Anharmonicity of the antiferrodistortive soft mode in barium zirconate BaZrO3

Anharmonicities; Antiferrodistortive; Atomic motion; Brillouin zone boundary; Cubic structure; Quantum fluctuation; Soft modes; Soft-phonon mode; Temperature dependence; Theoretical study; Electronic, Optical and Magnetic Materials; Condensed Matter Physics; Physics - Materials Science

Abstract :

[en] Barium zirconate (BaZrO3) is one of the very few perovskites that is claimed to retain an average cubic structure down to 0K, while being energetically very close to an antiferrodistortive phase obtained by condensation of a soft phonon mode at the R point of the Brillouin zone boundary. In this work, we report a combined experimental and theoretical study of the temperature dependence of this soft phonon mode. Inelastic neutron and x-ray scattering measurements on single crystals show that it softens substantially from 9.4meV at room temperature to 5.6meV at 2K. In contrast, the acoustic mode at the same R point is nearly temperature independent. The effect of the anharmonicity on the lattice dynamics is investigated nonperturbatively using direct dynamic simulations as well as a first-principles-based self-consistent phonon theory, including quantum fluctuations of the atomic motion. By adding cubic and quartic anharmonic force constants, quantitative agreement with the neutron data for the temperature dependence of the antiferrodistortive mode is obtained. The quantum fluctuations of the atomic motion are found to be important to obtain the proper temperature dependence at low temperatures. The mean-squared displacements of the different atoms are determined as function of temperature and are shown to be consistent with available experimental data. Adding anharmonicity to the computed fluctuations of the Ba-O distances also improves the comparison with available extended x-ray absorption fine structure data at 300K.

Disciplines :

Physics

Author, co-author :

Rosander, Petter; Department of Physics, Chalmers University of Technology, Göteborg, Sweden

Fransson, Erik ; Department of Physics, Chalmers University of Technology, Göteborg, Sweden

MILESI-BRAULT, Cosme ; University of Luxembourg > Faculty of Science, Technology and Medicine > Department of Physics and Materials Science > Team Mael GUENNOU ; Materials Research and Technology Department, Luxembourg Institute of Science and Technology, Belvaux, Luxembourg ; Institute of Physics of the Czech Academy of Sciences, Prague, Czech Republic

TOULOUSE, Constance ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Physics and Materials Science (DPHYMS)

Bourdarot, Frédéric ; Service de Modélisation et d'Exploration des Mateériaux, Université Grenoble Alpes et Commissariat À l'Énergie Atomique, INAC, Grenoble, France

Piovano, Andrea ; Institut Laue-Langevin (ILL), Grenoble, France

Bossak, Alexei ; European Synchrotron Radiation Facility, Grenoble, France

GUENNOU, Mael ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Physics and Materials Science (DPHYMS)

Wahnström, Göran ; Department of Physics, Chalmers University of Technology, Göteborg, Sweden

External co-authors :

yes

Language :

English

Title :

Anharmonicity of the antiferrodistortive soft mode in barium zirconate BaZrO3

Publication date :

July 2023

Journal title :

Physical Review. B

ISSN :

2469-9950

eISSN :

2469-9969

Publisher :

American Physical Society

Volume :

108

Issue :

Peer reviewed :

Peer Reviewed verified by ORBi

Additional URL :

https://link.aps.org/article/10.1103/PhysRevB.108.014309

Funders :

Vetenskapsrådet
Vetenskapsrådet

Funding text :

R. Haumont and R. Saint-Martin from the ICMMO-UMR 8182, Université Paris Saclay, are acknowledged for their help in the preparation of the single crystals used for the INS experiments. F. Eriksson and P. Erhart are thanked for useful discussions in connection to the software hiphive . Funding from the Swedish Energy Agency (Grant No. 45410-1), the Swedish Research Council (Grants No. 2018-06482 and No. 2020-04935), and the Excellence Initiative Nano at Chalmers is gratefully acknowledged. The computations were performed by resources provided by the Swedish National Infrastructure for Computing (SNIC), partially funded by the Swedish Research Council through Grant Agreement No. 2018-05973. C. Milesi-Brault was supported by the Operational Programme Research, Development, and Education (financed by European Structural and Investment Funds and by the Czech Ministry of Education, Youth, and Sports), Project No. SOLID21-CZ.02.1.01/0.0/0.0/16_019/0000760.

