Γ -Limit for Two-Dimensional Charged Magnetic Zigzag Domain Walls

Hans Knüpfer, Wenhui Shi

Research output: Contribution to journalArticleResearchpeer-review

2 Citations (Scopus)

Abstract

Charged domain walls are a type of domain wall in thin ferromagnetic films which appear due to global topological constraints. The non-dimensionalized micromagnetic energy for a uniaxial thin ferromagnetic film with in-plane magnetization m∈ S1 is given by Eε[m]=ε‖∇m‖L22+1ε‖m·e2‖L22+πλ2|lnε|‖∇·(m-M)‖H˙-122,where M is an arbitrary fixed background field to ensure global neutrality of magnetic charges. We consider a material in the form a thin strip and enforce a charged domain wall by suitable boundary conditions on m. In the limit ε→ 0 and for fixed λ> 0 , corresponding to the macroscopic limit, we show that the energy Γ -converges to a limit energy where jump discontinuities of the magnetization are penalized anisotropically. In particular, in the subcritical regime λ≦ 1 , one-dimensional charged domain walls are favorable, in the supercritical regime λ> 1 , the limit model allows for zigzaging two-dimensional domain walls.

Original languageEnglish
Pages (from-to)1875-1923
Number of pages49
JournalArchive for Rational Mechanics and Analysis
Volume239
DOIs
Publication statusPublished - 4 Feb 2021

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