Domain structure of ultrathin ferromagnetic elements in the presence of Dzyaloshinskii-Moriya Interaction

Cyrill B. Muratov, Valeriy V. Slastikov

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Recent advances in nanofabrication make it possible to produce multilayer nanostructures composed of ultrathin film materials with thickness down to a few monolayers of atoms and lateral extent of several tens of nanometers. At these scales, ferromagnetic materials begin to exhibit unusual properties, such as perpendicular magnetocrystalline anisotropy and antisymmetric exchange, also referred to as Dzyaloshinskii-Moriya interaction (DMI), because of the increased importance of interfacial effects. The presence of surface DMI has been demonstrated to fundamentally alter the structure of domain walls. Here we use the micromagnetic modelling framework to analyse the existence and structure of chiral domain walls, viewed as minimizers of a suitable micromagnetic energy functional. We explicitly construct the minimizers in the one-dimensional setting, both for the interior and edge walls, for a broad range of parameters. We then use the methods of Γ -convergence to analyse the asymptotics of the two-dimensional magnetization patterns in samples of large spatial extent in the presence of weak applied magnetic fields.

Original languageEnglish (US)
Article number20160666
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2197
StatePublished - Jan 1 2017

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • General Engineering
  • General Physics and Astronomy


  • Chiral domain walls
  • Dzyaloshinskii-moria interaction
  • G -convergence
  • Gradient theory of phase transitions
  • Magnetic skyrmions
  • Micromagnetics


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