[Paper Review] Double bit in-plane magnetic skyrmions on a track

Kyoung‐Woong Moon, Jungbum Yoon+2 more|arXiv (Cornell University)|Nov 30, 2018

Magnetic properties of thin films53 references54 citations

TL;DR

This paper proposes a new type of magnetic skyrmion in in-plane magnetic anisotropy (IMA) systems, where skyrmions with opposite topological charges can coexist in the same background magnetization. Unlike conventional perpendicular magnetic skyrmions, these in-plane skyrmions enable double-bit information transfer in a single magnetic wire via spin Hall effect and current-driven motion, demonstrating a novel pathway for skyrmion-based racetrack memory with higher information density.

ABSTRACT

A magnetic skyrmion isusually refers to a twisted spin texture surrounded by uniformly aligned out-of-plane spinsin the background of a uniformly magnetized state. The invariance of the magnetic skyrmion conserves its topological charge under any continuous transformations of the spin textures, leads to which represents the robustness of a magnetic skyrmion their texture against external perturbations, making it ideal to use skyrmions as . Such a behaviour is required for an ideal information carriers. To date, most magnetic skyrmion studies have been performedfocused on in perpendicularly magnetized systems, where the skyrmion topological number is determined by the relative orientation between the core and /outer perpendicular magnetization directions of the skyrmion is either up/down or down/up. Here we show that there also exists a new type of magnetic skyrmion with surrounding spins to be uniformly aligned to the in-plane direction. By continuous transformation and relaxation of the spin textures of out-of-plane skyrmions, we showed that an in-plane skyrmion, where the background magnetization is in the in-plane direction, is also possible. Different from the conventional perpendicular magnetic skyrmionsContrary to the skyrmions in a perpendicularly magnetized state, the in-plane magnetic skyrmions with opposite signs of topological charges can inherentlycharges can inherently coexist in the in-plane magnetization system coexist. Moreover, the iIn-plane skyrmions of opposite charge can move together by an electric current and exhibit with an opposite spin Hall effect. These findings showdemonstrate the inherent possibility of a double-bit transfer in a single magnetic wire that is not possible in a perpendicularly magnetized system.

Motivation & Objective

• To explore the existence and stability of magnetic skyrmions in in-plane magnetic anisotropy (IMA) systems, contrasting them with conventional perpendicular magnetic anisotropy (PMA) skyrmions.
• To investigate whether skyrmions with opposite topological charges can coexist in the same magnetic background, a feature not possible in PMA systems.
• To demonstrate the feasibility of double-bit information transfer using coexisting in-plane skyrmions in a single magnetic wire.
• To analyze the dynamics and motion of in-plane skyrmions under spin-transfer torque (SMT) and spin Hall effect, identifying their distinct transport behavior.

Proposed method

• Performed micromagnetic simulations using the mumax code to model and relax skyrmion configurations in IMA systems with interfacial Dzyaloshinskii–Moriya interaction (iDMI).
• Used Thiele's equation approach to derive skyrmion dynamics under spin-transfer torque (SMT) and spin-orbit torque (SOT), incorporating non-adiabaticity and damping effects.
• Defined the topological charge Q via the integral Q = (1/4π)∫𝐦∙(𝜕𝑥𝐦 × 𝜕𝑦𝐦)𝑑𝑥𝑑𝑦 to confirm skyrmion stability and classify states.
• Constructed phase diagrams by varying iDMI energy density (Dind) and saturation magnetization (MS), identifying conditions for IMA skyrmion stability.
• Applied periodic boundary conditions and simulated skyrmion motion under SMT (velocity u = 5–10 m/s) and SOT (τd = 4–8 mT) to study transport behavior.
• Validated the IMA skyrmion structure as a vortex-antivortex pair with opposite core polarities, confirming net topological charge of ±1.

Experimental results

Research questions

• RQ1 Can magnetic skyrmions with opposite topological charges coexist in a single in-plane magnetic anisotropy (IMA) system with uniform background magnetization?
• RQ2 What is the mechanism enabling the formation and stability of in-plane skyrmions in IMA systems, and how does it differ from conventional PMA skyrmions?
• RQ3 How do the dynamics of in-plane skyrmions differ under spin-transfer torque (SMT) and spin Hall effect, and can they be used for double-bit information transfer?
• RQ4 What are the critical material parameters (e.g., Dind, MS) that determine the stability of in-plane skyrmions, and how do they compare to stripe domain conditions?
• RQ5 Can the Thiele equation formalism be adapted to describe the motion of in-plane skyrmions with asymmetric spin textures and non-uniform Dij tensors?

Key findings

• In-plane magnetic skyrmions with opposite topological charges (+1 and −1) can coexist in the same uniform in-plane magnetization background, a feature impossible in conventional PMA systems.
• The IMA skyrmion structure is a vortex-antivortex pair with opposite core polarities, resulting in a net topological charge of ±1, confirmed via topological charge integral.
• Micromagnetic simulations show that IMA skyrmions are stabilized when |HDMI| > MS, which occurs when Dind < 1.11|Dind|/√(μ₀A) (the 'stripe condition'), with stable skyrmions existing slightly below this threshold.
• Under spin-transfer torque (SMT), both opposite-charge skyrmions move in the same direction but exhibit opposite spin Hall effect, enabling double-bit encoding.
• Thiele’s equations predict that skyrmion velocities depend on non-adiabaticity (β) and damping (α), with Vx = (β/α)ux and Vx = 1/(αDxx)wx for SMT and SOT-driven motion, respectively.
• In a confined wire structure, both skyrmions can be coherently driven by SMT, demonstrating the feasibility of double-bit transfer in a single magnetic track.