Creation of domain-wall skyrmions in chiral magnets with Landau-Lifshitz-Gilbert dynamics and demagnetization

TL;DR

This work analyzes the absorption of a bulk magnetic skyrmion into an empty domain wall in chiral magnets using Landau-Lifshitz-Gilbert dynamics with and without demagnetization. It develops a dimensionless model with parameters $\kappa$ (effective DMI) and $\eta$ (demagnetization strength), distinguishes Bloch and Néel DMI, and investigates both stationary solitons and their dynamics, including a 1D Kibble-Zurek mechanism on an unstable DW that can generate DW-skyrmion–anti-DW-skyrmion pairs. Numerical simulations (RK4 in 2D with Poisson-based demag) map phase diagrams for capture, annihilation, and repulsion across four cases (Bloch/Néel with/without demag) and derive Thiele equations for DW motion, finding good agreement with full LLG results. The study highlights conditions under which skyrmions are absorbed into DWs, how demagnetization modifies soliton sizes, and how a Kibble-Zurek-like process can dynamically generate complex DW-bound topological structures, informing potential DW-based data storage approaches.

Abstract

Absorption of an isolated bulk magnetic skyrmion into an empty domain wall in a chiral ferromagnetic system is studied using the Landau-Lifshitz-Gilbert equation with and without the demagnetization effect taken into account. The full phase diagram of creation versus repulsion or annihilation is mapped out in case of both Bloch-type and Néel-type DMI, with and without demagnetization. Finally, the unstable domain wall, realizable with a setup of several external magnets, contains the theoretical possibility of producing a 1-dimensional version of the Kibble-Zurek mechanism, which in turn can create a number of skyrmion-anti-skyrmion pairs engulfed in the domain wall: We denote them domain-wall-skyrmion-anti-domain-wall-skyrmion pairs.

Figures (17)

• Figure 1: (a) profile, (b) energy density, (c) topological charge density and (d) demagnetization energy density the magnetic (Néel) skyrmion. The dashed lines correspond to both Bloch-type and Néel-type magnetic skyrmions without the demagnetization taken into account and the solid lines correspond to the Néel-type magnetic skyrmions with $\eta=0.3$. The DMI coupling is varied from 0.3 to 0.55, and everything is plotted in dimensionless units, see the text.
• Figure 2: (a) Bloch without demag., (b) Néel without demag., (c) Bloch with demag. and (d) Néel with demag. The arrows display the magnetization vector in the plane and are in one-to-one correspondence with the coloring of the skyrmions. For instance, and arrow pointing in the $\hat{x}$-direction corresponds to red. Black and white correspond to $n_3=+1$ and $n_3=-1$, respectively. From now on, we will display the skyrmions using only the coloring, which has the same information as the arrows.
• Figure 3: Setup of DW and isolated skyrmion as initial condition. This figure is taken from Ref. Gudnason:2024shv.
• Figure 4: Sketch of a setup that could give rise to the magnetic fields described in Eq. \ref{['eq:extpot']}.
• Figure 5: Final states of evolution of the LLG equation from the initial condition \ref{['eq:u_composite']} in the case of Bloch DMI without demagnetization (and equivalently Néel DMI without demagnetization by the map from Fig. \ref{['fig:Bloch_Neel_coloring']}(a) to Fig. \ref{['fig:Bloch_Neel_coloring']}(b)). The columns display the color code for the final state, the magnetization vector (for a map to vectors, see Fig. \ref{['fig:Bloch_Neel_coloring']}), the DMI energy density, the total energy density and finally the topological charge density. The rows correspond to a DW-skyrmion (green/C), an empty DW (red/A), a bulk skyrmion (blue/B), two DW-skyrmions (yellow/D), a DW-skyrmion and a bulk skyrmion (magenta/F), an anti-DW-skyrmion and a bulk skyrmion (purple/G) and finally a DW-skyrmion-anti-DW-skyrmion pair with a bulk skyrmion (cyan/H).