Shape of a skyrmion.

Area of Science:

• Condensed Matter Physics
• Quantum Mechanics
• Spintronics

Background:

• Magnetic skyrmions are topologically protected spin structures with potential applications in data storage and computing.
• Precisely determining their shape is crucial for understanding their behavior and optimizing device performance.
• Existing methods may lack accuracy or applicability to complex scenarios.

Purpose of the Study:

• To develop a novel, accurate method for characterizing the shape of two-dimensional magnetic skyrmions.
• To provide a theoretical framework applicable to various magnetic systems and phenomena.
• To validate the proposed method through established simulation techniques.

Main Methods:

• Parameterizing skyrmion shape using the position-dependent orientation of magnetic moments.
• Employing an expansion based on eigenfunctions of the Schrödinger equation for a harmonic oscillator.
• Performing variational calculations up to the next-to-next-to-leading order.
• Verifying results with lattice simulations based on the Landau-Lifshitz-Gilbert equation.

Main Results:

• The proposed method accurately determines the shape of two-dimensional magnetic skyrmions.
• The theoretical framework is validated by Landau-Lifshitz-Gilbert equation simulations.
• The method is successfully applied to analyze the dissipative matrix in the Thiele equation.
• The approach is extended to study interacting skyrmions in bilayer systems.

Conclusions:

• The developed method offers a robust and accurate way to determine magnetic skyrmion shapes.
• This work provides a valuable tool for theoretical and computational studies in spintronics.
• The findings pave the way for designing and controlling novel magnetic devices.