Domain Wall Automotion by Cross Section Tailoring in Ferromagnetic Nanostripes

Curvilinear magnetism of nanostripes is a prospective playground both for fundamental research and numerous applications. By tailoring geometrical properties of the ferromagnetic stripes and wires there appear new possibilities to control its magnetic properties such as the dynamics of the domain walls. Deterministic fast motion of the domain walls is a key element in the constructions of ultra-fast, high-capacity, and non-volatile magnetic memory and logic devices. Here, we study theoretically the magnetic response of curved ferromagnetic nanostripes with varying cross section using a recently proposed effective model of curved biaxial stripe. We show that non zero gradient of stripe cross section results in the additional driving force for domain wall. The equations of motion of the domain wall are derived and analysed using the collective variable approach. We illustrate the influence of varying cross section by several specific geometries: a straight stripe with zero curvature and a circular arc with constant curvature. For these geometries, we derived (i) the asymptotic values of the domain wall velocity as a function of cross-section gradient, (ii) values of cross section-induced Walker threshold and curvature-induced corrections. All our analytical predictions are well-confirmed by the full scale micromagnetic simulations.