Critical Fields in Ferromagnetic Thin Films: Identification of Four Regimes

Cantero-Álvarez, Rubén; Otto, Félix

doi:10.1007/s00332-004-0683-0

Cited by 10 publications

(9 citation statements)

References 16 publications

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“…In [2], an idealized sample geometry of width and of thickness t with t was considered. This sample geometry is idealized in the sense that instead of a finite extent in x 1 -direction, we impose an (artificial) periodicity L, i.e.…”

Section: Previous Resultsmentioning

confidence: 99%

“…Hence in [2] a linear stability analysis of the saturated state m ≡ (1, 0, 0) was carried out. Since the Hessian of E is not explicitly diagonalizable, the analysis is not obvious and several Ansätze for unstable modes, i.e.…”

Section: Previous Resultsmentioning

confidence: 99%

“…In [2], it was proven that there are exactly four qualitatively different regimes depending on the non-dimensional parameters td −1 and d −1 . In the regime d 2 −1 t (d ) 1/2 the unstable mode is in-plane and does not depend on the thickness direction, i.e.…”

Section: Previous Resultsmentioning

confidence: 99%

“…The states observed in a quasi-static experiment are related to (local) minima of some suitable energy. The analysis of the concertina pattern, which was started in [2] and was pursued in [4], is based on the 3-d micromagnetic energy which we introduce now. For a sample Ω ⊂ R 3 and a magnetization m : Ω → R 3 the energy is given by…”

Section: Micromagnetic Energymentioning

confidence: 99%

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The concertina pattern

Otto

Steiner

2010

Calc. Var.

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This is a continuation of a series of papers on the concertina pattern. The concertina pattern is a ubiquitous metastable, nearly periodic magnetization pattern in elongated thin film elements. In previous papers, a reduced variational model for this pattern was rigorously derived from 3-d micromagnetics. Numerical simulations of the reduced model reproduce the concertina pattern and show that its optimal period w opt is an increasing function of the applied external field h ext . The latter is an explanation of the experimentally observed coarsening. Domain theory, which can be heuristically derived from the reduced model, predicts and quantifies this dependence of w opt on h ext . In this paper, we rigorously extract these heuristic observations of domain theory directly from the reduced model. The main ingredient of the analysis is a new type of estimate on solutions of a perturbed Burgers equation.

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Section: Previous Resultsmentioning

confidence: 99%

Section: Previous Resultsmentioning

confidence: 99%

Section: Previous Resultsmentioning

confidence: 99%

Section: Micromagnetic Energymentioning

confidence: 99%

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The concertina pattern

Otto

Steiner

2010

Calc. Var.

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“…So hat er in seinen frühen Arbeiten, inspiriert durch seinen akademischen Lehrer Stephan Luckhaus, einen neuen Zugang zu einer Vielzahl dissipativer Evolutionsgleichungen entwickelt, indem er sie als Gradientenfluss bezüglich einer geeigneten unendlichdimensionalen Riemannschen Metrik auffasst, die eng mit der Physik des zugrundeliegenden Problems verbunden ist (häufig ist dies die Wassersteinmetrik) [11,15] Ziehharmonikamuster, das bei Reduktion des magnetischen Feldes nach der Sättigung auftritt [2]. Sie konnten zeigen, dass es neben den drei in der bisherigen physikalischen Literatur diskutierten Instabilitä-ten eine vierte gibt (und die Liste damit vollständig ist), und eine Beziehung für die Größe der Struktur ableiten.…”

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