Magnetostatics of Magnetic Skyrmion Crystals

Magnetic skyrmion crystals are topological magnetic textures arising in the chiral ferromagnetic materials with Dzyaloshinskii-Moriya interaction. The magnetostatic fields generated by magnetic skyrmion crystals are first studied by micromagnetic simulations. For N\'eel-type skyrmion crystals, the fields will vanish on one side of the crystal plane, which depend on the helicity; while for Bloch-type skyrmion crystals, the fields will distribute over both sides, and are identical for the two helicities. These features and the symmetry relations of the magetostatic fields are understood from the magnetic scalar potential and magnetic vector potential of the hybridized triple-Q state. The possibility to construct magnetostatic field at nanoscale by stacking chiral ferromagnetic layers with magnetic skyrmion crystals is also discussed, which may have potential applications to trap and manipulate neutral atoms with magnetic moments.