On-column 2p bound state with topological charge \pm1 excited by an atomic-size vortex beam in an aberration-corrected scanning transmission electron microscope

TL;DR

This paper demonstrates that atomic-size vortex beams with topological charge ±1 can be coupled to 2p columnar bound states in crystals, propagating over 50 nm without dispersion, enabling advanced atomic-scale magnetic probing.

Contribution

It introduces a method to extend vortex beam propagation in crystals by coupling to 2p states, with numerical solutions and formulas for optimizing experimental parameters.

Findings

Atomic vortex beams can couple to 2p columnar states.

Vortex beams propagate over 50 nm without losing topological charge.

Provided numerical data for Co and Dy elements for experimental design.

Abstract

Atomic-size vortex beams have great potential in probing materials' magnetic moment at atomic scales. However, the limited depth of field of vortex beams constrains the probing depth in which the helical phase front is preserved. On the other hand, electron channeling in crystals can counteract beam divergence and extend the vortex beam without disrupting its topological charge. Specifically, in this paper, we report atomic vortex beams with topological charge \pm1 can be coupled to the 2p columnar bound states and propagate for more 50 nm without being dispersed and losing its helical phase front. We gave numerical solutions to the 2p columnar orbitals and tabulated the characteristic size of the 2p states of two typical elements, Co and Dy, for various incident beam energies and various atomic densities. The tabulated numbers allow estimates of the optimal convergence angle for maximal coupling to 2p columnar orbital. We also have developed analytic formulae for beam energy, convergence-angle, and hologram dependent scaling for various characteristic sizes. These length scales are useful for the design of pitch-fork apertures and operations of microscopes in the vortex-beam imaging mode.