Partial breakdown of translation symmetry at a structural quantum critical point associated with a ferroelectric soft mode

Y. Ishii, A. Yamamoto, N. Sato, Y. Nambu, S. Ohira-Kawamura, N. Murai, K. Ohara, S. Kawaguchi, T. Mori, and S. Mori

Phys. Rev. B 106, 134111 – Published 27 October 2022

Abstract

We report that complete suppression of a phonon-driven structural phase transition causes partial breakdown of a three-dimensional translation symmetry in a well-defined sublattice. This state is revealed for a dielectric compound, ${Ba}_{1 - x} {Sr}_{x} {Al}_{2} O_{4}$ , that comprises an ${AlO}_{4}$ network incorporated into a hexagonal Ba(Sr) sublattice. Pair distribution function analyses and inelastic neutron scattering experiments provide clear-cut evidence of the ${AlO}_{4}$ network forming a continuum of Al-O short-range correlations similar to glasses, whereas the Ba(Sr) sublattice preserves the original translational symmetry. This glassy network significantly dampens the phonon spectrum and transforms it into the broad one resembling those typically observed in glass materials.

Received 13 June 2022
Revised 31 August 2022
Accepted 13 September 2022

DOI:https://doi.org/10.1103/PhysRevB.106.134111

Physics Subject Headings (PhySH)

Phase transitions Quantum criticality Thermal conductivity

Ferroelectrics

Inelastic neutron scattering X-ray pair-distribution function analysis

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Y. Ishii ^1,*, A. Yamamoto², N. Sato ^3,4, Y. Nambu ^5,6,7, S. Ohira-Kawamura⁸, N. Murai⁸, K. Ohara ⁹, S. Kawaguchi⁹, T. Mori ³, and S. Mori¹

¹Department of Materials Science, Osaka Metropolitan University, Sakai, Osaka 599-8531, Japan
²Department of Materials Science, Osaka Prefecture University, Sakai, Osaka 599-8531, Japan
³International Center for Materials Nanoarchitectonics (WPI-MANA), National Institute for Materials Science (NIMS), Tsukuba, Ibaraki 305-0044, Japan
⁴International Center for Young Scientists, NIMS, Tsukuba, Ibaraki 305-0047, Japan
⁵Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan
⁶Organization for Advanced Studies, Tohoku University, 2-1-1 Katahira, Sendai 980-8577, Japan
⁷FOREST, Japan Science and Technology Agency, Kawaguchi, Saitama 332-0012, Japan
⁸Materials and Life Science Division, J-PARC Center, Tokai, Ibaraki 319-1195, Japan
⁹Japan Synchrotron Radiation Research Institute (JASRI), SPring-8, Sayo, Hyogo 679-5198, Japan

