A theoretical study on the statics and dynamics of magnetic domain walls and skyrmions
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This thesis conducts a comprehensive theoretical study and numerical simulations on the statics and dynamics of magnetic domain walls (DWs) and skyrmions, two prominent examples of topological solitons in magnetic materials. For DWs, the focus is on their motion in ferrimagnetic nanowires, driven by external magnetic fields or spin-polarized currents. The research addresses challenges like the Walker breakdown, which limits DW speed. A significant finding is that high-speed DW motion occurs near the angular momentum compensation point (AMCP). The study uses energy conservation principles to explain DW dynamics, proving that static DWs cannot exist under uniform external fields and deriving a velocity formula consistent with experimental results. In the skyrmion section, the thesis inv...[ Read more ]Keywords:
Skyrmion
Statics
Dynamics
Domain wall (magnetism)
We study classical solutions of the vector O(3) sigma model in (2 + 1) dimensions, spontaneously broken to . The model possesses Skyrmion-type solutions as well as stable domain walls which connect different vacua. We show that different types of waves can propagate on the wall, including waves carrying a topological charge. The domain wall can also absorb Skyrmions and, under appropriate initial conditions, it is possible to emit a Skyrmion from the wall.
Skyrmion
Domain wall (magnetism)
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Recent work on magnetic phase transition in nanoscale systems indicates that new physical phenomena, in particular, the Bloch wall width narrowing, arise as a consequence of geometrical confinement of magnetization and leads to the introduction of geometrically constrained domain wall models. In this paper, we present a systematic mathematical analysis on the existence of the solutions of the basic governing equations in such domain wall models. We show that, when the cross section of the geometric constriction is a simple step function, the solutions may be obtained by minimizing the domain wall energy over the constriction and solving the Bogomol’nyi equation outside the constriction. When the cross section and potential density are both even, we establish the existence of an odd domain wall solution realizing the phase transition process between two adjacent domain phases. When the cross section satisfies a certain integrability condition, we prove that a domain wall solution always exists which links two arbitrarily designated domain phases.
Domain wall (magnetism)
Fictitious domain method
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The pinning phenomena of the domain wall in the presence of exchange bias is studied analytically. The analytic solution of the domain wall spin configuration is presented. Unlike the traditional solution which is symmetric, our new solution could exhibit the asymmetry of the domain wall spin profile. Using the solution, the domain wall position, its width, its stability, and the depinning field are discussed analytically.
Domain wall (magnetism)
Position (finance)
Micromagnetics
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Domain wall skyrmions are skyrmions trapped inside a domain wall. We investigate domain wall skyrmions in chiral magnets using a fully analytic approach. Treating the Dzyaloshinskii-Moriya (DM) interaction perturbatively, we construct the low-energy effective theory of a magnetic domain wall in an $O(3)$ sigma model with the DM interaction and an easy-axis potential term, yielding a sine-Gordon model. We then construct domain wall skyrmions as sine-Gordon solitons along the domain wall. We also construct domain wall skyrmions on top of a pair of a domain wall and an anti-domain wall. One of characteristic feature of domain wall skyrmions is that both skyrmions and anti-skyrmions are equally stable inside the domain wall, unlike the bulk in which only one of them is stable.
Skyrmion
Domain wall (magnetism)
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We present a model for the dynamics of current-driven and field-driven domain-wall lines at nonzero temperature. We compute thermally averaged drift velocities from the Fokker-Planck equation that describes the nonzero-temperature dynamics of the domain wall. As special limits of this general description, we describe rigid domain walls as well as vortex domain walls. In these limits, we also determine depinning times of the domain wall from an extrinsic pinning potential. We compare our theory with previous theoretical and experimental works.
Domain wall (magnetism)
Dynamics
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Domain-wall skyrmions are skyrmions trapped inside a domain wall. We investigate domain-wall skyrmions in chiral magnets using a fully analytic approach. Treating the Dzyaloshinskii-Moriya (DM) interaction perturbatively, we construct the low-energy effective theory of a magnetic domain wall in an $O(3)$ sigma model with the DM interaction and an easy-axis potential term, yielding a sine-Gordon model. We then construct domain-wall skyrmions as sine-Gordon solitons along the domain wall. We also construct domain-wall skyrmions on top of a pair of a domain wall and an anti-domain wall. One characteristic feature of domain-wall skyrmions is that both skyrmions and antiskyrmions are equally stable inside the domain wall, unlike the bulk in which only one of them is stable.
Skyrmion
Domain wall (magnetism)
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We study classical solutions of a particular version of the modified Skyrme model in 3+1 dimensions. The model possesses Skyrmion solutions as well as stable domain walls that connect different vacua of the theory. We show that there is an attractive interaction between Skyrmions and domain walls. Thus Skyrmions can be captured by the domain walls. We show also that, when the mass term is of a special type, the model possesses bound states of Skyrmions and of the domain wall. They look similar to deformed two-dimensional Skyrmions captured by the wall. The field configurations of these solutions can be interpreted as having come from the evolution of the three-dimensional Skyrmions captured by the domain wall. For more conventional choices of the mass term in the model, the attraction between the Skyrmions and the wall leads to the capture of the Skyrmions which are then turned into topological waves which spread out on the wall. We have observed, numerically, such captures and the emission of the waves. We speculate that this observation may be useful in the explanation of the problem of baryogenesis and baryon-antibaryon asymmetry of the Universe.
Skyrmion
Domain wall (magnetism)
Baryon asymmetry
Baryon number
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Stresses and strains within domain walls are important for understanding the interaction of domain walls with point defects, and the surface structure of the domain walls. Unfortunately, attempts to determine these properties of the domain wall by diffraction or other methods fail because of the low resolution of the technique. We outline a method for estimating local stresses and strains within the domain wall using Landau theories of phase transitions based on elastic data. We apply this method to the materials V3Si, TeO2 (paratellurite), and SiO2 (quartz).
Domain wall (magnetism)
Strain (injury)
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We investigate domain wall excitations in a two-component Bose–Einstein condensate with two-body interactions and pair-transition effects. It is shown that domain wall excitations can be described exactly by kink and anti-kink excitations in each component. The domain wall solutions are given analytically, which exist with different conditions compared with the domain wall reported before. Bubble-droplet structure can be also obtained from the fundamental domain wall, and their interactions are investigated analytically. Especially, domain wall interactions demonstrate some striking particle transition dynamics. These striking transition effects make the domain wall admit quite different collision behavior, in contrast to the collision between solitons or other nonlinear waves. The collisions between kinks induce some phase shift, which makes the domain wall change greatly. Their collisions can be elastic or inelastic with proper combination of fundamental domain walls. These characters can be used to manipulate one domain wall by interacting with other ones.
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Component (thermodynamics)
Particle (ecology)
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Abstract We describe a group-theoretical procedure that enables one to find necessary conditions for the appearance of spontaneous magnetization in domain walls. We illustrate the derivation of wall symmetries on example of Cr2O3 and present a brief summary of a systematic analysis of domain walls in antiferromagnetic non-ferroelastic and magnetoelectric phases which shows that in more than 50% of possible domain walls a spontaneous magnetization may appear. Key Words: Non-ferroelastic domain structuresmagnetoelectric domain structuresantiferromagnetic domain structuresstructural domain wallsmagnetic domain wallssymmetry analysis of domain structures
Domain wall (magnetism)
Magnetoelectric effect
Ferroelasticity
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