Pith. sign in

REVIEW 3 major objections 4 minor 60 references

Tilt-driven ferrielectricity in PbZrO$_3$

T0 review · 3 major / 4 minor · reviewed 2026-08-01 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read An added oxygen tilt can turn antiferroelectric PbZrO3 into a polar ferrielectric phase.

desk verdict A genuinely new symmetry route to ferrielectricity in PbZrO3, with solid DFT support, but the finite-temperature ordering and the STEM identification are weaker than the central mechanism. read the letter →

arxiv 2607.27752 v1 pith:ZVHEGSQ4 submitted 2026-07-30 cond-mat.mtrl-sci

Huazhang Zhang , Ying Liu , Carson Carroll , Saptam Ganguly , Bin Xu , Xiaozhou Liao , Gustau Catalan , Philippe Ghosez
show 1 more author
Nicholas C. Bristowe
This is my paper · ORCID
classification cond-mat.mtrl-sci
keywords ferrielectricityantiferroelectricityPbZrO3octahedraltiltsimproperferroelectricityfirst-principlesSTEMimagingperovskite
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper argues that a hidden polar phase of PbZrO3 is created by adding an oxygen octahedral tilt to its known antiferroelectric structure. The tilt breaks a symmetry constraint that keeps the two antiparallel lead displacements equal in size, so the compensated 'up-up-down-down' pattern becomes an uncompensated 'up-up-down-down' pattern with a net polarization. First-principles calculations show this Pmc2_1 phase is dynamically stable under lattice contraction and gains free-energy advantage near room temperature. Atomic-resolution imaging in thin films and single crystals finds the asymmetric oxygen-chain rippling and uncompensated lead displacements that mark this phase. A sympathetic reader would care because it offers a kinetically easy, symmetry-governed route to ferrielectricity and a new kind of competitive improper ferroelectricity.

What carries the argument

The M2+ in-phase octahedral tilt mode is the trigger. Condensing M2+ into the Pbam structure breaks inversion-related equivalence; it couples with inherited Pbam modes (Sigma2 and S2) to activate the S1 modulated-tilt mode and the Gamma4- polar mode via quadratic-linear-linear and quadrilinear couplings. The net polarization is set by the competition between M2+ and S1, which can push the polarization continuously through zero and reverse its sign without reversing the driving modes themselves.

What would settle it

A direct test would be to measure the oxygen-chain rippling and lead displacements in a clean, defect-poor PbZrO3 sample under controlled hydrostatic pressure around 5 GPa; if no fourfold-periodic uncompensated 'up-up-down-down' pattern with asymmetric ripples appears, the central claim fails. More cheaply, recompute the 10 GPa Gibbs free-energy difference between Pmc2_1 and Ima2 with a phonon method that does not discard imaginary modes; if Ima2 remains lower through 500 K, the room-temperature stabilization argument collapses.

Watch

Extended reading notes

Core claim

The central claim is that Pbam antiferroelectric PbZrO3 can be transformed into a polar Pmc2_1 ferrielectric phase by condensing an additional M2+ in-phase oxygen octahedral tilt. In Pbam, the 'up-up-down-down' lead displacements are related by a symmetry operation that forces the two antiparallel sublattices to have equal magnitudes, so the structure is nonpolar. The added tilt breaks that operation and makes the oxygen-chain ripples between the 'up-up' and 'down-down' pairs unequal, which removes the equality constraint and lets one antiparallel sublattice become larger. The result is an uncompensated 'up-up-down-down' pattern with a net polarization that belongs to space group Pmc2_1. The

Load-bearing premise

The finite-temperature conclusion depends on quasi-harmonic phonon free energies in which imaginary modes of Pbam are discarded, and the energy differences separating Pmc2_1 from Ima2 are only a few meV per formula unit; an error of that size could reverse the ordering in Fig. 3(b). The STEM evidence also relies on regions near a chemically intermixed interface or containing Pb vacancies, so alternative local distortions are not excluded.

