Dynamics of transverse domain wall in bilayer ferromagnetic-heavy metal nanostructures: Interplay of spin-orbit torque, dry-friction dissipation, and the interfacial Dzyaloshinskii-Moriya interaction

This work deals with the static and dynamic characteristics of the transverse Bloch domain wall within a bilayer nanostructure comprising a ferromagnetic layer and a non-magnetic heavy metal layer. We examine the spatiotemporal evolution of magnetization within the ferromagnetic layer using the one-dimensional Extended Landau-Lifshitz-Gilbert equation under the combined impact of axial and transverse magnetic fields, spin-polarized electric currents, interfacial Dzyaloshinskii-Moriya interaction, nonlinear dry-friction damping, Rashba, and Spin-Hall effect. To characterize the domain wall motion, we first compute the magnetization profile in the two distant domains and analyze the static profile solely influenced by the external transverse magnetic field. We present a new Walker's type trial function and, applying a small angle approximation approach, establish an analytical expression of the dynamical quantities: domain wall velocity, displacement, moving domain wall profile, and excitation angles. Finally, the results are illustrated via numerical investigation.