The Concertina Pattern: A Bifurcation in Ferromagnetic Thin Films

Cantero-Álvarez, Rubén; Otto, Félix; Steiner, Jutta

doi:10.1007/s00332-006-0805-y

Cited by 10 publications

(24 citation statements)

References 12 publications

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“…In [4], the type of bifurcation in the oscillatory buckling regime was investigated. The goal was to find local minimizers near m ≡ (1, 0, 0) for h ext > h crit which are of concertina type.…”

Section: Previous Resultsmentioning

confidence: 99%

“…The numerical simulations presented in [4], where the magnetization was restricted to be w * -periodic, i.e. L = w * , show:…”

Section: Previous Resultsmentioning

confidence: 99%

“…In order to get a better understanding of the experimentally observed coarsening and to determine the dependence of the optimal period w opt of the concertina on the external field w optĥ * ext w * ĥ ext h ext , let us now present some new numerical results based on the finite difference discretization of the energy introduced in [4]. For details we refer to Appendix A.…”

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%

“…The numerical simulations presented in [4], where the magnetization was restricted to be w * -periodic, i.e. L = w * , show:…”

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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“…It is even not obvious whether minimizers of the reduced energy functional exist at all. However, one can show that the reduced energy is coercive for all values of the external fieldĥ ext , see Theorem 4 in [CÁOS07,p.236]. This in particular implies that there always exists a global minimizer of the reduced energy -which corresponds to a local minimizer of the original energy (1), see Theorem 5 in [CÁOS07, p.237] -in particular for fields larger than the critical field.…”

Section: Bifurcationmentioning

confidence: 99%

Formation and coarsening of the concertina magnetization pattern in elongated thin-film elements

et al. 2012

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The concertina is a magnetization pattern in elongated thin-film elements of a soft material. It is a ubiquitous domain pattern that occurs in the process of magnetization reversal in direction of the long axis of the small element.Van den Berg argued that this pattern grows out of the flux closure domains as the external field is reduced. Based on experimental observations and theory, we argue that in sufficiently elongated thin-film elements, the concertina pattern rather bifurcates from an oscillatory buckling mode.Using a reduced model derived by asymptotic analysis and investigated by numerical simulation, we quantitatively predict the average period of the concertina pattern and qualitatively predict its hysteresis. In particular, we argue that the experimentally observed coarsening of the concertina pattern is due to secondary bifurcations related to an Eckhaus instability.We also link the concertina pattern to the magnetization ripple and discuss the effect of a weak (crystalline or induced) anisotropy.

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Magnetic Domains in Thin Ferromagnetic Films with Strong Perpendicular Anisotropy

Knüpfer

Muratov

Nolte

2018

Arch Rational Mech Anal

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We investigate the scaling of the ground state energy and optimal domain patterns in thin ferromagnetic films with strong uniaxial anisotropy and the easy axis perpendicular to the film plane. Starting from the full three-dimensional micromagnetic model, we identify the critical scaling where the transition from single domain to multidomain ground states such as bubble or maze patterns occurs. Furthermore, we analyze the asymptotic behavior of the energy in two regimes separated by a transition. In the single domain regime, the energy Γ-converges towards a much simpler two-dimensional and local model. In the second regime, we derive the scaling of the minimal energy and deduce a scaling law for the typical domain size.

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The Concertina Pattern: A Bifurcation in Ferromagnetic Thin Films

Cited by 10 publications

References 12 publications

The concertina pattern

The concertina pattern

Formation and coarsening of the concertina magnetization pattern in elongated thin-film elements

Magnetic Domains in Thin Ferromagnetic Films with Strong Perpendicular Anisotropy

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