Magnetic kagome lattices have attracted much attention because the interplay of band topology with magnetism and electronic correlations give rise to various exotic quantum states. A common structural distortion in the kagome lattice is the breathing mode, which can significantly influence the magnetism and band characteristics. However, the control of breathing mode and the associated topological phenomena remain rarely explored. Here, we demonstrate that the coupling of breathing modes with ferroelectricity, magnetism, and band topology in the $M_3{X}_8$ monolayer system enables electric field manipulation of topological spin structure and electronic states. The breathing mode mainly occurs in materials containing early $4d/5d$ transition metal elements and can be reversed or even suppressed via ferroelectric switching in low-barrier materials. Importantly, electric field-induced switching of the breathing mode can alter the chirality of the topological spin structure, or trigger a transition from a topological trivial insulator to a Chern insulator. This work paves the way for exploring novel physical phenomena driven by breathing mode in kagome materials.

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• Chern insulators
• Ferroelectricity
• Skyrmions
• Topological phase transition
• 2-dimensional systems
• Kagome lattice
• Multiferroics
• First-principles calculations
• Tight-binding model