Micromagnetic Investigation of Periodic Cross-Tie/Vortex Wall Geometry

A systematic series of micromagnetic simulations on periodic cross-tie/vortex wall structures in an ideal soft film at various widths, thicknesses, and period lengths is performed. For each width and thickness a natural period length is found which has minimal energy density for walls of this type. For each width, a critical thickness is determined below which the natural period length is infinite; for films thinner than this, the pure Néel wall has lower energy than any cross-tie/vortex wall. Details of the origin of the energy reduction in cross-tie/vortex walls as compared to Néel walls are also examined, and canting inside cross-tie and vortex structures in films thicker than 1 ℓex is explained