Abstract: The influence of magnetic anisotropy, post-processing conditions, and defects on the domain wall (DW) dynamics of amorphous and nanocrystalline Fe-, Ni-, and Co-rich microwires with spontaneous and annealing-induced magnetic bistability has been thoroughly analyzed, with an emphasis placed on the influence of magnetoelastic, induced and magnetocrystalline anisotropies. Minimizing magnetoelastic anisotropy, either by the selection of a chemical composition with a low magnetostriction coefficient or by heat treatment, is an appropriate route for DW dynamics optimization in magnetic microwires. Stress-annealing allows further improvement of DW velocity and hence is a promising method for optimization of DW dynamics in magnetic microwires. The origin of current-driven DW propagation in annealing-induced magnetic bistability is attributed to magnetostatic interaction of outer domain shell with transverse magnetization orientation and inner axially magnetized core. The beneficial influence of the stress-annealing on DW dynamics has been explained considering that it allows increasing of the volume of outer domain shell with transverse magnetization orientation at the expense of decreasing the radius of inner axially magnetized core. Such transverse magnetic anisotropy can similarly aect the DW dynamics as the applied transverse magnetic field and hence is beneficial for DW dynamics optimization. Stress-annealing allows designing the magnetic anisotropy distribution more favorable for the DW dynamics improvement. Results on DW dynamics in various families of nanocrystalline microwires are provided. The role of saturation magnetization on DW mobility improvement is discussed. The DW shape, its correlation with the magnetic anisotropy constant and the microwire diameter, as well as manipulation of the DW shape by induced magnetic anisotropy are discussed. The engineering of DW propagation through local stress-annealing and DW collision is demonstrated.

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