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. |
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| 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] |
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| Database: | Engineering Source |
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| 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] |
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| ISSN: | 00039527 |
| DOI: | 10.1007/s00205-021-01606-x |
