Simultaneous Electrostatic and Magnetic Vector Potential Phase Retrieval Using Electron Ptychography

While the observation of magnetic structure with nanometer spatial resolution has been successfully achieved with various transmission electron microscopy (TEM) techniques such as Lorentz TEM, off-axis electron holography, differential phase contrast (DPC), and more recently, Lorentz scanning TEM, atomic-scale imaging of magnetization remains challenging.This can be traced back to the extremely small phase-shifts acquired by the electron beam due to the magnetic vector potential, A(x, y, z), compared to those acquired due to the electrostatic potential of the sample, V(x, y, z): φ(x, y) = φ e (x, y) + φ m (x, y) = σ ∫ V(x, y, z)dze h -∫ A z (x, y, z)dz,