Available on ORBilu :

since 22 December 2023

Statistics

Number of views

132 (3 by Unilu)

Number of downloads

0 (0 by Unilu)

More statistics

Scopus citations^®

Scopus citations^®
without self-citations

OpenAlex citations

Bibliography

A. S. Bhalla, R. Guo, and R. Roy, The perovskite structure-a review of its role in ceramic science and technology, Mater. Res. Innov. 4, 3 (2000) 1432-8917 10.1007/s100190000062.
A. Glazer, A brief history of tilts, Phase Transit. 84, 405 (2011) 0141-1594 10.1080/01411594.2010.544732.
C. J. Howard and H. T. Stokes, Structures and phase transitions in perovskites-a group-theoretical approach, Acta Crystallogr., Sect. A 61, 93 (2005) 0108-7673 10.1107/S0108767304024493.
N. Sai and D. Vanderbilt, First-principles study of ferroelectric and antiferrodistortive instabilities in tetragonal (Equation presented), Phys. Rev. B 62, 13942 (2000) 0163-1829 10.1103/PhysRevB.62.13942.
K. S. Knight, Low-temperature thermophysical and crystallographic properties of (Equation presented) perovskite, J. Mater. Sci. 55, 6417 (2020) 0022-2461 10.1007/s10853-020-04453-5.
M. Sebastian, Dielectric Materials for Wireless Communication (Elsevier, Amsterdam, 2010).
R. Vassen, X. Cao, F. Tietz, D. Basu, and D. Stöver, Zirconates as new materials for thermal barrier coatings, J. Am. Ceram. Soc. 83, 2023 (2000) 0002-7820 10.1111/j.1151-2916.2000.tb01506.x.
K. Kreuer, Proton-conducting oxides, Annu. Rev. Mater. Res. 33, 333 (2003) 1531-7331 10.1146/annurev.matsci.33.022802.091825.
D. Clark, H. Malerød-Fjeld, M. Budd, I. Yuste-Tirados, D. Beeaff, S. Aamodt, K. Nguyen, L. Ansaloni, T. Peters, P. K. Vestre, D. K. Pappas, M. I. Valls, S. Remiro-Buenamañana, T. Norby, T. S. Bjørheim, J. M. Serra, and C. Kjølseth, Single-step hydrogen production from (Equation presented), and biogas in stacked proton ceramic reactors, Science 376, 390 (2022) 0036-8075 10.1126/science.abj3951.
P. S. Dobal, A. Dixit, R. S. Katiyar, Z. Yu, R. Guo, and A. S. Bhalla, Micro-Raman scattering and dielectric investigations of phase transition behavior in the (Equation presented) system, J. Appl. Phys. 89, 8085 (2001) 0021-8979 10.1063/1.1369399.
W. Zhong and D. Vanderbilt, Competing Structural Instabilities in Cubic Perovskites, Phys. Rev. Lett. 74, 2587 (1995) 0031-9007 10.1103/PhysRevLett.74.2587.
J. W. Bennett, I. Grinberg, and A. M. Rappe, Effect of symmetry lowering on the dielectric response of (Equation presented), Phys. Rev. B 73, 180102 (R) (2006) 1098-0121 10.1103/PhysRevB.73.180102.
A. R. Akbarzadeh, I. Kornev, C. Malibert, L. Bellaiche, and J. M. Kiat, Combined theoretical and experimental study of the low-temperature properties of (Equation presented), Phys. Rev. B 72, 205104 (2005) 1098-0121 10.1103/PhysRevB.72.205104.
A. Bilić and J. D. Gale, Ground state structure of (Equation presented): A comparative first-principles study, Phys. Rev. B 79, 174107 (2009) 1098-0121 10.1103/PhysRevB.79.174107.
P. Chen, M. N. Grisolia, H. J. Zhao, O. E. González-Vázquez, L. Bellaiche, M. Bibes, B.-G. Liu, and J. Íñiguez, Energetics of oxygen-octahedra rotations in perovskite oxides from first principles, Phys. Rev. B 97, 024113 (2018) 2469-9950 10.1103/PhysRevB.97.024113.
D. Amoroso, A. Cano, and P. Ghosez, First-principles study of (Equation presented) and (Equation presented) solid solutions, Phys. Rev. B 97, 174108 (2018) 2469-9950 10.1103/PhysRevB.97.174108.
