Ab Initio Spin Hamiltonian and Topological Noncentrosymmetric Magnetism in Twisted Bilayer CrI₃

Twist engineering of van der Waals magnets has emerged as an outstanding platform for manipulating exotic magnetic states. However, the complicated form of spin interactions in the large moiré superlattice obstructs a concrete understanding of such spin systems. To tackle this problem, for the first time, we developed a generic ab initio spin Hamiltonian for twisted bilayer magnets. Our atomistic model reveals that strong AB sublattice symmetry breaking due to the twist introduces a promising route to realize the novel noncentrosymmetric magnetism. Several unprecedented features and phases are uncovered including the peculiar domain structure and skyrmion phase induced by noncentrosymmetricity. The diagram of those distinctive magnetic phases has been constructed, and the detailed nature of their transitions analyzed. Further, we established the topological band theory of moiré magnons relevant to each of these phases. By respecting the full lattice structure, our theory provides the characteristic features that can be detected in experiments.