Researchers have mapped the internal structure of the cuprate superconductor La1.675⁢Eu0.2⁢Sr0.125⁢CuO4 using scanning three-dimensional x-ray diffraction, a technique that overcomes longstanding challenges in visualizing bulk material at a microscopic level. The work reveals remarkably broad, tetragonallike domain wall regions within the material’s orthorhombic crystal structure, suggesting a more disordered internal structure than previously understood.

Characterizing these structural domains at the ID11 beamline between 300 and 100 K further exposes a fine microstructure of orthorhombiclike stripes embedded within a tetragonal matrix, a finding with significant consequences for interpreting the interplay between structural and electronic heterogeneity in these complex materials. Domain walls reach approximately 150 nanometers. This advance establishes 3DXRD as a powerful tool for understanding how microstructure governs material functionality.

3DXRD Resolves Bulk Microstructure in La1.675⁢Eu0.2⁢Sr0.125⁢CuO4

Scanning three-dimensional x-ray diffraction (3DXRD) has revealed unexpectedly wide regions where the crystal structure shifts within the cuprate superconductor La1. 675⁢Eu0. 2⁢Sr0. 125⁢CuO4, challenging previous assumptions about the material’s internal order. These domain walls, measuring in the hundreds of nanometers, appear tetragonal-like within a crystal structure generally considered orthorhombic, indicating a degree of structural disorder not previously observed in bulk samples of this material.

The technique employed offers an advantage over methods like transmission electron microscopy, which typically only probes surface features, by providing a cross-sectional view through the entire material volume. This detailed mapping of the bulk microstructure was achieved at the ID11 beamline of the European Synchrotron Radiation Facility (ESRF), characterizing the structural domains of the cuprate between 300 and 100 K. Cooling the material to 100 K further exposed a refined microstructure, revealing fine stripes with an orthorhombic-like arrangement embedded within the dominant tetragonal matrix.

The observed changes suggest a dynamic relationship between the arrangement of charge stripes and the superconducting properties of the cuprate. The ability to visualize these structures in three dimensions opens new avenues for quantitatively linking microstructure and mesostructure to macroscopic material properties. While current 3DXRD capabilities do not extend to directly mapping the weak reflections of charge density waves (CDW), the researchers anticipate that future advances in beamline technology could enable sub-100-nanometer resolution mapping of both structure and CDW order.

Such a development would facilitate establishing direct, spatially resolved correlations between structure and electronic behavior, significantly enhancing understanding of competing orders within complex oxides. Researchers emphasize that the focus of this work remains on resolving the bulk microstructure, rather than the electronic response itself.

Given the established correlation length of both superconductivity and CDW order parameters falls between 2 and 15 nanometers in cuprates, the team concludes that the symmetry breaking associated with these domain wall structures shapes the competition between superconductivity and CDW order. This suggests the domain walls are an active element influencing it. The versatility of scanning 3DXRD extends beyond cuprate superconductors, offering a powerful approach for resolving bulk microstructures in any phase transition considered ferroelastic or coelastic.

The method is effective when domain structures measure upward of 70 nanometers in length, encompassing martensitic transitions driven by strain, and nearly all structural and magnetic phase transitions where strain couples to the primary order parameter. “Scanning 3DXRD enables direct visualization of bulk microstructural heterogeneity with a level of detail that has not previously been accessible across such length scales,” the researchers write, highlighting the technique’s potential for broad application in materials science.

Tetragonal-Orthorhombic Phase Transitions Drive Microstructural Complexity

The persistence of these domain walls down to at least 10 K in LESCO and isostructural compounds indicates a coupling to electronic phase separation, potentially linking superconductivity and charge density wave order. This direct visualization of bulk microstructural heterogeneity represents an advancement in the field, enabling researchers to move beyond indirect measurements and directly observe the organization of phases within a material. Beyond cuprates, the versatility of scanning 3DXRD extends to a broad range of layered perovskite structures, including high-pressure superconductors exhibiting complex structural phase transitions driven by octahedral rotations and tilting.

The variation in calculated strains suggests domain sizes range from in LESCO to in Tl-2201, and down to in Bi-2223, demonstrating the technique’s sensitivity to subtle structural differences. This observation underscores the importance of understanding how interfaces formed during phase transitions can become active elements, hosting properties absent in the surrounding bulk.

While conductive atomic force microscopy shows promise for certain materials, anion migration currently prevents reliable interpretation in LESCO, highlighting the need for complementary techniques. “Any phase transition that may be considered as ferroelastic or coelastic can be imaged using our implementation of scanning 3DXRD,” the researchers state, emphasizing the broad applicability of the method. In-plane superconducting correlations may persist despite the suppression of bulk superconductivity by CDW order, a phenomenon that demands further investigation.

Broad Domain Walls Coexist Within 214 Cuprate Superconductors

Strain maps of La1. These features are not isolated defects but extended areas exhibiting near-zero strain, a scale orders of magnitude larger than typically observed in ferroelastic or ferroelectric domain walls.

Analysis of absolute strain magnitude uncovered submicron variation at all temperatures, resembling tweed domain structures, and the spatial resolution of the reconstructions is at least 70 nanometers. This resolution, based on the determined strain resolution of the experiment, allowed researchers to map the temperature evolution of structural domains, demonstrating a transition from bimodal distribution at 300 K to a more homogeneous, though still asymmetric, distribution at 100 K.

