Quantitative magnetic mapping in TEM through accurate 2D thickness determination

Abstract

Off-axis Electron Holography and Electron Magnetic Circular Dichroism are powerful Transmission Electron Microscopy (TEM) techniques capable of mapping magnetic information with near-atomic spatial resolution. However, the magnetic signals obtained is semi-quantitative due to factors such as thickness variations and local crystallographic changes. Precise determination of spatial thickness variations can make these techniques more quantitative. Electron Energy Loss Spectroscopy (EELS) provides a method to measure thickness variations within a region of interest. The absolute thickness depends on reliable estimates of the inelastic mean free path ($\lambda$), which is often unknown for many materials. Alternative techniques, such as Scanning Electron Microscopy (SEM) and Convergent Beam Electron Diffraction (CBED), either lack spatial resolution in thickness mapping or are accurate only within a limited thickness range. Here, we present a straightforward approach to precisely determine the inelastic mean free path ($\lambda$), enabling accurate thickness measurements from EELS maps. We compare these thickness measurements with CBED- and SEM-based methods, identifying discrepancies, particularly in thinner samples ($<100\mathrm{nm}$). Finally, we demonstrate how this calibrated thickness measurement can provide quantitative magnetic maps using TEM-based magnetic measurements.