Exploiting symmetries in skyrmionic micromagnetic simulations: Cylindrical and radial meshes

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Micromagnetic simulations are an essential tool in the theoretical study of magnetic skyrmions. When confined
into nanometric samples, these structures can serve as bits of information among other possible applications.
Accurate simulations are one of the major sources of theoretical results. In the case of confined skyrmions, it
is known that the boundaries play a critical role in their stabilization. However, most of the micromagnetic
simulations are done using a finite-difference method with quadrilateral meshes, that do not exactly fit the
boundaries. The use of this mesh can introduce a significant numerical error that can completely change
the results of the simulations. We present here two different finite-difference meshes to study skyrmions in
confined disks, taking advantage of the symmetry of that geometry. A two-dimensional cylindrical mesh for
non-symmetric scenarios but geometrically symmetric (boundary conditions) that reduces the propagation of
the numerical error, and the particular case of a one dimensional mesh for axisymmetric scenarios where the
computation time is hugely reduced.
Original languageEnglish
Article number168972
Pages (from-to)1-7
Number of pages7
JournalJournal of Magnetism and Magnetic Materials
Publication statusPublished - 1 May 2022


  • Micromagnetism
  • Simulation
  • Skyrmions


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