Collective coordinate models of domain wall motion in perpendicularly magnetized systems under the spin hall effect and longitudinal fields

Recent studies on heterostructures of ultrathin ferromagnets sandwiched between a heavy metal layer and an oxide have highlighted the importance of spin-orbit coupling (SOC) and broken inversion symmetry in domain wall (DW) motion. Specifically, chiral DWs are stabilized in these systems due to the Dzyaloshinskii-Moriya interaction (DMI). SOC can also lead to enhanced current induced DW motion, with the Spin Hall effect (SHE) suggested as the dominant mechanism for this observation. The efficiency of SHE driven DW motion depends on the internal magnetic structure of the DW, which could be controlled using externally applied longitudinal in-plane fields. In this work, micromagnetic simulations and collective coordinate models are used to study current-driven DW motion under longitudinal in-plane fields in perpendicularly magnetized samples with strong DMI. Several extended collective coordinate models are developed to reproduce the micromagnetic results. While these extended models show improvements over traditional models of this kind, there are still discrepancies between them and micromagnetic simulations which require further work.