Quantum mechanical treatment of atomic-resolution differential phase contrast imaging of magnetic materials

Utilizing the Pauli equation based multislice method, introduced in a previous paper [A. Edstrom, A. Lubk, and J. Rusz, Phys. Rev. Lett. 116, 127203 (2016)], we study the atomic-resolution differential phase contrast (DPC) imaging on an example of a hard magnet FePt with in-plane magnetization. Simulated center-of-mass pattern in a scanning transmission electron microscopy experiment carries information about both electric and magnetic fields. The momentum transfer remains curl free, which has consequences for interpretation of the integrated DPC technique. The extracted magnetic component of the pattern is compared to the expected projected microscopic magnetic field as obtained by density functional theory calculation. Qualitative agreement is obtained for low sample thicknesses and a suitable range of collection angles.