[Paper Review] Composite Skyrmion bags in two-dimensional materials

David Foster, Charles Kind+4 more|arXiv (Cornell University)|Jun 7, 2018

Metamaterials and Metasurfaces ApplicationsMaterials Science32 references4 citations

TL;DR

This paper proposes composite Skyrmion bags—topologically stable, nested configurations of multiple Skyrmions in 2D magnetic and liquid crystal systems—that behave as single, robust entities under current drive. Using Yukawa-type dipole interactions derived from high-energy physics, the authors demonstrate experimentally and via simulations that these bags are stable, interact like single Skyrmions, and enable higher-density, more robust racetrack memory devices.

ABSTRACT

Skyrmions are particle-like topological excitations, studied in various condensed matter systems and models of high-energy physics (HEP). They occur as stable spin textures in certain planar magnetic materials and as configurations in chiral nematic liquid crystals, having been originally proposed as model of atomic nuclei. Since magnetic Skyrmions can be accelerated with a current, they have the potential to encode bits in low-power magnetic storage devices. Drawing on techniques from HEP, we demonstrate that magnetic and liquid crystal Skyrmions interact like orientation dependent, localised particles, explaining previously observed Skyrmion behaviour. This interaction motivates the construction of Skyrmion bags: textures of high topological degree which we realise experimentally in liquid crystals, and in magnetic materials by computer simulations. These Skyrmion bags configurations are nested multiple Skyrmions, which act like single Skyrmions in pairwise interaction, and under the influence of a current in magnetic materials. These results emphasize equivalent Skyrmion behaviour in different physical systems, and suggest new, high-density magnetic memory storage devices based on Skyrmion bags.

Motivation & Objective

• To understand the nature of Skyrmion-Skyrmion interactions in 2D magnetic and chiral nematic liquid crystal systems.
• To develop a unified theoretical framework for higher-degree topological textures based on Yukawa-type dipole interactions.
• To explore the stability and dynamics of composite Skyrmion bags as candidates for high-density magnetic memory.
• To demonstrate experimentally and numerically that Skyrmion bags behave as single, current-driven entities with enhanced robustness.

Proposed method

• Adapted a 2D high-energy physics model (Piette & Zakrzewski, 1994) to describe Skyrmion interactions in 2D materials.
• Derived a Yukawa-type interaction potential between Skyrmions based on the Dzyaloshinskii-Moriya interaction (DMI) and gradient energy terms.
• Used asymptotic analysis of the Skyrmion profile function to model long-range dipole-like interactions dependent on relative orientation.
• Mapped internal Skyrmion packing inside bags to the circle packing problem, identifying stable configurations (e.g., S(13) with two optimal arrangements).
• Performed dynamical micromagnetic simulations (MuMax3) to study current-driven motion of Skyrmion bags in racetrack geometry.
• Conducted experimental observations in chiral nematic liquid crystals to validate the predicted repulsive interaction and bag formation.

Experimental results

Research questions

• RQ1 How do magnetic and liquid crystal Skyrmions interact at long range, and what governs their orientation-dependent repulsion?
• RQ2 Can composite textures of multiple Skyrmions—Skyrmion bags—be stabilized in 2D systems with high topological charge?
• RQ3 Do Skyrmion bags behave as single, current-driven entities, suitable for racetrack memory applications?
• RQ4 What is the relationship between internal Skyrmion packing and the stability of composite bags?
• RQ5 Can the S(13) configuration of Skyrmion bags support two distinct, switchable states for data encoding?

Key findings

• The interaction between Skyrmions is a Yukawa-type repulsion dependent on relative orientation, with potential $V_{\text{int}} \approx \frac{C^2 \mu_J}{\pi} \cos\gamma \frac{e^{-\sqrt{\mu_J} R}}{\sqrt{R}}$, where $\gamma$ is the relative orientation angle.
• Skyrmion bags with topological degree $n$ exhibit a radius that increases approximately linearly with $n$ up to $S(15)$, as confirmed by MuMax3 simulations.
• The $S(13)$ Skyrmion bag configuration supports two distinct, stable geometric arrangements, corresponding to the two known optimal circle packings, enabling binary data encoding.
• Dynamical micromagnetic simulations show that magnetic Skyrmion bags can be driven by electrical current in racetrack devices with behavior analogous to single Skyrmions.
• Experimental observations in chiral nematic liquid crystals confirm the predicted repulsive interaction between Skyrmions, validating the theoretical model.
• The internal structure of Skyrmion bags is stabilized by repulsive interactions and topological constraints, with the central anti-Skyrmion region favoring $\gamma = \pi/2$ for energy minimization.