A. Perrichon, E. Jedvik Granhed, G. Romanelli, A. Piovano, A. Lindman, P. Hyldgaard, G. Wahnström, and M. Karlsson, Unraveling the ground-state structure of (Equation presented) by neutron scattering experiments and first-principles calculations, Chem. Mater. 32, 2824 (2020) 0897-4756 10.1021/acs.chemmater.9b04437.
R. A. Evarestov, Hybrid density functional theory LCAO calculations on phonons in Ba(Ti,Zr,Hf)(Equation presented), Phys. Rev. B 83, 014105 (2011) 1098-0121 10.1103/PhysRevB.83.014105.
C. Toulouse, D. Amoroso, C. Xin, P. Veber, M. C. Hatnean, G. Balakrishnan, M. Maglione, P. Ghosez, J. Kreisel, and M. Guennou, Lattice dynamics and Raman spectrum of (Equation presented) single crystals, Phys. Rev. B 100, 134102 (2019) 2469-9950 10.1103/PhysRevB.100.134102.
I. Levin, M. G. Han, H. Y. Playford, V. Krayzman, Y. Zhu, and R. A. Maier, Nanoscale-correlated octahedral rotations in (Equation presented), Phys. Rev. B 104, 214109 (2021) 2469-9950 10.1103/PhysRevB.104.214109.
C. Xin, P. Veber, M. Guennou, C. Toulouse, N. Valle, M. Ciomaga Hatnean, G. Balakrishnan, R. Haumont, R. Saint Martin, M. Velazquez, A. Maillard, D. Rytz, M. Josse, M. Maglione, and J. Kreisel, Single crystal growth of (Equation presented) from the melt at (Equation presented) using optical floating zone technique and growth prospects from (Equation presented) flux at (Equation presented), CrystEngComm 21, 502 (2019) 1466-8033 10.1039/C8CE01665H.
P. Souvatzis, O. Eriksson, M. I. Katsnelson, and S. P. Rudin, Entropy Driven Stabilization of Energetically Unstable Crystal Structures Explained from First Principles Theory, Phys. Rev. Lett. 100, 095901 (2008) 0031-9007 10.1103/PhysRevLett.100.095901.
O. Hellman, I. A. Abrikosov, and S. I. Simak, Lattice dynamics of anharmonic solids from first principles, Phys. Rev. B 84, 180301 (R) (2011) 1098-0121 10.1103/PhysRevB.84.180301.
L. Monacelli, R. Bianco, M. Cherubini, M. Calandra, I. Errea, and F. Mauri, The stochastic self-consistent harmonic approximation: Calculating vibrational properties of materials with full quantum and anharmonic effects, J. Phys.: Condens. Matter 33, 363001 (2021) 0953-8984 10.1088/1361-648X/ac066b.
K. Esfarjani and Y. Liang, Thermodynamics of anharmonic lattices from first principles, in Nanoscale Energy Transport, edited by B. Liao (IOP Publishing, Bristol, 2020), Chap. 7.
T. Tadano and S. Tsuneyuki, Self-consistent phonon calculations of lattice dynamical properties in cubic (Equation presented) with first-principles anharmonic force constants, Phys. Rev. B 92, 054301 (2015) 1098-0121 10.1103/PhysRevB.92.054301.
J. Zheng, D. Shi, Y. Yang, C. Lin, H. Huang, R. Guo, and B. Huang, Anharmonicity-induced phonon hardening and phonon transport enhancement in crystalline perovskite (Equation presented), Phys. Rev. B 105, 224303 (2022) 2469-9950 10.1103/PhysRevB.105.224303.
F. Eriksson, E. Fransson, and P. Erhart, The hiphive package for the extraction of high-order force constants by machine learning, Adv. Theory Simul. 2, 1800184 (2019) 2513-0390 10.1002/adts.201800184.
A. H. Larsen, J. J. Mortensen, J. Blomqvist, I. E. Castelli, R. Christensen, M. Dułak, J. Friis, M. N. Groves, B. Hammer, C. Hargus, E. D. Hermes, P. C. Jennings, P. B. Jensen, J. Kermode, J. R. Kitchin, E. L. Kolsbjerg, J. Kubal, K. Kaasbjerg, S. Lysgaard, J. B. Maronsson, The atomic simulation environment-a Python library for working with atoms, J. Phys.: Condens. Matter 29, 273002 (2017) 0953-8984 10.1088/1361-648X/aa680e.
Z. Fan, W. Chen, V. Vierimaa, and A. Harju, Efficient molecular dynamics simulations with many-body potentials on graphics processing units, Comput. Phys. Commun. 218, 10 (2017) 0010-4655 10.1016/j.cpc.2017.05.003.
