Hopfion rings in a cubic chiral magnet.

Area of Science:

• Condensed Matter Physics
• Materials Science
• Nanotechnology

Background:

• Magnetic skyrmions and hopfions are topological solitons with particle-like properties, making them promising for spintronics.
• Skyrmions are 2D vortex-like structures, while hopfions are 3D ring-shaped solitons.
• Direct observation of magnetic hopfions has been challenging, with prior reports limited to synthetic materials.

Purpose of the Study:

• To present the first direct observations of magnetic hopfions in crystalline materials.
• To investigate the formation of hopfions in coupled states with skyrmion strings.
• To develop a protocol for nucleating hopfion rings and provide a unified classification.

Main Methods:

• Transmission electron microscopy (TEM) was employed for direct observation.
• Lorentz imaging and electron holography were used for verification.
• Micromagnetic simulations were conducted for comparison and validation.

Main Results:

• Direct visualization of hopfions forming coupled states with skyrmion strings in B20-type FeGe plates.
• A reproducible protocol for nucleating hopfion rings was successfully developed and verified.
• Experimental results showed excellent agreement with micromagnetic simulations.

Conclusions:

• This study provides the first direct experimental evidence of hopfions in crystals.
• The findings offer insights into the diversity and behavior of topological solitons in 3D chiral magnets.
• The developed methods and classification contribute to understanding complex magnetic structures for future applications.