GoKawiilSample preparation
Commercial SrTiO 3 single crystals (MTI) were used for this study. The SrTiO 3 lamella was prepared using standard gallium focused ion beam (FEI Helios 660) lift-out and thinning. The samples were thinned down using an accelerating ion voltage of 30 kV with a decreasing current from 100 pA to 40 pA, and then with a fine polishing process using an accelerating voltage of 5 kV and 2 kV, and a current of 41 pA and 23 pA.
The STEM lamella sample is supported on a copper post of the focused ion beam grid on only one side, making the sample free to naturally contract with temperature (Extended Data Fig. 1). This mounting geometry ensures minimal strain imparted to the lamella while maintaining thermal coupling for stable cryogenic experiment. The thickness of the sample within the imaging region is estimated using the zero-loss peak in electron energy loss spectroscopy data (Supplementary Fig. 10). Thickness varies from about 53 to 69 nm across the relatively large 140 × 140 nm2 field of view.
Liquid helium cryogenic electron microscopy
Cryogenic STEM experiments were performed using an h-Bar Instruments ULT holder which uses continuous flow through a heat exchanger that is mechanically decoupled from the sample to reduce vibrations47,54. Variable temperatures are enabled by an integrated heater and proportional–integral–derivative (PID) control. The sample drift rate at low temperature is measured as 0.37 Å s–1 at base temperature through image tracking, lower than the usual range (0.6–1.0 Å s–1) for collecting a high-resolution image in conventional side-entry liquid nitrogen cryogenic holders55,56. For each temperature step during heating, we realign the sample location to the same region after waiting for temperature to stabilize and sample drift to become negligible. A complete 4D-STEM dataset is acquired in about 2 min, so drift during acquisition produces at most about 4 nm, far smaller than the observed domain size scale.
Four dimensional scanning transmission electron microscopy
Advances in pixelated detectors, particularly direct electron detectors with high dynamic range41,57, have enabled the simultaneous capture of both intense Bragg reflections and more subtle features such as Kikuchi bands (more than 104 weaker than Bragg spots), which arise from multiple scattering processes in the crystal lattice. 4D-STEM measurements were performed in an aberration-corrected scanning transmission electron microscope (Thermo Fisher Scientific Spectra 300) operated at 300 kV. 4D-STEM datasets were collected by a first-generation electron microscopy pixel array detector, using a 1 mrad convergence semi-angle. The probe current was 30 pA. The real-space sampling was 140 × 140 nm2 for each dataset, with about 0.69 nm pixel size. The reciprocal space area spans 14 × 14 Å−2, with a pixel size of around 0.1 Å−1. Each diffraction pattern was acquired with 1 ms dwell time, with an additional 0.86 ms for readout time.
Visualization of Friedel-pair asymmetry in Kikuchi bands
Polarity-induced asymmetry in nanobeam electron diffraction is revealed by plotting the antisymmetric component of the diffraction pattern. We first establish the asymmetry in simulated data. Extended Data Fig. 3a shows two simulated diffraction patterns, I(k), with P-down and P-up structures (the same simulated patterns in Fig. 2c). We define the antisymmetric component d(k) = I(k) – I(–k), in the 2D diffraction pattern which is sensitive to polarity. The 2D pattern contains intense features at small k. Multiplying diffraction intensity by |k|2 reduces the dominance of the very strong low-k signal and amplifies high-k features of the Kikuchi bands, allowing structural information in the outer parts of reciprocal space to become visible. To visualize the differences in the high-k Kikuchi bands, we thus plot A(k) = |k|2d(k) = |k|2(I(k) – I(–k)). Extended Data Fig. 3c shows clear asymmetry along the k y direction when comparing P-up and P-down diffraction patterns. Line profiles (Extended Data Fig. 3d) further help visualize this asymmetry.
The connection between polarity and intensity asymmetry is revealed in the experimental data as well. To better visualize the intensity asymmetry in the experimental data, we average diffraction patterns from 3 × 3 nm2 regions (5 × 5 pixels), which is smaller than the typical domain size of about 20 nm, to improve the signal-to-noise ratio. We reproduce results consistent with the simulations by plotting A(k) from regions with P-up and P-down regions (Extended Data Fig. 3e–h).
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