Comparison between collective coordinate models for domain wall motion in PMA nanostrips in the presence of the Dzyaloshinskii-Moriya interaction

Abstract

Lagrangian-based collective coordinate models for magnetic domain wall (DW) motion rely on an ansatz for the DW profile and a Lagrangian approach to describe the DW motion in terms of a set of time-dependent collective coordinates: the DW position, the DW magnetization angle, the DW width and the DW tilting angle. Another approach was recently used to derive similar equations of motion by averaging the Landau-Lifshitz-Gilbert equation without any ansatz, and identifying the relevant collective coordinates afterwards. In this paper, we use an updated version of the semi-analytical equations to compare the Lagrangian-based collective coordinate models with micromagnetic simulations for field- and STT-driven (spin-transfer torque-driven) DW motion in Pt/CoFe/MgO and Pt/Co/AlOx nanostrips. Through this comparison, we assess the accuracy of the different models, and provide insight into the deviations of the models from simulations. It is found that the lack of terms related to DW asymmetry in the Lagrangian-based collective coordinate models significantly contributes to the discrepancy between the predictions of the most accurate Lagrangian-based model and the micromagnetic simulations in the field-driven case. This is in contrast to the STT-driven case where the DW remains symmetric

Simulation and Modeling of Racetrack Memories With VCMA Synchronization

“…3), the average speed of a domain wall evaluated by the analytical model shows an offset of ≈30% with respect the average speed evaluated by Mumax3. This offset is in good agreement with the one evaluated in [16] and [19] for the two-collective coordinates model. It is observed that as the current density increases in the heavy metal layer up to a maximum of 3.5 × 10 11 A/m 2 , due to the SOT effect the average speed of a domain wall increases.…”

Depinning exponents of thin film domain walls depend on disorder strength

“…Our model should find applications in modelling DW dynamics in a wide range of contexts where DW velocities are not so high that spin wave emission from the moving DW [37][38][39] (not captured by our line model) becomes important, including creep motion of DWs [5] and Barkhausen noise [6]. Finally, extensions to bubble geometry would be useful, e.g., for studying effects due to the Dzyaloshinskii-Moriya interaction [40,41].…”

Collective coordinate descriptions of magnetic domain wall motion in perpendicularly magnetized nanostructures under the application of in-plane fields

“…1. Integrating ansatz 1 from 0 to π: This model does not take into account the canting in the domains, and was presented in one of our previous works [16]. 2.…”

“…Alternatively, simpler models may be extracted from the LLG equation to analyze the motion of specific topological defects of interest, such as vortices and DWs [8,9,10,11,12,13,14,15,16,17]. The sim-plified nature of these collective coordinate models (CCMs) is due to the introduction of an ansatz which characterizes the structure of the spin texture of interest.…”