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- Title
Onset of pattern formation in thin ferromagnetic films with perpendicular anisotropy.
- Authors
Brietzke, Birger; Knüpfer, Hans
- Abstract
We consider the onset of pattern formation in an ultrathin ferromagnetic film of the form Ω t : = Ω × [ 0 , t ] for Ω ⋐ R 2 with preferred perpendicular magnetization direction. The relative micromagnetic energy is given by E [ M ] = ∫ Ω t d 2 | ∇ M | 2 + Q ∫ Ω t (M 1 2 + M 2 2) + ∫ R 3 | H (M) | 2 - ∫ R 3 | H (e 3 χ Ω t) | 2 , describing the energy difference for a given magnetization M : R 3 → R 3 with | M | = χ Ω t and the uniform magnetization e 3 χ Ω t . For t ≪ d , we derive the scaling of the minimal energy and a BV-bound in the critical regime, where the base area of the film has size of order | Ω | 1 2 ∼ (Q - 1) - 1 2 d e 2 π d t Q - 1 . We furthermore investigate the onset of non-trivial pattern formation in the critical regime depending on the size of the rescaled film.
- Subjects
PERPENDICULAR magnetic anisotropy; THIN films; ANISOTROPY; THRESHOLD energy; MAGNETIZATION
- Publication
Calculus of Variations & Partial Differential Equations, 2023, Vol 62, Issue 4, p1
- ISSN
0944-2669
- Publication type
Article
- DOI
10.1007/s00526-023-02459-w