Radial stabilization of magnetic Skyrmions under strong external magnetic field

Abstract The Skyrmion number density, q ≡ n → · ∂ x n → × ∂ y n → / 4 π , is one of the key quantities that characterizes the topological properties of Skyrmionic spin textures. In this work, we propose a topologically supported stabilization mechanism for two-dimensional magnetic Skyrmions using a Hamiltonian that includes a term proportional to the square of the Skyrmion number density, q 2 . This term, derived from the generalization of the harmonic map, preserves inversion symmetry and remains significant under strong external magnetic fields where conventional exchange interactions are suppressed. Through scaling analysis and micromagnetic calculations using the Landau–Lifshitz-Gilbert equation, we show that this q 2 term stabilizes single Skyrmion configurations. We also derive an energy bound that confirms the topological protection of these configurations under radial perturbation. Our results provide a framework for realizing Skyrmions in materials without broken inversion symmetry, particularly in systems subjected to strong external magnetic fields, where conventional exchange interactions are significantly weaker than the Zeeman effect.