Parameterization of magnetic vector potentials and fields for efficient multislice calculations of elastic electron scattering

Abstract

The multislice method 1 , which simulates the propagation of the incident electron wavefunction through a crystal, is a well-established method for analyzing the multiple scattering effects that an electron beam may undergo.The inclusion of magnetic effects into this method 2,3 proves crucial towards simulating magnetic differential phase contrast images at atomic resolution 4 , enhanced magnetic interaction of vortex beams with magnetic materials 3,5 , calculating magnetic Bragg spots 6 , or searching for magnon signatures 7 , to name a few examples. Inclusion of magnetism poses novel challenges to the efficiency of the multislice method for larger systems, especially regarding the consistent computation of magnetic vector potentials A and magnetic fields B over large supercells. We present in this work a tabulation of parameterized magnetic values for the first three rows of transition metal elements computed from atomic density functional theory calculations 8,9 , allowing for the efficient computation of approximate A and B across large crystals using only structural and magnetic moment size and direction information. Ferromagnetic bcc Fe and tetragonal FePt are chosen as examples in this work to showcase the performance of the parameterization versus directly obtaining A and B from the unit cell spin density by density functional theory calculations 5 , both for the quantities themselves and the resulting magnetic signal from their respective use in multislice calculations.