Twisted domain walls and skyrmions in perpendicularly magnetized multilayers

Abstract

We present an analytical theory to describe three-dimensional magnetic textures in perpendicularly magnetized magnetic multilayers that arise in the presence of magnetostatic interactions and the Dzyaloshinskii-Moriya interaction (DMI). We demonstrate that domain walls in multilayers develop a complex twisted structure, which persists even for films with strong DMI. The origin of this twist is surface-volume stray field interactions that manifest as a depth-dependent effective field whose form mimics the DMI effective field. We find that the wall twist has a minor impact on the equilibrium skyrmion or domain size, but can significantly affect current-driven dynamics. Our conclusions are based on the derived analytical expressions for the magnetostatic energy and confirmed by micromagnetic simulations. arXiv:1809.01247v1 [cond-mat.mtrl-sci]

Walker Breakdown with a Twist: Dynamics of Multilayer Domain Walls and Skyrmions Driven by Spin-Orbit Torque

“…3(a), where our analytical results are overlayed with the 3D micromagnetically-modeled results, using the same material parameters. We note that the velocities are substantially lower than those predicted previously [42,43] with models that imposed stationary dynamics (dot-dashed lines in Fig. 7(a) of Appendix A) on twisted DWs, emphasizing the qualitative and quantitative impact of precession on v(j).…”

“…We assume a saturation magnetization M s = 1.4 × 10 6 A/m, quality factor Q = 2K u /µ 0 M 2 s = 1.4 (where K u is the uniaxial magnetocrystalline anisotropy constant and µ 0 is the vacuum permeability), exchange stiffness A = 1.0 × 10 −11 J/m, and interfacial DMI, D = 1.0 mJ/m 2 , representative of typical experimental skyrmion-hosting multilayers [10,21,45,51,53,54]. The static DW profile in such a material exhibits a twisted character as shown elsewhere [39,41,42] and depicted in Fig. 1(a).…”

“…5(a), which depicts the location of the Walker layer, i cr , as a function of the number of multilayer repeats N and DMI. Comparing layer [42] (if it exists), we can conclude that the correlation between i cr and i Bloch is indeed very high. There are two notable differences: (i) at no DMI, there is no Walker breakdown in the system as it is completely immobile and (ii) at high DMI all the DWs are Néel.…”

“…Here, we also assumed that the DW width is constant in all layers. This assumption, though an approximation [41,42], still accurately captures the average width of the DW, ∆ = i ∆ i /N [42]. The total cross-sectional DW energy density σ 1,N tot = +∞ −∞ E 1,N tot (x)dx can then be integrated with respect to x, which after including the magnetostatic energy of an infinitely extended (L x , L y → ∞) multilayer film as calculated in Ref.…”

“…Walker breakdown is precluded by symmetry for SOT-driven motion in conventional single ultrathin ferromagnetic layers [37,38], since at high drive, ψ tends asymptotically toward the hard axis but is never driven into precession. However, recently it has been found that in in multilayers of ferromagnet and heavy-metal, DWs and skyrmions can exhibit throughthickness twists [39][40][41][42][43][44] such that the statics and dynamics can no longer be described using a single value of ψ. Micromagnetic simulations of such twisted multilayer skyrmions [42] have evidenced dynamical instabilities reminiscent of Walker breakdown during SOTdriven motion, wherein Bloch line nucleation and motion in a subset of layers leads to a significantly diminished skyrmion velocity and skyrmion Hall angle. These behaviors are a result of complex surface-volume stray field interactions whose influence on the dynamics remains largely unexplored.…”