[Paper Review] Positional stability of skyrmions in a racetrack memory with notched geometry

Md Golam Morshed, Hamed Vakili+1 more|arXiv (Cornell University)|Oct 26, 2021

Magnetic properties of thin films66 references36 citations

TL;DR

This paper investigates the positional stability of magnetic skyrmions in a racetrack memory with notched geometry using micromagnetic simulations. It demonstrates that notch-induced constriction of skyrmion size generates energy barriers up to ~45 kBT, enabling years-long positional stability at ~10^10 A/m² current density, with analytical models confirming the mechanism and outperforming alternative pinning methods.

ABSTRACT

Magnetic skyrmions are chiral spin textures with attractive features, such as ultra-small size, solitonic nature, and easy mobility with small electrical currents that make them promising as information-carrying bits in low-power high-density memory, and logic applications. However, it is essential to guarantee the positional stability of skyrmions for reliable information extraction. Using micromagnetic simulations for the minimum energy path (MEP), we compute the energy barriers associated with stabilizing notches along a racetrack. We vary material parameters, specifically, the strength of the chiral Dzyaloshinskii-Moriya interactions (DMI), the notch geometry, and the thickness of the racetrack to get the optimal barrier height. We find that the reduction of skyrmion size as it squeezes past the notch gives rise to the energy barrier. We find a range of energy barriers up to ~ 45 kBT for a racetrack of 5 nm thickness that can provide years long positional lifetime of skyrmions for long-term memory applications while requiring a moderate amount of current (~ 10^10 A/m2) to move the skyrmions. Furthermore, we derive quasi-analytical equations to estimate the energy barrier. We also explore other pinning mechanisms, such as a local variation of material parameters in a region, and find that notched geometry provides the highest energy barrier. Our results open up possibilities to design practical skyrmion-based racetrack geometries for spintronics applications.

Motivation & Objective

• To investigate the energy barriers that stabilize skyrmions at notched geometries in racetrack memory.
• To determine the optimal material and geometric parameters for maximizing skyrmion positional stability.
• To compare notched geometry with other pinning mechanisms such as local material parameter variations.
• To derive quasi-analytical models for predicting energy barriers in notched racetracks.
• To evaluate the operational current requirements for skyrmion unpinning in practical memory applications.

Proposed method

• Used micromagnetic simulations with MuMax3 to solve the Landau-Lifshitz-Gilbert equation for skyrmion dynamics.
• Employed the string method to compute the minimum energy path (MEP) for skyrmion traversal through notches.
• Varied Dzyaloshinskii-Moriya interaction (DMI) strength, notch radius, and racetrack thickness to explore parameter space.
• Derived empirical and quasi-analytical equations for energy barriers based on skyrmion size reduction during notch passage.
• Compared simulated energy barriers with analytical models for skyrmions on an infinite plane plus a phenomenological confinement correction.
• Evaluated unpinning current requirements to assess compatibility with low-power electronic circuits.

Experimental results

Research questions

• RQ1 What is the magnitude of the energy barrier generated by a notch in a skyrmion racetrack, and how does it depend on DMI, notch geometry, and thickness?
• RQ2 How does the reduction in skyrmion size during passage through a notch contribute to the energy barrier?
• RQ3 How do notched geometries compare to other pinning mechanisms (e.g., local material parameter variations) in terms of energy barrier height?
• RQ4 Can quasi-analytical equations accurately predict the energy barrier in notched racetracks based on skyrmion size and geometric constraints?
• RQ5 What is the required current density to unpin skyrmions from notches, and is it compatible with low-power spintronic applications?

Key findings

• Energy barriers up to ~45 kBT are achieved in a 5 nm thick racetrack, enabling skyrmion positional lifetimes of years for long-term memory.
• The energy barrier arises from the constriction-induced reduction in skyrmion size as it passes through the notch.
• Notched geometry produces the highest energy barrier among tested pinning mechanisms, outperforming local variations in material parameters.
• A quasi-analytical model based on skyrmion energy on an infinite plane with a phenomenological confinement correction matches simulation data with excellent accuracy.
• The required unpinning current is ~10^10 A/m², which is moderate and suitable for integration with low-power electronic circuits.
• The study identifies a 'Goldilocks' regime in parameter space balancing stability and operational current for practical skyrmion-based memory.