Fig. 6: Estimation of the error in the out-of-plane magnetisation component mz at the left boundary of a one-dimensional ferromagnet defined in the domain [− ℓ/2, ℓ/2], with ℓ = 100 nm.
The system includes exchange and DM interactions only. The error is computed as a function of the number of mesh discretisation sites N = ℓ/h, where h is the distance between mesh sites. The numerical solution is compared to a kink-soliton solution at the sample edge86. The mz curve is extrapolated to x = − ℓ/2 and x = ℓ/2 since the mesh points at the domain extrema do not lie exactly at the mesh boundaries. The one-dimensional system is simulated using different approximations of the exchange interactions: 6-neighbour (6 Nb) and 12-neighbour (12 Nb) stencils, and free (no label) or Robin boundary conditions (BC), as well as various finite-difference micromagnetic codes, as specified in the legend. The faded dashed line serves as a reference for inverse cubic scaling of the error with the number of mesh points.