E. Fransson, M. Slabanja, P. Erhart, and G. Wahnström, dynasor, a tool for extracting dynamical structure factors and current correlation functions from molecular dynamics simulations, Adv. Theory Simul. 4, 2000240 (2021) 2513-0390 10.1002/adts.202000240.
G. Kresse and J. Furthmüller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B 54, 11169 (1996) 0163-1829 10.1103/PhysRevB.54.11169.
G. Kresse and J. Furthmüller, Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set, Comput. Mater. Sci. 6, 15 (1996) 0927-0256 10.1016/0927-0256(96)00008-0.
J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized Gradient Approximation Made Simple, Phys. Rev. Lett. 77, 3865 (1996) 0031-9007 10.1103/PhysRevLett.77.3865.
J. P. Perdew, A. Ruzsinszky, G. I. Csonka, O. A. Vydrov, G. E. Scuseria, L. A. Constantin, X. Zhou, and K. Burke, Restoring the Density-Gradient Expansion for Exchange in Solids and Surfaces, Phys. Rev. Lett. 100, 136406 (2008) 0031-9007 10.1103/PhysRevLett.100.136406.
K. Berland and P. Hyldgaard, Exchange functional that tests the robustness of the plasmon description of the van der Waals density functional, Phys. Rev. B 89, 035412 (2014) 1098-0121 10.1103/PhysRevB.89.035412.
M. Dion, H. Rydberg, E. Schröder, D. C. Langreth, and B. I. Lundqvist, Van der Waals Density Functional for General Geometries, Phys. Rev. Lett. 92, 246401 (2004) 0031-9007 10.1103/PhysRevLett.92.246401.
J. Heyd, G. E. Scuseria, and M. Ernzerhof, Hybrid functionals based on a screened coulomb potential, J. Chem. Phys. 118, 82078215 (2003) 0021-9606 10.1063/1.1564060.
J. Heyd, G. E. Scuseria, and M. Ernzerhof, Erratum: "Hybrid functionals based on a screened Coulomb potential" [J. Chem. Phys. 118, 8207 (2003)], J. Chem. Phys. 124, 219906 (2006) 0021-9606 10.1063/1.2204597.
Y. Jiao, E. Schröder, and P. Hyldgaard, Extent of Fock-exchange mixing for a hybrid van der Waals density functional J. Chem. Phys. 148, 194115 (2018) 10.1063/1.5012870.
P. E. Blöchl, Projector augmented-wave method, Phys. Rev. B 50, 17953 (1994) 0163-1829 10.1103/PhysRevB.50.17953.
G. Kresse and D. Joubert, From ultrasoft pseudopotentials to the projector augmented-wave method, Phys. Rev. B 59, 1758 (1999) 0163-1829 10.1103/PhysRevB.59.1758.
X. Gonze, J. C. Charlier, D. C. Allan, and M. P. Teter, Interatomic force constants from first principles: The case of (Equation presented)-quartz, Phys. Rev. B 50, 13035 (1994) 0163-1829 10.1103/PhysRevB.50.13035.
X. Gonze and C. Lee, Dynamical matrices, Born effective charges, dielectric permittivity tensors, and interatomic force constants from density-functional perturbation theory, Phys. Rev. B 55, 10355 (1997) 0163-1829 10.1103/PhysRevB.55.10355.
A. Togo and I. Tanaka, First principles phonon calculations in materials science, Scr. Mater. 108, 1 (2015) 1359-6462 10.1016/j.scriptamat.2015.07.021.
F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, and E. Duchesnay, Scikit-learn: Machine learning in Python, J. Mach. Learn. Res. 12, 2825 (2011) 10.5555/1953048.2078195.
See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevB.108.014309 for details about the force constant potential, phonon dispersions, fitting of the INS and IXS data, fitting of the dynamical structure factor, comparison between the self-consistent phonon model and the effective harmonic model. The Supplemental Material also contains Refs. [64,65].
