Uniqueness of one-dimensional Néel wall profiles

Cyrill B. Muratov, Xiaodong Yan

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

We study the domain wall structure in thin uniaxial ferromagnetic films in the presence of an in-plane applied external field in the direction normal to the easy axis. Using the reduced one-dimensional thinfilm micromagnetic model, we analyse the critical points of the obtained non-local variational problem. We prove that the minimizer of the one-dimensional energy functional in the form of the Néel wall is the unique (up to translations) critical point of the energy among all monotone profiles with the same limiting behaviour at infinity. Thus, we establish uniqueness of the one-dimensional monotone Néel wall profile in the considered setting. We also obtain some uniform estimates for general one-dimensional domain wall profiles.

Original languageEnglish (US)
Article number20150762
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume472
Issue number2187
DOIs
StatePublished - Mar 2016

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Engineering(all)
  • Physics and Astronomy(all)

Keywords

  • Critical point
  • Domain wall
  • Uniqueness

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