Curved domain walls dynamics driven by magnetic field and electric current in hard ferromagnets

The propagation of curved domain walls in hard ferromagnetic materials is studied by applying a reductive perturbation method to the generalized Landau–Lifshitz–Gilbert equation. The extended model herein considered explicitly takes into account the effects of a spin-polarized current as well as those arising from a nonlinear dissipation.Under the assumption of steady regime of propagation, the domain wall velocity is derived as a function of the domain wall curvature, the nonlinear damping coefficient, the magnetic field and the electric current. Threshold and Walker-like breakdown conditions for the external sources are also determined. The analytical results are evaluated numerically for different domain wall surfaces (planes, cylinders and spheres) and their physical implications are discussed.