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Register a new userAnalytic form of head-to-head domain walls in thin ferromagnetic cylinders
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The one-dimensional problem of a static head-to-head domain wall structure in a thin soft-magnetic nanowire with circular cross-section is treated within the framework of micromagnetic theory. A radius-dependent analytic form of the domain wall profile is derived by decomposing the magnetostatic energy into a monopolar and a dipolar term. We present a model in which the dipolar term of the magnetostatic energy resulting from the transverse magnetization in the center of the domain wall is calculated with Osborns formulas for homogeneously magnetized ellipsoids [Phys. Rev. 67, 351 (1945)]. The analytic results agree almost perfectly with simulation data as long as the wire diameter is sufficiently small to prevent inhomogeneities of the magnetization along the cross-section. Owing to the recently demonstrated negligible Doring mass of these walls, our results should also apply to the dynamic case, where domain walls are driven by spin-transfer toque effects and/or an axial magnetic field.
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So far magnetic domain walls in one-dimensional structures have been described theoretically only in the cases of flat strips, or cylindrical structures with a compact cross-section, either square or disk. Here we describe an extended phase diagram unifying the two pictures, extensively covering the (width,thickness) space. It is derived on the basis of symmetry and phase-transition arguments, and micromagnetic simulations. A simple classification of all domain walls in two varieties is proposed on the basis of their topology: either with a combined transverse/vortex character, or of the Bloch-point type. The exact arrangement of magnetization within each variety results mostly from the need to decrease dipolar energy, giving rise to asymmetric and curling structures. Numerical evaluators are introduced to quantify curling, and scaling laws are derived analytically for some of the iso-energy lines of the phase diagram.
We present a quantitative investigation of magnetic domain wall pinning in thin magnets with perpendicular anisotropy. A self-consistent description exploiting the universal features of the depinning and thermally activated sub-threshold creep regimes observed in the field driven domain wall velocity, is used to determine the effective pinning parameters controlling the domain wall dynamics: the effective height of pinning barriers, the depinning threshold, and the velocity at depinning. Within this framework, the analysis of results published in the literature allows for a quantitative comparison of pinning properties for a set of magnetic materials in a wide temperature range. On the basis of scaling arguments, the microscopic parameters controlling the pinning: the correlation length of pinning, the collectively pinned domain wall length (Larkin length) and the strength of pinning disorder, are estimated from the effective pinning and the micromagnetic parameters. The analysis of thermal effects reveals a crossover between different pinning length scales and strengths at low reduced temperature.
We study from first-principles the structural and electronic properties of head-to-head (HH) and tail-to-tail (TT) 180$^circ$ domain walls in isolated free-standing PbTiO$_{3}$ slabs. For sufficiently thick domains ($n$ = 16 unit cells of PbTiO$_{3}$), a transfer of charge from the free surfaces to the domain walls to form localized electron (in the HH) and hole (in the TT) gases in order to screen the bound polarization charges is observed. The electrostatic driving force behind this electronic reconstruction is clearly visible from the perfect match between the smoothed free charge densities and the bound charge distribution, computed from a finite difference of the polarization profile obtained after the relaxation of the lattice degrees of freedom. The domain wall widths, of around six unit cells, are larger than in the conventional 180$^circ$ neutral configurations. Since no oxygen vacancies, defects or dopant atoms are introduced in our simulations, all the previous physical quantities are the intrinsic limits of the system. Our results support the existence of an extra source of charge at the domains walls to explain the enhancement of the conductivity observed in some domains walls of prototypical, insulating in bulk, perovskite oxides.
We report a comparative study of magnetic field driven domain wall motion in thin films made of different magnetic materials for a wide range of field and temperature. The full thermally activated creep motion, observed below the depinning threshold, is shown to be described by a unique universal energy barrier function. Our findings should be relevant for other systems whose dynamics can be modeled by elastic interfaces moving on disordered energy landscapes.
We present a characterization of the domain wall solutions arising as minimizers of an energy functional obtained in a suitable asymptotic regime of 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 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 $Gamma$-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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