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

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Title: Γ-Limit for Two-Dimensional Charged Magnetic Zigzag Domain Walls.
Authors: Knüpfer, Hans1 (AUTHOR) hans.knuepfer@math.uni-heidelberg.de, Shi, Wenhui2 (AUTHOR)
Source: Archive for Rational Mechanics & Analysis. Mar2021, Vol. 239 Issue 3, p1875-1923. 49p.
Subjects: Magnetic domain walls, Domain walls (String models), Thin films, Magnetization
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 ∈ S 1 is given by E ε [ m ] = ε ‖ ∇ m ‖ L 2 2 + 1 ε ‖ m · e 2 ‖ L 2 2 + π λ 2 | ln ε | ‖ ∇ · (m - M) ‖ H ˙ - 1 2 2 , 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. [ABSTRACT FROM AUTHOR]
Copyright of Archive for Rational Mechanics & Analysis is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Γ-Limit for Two-Dimensional Charged Magnetic Zigzag Domain Walls.
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  Data: <searchLink fieldCode="JN" term="%22Archive+for+Rational+Mechanics+%26+Analysis%22">Archive for Rational Mechanics & Analysis</searchLink>. Mar2021, Vol. 239 Issue 3, p1875-1923. 49p.
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  Group: Ab
  Data: 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 ∈ S 1 is given by E ε [ m ] = ε ‖ ∇ m ‖ L 2 2 + 1 ε ‖ m · e 2 ‖ L 2 2 + π λ 2 | ln ε | ‖ ∇ · (m - M) ‖ H ˙ - 1 2 2 , 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. [ABSTRACT FROM AUTHOR]
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  Label:
  Group: Ab
  Data: <i>Copyright of Archive for Rational Mechanics & Analysis is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Text: English
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        Type: general
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