Three-dimensional study of the vector potential of magnetic structures

Area of Science:

• Condensed matter physics
• Magnetism
• Superconductivity

Background:

• The vector potential is crucial in condensed matter physics, particularly for understanding superconductivity and magnetism.
• Experimental visualization of the vector potential in magnetic nanostructures is essential for advancing these fields.

Purpose of the Study:

• To experimentally measure and visualize the three-dimensional vector potential in and around a magnetic Permalloy structure.
• To demonstrate a novel method for probing vector potentials at high resolution.

Main Methods:

• Utilized a combination of electron wave phase reconstruction and electron tomographic reconstruction.
• Employed a transmission electron microscope in Lorentz mode to record tomographic tilt series.

Main Results:

• Successfully measured and visualized the 3D vector potential in a magnetic Permalloy structure.
• Achieved a resolution of approximately 13 nm for probing the vector potential.
• Presented measurements for a square Permalloy structure with an internal closure domain configuration.

Conclusions:

• The developed method enables high-resolution experimental measurement of the 3D vector potential.
• This technique provides valuable insights into the magnetic properties of nanostructures.
• The findings contribute to a deeper understanding of magnetism and related phenomena.