Micromagnetics on Curved Geometries Using Rectangular Cells: Error Correction and Analysis

This paper presents an edge field correction for micromagnetic computations of arbitrarily shaped objects on rectangular grids. The correction is compatible with fast Fourier transform techniques and involves factors that are precomputed using the standard self-magnetostatic algorithms applied on a local, refined mesh. To evaluate this correction, we introduce a quantitative measure that is based on calculating an edge mode resonance for different orientations of an edge with respect to the rectangular mesh. Applied to a 350-nm Permalloy square, we find up to a 50% frequency shift for the uncorrected approach, but less than a 5% shift using the proposed method. We also study vortex expulsion in a 220-nm Permalloy square, and again find that the proposed correction significantly reduces the dependence of the expulsion field on the orientation angle of the sample square with the mesh