Magnetic Domains in Thin Ferromagnetic Films with Strong Perpendicular Anisotropy

Hans Knüpfer, Cyrill B. Muratov, Florian Nolte

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


We investigate the scaling of the ground state energy and optimal domain patterns in thin ferromagnetic films with strong uniaxial anisotropy and the easy axis perpendicular to the film plane. Starting from the full three-dimensional micromagnetic model, we identify the critical scaling for which the transition from single domain to multidomain ground states such as bubble or maze patterns occurs as the film thickness goes to zero and the lateral extent goes to infinity. Furthermore, we analyze the asymptotic behavior of the energy in these two asymptotic regimes. In the single domain regime, the energy Γ-converges towards a much simpler two-dimensional and local model. In the multidomain regime, we derive the scaling of the minimal energy and deduce a scaling law for the typical domain size.

Original languageEnglish (US)
Pages (from-to)727-761
Number of pages35
JournalArchive for Rational Mechanics and Analysis
Issue number2
StatePublished - May 2 2019

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering


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