^*yishii@omu.ac.jp

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Issue

Vol. 106, Iss. 13 — 1 October 2022

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Images

Figure 1
Relationship between the (a) Ba sublattice and (b) ${AlO}_{4}$ network of the high-temperature phase of ${BaAl}_{2} O_{4}$ (space group $P 6_{3} 22$ ). Solid boxes indicate the multiple unit cells. (c) Ideal crystal structure of the high-temperature phase. The cell parameters determined by using laboratory x-ray diffraction are $a = 5.232 6 (3)$ Å and $c = 8.8174 (7)$ Å at 500 K. (d) Split atom model used as an average structure model for $x \geq 0.05$ . In this model, the Ba, O1, and O2 sites are split into several seats with lowered symmetries and partial occupancies. Panels (e) and (f) describe the relationship between the ideal and split positions of Ba and O1 atoms, respectively. (e) Ba atoms are accommodated at the $2 b$ site at $z = 1 / 4$ in the ideal $P 6_{3} 22$ structure. When the Ba atoms have a small displacement ( $\pm δ$ ) along the $c$ axis from the ideal site, they can be accommodated at the $4 e$ site with lowered symmetry. (f) O1 atoms are accommodated at the $2 d$ site in the ideal structure. Al atoms are not shown here. Because the $2 d$ site is on the threefold axis along the $c$ axis, the three seats of the $6 h$ site are generated in the split atom model.
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Figure 2
Full phase diagram of ${Ba}_{1 - x} {Sr}_{x} {Al}_{2} O_{4}$ [9, 11, 12, 22, 23, 24]. The phase boundaries are determined using powder x-ray diffraction (filled circles), synchrotron x-ray diffraction experiments for single crystals (open circles), and dielectric measurements (diamonds). $T^{*}$ denotes the temperature at which thermal diffuse scattering caused by the $M_{2}$ and $K_{2}$ soft modes shows a maximum intensity. The $K_{2}$ mode is another dominant soft mode in the high-temperature phase of ${BaAl}_{2} O_{4}$ , and the $P 6_{3} (\sqrt{3} a)$ structure is the condensed state of the $K_{2}$ mode [24]. The Supplemental Material provides further details of the phase diagram of ${Ba}_{1 - x} {Sr}_{x} {Al}_{2} O_{4}$ [13].
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Figure 3
(a) Synchrotron powder x-ray diffraction profiles in the range of $Q = 2.55$ –2.65 $Å^{- 1}$ for ${Ba}_{1 - x} {Sr}_{x} {Al}_{2} O_{4}$ ( $x = 0$ –0.1) samples at 15 K. The 1/2 3/2 1 superlattice reflection observed at $Q \approx 2.6 Å^{- 1}$ disappears between $x = 0.06$ and 0.1. (b) FWHM as a function of Sr composition ( $x$ ). (c) Correlation length ( $ξ$ ) converted from the FWHM value. The value of $ξ$ decreases with $x$ and reaches $\approx 20$ nm at $x = 0.06$ . This length corresponds to only $\approx 20$ unit cells of the low-temperature phase.
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Figure 4
(a) Experimentally derived PDFs $[g (r)]$ at 300 K of ${Ba}_{1 - x} {Sr}_{x} {Al}_{2} O_{4}$ with $x = 0$ –0.3 (solid curves). The $g (r)$ curves for different compositions are plotted with a relative offset. Model calculations (broken curves) are also performed for each composition by using the average structures obtained with powder x-ray structural refinements [12]. Partial $g (r)$ curves for the average structure of $x = 0$ are shown at the bottom. The peak assigned as Al-O comes from the Al-O1 and Al-O2 correlations in the ${AlO}_{4}$ tetrahedra. (b), (c), and (d) Peak positions of the Al-O, Ba-Al, and Ba-Ba correlations, respectively.
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Figure 5
Dynamical structure factor, $S (Q, E$ ), for ${Ba}_{1 - x} {Sr}_{x} {Al}_{2} O_{4}$ powder samples of (a) $x = 0$ , (b) 0.03, (c) 0.07, (d) 0.2, and (e) 0.3 measured at 100 K with $E_{i} = 17.255$ meV. The insets show an enlarged view in the range of $E = 1.0$ –2.4 meV and $| Q | = 2$ –3 Å obtained with $E_{i} = 8.485$ meV. The Al sample can background has been subtracted from each scan. (f) $S (Q, E)$ calculated using the oclimax program [17] based on the phonon calculation for ${BaAl}_{2} O_{4}$ . (g) Phonon-dispersion relations calculated on the ferroelectric $P 6_{3}$ ( $2 a$ ) structure of ${BaAl}_{2} O_{4}$ . The calculation uses a $2 \times 2 \times 3$ supercell of the unit cell. (h) Inelastic spectra energy integrated over the energy transfer $E = 1$ –2.3 meV with $E_{i} = 8.485$ meV. The inset presents the maximum intensity of the peak at $Q \approx 2.5$ Å $^{- 1}$ . (i) Inelastic spectra $Q$ integrated over $| Q | = 2$ –4 Å $^{- 1}$ with $E_{i} = 17.255$ meV. Profiles are offset by 0.09 for clarity. The intensities in panels (h) and (i) are normalized using a coherent cross section of the 111 nuclear peak whose structure factor is independent of the Ba/Sr ratio.
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Figure 6
Log-log plots of the thermal conductivity as a function of temperature for ${Ba}_{1 - x} {Sr}_{x} {Al}_{2} O_{4}$ of (a) $x = 0$ –0.3 and (b) $x = 0.4$ –1. Error bars are smaller than the symbol size. Broken lines show the power fit using $κ \propto T^{α}$ for the experimental data of $x = 0$ and $x = 1$ . A plateau is observed for $x = 0.07$ –0.4 near 10 K, as indicated by an arrow. The inset shows the power exponent $α$ plotted against $x$ .
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