Approaching the Topological Low-Energy Physics of the F Model in a Two-Dimensional Magnetic Lattice.

We demonstrate that the physics of the F model can be approached very closely in a two-dimensional artificial magnetic system. Faraday lines spanning across the lattice and carrying a net polarization, together with chiral Faraday loops characterized by a zero magnetic susceptibility, are imaged in real space using magnetic force microscopy. Our measurements reveal the proliferation of Faraday lines and Faraday loops as the system is brought from low- to high-energy magnetic configurations. They also reveal a link between the Faraday loop density and icelike spin-spin correlations in the magnetic structure factor. Key for this Letter, the density of topological defects remains small, on the order of 1% or less, and negligible compared to the density of Faraday loops. This is made possible by replacing the spin degree of freedom used in conventional lattices of interacting nanomagnets by a micromagnetic knob, which can be finely tuned to adjust the vertex energy directly, rather than modifying the two-body interactions.

Beam shaping and probe characterization in the scanning electron microscope.

Here we demonstrate the use of nanofabricated grating holograms to diffract and shape electrons in a scanning electron microscope. The diffraction grating is placed in an aperture in the column. The entire diffraction pattern can be passed through the objective lens and projected onto the specimen, or an intermediate aperture can be used to select particular diffracted beams. We discuss several techniques for characterizing the diffraction pattern. The grating designs can incorporate features that can influence the phase and intensity of the diffracted SEM probe. We demonstrate this by producing electron vortex beams.