Related papers: Stability of precessing domain walls in ferromagne…
We report the existence of a new regime for domain wall motion in uniaxial and near-uniaxial ferromagnetic nanowires, characterised by applied magnetic fields sufficiently strong that one of the domains becomes unstable. There appears a new…
We consider a ferromagnetic nanowire and we focus on an asymptotic regime where the Dzyaloshinskii-Moriya interaction is taken into account. First we prove a dimension reduction result via $\Gamma$-convergence that determines a limit…
The Landau--Lifshitz equation describes the behaviour of magnetic domains in ferromagnetic structures. Recently such structures have been found to be favourable for storing digital data. Stability of magnetic domains is important for this.…
We consider an infinite ferromagnetic nanowire, with an energy functional $E$ with easy-axis in the direction $e_1$ and a constant external magnetic field $H_{ext} = h_0 e_1$ along the same direction. The evolution of its magnetization is…
We study the dynamics of a domain wall under the influence of applied magnetic fields in a one-dimensional ferromagnetic nanowire, governed by the Landau--Lifshitz--Gilbert equation. Existence of travelling-wave solutions close to two known…
We consider a ferromagnetic nanowire, with an energy functional E with easy-axis in the direction $e_1$, and which takes into account the Dzyaloshinskii-Moriya interaction. We consider configurations of the magnetization which are…
Spin wave equations in the non-equilibrium precessing state of a ferromagnetic system are found. They show a spin-wave instability towards growing domains of stable magnetization. Precession of the uniform magnetization mode is described by…
We study the stability of travelling wall profiles for a one dimensional model of ferromagnetic nanowire submitted to an exterior magnetic field. We prove that these profiles are asymptotically stable modulo a translation-rotation for small…
We address the dynamics of magnetic domain walls in ferromagnetic nanowires under the influence of external time-dependent magnetic fields. We report a new exact spatiotemporal solution of the Landau-Lifshitz-Gilbert equation for the case…
This article is concerned with the dynamics of magnetic domain walls (DWs) in nanowires as solutions to the classical Landau-Lifschitz-Gilbert equation augmented by a typically non-variational Slonczewski term for spin-torque effects.…
A simplified model is introduced and analysed to show, that for the Landau-Lifshitz equation stable, steady state solutions of domain type exist in ferromagnetic systems, strongly driven by external transverse fields. These dynamic domain…
Bistable nanomagnets store a binary bit of information. Exchange coupled nanomagnets can increase the thermal stability at low dimensions. Here we show that the antiferromagnetically (AFM) coupled nanomagnets can be highly stable at low…
Motivated by the difference between the dynamics of magnetization textures in ferromagnets and antiferromagnets, the Landau-Lifshitz equation of motion is explored. A typical one-dimensional domain wall in a bulk ferromagnet with biaxial…
It was proved by Karch and Pilarzyc that Landau solutions are asymptotically stable under any $L^2$-perturbation. In our earlier work with L. Li, we have classified all $(-1)$-homogeneous axisymmetric no-swirl solutions of incompressible…
We give a survey on some recent results concerning the Landau-Lifshitz equation, a fundamental nonlinear PDE with a strong geometric content, describing the dynamics of the magnetization in ferromagnetic materials. We revisit the Cauchy…
We develop a systematic asymptotic description for domain wall motion in one-dimensional magnetic nanowires under the influence of small applied magnetic fields and currents and small material anisotropy. The magnetization dynamics, as…
We study the linear stability of entire radial solutions $u(re^{i\theta})=f(r)e^{i\theta}$, with positive increasing profile $f(r)$, to the anisotropic Ginzburg-Landau equation \[ -\Delta u -\delta (\partial_x+i\partial_y)^2\bar u…
In this article we study the problem of nonlinear Landau damping for the Vlasov-Poisson equations on the torus. As our main result we show that for perturbations initially of size $\epsilon>0$ and time intervals $(0,\epsilon^{-N})$ one…
In this paper we study, in dimension two, the stability of the solutions of some nonlinear elliptic equations with Neumann boundary conditions, under perturbations of the domains in the Hausdorff complementary topology.
The dynamics of magnetization near a stable equilibrium in ferromagnetic nanomagnets are examined within the Landau--Lifshitz--Gilbert (LLG) framework. For a small angle precession, the dependence of ferromagnetic resonance (FMR) frequency,…