Atomically- resolved measurement of competing spin Hamiltonian energies

The ground states and dynamics of all magnetic materials are fundamentally governed by the competition among spin Hamiltonian energies, including symmetric super-exchange, antisymmetric Dzyaloshinskii-Moriya interaction (DMI), Zeeman energy, and single-ion anisotropy (SIA). However, quantifying these competing terms at the atomic scale remains a grand challenge due to the lack of techniques capable of resolving three-dimensional (3D) spin vectors locally. This project aims to develop and apply a transformative beam-shift fourdimensional electron magnetic circular dichroism (4D-EMCD) technique to achieve atomicscale 3D vector magnetometry with atomic resolution. Focusing on canted antiferromagnets, we will map the field-induced asymmetric rotation of the two spin sublattices under a 2.5 T magnetic field. By explicitly decoupling the local Hamiltonian energies plane-by-plane, the project will elucidate that this structural asymmetry originates from the delicate competition between SIA and differential Zeeman energies of antiparallel spins. This small-scale project will bridge the gap between atomic structure and Hamiltonian mechanics, establishing a robust experimental and analytical pipeline for topological spintronics and altermagnets.