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...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article (Journal) Chapter/Article |
| Language: | English |
| Published: |
20 May 2022
|
| In: |
Arxiv
Year: 2022, Pages: 1-27 |
| DOI: | 10.48550/arXiv.2205.10061 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.48550/arXiv.2205.10061 Verlag, lizenzpflichtig, Volltext: http://arxiv.org/abs/2205.10061 
|
| Author Notes: | Birger Brietzke and Hans Knüpfer |
| Summary: | 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. |
|---|---|
| Item Description: | Gesehen am 14.10.2022 |
| Physical Description: | Online Resource |
| DOI: | 10.48550/arXiv.2205.10061 |