A. Piovano, A. Ivanov, S. Roux, and F. Charpenay, The science division projects in8 monochromator and thermes secondary spectrometer: enhancing the performance of the thermal neutron TAS-IN8, ILL Annual Report 2020, 76 (2020).
M. Guennou, R. Haumont, M. Maglione, and A. Piovano, Experimental report on proposal 7-02-190, Institut Laue-Langevin (ILL), 2021 (unpublished).
M. Guennou, F. Bourdarot, M. Maglione, C. Toulouse, and C. Xin, Experimental report on proposal 7-02-180, Institut Laue-Langevin (ILL), 2019 (unpublished), doi: 10.5291/ILL-DATA.7-02-180.
M. Krisch and F. Sette, Inelastic x-ray scattering from phonons, in Light Scattering in Solid IX, edited by M. Cardona and R. Merlin (Springer, Berlin, 2007), Chap. 5, pp. 317-370.
A. Girard, T. Nguyen-Thanh, S. M. Souliou, M. Stekiel, W. Morgenroth, L. Paolasini, A. Minelli, D. Gambetti, B. Winkler, and A. Bosak, A new diffractometer for diffuse scattering studies on the ID28 beamline at the ESRF, J. Synchrotron Radiat. 26, 272 (2019) 1600-5775 10.1107/S1600577518016132.
V. F. Sears, Neutron scattering lengths and cross sections, Neutron News 3, 26 (1992) 1044-8632 10.1080/10448639208218770.
T. Weber, R. Georgii, and P. Böni, Takin: An open-source software for experiment planning, visualisation, and data analysis, SoftwareX 5, 121 (2016) 2352-7110 10.1016/j.softx.2016.06.002.
T. Weber, Update 1.5 to "takin: An open-source software for experiment planning, visualisation, and data analysis", SoftwareX 6, 148 (2017) 2352-7110 10.1016/j.softx.2017.06.002.
T. Weber, Update 2.0 to "takin: An open-source software for experiment planning, visualisation, and data analysis", SoftwareX 14, 100667 (2021) 2352-7110 10.1016/j.softx.2021.100667.
J. Brorsson, A. Hashemi, Z. Fan, E. Fransson, F. Eriksson, T. Ala-Nissila, A. V. Krasheninnikov, H.-P. Komsa, and P. Erhart, Efficient calculation of the lattice thermal conductivity by atomistic simulations with ab initio accuracy, Adv. Theory Simul. 5, 2100217 (2022) 2513-0390 10.1002/adts.202100217.
E. Metsanurk and M. Klintenberg, Sampling-dependent systematic errors in effective harmonic models, Phys. Rev. B 99, 184304 (2019) 2469-9950 10.1103/PhysRevB.99.184304.
E. J. Granhed, G. Wahnström, and P. Hyldgaard, (Equation presented) stability under pressure: The role of nonlocal exchange and correlation, Phys. Rev. B 101, 224105 (2020) 2469-9950 10.1103/PhysRevB.101.224105.
P. Fornasini and R. Grisenti, On EXAFS Debye-Waller factor and recent advances, J. Synchrotron Radiat. 22, 1242 (2015) 1600-5775 10.1107/S1600577515010759.
A. I. Lebedev and I. A. Sluchinskaya, Structural instability in (Equation presented) crystals: Calculations and experiment, Phys. Solid State 55, 1941 (2013) 1063-7834 10.1134/S1063783413090229.
T. Tadano, Y. Gohda, and S. Tsuneyuki, Anharmonic force constants extracted from first-principles molecular dynamics: Applications to heat transfer simulations, J. Phys.: Condens. Matter 26, 225402 (2014) 0953-8984 10.1088/0953-8984/26/22/225402.
E. Fransson, P. Rosander, F. Eriksson, J. M. Rahm, T. Tadano, and P. Erhart, Limits of the phonon quasi-particle picture at the cubic-to-tetragonal phase transition in halide perovskites, Commun. Phys. 6, 173 (2023) 10.1038/s42005-023-01297-8.
P. Korotaev, M. Belov, and A. Yanilkin, Reproducibility of vibrational free energy by different methods, Comput. Mater. Sci. 150, 47 (2018) 0927-0256 10.1016/j.commatsci.2018.03.057.
A. Castellano, F. Bottin, J. Bouchet, A. Levitt, and G. Stoltz, Ab initio canonical sampling based on variational inference, Phys. Rev. B 106, L161110 (2022) 2469-9950 10.1103/PhysRevB.106.L161110.