Ginzburg-Landau micromagnetic model to study domain wall dynamics in thin ferromagnetic systems

Fully understanding domain wall motion in ferromagnetic systems is considered to be essential for the design of new magneto-electronic devices. Along with experiments, numerical simulations are therefore a key to gaining insight into the underlying mechanisms. However, simulating model systems at time and length scales comparable with those of experiments still represents a great challenge. Here, we present a simplified micromagnetic model --halfway between full micromagnetism and Ginzburg-Landau theory-- to study the dynamics of domain walls in quasi two-dimensional ferromagnetic systems with perpendicular magnetic anisotropy (PMA). Our approach relies on the local parametrization of the in-plane magnetization in terms of its out-of-plane component. We show that our model quantitatively reproduces previous experimental velocity-field data in the archetypal PMA Pt/Co/Pt ultra-thin films in the three dynamical regimes of domain wall motion (creep, depinning and flow). In addition, we present a statistical analysis of the domain wall width parameter, showing that our model can provide detailed nano-scale information while reaching length and time scales comparable to experiments.