Domain wall mobility in nanowires: Transverse versus vortex walls

TLDR

The study numerically investigates domain‑wall motion in ferromagnetic cylindrical nanowires by solving the Landau–Lifshitz–Gilbert equation for a classical spin model. The simulations incorporate exchange, crystalline anisotropy, dipole–dipole interactions, and a driving magnetic field within the LLG framework. For diameters below the exchange length the transverse wall dominates and its mobility follows the one‑dimensional Slonczewski result, while larger diameters trigger a vortex wall that markedly increases mobility, following the Walker formula and scaling as 1/α² for small damping.

Abstract

The motion of domain walls in ferromagnetic, cylindrical nanowires is investigated numerically by solving the Landau-Lifshitz-Gilbert equation for a classical spin model in which energy contributions from exchange, crystalline anisotropy, dipole-dipole interaction, and a driving magnetic field are considered. Depending on the diameter, either transverse domain walls or vortex walls are found. The transverse domain wall is observed for diameters smaller than the exchange length of the given material. Here, the system behaves effectively one-dimensional and the domain wall mobility agrees with a result derived for a one-dimensional wall by Slonczewski. For low damping the domain wall mobility decreases with decreasing damping constant. With increasing diameter, a crossover to a vortex wall sets in which enhances the domain wall mobility drastically. For a vortex wall the domain wall mobility is described by the Walker-formula, with a domain wall width depending on the diameter of the wire. The main difference is the dependence on damping: for a vortex wall the domain wall mobility can be drastically increased for small values of the damping constant up to a factor of $1/\alpha^2$.