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Analytical multi-domain solutions to the dynamical (Landau-Lifshitz-Gilbert) equation of a one-dimensional ferromagnet including an external magnetic field and spin-polarized electric current are found using the Hirota bilinearization method. A standard approach to solve the Landau-Lifshitz equation (without the Gilbert term) is modified in order to treat the dissipative dynamics. I establish the relations between the spin interaction parameters (the constants of exchange, anisotropy, dissipation, external-field intensity, and electric-current intensity) and the domain-wall parameters (width and velocity) and compare them to the results of the Walker approximation and micromagnetic simulations. The domain-wall motion driven by a longitudinal external field is analyzed with especial relevance to the field-induced collision of two doma...
Multi-domain solutions to the time-dependent Ginzburg-Landau equation in presence of an external field are analyzed using the Hirota bilinearization method. Domain-wall collisions are studied in detail considering different regimes of the critical parameter. I show the dynamics of the Ising and Bloch domain walls of the Ginzburg-Landau equation in the bistable regime to be similar to that of the Landau-Lifshitz domain walls. Domain-wall reflections lead to the appearance of bubble and pattern structures. Above the Bloch-Ising transition point, spatial structures are determined by the collisions of fronts propagating into an unstable state. Mutual annihilation of such fronts is described.
Interactions of domain walls (DWs) are analyzed with relevance to formation of stationary bubbles (complexes of two DWs) and complexes of many domains in one dimensional systems. I investigate the domain structures in ferromagnets which are described with the Landau-Lifshitz equation as well as the domains in critical systems described with the Ginzburg-Landau equation. Supplementing previous author studies on the creation of hard bubbles [formed by one Bloch DW and one Neel (Ising) DW] in the presence of an external (magnetic) field, the soft bubbles consisting of two Bloch DWs or two Neel (Ising) DWs are studied in detail. The interactions of two DWs of the same kind are studied in the framework of a perturbation calculus.
Interaction of domain walls (DWs) in ferromagnetic stripes is studied with relevance to the formation of stable complexes of many domains. Two DW system is described with the Landau-Lifshitz-Gilbert equation including regimes of narrow and wide stripes which correspond the presence of transverse and vortex DWs. The DWs of both kinds are characterized with their chiralities (the direction of the magnetization rotation in the stripe plane) and polarities (the magnetization orientation in the center of a vortex and/or halfvortices), hence, their interactions are analyzed with dependence on these properties. In particular, pairs of the DWs of opposite or like both chiralities and polarities are investigated as well as pairs of opposite (like) chiralities and of like (opposite) polarities. Conditions of the creation of stationary magnetic...
Two effects of oscillatory transformations of vortex textures in flat nanomagnets due to the application of an external field or a spin-polarized electric current are analytically described with relevance to soft-magnetic structures of submicrometer sizes (whose thickness is significantly bigger than the magnetostatic exchange length). These are changes of a domain wall (DW) structure in a long magnetic stripe (oscillations between a transverse DW, a vortex DW, and an antivortex DW) and periodic vortex-core reversals in a circular magnetic dot which are accompanied by oscillatory displacements of the vortex from the dot center. In nanostructures of smaller thicknesses (comparable to the exchange length), where nonlocal magnetostatic effects are very strong because of fast spatial variation of the magnetization, similar phenomena have...
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