DMI Study Materials

Accordingly, we only show the interfacial and bulk DMI solutions in figures 1(a) and (b), respectively. In the plots, data points from the simulations are compared with the solutions of equations (11) and (12). In general, OOMMF and Fidimag produce similar results that perfectly agree with the theoretical curves obtained from the solutions of the differential equations (as shown in figure 1). Specifically, in the interfacial case the average relative error (between the semi-analytical and simulation curves) for the mx component is about 3.8% and for mz is about 0.3%. Equivalent magnitudes are found for the bulk DMI system. Smaller errors are obtained when reducing the mesh spacing, for instance, the DMI Study Materials previous magnitudes reduce to 0.44% and 0.03% for mx and mz, respectively, when using a mesh discretisation of 0.1 nm in the x-direction. In the case of MuMax3, a similar agreement is found when imposing periodic boundary conditions along the y-direction of the one-dimensional system (with a single repetition across the width although the Exam Dumps number should not affect the results since we are not considering dipolar interactions) because the DMI calculation is implemented with Neumann boundary conditions [31, 45] rather than free boundaries8 (see section S2 of the supplementary material for a comparison when not using periodic boundaries).

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