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Register a new userParadigm shift for quantum paraelectric: softening of longitudinal modes
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Authors
Yaron Kedem
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We revisit the quantum phase transition from a paraelectric state to a ferroelectric one and in particular the widespread distinction between a longitudinal modes to transverse one. In contrast to transitions at finite temperature, for a quantum phase transition breaking a discrete symmetry the splitting between the modes is irrelevant. We show that an anisotropy in the context of a quantum phase transition leads to a different behavior, compared to a classical transition, and suggest an experiment to observe it. The result is essential for explaining the pairing mechanism in strontium titanate.
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Accurately determining the crystallographic structure of a material, organic or inorganic, is a critical primary step in material development and analysis. The most common practices involve analysis of diffraction patterns produced in laboratory XRD, TEM, and synchrotron X-ray sources. However, these techniques are slow, require careful sample preparation, can be difficult to access, and are prone to human error during analysis. This paper presents a newly developed methodology that represents a paradigm change in electron diffraction-based structure analysis techniques, with the potential to revolutionize multiple crystallography-related fields. A machine learning-based approach for rapid and autonomous identification of the crystal structure of metals and alloys, ceramics, and geological specimens, without any prior knowledge of the sample, is presented and demonstrated utilizing the electron backscatter diffraction (EBSD) technique. Electron backscatter diffraction patterns are collected from materials with well-known crystal structures, then a deep neural network model is constructed for classification to a specific Bravais lattice or point group. The applicability of this approach is evaluated on diffraction patterns from samples unknown to the computer without any human input or data filtering. This is in comparison to traditional Hough transform EBSD, which requires that you have already determined the phases present in your sample. The internal operations of the neural network are elucidated through visualizing the symmetry features learned by the convolutional neural network. It is determined that the model looks for the same features a crystallographer would use, even though it is not explicitly programmed to do so. This study opens the door to fully automated, high-throughput determination of crystal structures via several electron-based diffraction techniques.
The lattice dynamics of the $rm YMnO_3$ magneto-electric compound has been investigated using density functional calculations, both in the ferroelectric and the paraelectric phases. The coherence between the computed and experimental data is very good in the low temperature phase. Using group theory, modes continuity and our calculations we were able to show that the phonons modes observed by Raman scattering at 1200K are only compatible with the ferroelectric $P6_{3} cm$ space group, thus supporting the idea of a ferroelectric to paraelectric phase transition at higher temperature. Finally we proposed a candidate for the phonon part of the observed electro-magnon. This mode, inactive both in Raman scattering and in Infra-Red, was shown to strongly couple to the Mn-Mn magnetic interactions.
Motivated by recent experimental findings, we study the contribution of a quantum critical optical phonon branch to the thermal conductivity of a paraelectric system. We consider the proximity of the optical phonon branch to transverse acoustic phonon branch and calculate its contribution to the thermal conductivity within the Kubo formalism. We find a low temperature power law dependence of the thermal conductivity as $T^{alpha}$, with $1 < alpha < 2$, (lower than $T^3$ behavior) due to optical phonons near the quantum critical point. This result is in accord with the experimental findings and indicates the importance of quantum fluctuations in the thermal conduction in these materials.
We demonstrate how the quantum paraelectric ground state of SrTiO$_3$ can be accessed via a microscopic $ab~initio$ approach based on density functional theory. At low temperature the quantum fluctuations are strong enough to stabilize the paraelectric phase even though a classical description would predict a ferroelectric phase. We find that accounting for quantum fluctuations of the lattice and for the strong coupling between the ferroelectric soft mode and lattice elongation is necessary to achieve quantitative agreement with experimental frequency of the ferroelectric soft mode. The temperature dependent properties in SrTiO$_3$ are also well captured by the present microscopic framework.
Analysis of the spheroidal modes of vibration of a free elastic sphere show that they can be qualitatively grouped into two categories: primarily longitudinal and primarily transverse. This is not a sharp distinction. However, there is a relatively stark contrast between the two kinds of modes. Primarily transverse modes have a small divergence and have frequencies that are almost functionally independent of the longitudinal speed of sound. Analysis of inelastic light scattering intensity from confined acoustic phonons in nanoparticles requires an understanding of this qualitative distinction between different spheroidal modes. In addition, some common misconceptions about spheroidal modes are corrected.
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