Domain structure of bulk ferromagnetic crystals in applied fields near saturation

Hans Knüpfer, Cyrill B. Muratov

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


We investigate the ground state of a uniaxial ferromagnetic plate with perpendicular easy axis and subject to an applied magnetic field normal to the plate. Our interest is in the asymptotic behavior of the energy in macroscopically large samples near the saturation field. We establish the scaling of the critical value of the applied field strength below saturation at which the ground state changes from the uniform to a multidomain magnetization pattern and the leading order scaling behavior of the minimal energy. Furthermore, we derive a reduced sharp interface energy, giving the precise asymptotic behavior of the minimal energy in macroscopically large plates under a physically reasonable assumption of small deviations of the magnetization from the easy axis away from domain walls. On the basis of the reduced energy and by a formal asymptotic analysis near the transition, we derive the precise asymptotic values of the critical field strength at which non-trivial minimizers (either local or global) emerge. The non-trivial minimal energy scaling is achieved by magnetization patterns consisting of long slender needle-like domains of magnetization opposing the applied field.

Original languageEnglish (US)
Pages (from-to)921-962
Number of pages42
JournalJournal of Nonlinear Science
Issue number6
StatePublished - Dec 2011

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • General Engineering
  • Applied Mathematics


  • Ansatz-free analysis
  • Magnetic domains
  • Self-similarity
  • Variational bounds


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