March 1, 2024

Physicists detect elusive ‘Bragg glass’ phase with machine learning tool

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CDWs in PDxErTe3. TheCrystal structure of pure ErTe3. Te planes have approximately square geometry. The crystal belongs to the WIwI space group, B denotes the out-of-plane axis, and The It is w are the axes in the plane. BSchematic25 showing Bragg peaks (circles) and CDW peaks (triangles) in the plane (The*–w*) reciprocal space. The peaks of satellites CDW-1 (up triangle) and CDW-2 (down triangle) are aligned along the w* It is The* axes, respectively. wScheme for the plan (The*–w*) intensity distribution of the pair of CDW satellite peaks (in (H,I± qw)) around a Bragg peak (in ( H, I )), with the following three characteristics of interest: peak intensity, peak width Γ(solid arrow) and the asymmetry in the diffuse scattering around the satellite peaks (dashed arrow). d, Table summarizing the diagnoses for classifying the three phases. The first line describes the intensity-temperature trajectory of the CDW. Only the pure sample with long-range order exhibits a sharp onset, marking the transition temperature Tw. On the other hand, Bragg glass cannot be distinguished from short-range order, because even after Bragg glass order breaks with increasing temperature, short-range fluctuations persist (due to disorder fixation) and contribute for CDW intensity. The second line illustrates a simplified temperature dependence of the CDW peak width Γ . Credit: Nature Physics (2024). DOI: 10.1038/s41567-023-02380-1

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CDWs in PDxErTe3. TheCrystal structure of pure ErTe3. Te planes have approximately square geometry. The crystal belongs to the WIwI space group,B denotes the out-of-plane axis, andThe It is ware the axes in the plane. BSchematic25 showing Bragg peaks (circles) and CDW peaks (triangles) in the plane ( The*–w*) reciprocal space. The peaks of satellites CDW-1 (up triangle) and CDW-2 (down triangle) are aligned along thew* It isThe* axes, respectively. wScheme for the plan (The*– w*) intensity distribution of the pair of CDW satellite peaks (in ( H, I± qw)) around a Bragg peak (in ( H , I)), with the following three characteristics of interest: peak intensity, peak widthΓ (solid arrow) and the asymmetry in the diffuse scattering around the satellite peaks (dashed arrow). d, Table summarizing the diagnoses for classifying the three phases. The first line describes the intensity-temperature trajectory of the CDW. Only the pure sample with long-range order exhibits a sharp onset, marking the transition temperatureTw. On the other hand, Bragg glass cannot be distinguished from short-range order, because even after Bragg glass order breaks with increasing temperature, short-range fluctuations persist (due to disorder fixation) and contribute for CDW intensity. The second line illustrates a simplified temperature dependence of the CDW peak widthΓ. Credit:Nature Physics (2024). DOI: 10.1038/s41567-023-02380-1

Cornell quantum researchers have detected an elusive phase of matter called the Bragg glass phase using large volumes of X-ray data and a new machine learning data analysis tool. The discovery resolves a long-standing question about whether this almost – but not quite – ordered state of Bragg glass can exist in real materials.

The article, “Bragg glass signatures in PdxErTe3 with X-ray diffraction temperature clustering (X-TEC)”, is published inNature Physics. The lead author is Krishnanand Madhukar Mallayya, a postdoctoral researcher in the Department of Physics in the Faculty of Arts and Sciences (A&S). Eun-Ah Kim, professor of physics (A&S), is the corresponding author. The research was conducted in collaboration with scientists at Argonne National Laboratory and Stanford University.

Researchers present the first evidence of a Bragg glass phase detected from X-ray scattering, which is a probe that accesses the entire mass of a material, as opposed to just the surface of a material, in a density wave of systematically disordered cargo. CDW material), PdxErTe3. They used comprehensive X-ray data and a new machine learning data analysis tool, X-ray Temperature Clustering (X-TEC).

“Despite its theoretical prediction three decades ago, concrete experimental evidence of CDW Bragg glass in most of the crystal was still lacking,” Mallayya said.

Theoretically, there is a sharp distinction between three phases: long-range order, Bragg glass and disordered state, Kim said. In the disordered state, the CDW correlation decays within a finite distance. In the long-range ordered state, the charge density wave correlation continues indefinitely.

In the Bragg glass phase, Kim continued, the CDW correlation decays so slowly that it will only completely disappear at infinite distances.

“The challenge is to detect these distinctions from experimental data that also reflect real-life issues such as noise and finite resolution of the experimental setup,” Kim said.

Researchers overcame key challenges through strategic synergy between materials, data and machine learning tools. On the materials front, they found, in collaboration with Stanford scientists, a family of CDW materials that will allow for a systematic study with control over the dirt to be used in the experiment – ​​PdxErTe3. On the data front, they collected large amounts of data at Argonne National Laboratory in collaboration with Argonne scientists.

On the machine learning front, they used X-TEC, a machine learning tool, to analyze the massive volume of data with a scalable and automated approach.

“An experimental detection of the Bragg glass phase via X-ray diffraction resolved the open question about the fate of CDW order subject to fouling,” Mallayya said.

Going beyond the specific scientific problem, the paper presents a new mode of research in the era of big data, Kim said: “Using machine learning tools and data scientific perspectives, we can go after challenging questions and track subtle signatures through a comprehensive data analysis approach.”

The researchers wrote that this detection of the order of Bragg glasses and the resulting phase diagram significantly advances our understanding of the complex interplay between disorder and fluctuations. Furthermore, using X-TEC to target fluctuations through a high-throughput measurement of “peak distribution” could revolutionize the way fluctuations are studied in dispersion experiments.

More information:
Krishnanand Mallayya et al, Bragg glass signatures in PdxErTe3 with X-ray diffraction temperature grouping,Nature Physics(2024). DOI: 10.1038/s41567-023-02380-1

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