Spin moir\'{e} engineering of topological magnetism and emergent electromagnetic fields

TL;DR

This paper explores how superposing spin helices, akin to optical moiré patterns, can systematically control topological magnetic textures and emergent electromagnetic fields, enabling new ways to engineer magnetic topologies.

Contribution

It introduces the concept of 'spin moiré' to engineer and control topological magnetic textures and emergent electromagnetic phenomena systematically.

Findings

Successive topological transitions via angle control between helices.

Emergent electromagnetic fields evolve systematically with spin texture changes.

Dimensional reduction from 3D hedgehog lattice to 2D skyrmion lattice or 1D conical state.

Abstract

A superposition of spin helices can yield topological spin textures, such as skyrmion and hedgehog lattices. Based on the analogy with the moir\'e 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.