$$\Gamma $$-Limit for Two-Dimensional Charged Magnetic Zigzag Domain Walls

Knüpfer, Hans; Shi, Wenhui

doi:10.1007/s00205-021-01606-x

Cited by 4 publications

(1 citation statement)

References 38 publications

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“…5 Zig-zag charged domain walls similar to those considered here are known to appear in magnetic thin films on scales of micrometers and larger. [33][34][35][36] Some of the triangles show features similar smoke-like features as those described here. The compensating electric charge used in the electrostatic considerations performed here is analogous to the notion of the magnetic charge due to orientation of the magnetization out of the plane of the film.…”

Section: E Experimental Contextsupporting

confidence: 72%

Zig-zag charged domain walls in ferroelectric PbTiO$_3$

Márton¹,

Gonçalves²,

Paściak³

et al. 2022

Preprint

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We report a theoretical investigation of a charged 180 • domain wall in ferroelectric PbTiO3, compensated by randomly distributed immobile charge defects. For this we utilize atomistic shellmodel simulations and continuous phase-field simulations in the framework of the Ginzburg-Landau-Devonshire model. We predict that domain walls form a zig-zag pattern and we discuss its properties in a broad interval of compensation-region widths, ranging from a couple to over a hundred nanometers.

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Section: E Experimental Contextsupporting

confidence: 72%

Zig-zag charged domain walls in ferroelectric PbTiO$_3$

Márton¹,

Gonçalves²,

Paściak³

et al. 2022

Preprint

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Transverse Domain Walls in Thin Ferromagnetic Strips

Morini

Muratov

Novaga

et al. 2023

Arch Rational Mech Anal

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We present a characterization of the domain wall solutions arising as minimizers of an energy functional obtained in a suitable asymptotic regime of the micromagnetics for infinitely long thin film ferromagnetic strips in which the magnetization is forced to lie in the film plane. For the considered energy, we provide the existence, uniqueness, monotonicity, and symmetry of the magnetization profiles in the form of 180 $$^\circ $$ ∘ and 360 $$^\circ $$ ∘ walls. We also demonstrate how this energy arises as a $$\Gamma $$ Γ -limit of the reduced two-dimensional thin film micromagnetic energy that captures the non-local effects associated with the stray field, and characterize its respective energy minimizers.

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The mathematics of thin structures

Babadjian¹,

Fratta

Fonseca

et al. 2022

Quart. Appl. Math.

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This article offers various mathematical contributions to the behavior of thin films. The common thread is to view thin film behavior as the variational limit of a three-dimensional domain with a related behavior when the thickness of that domain vanishes. After a short review in Section 1 of the various regimes that can arise when such an asymptotic process is performed in the classical elastic case, giving rise to various well-known models in plate theory (membrane, bending, Von Karmann, etc…), the other sections address various extensions of those initial results. Section 2 adds brittleness and delamination and investigates the brittle membrane regime. Sections 4 and 5 focus on micromagnetics, rather than elasticity, this once again in the membrane regime and discuss magnetic skyrmions and domain walls, respectively. Finally, Section 3 revisits the classical setting in a non-Euclidean setting induced by the presence of a pre-strain in the model.

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$$\Gamma $$-Limit for Two-Dimensional Charged Magnetic Zigzag Domain Walls

Cited by 4 publications

References 38 publications

Zig-zag charged domain walls in ferroelectric PbTiO$_3$

Zig-zag charged domain walls in ferroelectric PbTiO$_3$

Transverse Domain Walls in Thin Ferromagnetic Strips

The mathematics of thin structures

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