Spin Moiré Engineering of Emergent Electromagnetism

A superposition of waves generates interference fringes called Moiré. It has gained renewed interest in atomic layered materials such as twisted graphene. Here we pursue this idea in magnetism, by regarding a superposition of spin helices as spin Moiré. We find that the manipulation of the Moiré patterns by the angles between the superposed helices and the net magnetization yields successive topological transitions associated with pair annihilation of topological defects called hedgehogs and antihedgehogs. Accordingly, emergent electromagnetic fields arising from the noncoplanar spin textures show systematic evolution. We also show how the system undergoes the topological transitions, in addition to the magnetic phase transitions from the hedgehog lattice to a skyrmion lattice or a conical state associated with spin Moiré modulation. Our results indicate that the spin Moiré is an efficient picture for engineering the topology and the emergent electromagnetism in chiral magnets.