Domain wall creep and depinning: a scalar field model approach

Domain wall motion is at the heart of new magneto-electronic technologies and hence the need for a deeper understanding of domain wall (DW) dynamics in magnetic systems. In this context, numerical simulations using simple models can capture the main ingredients responsible for the complex observed DW behavior. We present a scalar-field model for the magnetization dynamics of quasi-two-dimensional systems with a perpendicular easy axis of magnetization which allows a direct comparison with typical experimental protocols, used in polar magneto-optical Kerr effect microscopy experiments. We show that the thermally activated creep and depinning regimes of DW motion can be reached, and the effect of different quenched disorder implementations can be assessed with the model. Moreover, our model has material-dependent tunable parameters and allows to reproduce experimental velocity-field curves. In particular, we show how the structural disorder should be modeled to reproduce Pt/Co/Pt velocity-field curves in a broad range of temperatures (ranging from 4K to room temperature). We also use this model to make a connection with DW with defects such as bubbles and overhangs. We examine in particular observables such as the two-dimensional structure factor both numerically and analytically.