Domain wall pinning in a circular cross-section wire with modulated diameter

37 pages, 14 figures, overview chapterDomain wall propagation in cylindrical nanowires with modulations of diameter is a key phenomenon to design physics-oriented devices, or a disruptive three-dimensional magnetic memory. This chapter presents a combination of analytical modelling and micromagnetic simulations, with the aim to present a comprehensive panorama of the physics of pinning of domain walls at modulations, when moved under the stimulus of a magnetic field or a spin-polarized current. For the sake of considering simple physics, we consider diameters of a few tens of nanometers at most, and accordingly domain walls of transverse type. Modeling with suitable approximations provides simple scaling laws, while simulations are more accurate, refining the results and defining the range of validity of the models. While pinning increases with the relative change of diameter, a key feature is the much larger efficiency of pinning at an increase of diameter upon considering current rather than field, due to the drastic decrease of current density related to the increase of diameter