Maps of absolute strain magnitude further enhanced these observations, revealing broad, low-transformation temperature (LTT)-like features within the low-temperature orthorhombic (LTO) phase at 300 K and subtle LTO-like filaments within the LTT phase at 100 K. The observed microstructure is not unique to this specific cuprate; a symmetry analysis of parent structures across the broader family of high-temperature superconductors reveals a striking generality, all based on the same symmetry. This suggests the observed domain wall behavior may be widespread within the 214 cuprate family and potentially other layered perovskite structures.

Infrared nanospectroscopy has previously revealed 60-100 nanometer wide ferroelastic walls, attributed to gradual rotation of octahedral tilt and rotation order parameters, and Néel-like ferroelectric domain walls, where polarization rotates rather than vanishes, have been predicted and observed in other systems. These findings support a broader understanding of wide domain boundaries as intrinsic structural features that can serve as functionally active elements.

The broader significance of this work, according to the researchers, lies in the experimental approach itself. The technique’s ability to directly visualize these structures with a level of detail not previously attainable promises to provide insights into the complex behavior of these materials and potentially guide the development of future superconducting technologies.

Structural Distortions Impact Charge Stripe Alignment & Superconductivity

The breadth of structural distortions within the cuprate superconductor La1.125⁢CuO4 directly impacts the alignment of charge stripes, a finding revealed through detailed scanning three-dimensional x-ray diffraction (3DXRD) measurements taken between 300 and 100 K. These walls, extending significantly beyond expectations, suggest a level of internal disorder previously underestimated in these complex materials and challenge assumptions of a homogeneous structural state underpinning superconductivity. Researchers found that these walls, where the sense of octahedral rotations reverses, induce corresponding charge stripe rotations, potentially frustrating interlayer Josephson coupling critical for superconductivity.

This structural basis for suppressing superconductivity is not coincidental, but instead appears linked to the critical octahedral tilting amplitude, suggesting a fundamental connection between microstructure and the composition-doping phase diagram of these materials. Cooling the material to 120 and 100 K appears to reduce microscale variation, indicating a transition toward a more homogeneous, albeit still distorted, structure.

These fine structural heterogeneities actively shape charge density wave (CDW) order and may create pathways for localized superconductivity. Recent studies have previously revealed 60-100 nanometer wide ferroelastic walls across multiple cuprates, but a detailed description of the underlying microstructure remained elusive until now. The present results suggest a natural framework for the microscopic coexistence of CDW order, superconductivity, and even antiferromagnetic order, offering a new perspective on the interplay of these competing phases.

“Such fine structural heterogeneity likely actively shapes CDW order and may provide filamentary pathways for localized or lower-dimensional superconductivity,” the researchers write. The observed distortions couple to symmetry-breaking strains along a direction between the oxygen-copper-oxygen planes, a phenomenon also seen in other cuprate families.

This coupling to symmetry-breaking strains is not limited to this specific composition; examples exist across the broader cuprate landscape, suggesting a common underlying mechanism governing structural heterogeneity and its impact on electronic properties. The work helps address a long-standing gap in understanding, suggesting that detailed characterization of the microstructure at the domain level is essential for accurately measuring and controlling superconductivity in these materials.

Symmetry-Mode Analysis Defines LTO and LTT Order Parameters

The transition from the LTO to LTT phase in the cuprate superconductor LESCO, occurring around 160 K, is not a simple shift but a complex rearrangement described through symmetry-mode analysis, a method detailing distorted structures as modifications of a high-symmetry parent structure. This analytical approach allows for a direct microscopic description of the order parameters governing the material’s behavior, utilizing software tools like isodistort to map these changes.

The absence of a clear group-subgroup relationship between LTO and LTT necessitates a region where both phases coexist, a phenomenon observed in LESCO and isostructural LBCO down to temperatures as low as 10 K. While charge density wave order is generally understood to suppress bulk superconductivity, in-plane superconducting correlations may still exist within the material.

Distinguishing between LTO and LTT domains proved challenging due to a lack of systematic absence conditions in the lower-temperature LTT structure; instead, researchers focused on variations in ferroelastic strain, which functions as a secondary order parameter for octahedral tilting. Iterative reconstructions, based on the spatial distribution of local average unit cell parameters, revealed a strong correlation between reconstructions derived from reflection intensities and those from peak positions, validating the methodology employed.

These reconstructions demonstrate that the observed domain walls are not merely boundaries, but effectively extended regions resembling the LTT phase embedded within the LTO matrix. The substantial thickness of these walls, reaching approximately 150 nanometers, could explain coherent scattering signals previously misinterpreted as distinct phases in conventional x-ray diffraction.

This offers a potential explanation for the phase coexistence reported in LESCO and related cuprates, though the ability to resolve these structures depends not only on the coherence of the order parameters within the material but also on the resolution of the instrument and the coherence of the radiation source used for measurement. The study concludes that the superconducting or charge density wave order parameters will perceive the domain wall symmetry as a bulk property.

As ferroelastic strains decrease, the energy and width of these domain walls fall rapidly, a consequence of their quadratic dependence on strain. Reductions in LTO transition temperatures and associated ferroelastic strains are common across 214 cuprates, influenced by factors like doping effects. The presence of such domain wall structures is not limited to this specific material, but is expected to occur in a wider range of cuprate superconductors.

👉 More information
🗞 Giant Domain Walls and Intrinsic Heterogeneity in 214 Cuprate Superconductors
✍️ Evie Ladbrook, Jon P. Wright and Mark S. Senn
🧠 DOI: http://link.aps.org/doi/10.1103/r62x-kt5j

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