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

Abstract

-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 o f 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 the m and micromagnetic simulations which require further work.Index: magnetic DW motion -PMA material -spin Hall effect (SHE)

Measuring interfacial Dzyaloshinskii-Moriya interaction in ultra-thin magnetic films

“…Furthermore, considering experiments of fast current-driven DW motion (Ryu et al, 2012), Boulle et al (2013) proposed to include DW tilting as an additional time-dependent variable χ(t) (defined as the angle of the DW normal plane with respect to the positive x-axis), which led to the development of the q − Φ − χ model. Very recently the 1D model was extended to implement all four collective coordinates, namely q − Φ − ∆ − χ, with the aim of improving the agreement with experimental observations and micromagnetic simulations when large in-plane fields are applied (Nasseri et al, 2017). The same authors later showed that the simple two coordinate q − Φ model can grant higher accuracy when combined with an ansatz (which links collective coordinates to magnetization components) that takes into account magnetization canting within the domains under an in-plane field (Nasseri et al, 2018).…”

Chiral domain wall dynamics in magnetic heterostructures with bulk Dzyaloshinskii-Moriya interactions

“…can be proposed with R ≡ η[(x − q) cos χ + y sin χ]/∆. By integrating the resulting dynamical equations over infinite strip length and finite width, the so-called "q − ϕ − χ" [40] or "q − ϕ − χ − ∆" [51,52] models, emerge. However they are too complicated to provide clear physical pictures in analyzing chiral wall dynamics.…”

Determination of the Dzyaloshinskii-Moriya interactions

“…For ideal narrow-strip shaped heterostructures when considering the DMI-induced wall tiling χ [28] and canting θ ∞ [37] in domains from in-plane fields, a more complicated wall ansatz tan ϑ 2 = e R + tan(θ ∞ /2) 1 + e R tan(θ ∞ /2) , φ = ϕ(t) (10) can be proposed with R ≡ η[(x − q) cos χ + y sin χ]/∆. By integrating the resulting dynamical equations over strip surface in xy−plane, alternative Lagrangian-based collective coordinate models, such as the "q − ϕ − χ" [28] or "q − ϕ − χ − ∆" [38,39] models, emerge. However they are too complicated to provide clear criteria in constructing operable procedures and explaining experimental data.…”