Ginzburg–Landau Vortices Driven by the Landau–Lifshitz–Gilbert Equation

Kurzke, Matthias; Melcher, Christof; Moser, Roger; Spirn, Daniel

doi:10.1007/s00205-010-0356-0

Cited by 26 publications

(37 citation statements)

References 42 publications

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“…From an analytical perspective, the stabilization of magnetic vortices is essentially due to curling boundary conditions induced by stray-field interaction (e.g. [15]) rather than intrinsic effects as in the case of skyrmions. Our goal is to investigate the range of existence of isolated skyrmions emerging as energy minimizers in a simplified ferromagnetic model in the plane, including DM and Zeeman interaction.…”

Section: Introduction and Statement Of The Main Resultsmentioning

confidence: 99%

Chiral skyrmions in the plane

Melcher

2014

Proc. R. Soc. A.

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127

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Magnets without inversion symmetry are a prime example of a solid-state system featuring topological solitons on the nanoscale, and a promising candidate for novel spintronic applications. Magnetic chiral skyrmions are localized vortex-like structures, which are stabilized by antisymmetric exchange interaction, the so-called Dzyaloshinskii-Moriya interaction. In continuum theories, the corresponding energy contribution is, in contrast to the classical Skyrme mechanism from nuclear physics, of linear gradient dependence and breaks the chiral symmetry. In the simplest possible case of a ferromagnetic energy in the plane, including symmetric and antisymmetric exchange and Zeeman interaction, we show that the least energy in a class of fields with unit topological charge is attained provided the Zeeman field is sufficiently large.

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Section: Introduction and Statement Of The Main Resultsmentioning

confidence: 99%

Chiral skyrmions in the plane

Melcher

2014

Proc. R. Soc. A.

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127

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“…magnetic vortices, is concerned. Recent results show that in the presence of strong potentials of Ginzburg-Landau type, conventional energy bounds can be bypassed by certain well-preparedness assumptions on the initial data that prevent the formation of (extra) bubbles, see [21,20].…”

Section: Introduction and Resultsmentioning

confidence: 99%

Global solvability of the Cauchy problem for the Landau-Lifshitz-Gilbert equation in higher dimensions

Melcher¹

2012

Indiana Univ. Math. J.

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We prove existence, uniqueness and asymptotics of global smooth solutions for the Landau-Lifshitz-Gilbert equation in dimension n ≥ 3, valid under a smallness condition of initial gradients in the L n norm. The argument is based on the method of moving frames that produces a covariant complex Ginzburg-Landau equation, and a priori estimates that we obtain by the method of weighted-in-time norms as introduced by Fujita and Kato.

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“…Moreover in stereographic coordinates (11) ∇m · (m × ∂ t m) = −∇m · λ −2 ∆m + κ(m · ν)ν and taking the curl (∇×) we obtain the conservation law [16] (20)…”

Section: Notation and Preliminariesmentioning

confidence: 99%

“…In fact, J = −∇ x ×x comes about by taking into account (16), and the corresponding term is dropping out by skew-symmetry. In the last step we used ∂ν ∂χ =ê 3 × ν.…”

Section: Notation and Preliminariesmentioning

confidence: 99%

Curvature-stabilized skyrmions with angular momentum

Melcher

Sakellaris

2019

Lett Math Phys

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We examine skyrmionic field configurations on a spherical ferromagnet with large normal anisotropy. Exploiting variational concepts of angular momentum we find a new family of localized solutions to the Landau-Lifshitz equation that are topologically distinct from the ground state and not equivariant. Significantly, we observe an emergent spin-orbit coupling on the level of magnetization dynamics in a simple system without individual rotational invariance in spin and coordinate space.

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Ginzburg–Landau Vortices Driven by the Landau–Lifshitz–Gilbert Equation

Cited by 26 publications

References 42 publications

Chiral skyrmions in the plane

Chiral skyrmions in the plane

Global solvability of the Cauchy problem for the Landau-Lifshitz-Gilbert equation in higher dimensions

Curvature-stabilized skyrmions with angular momentum

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