General magnetostatic shape–shape interactions

M. Beleggia, M. De Graef

Research output: Contribution to journalJournal articleResearchpeer-review


The magnetostatic interaction energy between two magnetic elements of arbitrary shape is presented as a convolution between the cross-correlation of the particle shapes and the dipolar tensor field. A generalized dipole–dipole interaction is derived, where the magnetic moments associated with the two particles interact through a magnetometric tensor field, carrying all the shape information. Example computations are given in order to verify the correctness of the formalism. The well-known result of the interaction between prisms, employed in most micromagnetic simulations, is correctly retrieved. The numerical accuracy of the method is also compared to a simple analytical result. Finally, one additional example computation, two interlaced interacting rings, is presented to show the generality of the formalism.
Original languageEnglish
JournalJournal of Magnetism and Magnetic Materials
Issue number1-2
Pages (from-to)L1-L10
Publication statusPublished - 2005
Externally publishedYes


  • Magnetostatic energy
  • Shape amplitude
  • Magnetic nanoparticles


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