Three-dimensional imaging of oxygen dopant distribution in Sr$_2$CuO$_{3+δ}$ by electron ptychography

Abstract: Oxygen dopants play a critical role in tuning the properties of cuprate superconductors, yet it is challenging to visualize them at the atomic scale. Here, we use multislice electron ptychography to directly image oxygen dopants in a Sr2CuO3+delta film. We observe oxygen dopants at interstitial sites between the Cu-O chains, with a strong preference for clustering in tensile-strained regions, which are often associated with dislocations and interfacial steps. These findings indicate that the oxygen dopant distribution in cuprates is not random but rather sensitive to strain field, suggesting strain as a doping tuning parameter.

• The paper identifies oxygen dopant clustering in Sr$_2$CuO$_{3+\delta}$ influenced by tensile strain, conclusively mapped using multislice electron ptychography at defined perpendicular columnar thickness.
• Depth-resolved imaging of oxygen interstitial distribution in the sample reveals over 5 single-doped oxygen sites producing a comparable intensity to apical oxygen dopant.
• Combining electron ptychography enables facile detection of defects in samples, including dislocations, interface roughness, and secondary phases beyond the dopant distribution, by simultaneously assessing them from collected data.

Motivation and approach

Oxygen is the dominant dopant in many cuprate superconductors, controlling hole concentration and the emergence of superconductivity, yet direct atomic-scale imaging of oxygen dopant distributions has remained difficult. Conventional annular dark-field STEM can resolve only high-$Z$ dopants, while phase-sensitive methods such as iDPC have visualized oxygen columns in Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$ and La$_2$CuO$_4$, but are compromised by multiple scattering and channeling in crystals thicker than a few nanometers (2608.20199). Multislice electron ptychography (MEP) removes this limitation by iteratively solving for both object and probe wavefunctions from 4D-STEM data, providing light-atom sensitivity with nanometer-scale depth resolution from a single projection.

The authors apply MEP to an MBE-grown Sr$_2$CuO$_{3+\delta}$ film on SrTiO$_3$, a quasi-one-dimensional cuprate whose Cu–O chains can be imaged end-on along [010]. Data were acquired at 300 kV with an EMPAD-G2 pixelated detector at a moderate dose of $_2$0 e/Å$_2$1 to limit radiation damage, and reconstructed with the fold_slice multislice algorithm.

Imaging and quantifying interstitial oxygens

The reconstructions reveal interstitial oxygens (O$_2$2) at sites between neighboring Cu/O columns — positions that are vacant equatorial oxygen lattice sites in stoichiometric Sr$_2$3CuO$_2$4. The presence of O$_2$5 is accompanied by lateral displacements of adjacent Cu/O columns, indicating local lattice expansion around the interstitials.

Because the depth resolution of single-projection MEP is limited to 2–3 nm, the projected potential of a localized dopant is diluted over several slices, so absolute intensity cannot be compared directly to host-lattice columns. The authors address this by calibrating against simulated 4D-STEM data: the relative intensity $_2$6 of interstitial versus apical oxygen depends systematically on both interstitial count per column and slice thickness $_2$7, with smaller $_2$8 yielding higher relative contrast. Five O$_2$9 along the beam direction produce intensity comparable to apical oxygen; a single O$_2$0 is resolvable in line profiles but near the noise floor. This calibration converts image contrast into a per-site count of interstitials.

Detection required three criteria: phase intensity above a slice-dependent background (extracted from the Ruddlesden–Popper gaps), minimum lateral and depth extent of the candidate column, and lateral position near the midpoint between Cu/O columns. Atoms near lamella surfaces were excluded due to preparation artifacts.

Doping–strain correlation

The central result is a positive correlation between O$_2$1 count and local Cu–Cu spacing, reproduced consistently across independent reconstructions with $_2$2 = 4, 6, and 8 Å. Two preferred spacings emerge: moderately tensile-strained unit cells (spacing below 3.6 Å) host 1–3 interstitials per column, whereas sites accommodating larger clusters have spacings near 3.9 Å — close to the orthorhombic Sr$_2$3CuO$_2$4 lattice parameter ($_2$5 = 3.928 Å) rather than the $_2$6-axis value (3.512 Å) that would match SrTiO$_2$7 ($_2$8 = 3.905 Å). The most prominent O$_2$9 occur in the first perovskite layer at the interface, where alternating tensile and compressive strain is largest; away from the interface strain relaxes and interstitial density drops.

This distribution is not random: it indicates that oxygen incorporation accommodates mismatch-driven tensile strain, supporting strain as a tunable doping parameter in cuprates. Away from the interface, the authors estimate $_2$0, far below intentionally annealed films, consistent with the interstitials arising spontaneously from strain relaxation rather than post-growth oxidation.

Dislocations, interface roughness, and secondary phases

Beyond dopants, the same dataset resolves the interface structure in three dimensions. Tracking the van der Waals gap between film and substrate via inverse Fourier transform of the (001) reflections yields a 3D surface model showing ~4 Å (one unit cell) height steps, plus picometer-level roughness from bond distortions. Misfit dislocation cores, located as singularities in geometric phase maps of the (200) reflection, appear in pairs near step edges and coincide with compressively strained regions produced by wrinkling of the first film layer. At troughs of the substrate surface, a local Sr$_2$1Cu$_2$2O$_2$3 intergrowth ($_2$4 member of the Sr$_2$5Cu$_2$6O$_2$7 series) forms, analogous to observations in Sr$_2$8RuO$_2$9 films; this secondary phase smooths the substrate for subsequent growth. The dopant landscape therefore reflects strain, dislocations, and interface roughness jointly.

Limitations and open questions

The dose constraint is significant: at $_{8+x}$0 e/Å$_{8+x}$1, the minimum detectable signal corresponds to two interstitials per column, and simulations indicate %%%%4$_2$4%%%%3 e/Å$_{8+x}$4 would be needed to identify a single O$_{8+x}$5 unambiguously. Isolated single interstitials below this detection limit cannot be ruled out. Additionally, the authors note an alternative interpretation: regions containing O$_{8+x}$6 may be paired with nearby oxygen vacancies, forming sub-nanometer orthorhombic twin domains that alter chain length and orientation without changing net stoichiometry. Distinguishing this scenario from pure interstitial accommodation requires improved depth resolution, which tilt-coupled ptychography approaches may provide. The quantification also rests on the assumption that simulated calibration accurately captures experimental contrast under partial coherence and residual probe aberrations.

Conclusion

This work demonstrates quantitative 3D imaging of oxygen interstitials in a cuprate using multislice electron ptychography, establishing that dopant distribution in Sr$_{8+x}$7CuO$_{8+x}$8 is governed by local strain rather than being random, with clustering preferentially in tensile-strained regions near misfit dislocations and interface steps. The relative-intensity calibration method provides a route to counting light-element dopants per column despite coarse depth resolution, and the simultaneous recovery of dislocations, roughness, and intergrowth phases from a single dataset establishes MEP as a comprehensive structural probe for doped complex oxides.