Design of Skyrmion Bags with Tunable Topology in Symmetry-Broken 2D Lattices

Magnetic skyrmion bags, as high-order topological swirling spin textures, offer rich fundamental physics and distinct advantages for spintronic applications; however, their realization remains a formidable challenge, especially in two-dimensional (2D) systems. Here, through model analysis, we establish a theoretical framework for engineering skyrmion bags with tunable topology in symmetry-broken 2D ferromagnetic lattices. The physics correlates to the delicate interplay of isotropic exchange interaction, Dzyaloshinskii–Moriya interaction, and magnetic anisotropy, which can stabilize a rich variety of high-order topological spin states as well as the intriguing skyrmionium with zero topological charge. We further validate this mechanism in monolayer CrInTe 2 by using first-principles calculations and atomistic spin model simulations, revealing the existence of field-free skyrmion bags. Furthermore, we find that a weak magnetic field triggers a transition to skyrmioniums that maintains their structural integrity up to 240 K. Our results provide a compelling platform for exploring the high-order topological magnetism.