Three-beam convergent-beam electron diffraction for measuring crystallographic phases

Emergent chirality in a polar meron to skyrmion phase transition

Polar skyrmions are predicted to emerge from the interplay of elastic, electrostatic and gradient energies, in contrast to the key role of the anti-symmetric Dzyalozhinskii-Moriya interaction in magnetic skyrmions. Here, we explore the reversible transition from a skyrmion state (topological charge of -1) to a two-dimensional, tetratic lattice of merons (with topological charge of -1/2) upon varying the temperature and elastic boundary conditions in [(PbTiO₃)₁₆/(SrTiO₃)₁₆]₈ membranes. This topological phase transition is accompanied by a change in chirality, from zero-net chirality (in meronic phase) to net-handedness (in skyrmionic phase). We show how scanning electron diffraction provides a robust measure of the local polarization simultaneously with the strain state at sub-nm resolution, while also directly mapping the chirality of each skyrmion. Using this, we demonstrate strain as a crucial order parameter to drive isotropic-to-anisotropic structural transitions of chiral polar skyrmions to non-chiral merons, validated with X-ray reciprocal space mapping and phase-field simulations.

Evaluation of accuracy in the determination of crystal structure factors using large-angle convergent-beam electron diffraction patterns

The accuracy of electron density distribution analysis using large-angle convergent-beam electron diffraction (LACBED) patterns is evaluated for different convergence angles. An orbital ordered state of FeCr2O4 is used as an example of the analysis. Ideal orbital-ordered and non-ordered states are simulated by using orbital scattering factors. LACBED patterns calculated for the orbital-ordered state were used as hypothetical experimental data sets. Electron density distribution of the Fe 3d orbitals has been successfully reconstructed with a higher accuracy from LACBED patterns with convergence angles larger than 15.2 mrad, which is 4 times as large as that for conventional convergent-beam electron diffraction patterns. Excitation of particular Bloch waves with the aid of LACBED patterns has a key role in the accurate analysis of electron density distributions.

Structure refinement from 'digital' large angle convergent beam electron diffraction patterns

We use semi-automated data acquisition and processing to produce digital large angle CBED (D-LACBED) patterns. We demonstrate refinements of atomic coordinates and isotropic Debye-Waller factors for well-known materials using simulations produced with a neutral, spherical independent atom model. We find that atomic coordinate refinements in Al₂O₃ have sub-pm precision and accuracy. Isotropic DWFs are accurate for Cu, a simple fcc metal, but do not agree with X-ray measurements of GaAs or Al₂O₃. This lack of agreement is probably caused by bonding and change transfer between atoms. While it has long been appreciated that CBED is sensitive to bonding, examination of D-LACBED data shows that some regions exhibit large changes in diffracted intensity from small changes in the periodic crystal potential. Models of bonding will be essential to fully interpret D-LACBED data.