is formed when two periodic structures have a slightly mismatched period, resulting in unusual strongly correlated states in the presence of particle-particle interactions. The periodic structures can arise from the intrinsic crystal
The recently proposed theoretical concept of a Hunds metal is regarded as a key to explain the exotic magnetic and electronic behavior occuring in the strongly correlated electron systems of multiorbital metallic materials. However, a tuning of the a
Gapless Luttinger liquid is conventionally viewed as topologically trivial, unless it hosts degenerate ground states and or entanglement spectrum, which necessitates partial bulk degree of freedom to be gapped out. Here we predict an emergent gapless