Abstract text (incl. figure legends and references)

Magnetic materials consist of a domain structure where the magnetic fields of dipoles are grouped together and aligned to minimize magnetostatic energy. The formation of the magnetic domains is associated with magnetic anisotropies which tun the local configuration of spins. According to magneto-elastic coupling, magnetic anisotropies are coupled to local atomic displacement [1]. Therefore, a strain field within a material can induce rearrangement of the domain structure giving rise to the complicated magnetic responses of magnets [2]. For soft ferromagnetic metallic glass (SFMG), which originally possess an isotropic atomic structure, the magnetic domain rearrangement of SFMGs is extremely sensitive to the local deviatoric distortion at the atomic scale [1, 3]. Highly sensitive measurement of strain, magnetic field, and atomic structure in SFMGs at the nanometer scale is desired for new material designs.

Here, we developed Lorentz 4-dimensional scanning transmission electron microscopy (Ltz-4D-STEM) for correlative mapping of the magnetic structure, strain field, and atomic density of a Fe-based SFMG. A quasi-parallel electron probe is focused to ~10 nm diameter on the soft magnetic TEM sample under field-free conditions as illustrated in Figure 1A. Electron diffraction patterns are acquired from the nano-volume at each scan position during stepwise scanning of the probe over the area of interest. Diffraction patterns are shown in the background. As illustrated in Figure 1B, measuring the center positions of each local diffraction pattern provides a magnetic domain map. Measuring the strength and orientation of elliptical deviation of each local diffraction pattern provides strain fields and a corresponding map of elastic energy. Quantifying the area encircled by the 1st ring of each diffraction pattern provides an atomic packing density map [4]. Thus, this method simultaneously provides a correlative visualization of multi-field and atomic structure information with a pixel-level correlation. Figure 1C shows typical results from the Lorentz 4D-STEM. The magnetic field , first principal strain , and relative atomic packing density are simultaneously measured from a deformed SFMG.

Figure 1. Schematic illustration of Lorentz 4D-STEM. (A) The electron probe is focused on the soft magnetic TEM sample under field-free conditions. Spatially-resolved diffraction patterns are collected during scanning over a shear band in a deformed metallic glass. (B) Data processing: the center of mass (CoM) of a direct beam measures the momentum transfer in the diffraction pattern by the magnetic field (Lorentz forces) inside of the sample under the probe positions. The principal strains ( and ) are calculated from the elliptic distortion of the diffraction ring from a perfect circle. The local atomic packing density is quantified by the area encircled by the 1st ring of each diffraction pattern. (C) Obtained data, magnetic field , strain field and relative atomic packing density from a deformed soft magnetic Fe85.2Si0.5B9.5P4Cu0.8 MG ribbon.

[1] Shen et al, Nat. Commun. 9, 4414, (2018)

[2] Lei, N. et al. Nat. Commun. 4, 1378 (2013)

[3] Pascarelli, S. et al.. Phys. Rev. Lett. 99, 237204 (2007)

[4] Kang et al, Nat. Commun, Under review. Currently available at Nature portfolio https://doi.org/10.21203/rs.3.rs-1545335/v1 (2022)