Curved domain walls in the ferromagnetic nanostructures with Rashba and nonlinear dissipative effects

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This work reveals an analytical investigation of the curved domain wall motion in ferromagnetic nanostructures in the framework of the extended Landau-Lifshitz-Gilbert equation. To be precise, the study delineates the description of curved domain wall motion in the steady-state dynamic regime for metallic and semiconductor ferromagnets. The study is done under the simultaneous action of the Rashba field and nonlinear dissipative effects described via the viscous-dry friction mechanism. By means of reductive perturbation technique and realistic assumption on the considered parameters, we establish an analytical expression of the steady domain wall velocity that depends on mean curvature of domain wall surfaces, nonlinear dissipation coefficients, Rashba parameter, external magnetic field, and spin-polarized electric current. In particular, it is observed that the domain wall velocity, mobility, threshold, and Walker breakdown can be manipulated by the combined mechanism of the Rashba field and nonlinear dissipation coefficients. Finally, the obtained analytical results are illustrated numerically for the curved domain walls through constant-curvature surfaces under-considered scenarios. The results presented herein are in qualitatively good agreement with the recent observations.