Topological transitions by magnetization rotation in kagome monolayers of ferromagnetic Weyl semimetal Co-based shandite

Abstract

Co-based shandite Co$_3$Sn$_2$S$_2$ is a ferromagnet hosting Weyl fermions in the layered Co kagome structure. The band topology as well as the magnetism is predicted to vary drastically in the atomically thin films depending on the thickness and surface termination, and as an extreme case, the quantum anomalous Hall state is expected in a monolayer of the Co kagome lattice. Given that the bulk Weyl gap depends on the magnetization direction, here we theoretically study how the topological nature and transport properties vary with the magnetization direction in the systems with kagome monolayer with both Sn and S surface terminations. By using $ab \ initio$ calculations, we find that in the Sn-end monolayer the anomalous Hall conductivity shows successive discrete changes between different quantized values by rotating the magnetization, indicating several topological transitions between the anomalous quantum Hall insulators with different Chern numbers. Notably, when the magnetization is oriented in-plane and perpendicular to the Co-Co bond, the system exhibits a planar quantized anomalous Hall effect. We clarify that these peculiar behaviors are due to topological changes in the band structures associated with gap closing of the Weyl nodes. In contrast, the S-end monolayer shows rather continuous changes in the transport properties since the system is metallic, although the band structure contains many Weyl nodes. Our results pave the way for controlling Weyl fermions in atomically thin films of Co-based shandite, where the topological nature associated with the Weyl nodes appears more clearly than the bulk.