Programmable Topological Magnetic Textures in Above-Room-Temperature 2D Ferromagnet Fe₃GaTe₂

Topological invariants identify distinct topological states by remaining unchanged under continuous deformations, which reflects the robustness of topological phases against external perturbations. In magnetic systems, they characterize deformation-resistant spin textures and endow non-trivial configurations with exceptional stability; however, they also create inherent challenges in precise modulation of topological magnetic states. Here, we demonstrate the generation and programmable modulation of arbitrary topological numbers in a magnetic skyrmion bag system that is thermally stable in the 2D van der Waals (vdW) ferromagnet Fe₃GaTe₂ (FGaT) at above room temperature. The surface-interior energy-landscape decoupling has been uncovered by exploiting unusual perpendicular magnetic anisotropy (PMA) and the thickness-dependent demagnetization energy, which enables hierarchical reconstruction of surface branching domains while retaining the bulk topological backbone. The encoding of skyrmion bags with different topological structures is demonstrated to enable applications in binary and higher-radix information storage. This work establishes a comprehensive strategy for generating, reconfiguring and operating high-order topological states, which paves the way toward programmable, multi-state spintronic technologies.