Demagnetization in micromagnetics: Magnetostatic self-interactions of bulk chiral magnetic skyrmions

We develop a theoretical and numerical framework for three-dimensional bulk chiral magnets that includes the full magnetostatic dipole-dipole interaction and its back-reaction on the magnetization. Assuming translational invariance along one spatial direction, we analyze the effect of dipolar interactions on three Dzyaloshinskii-Moriya interaction (DMI) terms—Dresselhaus, Rashba, and Heusler—corresponding to Bloch, Néel, and antiskyrmion textures. In the absence of the dipolar interaction, these three DMI terms are gauge equivalent and yield degenerate skyrmion energies. Incorporating the nonlocal dipole-dipole interaction breaks this degeneracy: Bloch skyrmions remain unaffected, Néel skyrmions shrink slightly, and Heusler antiskyrmions lose axial symmetry and stabilize into square lattice crystals. The system is solved using a nonlocal numerical relaxation method that self-consistently computes the magnetostatic potential from Poisson's equation. Our results show that long-range dipolar interactions can stabilize bulk antiskyrmion crystals in translationally invariant three-dimensional chiral magnets.