Onset of pattern formation in thin ferromagnetic films with perpendicular anisotropy
We consider the onset of pattern formation in an ultrathin ferromagnetic film of the form Ωt:=Ω×[0,t] for Ω⋐R2 with preferred perpendicular magnetization direction. The relative micromagnetic energy is given by E[M]=∫Ωtd2|∇M|2+Q∫Ωt(M21+M22)+∫R3|H(M)|2−∫R3|H(e3χΩt)|2, describing the energy difference...
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| Main Authors: | , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
06 April 2023
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| In: |
Calculus of variations and partial differential equations
Year: 2023, Volume: 62, Issue: 4, Pages: 1-22 |
| ISSN: | 1432-0835 |
| DOI: | 10.1007/s00526-023-02459-w |
| Online Access: | Verlag, kostenfrei, Volltext: https://doi.org/10.1007/s00526-023-02459-w
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| Author Notes: | Birger Brietzke, Hans Knüpfer |
MARC
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| 520 | |a We consider the onset of pattern formation in an ultrathin ferromagnetic film of the form Ωt:=Ω×[0,t] for Ω⋐R2 with preferred perpendicular magnetization direction. The relative micromagnetic energy is given by E[M]=∫Ωtd2|∇M|2+Q∫Ωt(M21+M22)+∫R3|H(M)|2−∫R3|H(e3χΩt)|2, describing the energy difference for a given magnetization M:R3→R3 with |M|=χΩt and the uniform magnetization e3χΩt. 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|12∼(Q−1)−12de2πdtQ−1√. We furthermore investigate the onset of non-trivial pattern formation in the critical regime depending on the size of the rescaled film. | ||
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