Extended Data Fig. 10: Micromagnetic modeling and validation of continuous model.
From: Dipolar skyrmions and antiskyrmions of arbitrary topological charge at room temperature
The multilayer system can be simulated using a continuous quasi 2D model, where the magnetization is assumed to be homogenous along the z direction. Thus, the exchange interaction is assumed to be equal in all three directions. This is a reasonable approximation as the Co and Ni layers are ultra-thin and no spacer layers are involved. The average deviation θ from the mean value <m> along the OOP direction is smaller than 1 degree (a) for the layers marked in (b). The total simulation box consists of n = nx × ny × nz = 2000 × 2000 ×5 cells. Thus, 2000 × 2000 vectors were used for each ith layer to obtain the mean value <θ> and the corresponding error bars. If one compares the snapshots of magnetization states, induction maps, as well as LTEM over-focus images for all the layers as plotted in (c) then no substantial change can be observed. Scale bars correspond to 500 nm. The more important aspect regarding the correct micromagnetic modeling is the appropriate choice of lateral cell size which is crucial for the correct numerical investigation of the higher order spin textures. In (d) the topological charge is plotted against the chosen lateral cell size. For lateral discretization lengths smaller than 2.2 nm a Q = +5 ASK can be stabilized, as shown in (e,I), when the simulations are started with a rough parametrization of such a higher charged ASK. If the discretization length is increased to 2.25 nm, then the Q = +5 ASK decays into a Q = +2 type, as shown in (f,II). For cell sizes larger than 2.5 nm, no spin objects are stable, and one observes only the polarized ferromagnetic state.
