Phase contrast of spherical magnetic particles
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Updated: Oct 22, 2026

Optimizing Magnetic Force Microscopy Resolution and Sensitivity to Visualize Nanoscale Magnetic Domains
Published on: July 20, 2022
De Graef M1, Nuhfer, McCartney
1Department of Materials Science and Engineering, Carnegie Mellon University, Pittsburgh, PA 15213-3890, U.S.A.
Abstract:
This paper derives analytical expressions for the magnetic and electrostatic phase shifts of a plane electron wave upon traversing a spherical, uniformly magnetized particle with a non-zero mean inner potential. The Aharonov-Bohm phase shift is represented in terms of dimensionless parameters. Standard Foucault and Fresnel Lorentz image simulations are presented for a range of particle sizes and saturation inductions. We discuss the detection limits of the Lorentz techniques and compare them with the sensitivity of the electron holography method. We conclude the paper with experimental holography results for nanocrystalline cobalt particles; the observed phase changes are in good agreement with the analytical predictions.
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