On the computation of the magnetic phase shift for magnetic nano-particles of arbitrary shape using a spherical projection model

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• We model the magnetic phase shift of an electron wave using a multi-grid approach.
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• We derive closed-form expressions for the voxel-by-voxel update of the phase shift.
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• Comparison of simulated phase shifts with analytical expressions shows good agreement.
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• This approach can be integrated with iterative vector field electron tomography reconstructions.

The magnetic phase shift of an electron wave traveling through a magnetized object is computed by considering the object to be made up of a collection of uniformly magnetized spheres arranged on the nodes of a cubic grid. In the limit of vanishing grid size, this approach becomes equivalent to other numerical approaches. Update equations are derived for the change of the magnetic phase shift when the magnetization of a single object voxel is modified. Example phase shift calculations are presented for a uniformly magnetized sphere, circular disks with an infinitely sharp vortex core and a smooth core, and an oval disk with a pair of vortices and an antivortex.