Quantification of magnetization of nanostructures via three complementary methods

The quantitative measurement of magnetization in magnetic nanostructures plays a crucial role in advancing both fundamental understanding and applied research. Off-axis electron holography in a transmission electron microscope enables the retrieval of magnetic phase shifts induced by magnetic induction fields, thereby allowing precise quantification of magnetization. Using magnetite (Fe3O4) nanoparticles as a model system, we use off-axis electron holography to demonstrate three complementary methods for quantifying the magnetic properties of nanoparticles. These methods are the simple geometric approximation, the magnetic phase gradient integration, and the model-based iterative reconstruction, each providing unique capability, ranging from the rapid estimation of in-plane magnetic induction to highly detailed spatially resolved magnetization maps. We analyze the strengths, the limitations, and the applicability of each approach, emphasizing the potential of integrating these methods for a comprehensive analysis of the magnetization of nanomaterials.