Effects of interlayer Dzyaloshinskii-Moriya interaction on the shape and dynamics of magnetic twin-skyrmions

TL;DR

This work shows that interlayer Dzyaloshinskii–Moriya interaction (IL-DMI) stabilizes a three-dimensional twin-skyrmion in magnetic bilayers, with the skyrmion shape and helicity adapting to the IL-DMI direction while preserving the topological charge $Q=p m$. Using atomistic spin dynamics and continuum/Thiele analyses, the authors demonstrate that in-plane IL-DMI elongates the twin-skyrmion along the IL-DMI axis and induces opposite lateral shifts between layers, whereas out-of-plane IL-DMI enlarges the skyrmions and drives opposite helicity changes in the two layers. In current-perpendicular-to-plane driving, the skyrmion velocity and Hall angle can be tuned independently by IL-DMI orientation: in-plane IL-DMI couples elongation to motion, while out-of-plane IL-DMI mainly increases speed with little Hall-angle change. These results highlight IL-DMI as a controllable knob for 3D skyrmion transport in multilayers, with potential electric-field tunability via IL-DMI strength.

Abstract

Magnetic skyrmions have been proposed as promising candidates for storing information due to their high stability and easy manipulation by spin-polarized currents. Here, we study how these properties are influenced by the interlayer Dzyaloshinskii--Moriya interaction (IL-DMI), which stabilizes twin-skyrmions in magnetic bilayers. We find that the spin configuration of the twin-skyrmion adapts to the direction of the IL-DMI by elongating or changing the helicities in the two layers. Driving the skyrmions by spin-polarized currents in the current-perpendicular-to-plane configuration, we observe significant changes either in the skyrmion velocity or in the skyrmion Hall angle depending on the current polarization. These findings unravel further prospects for skyrmion manipulation enabled by the IL-DMI.

Figures (7)

• Figure 1: Effect of IL-DMI on Néel-type twin-skyrmions. A schematic of the physical system studied here is shown on the left, consisting of two magnetic layers and a non-magnetic layer between them. The contributions to the Hamiltonian in Eq. \ref{['eq:HamiltonianSplit']} from the different layers are written inside them. Without IL-DMI the material can host typical Néel-type skyrmions, as seen in (a). If the IL-DMI lies in the $xy$ plane, the twin-skyrmion becomes elongated along the direction of the IL-DMI vector, as seen in (b) and (c). Finally, if the IL-DMI points into the out-of-plane $z$ direction, the skyrmions in the two layers twist relative to each other by changing their helicities. The parameters are $J^{\text{IF}}=12meV$, $|\hbox{\boldmath$\mathrm{D}$}^\text{IF}|=3meV$, $|\hbox{\boldmath$\mathrm{J}$}^\text{IL}|=0.6meV$, $B^{z}=-3.5T$. The IL-DMI is $D^{\textrm{IL}}=\hbox{\boldmath$\mathrm{0}$}$ for (a), $D^{\textrm{IL}}=8meV\cdot \hat{\hbox{\boldmath$\mathrm{x}$}}$ for (b), $D^{\textrm{IL}}=8meV\cdot \hat{\hbox{\boldmath$\mathrm{y}$}}$ for (c), and $D^{\textrm{IL}}=1meV \cdot \hat{\hbox{\boldmath$\mathrm{z}$}}$ for (d).
• Figure 2: Elongation of Néel-type twin-skyrmions depending on the IEC $J^{\text{IL}}$ and IL-DMI $D_x^{\text{IL}}$. The parameters are $J^{\text{IF}}=6meV$, $|\hbox{\boldmath$\mathrm{D}$}^{\text{IF}}|=1.5meV$, $D_y^{\text{IL}}=D_z^{\text{IL}}=0$, and $B^{z}=1.4T$. For relaxing the structures, the damping parameter $\alpha=1$ was used, and the simulation was run for $5\times10^{6}$ time steps, i.e., 10ns. In the points shown in white, the elongation of the twin-skyrmion was unbounded.
• Figure 3: Change of twin-skyrmion size and helicity for out-of-plane IL-DMI. (a) Difference in helicity between the layers $\psi_1-\psi_2$ as a function of $D^{\textrm{IL}}_{z}$ and $J^{\textrm{IL}}$. Panel (b) shows line cuts along the lines colored correspondingly in panel (a); crosses represent simulation results while the line shows the numerical solution of the equations in the continuum limit, see Supplementary Note 1. (c) Twin-skyrmion size for the same parameters, with line cuts shown in panel (d). The system parameters are $J^{\text{IF}}=6meV$, $|\hbox{\boldmath$\mathrm{D}$}^{\text{IF}}|=1.5meV$, $D_x^{\text{IL}}=D_y^{\text{IL}}=0$, and $B^{z}=3.0T$. For relaxing the structures, the damping parameter $\alpha=1$ was used, and the simulation was run for $5\times10^{6}$ time steps, i.e., 10ns.
• Figure 4: Velocity of twin-skyrmions for in-plane IL-DMI. The current polarization $\hbox{\boldmath$\mathrm{P}$}$ is along the $+x$ direction, corresponding to an electric current along the $+y$ direction. (a) Simulations of the current-driven motion for selected values of the IL-DMI. The arrow illustrates the displacement over the same simulation time, with the skyrmion Hall angle measured with respect to the current direction. (b) Skyrmion Hall angle and (c) magnitude of skyrmion velocity as a function of IL-DMI. The parameters are $J^{\text{IF}}=6meV$, $|\hbox{\boldmath$\mathrm{D}$}^{\text{IF}}|=1.5meV$, $J^{\text{IL}}=1.75meV$, $D_z^{\text{IL}}=0$, $B^{z}=1.4T$, $\alpha=0.1$, and $\beta_d=1ns^{-1}$. The simulation ran for $2\times10^{6}$ time steps, i.e., $2ns$.
• Figure 5: Effect of the $D^{\text{IL}}_z$ on the twin-skyrmion velocity and size. Values of $D^{\text{IL}}_z$ greater than $0.6meV$ do not result in stable motion. The system parameters are: $J^{\text{IL}}=1.75meV$, $D^{\text{IL}}_x=D^{\text{IL}}_y=0$, $\hbox{\boldmath$\mathrm{B}$}=1.4T$, $\alpha=0.1$, and $\beta_d=1ns^{-1}$.