Oscillatory Buckling Mode in Thin-Film Nucleation

Cantero-Álvarez, Rubén; Otto, Félix

doi:10.1007/s00332-004-0684-z

Cited by 9 publications

(6 citation statements)

References 2 publications

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“…[3]. The experimentally observed period of the concertina pattern agrees with this theoretically predicted period of the unstable mode up to a factor of about 2 over a wide range of sample sizes t and .…”

Section: Previous Resultssupporting

confidence: 76%

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 Resultssupporting

confidence: 76%

The concertina pattern

Otto

Steiner

2010

Calc. Var.

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“…. This type of scaling of the stray field energy appears in many studies of thin ferromagnetic films [1,2,3,4,5,7,8,9,10,11,16,18] where new mathematical tools are developed in order to understand the structure of domain walls such as Néel walls, concertina pattern, Landau state etc. (for more details, see the review paper [6]).…”

Section: Derivation Of the Modelmentioning

confidence: 99%

“…white noise. Brownian motion is known to be slightly worse than C 1 2 and thus white noise slightly worse than C − 1 2 . Stochastic analysis has found two ways out of this border-line singular situation: Ito calculus and more recently Lyons' rough path theory (see [15]).…”

Section: Introductionmentioning

confidence: 99%

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The magnetization ripple: A nonlocal stochastic PDE perspective

Ignat

Otto

2019

Journal de Mathématiques Pures et Appliquées

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The magnetization ripple is a microstructure formed by the magnetization in a thinfilm ferromagnet. It is triggered by the random orientation of the grains in the polycrystalline material. In an approximation of the micromagnetic model, which is sketched in this paper, this leads to a nonlocal (and strongly anisotropic) elliptic equation in two dimensions with white noise as a right hand side. However, like in singular Stochastic PDE, this right hand side is too rough for the non-linearity in the equation. In order to develop a small-date well-posedness theory, we take inspiration from the recent roughpath approach to singular SPDE. To this aim, we develop a Schauder theory for the non-standard symbol |k 1 | 3 + k 2 2 .

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“…In [14] the author studies a similar problem for thin films and derives Γ-convergence result for the energies. In a series of papers the authors study the magnetization reversal process in thin films, identifying four different scaling regimes for the critical value of the applied external field, see [7,8,9,23,27]. In nanowires, it has been observed that there is a distinctive crossover between two different modes, which occurs at a critical diameter of the wire and it was suggested that the magnetization switching process can be understood by analyzing the micromagnetics energy minimization problem for different diameters of the cross section.…”

Section: The Transverse Wallmentioning

confidence: 99%

On the existence and stability of minimizers in ferromagnetic nanowires

Harutyunyan

2016

Journal of Mathematical Analysis and Applications

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We study static 180 degree domain walls in infinite magnetic wires with bounded, C 1 and rotationally symmetric cross sections. We prove an existence of global minimizers for the energy of micromagnetics for any bounded C 1 cross sections. Under some asymmetry of cross sections we prove a stability result for the minimizers, namely, we show that vectors of micromagnetics having an energy close to the minimal one, must be H 1 close to the actual minimizer, which is itself close to the minimizer of the limit energy up to a rotation and a translation.

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Oscillatory Buckling Mode in Thin-Film Nucleation

Cited by 9 publications

References 2 publications

The concertina pattern

The concertina pattern

The magnetization ripple: A nonlocal stochastic PDE perspective

On the existence and stability of minimizers in ferromagnetic nanowires

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