Depinning of domain walls in a notched ferromagnetic nanostrip: role of inertial and nonlinear damping effects

Abstract

Abstract In this work, we investigate theoretically the static and kinetic depinning field of a domain wall in a notched magnetic nanostrip under the generalized framework of the Landau–Lifshitz-Gilbert equation, which combines inertial and nonlinear viscous-dry friction damping effects. We assume a head-to-head transverse domain wall configuration and analyzed its motion subject to a time-varying external magnetic field. To deduce the equation ruling the spatio-temporal evoution of the magnetic domain wall, we adopt the Schryer and Walker trial function approach. The results show that static and kinetic depinning fields increase as the dry friction dissipation increases. Moreover, viscous dissipation exhibits a weak dependence on the kinetic depinning field and saturated domain wall velocity, while inertial damping due to the relaxation time of angular momentum significantly impacts the kinetic depinning field, depinning time, and breakdown velocity. Our numerical results are in good qualitative agreement with the recent observations reported in the literature.