Editorial extensions

If this is right

  • Above about 5 GPa hydrostatic pressure (approximately -1.2% linear strain), Pmc2_1 sits lower in enthalpy than Pbam and becomes dynamically stable; it remains a metastable competitor above 10 GPa.
  • The Pbam-to-Pmc2_1 path is group-subgroup and barrier-free in the dipole pattern, so the polar phase is kinetically reachable by adjusting dipole magnitudes rather than reversing dipoles, unlike the threefold Ima2 ferrielectric ground state.
  • At 10 GPa and near room temperature, QHA free-energy results put Pmc2_1 thermodynamically above Ima2, suggesting a heating path from Pmc2_1 directly to cubic without returning to Pbam.
  • Reciprocal couplings imply electric fields can excite M-point octahedral tilts, giving a way to control tilt order electrically.
  • Because the mechanism only needs polarization modulation plus in-phase tilts, it extends beyond PZO, as shown for PbSnO3 and 180-degree domain walls in the ferroelectric Q phase of NaNbO3.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If local Pb vacancies act as microscopic sources of lattice contraction, defect patterning could be used to imprint or erase Pmc2_1-like polar regions at the nanoscale in otherwise antiferroelectric films.
  • The ability to reverse polarization sign by tuning M2+/S1 amplitudes without reversing the driving modes suggests a continuous polarization-reversal route that might be observable as soft-mode behavior or as domains annihilating at zero net polarization.
  • The 'competitive' improper mechanism raises the possibility of multiple near-degenerate polar states with different polarization magnitudes; field cycling might show staircase-like or non-binary switching in energy-storage devices.
  • The same symmetry analysis could be applied to other Pbam antiferroelectrics such as PbHfO3 to predict pressure-induced ferrielectricity.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper proposes that the antiferroelectric Pbam phase of PbZrO3 can be converted into a polar Pmc2_1 ferrielectric phase by condensing an additional in-phase octahedral tilt (M2+ mode). Group-theoretic analysis identifies symmetry-allowed couplings by which the tilt, together with the pre-existing Pbam distortions, induces the polar Gamma4- mode through quadratic-linear-linear and quadrilinear terms. First-principles DFT relaxations show that Pmc2_1 becomes stable under hydrostatic pressure above about 5 GPa and under biaxial compressive strain, and that at 10 GPa it is dynamically stable and 3.6 meV/f.u. lower in enthalpy than Pbam. Quasi-harmonic calculations are used to argue that Pmc2_1 overtakes the Ima2 ferrielectric phase near room temperature. STEM-HAADF and iDPC imaging are presented as evidence of Pmc2_1-like structures in thin films and single crystals. The paper also extends the mechanism to PbSnO3 and to 180-degree domain walls in NaNbO3.

Significance. If the central mechanism is correct, the paper identifies a new symmetry-based route to ferrielectricity that is qualitatively different from previously studied FiE states: the Pmc2_1 phase is connected to the parent Pbam phase via a direct group-subgroup relation and can be reached without reversing any Pb displacements. The competitive improper coupling picture, in which polarization is determined by a subtle balance of M2+ and S1 modes, is a valuable conceptual extension of hybrid-improper ferroelectricity, and the predicted polarization reversal within a fixed phase by tuning nonpolar mode amplitudes is a striking and falsifiable consequence. The paper also provides direct DFT relaxations, phonon stability checks, and a transparent Landau fit. If the finite-temperature and experimental evidence were as robust as the symmetry argument, this would be a significant advance. As it stands, the theoretical mechanism is credible but the paper overreaches in its kinetic and experimental claims.

major comments (3)
  1. [Fig. 3(b) and QHA discussion] The finite-temperature ordering of Pmc2_1 above Ima2 rests on QHA phonon free energies with imaginary modes of Pbam excluded and enthalpy differences of only a few meV/f.u. (3.6 meV/f.u. at 10 GPa). QHA errors from anharmonicity and from the treatment of dynamically unstable phases are easily of this magnitude; a small correction could reverse the room-temperature ordering. The paper acknowledges the approximation but still concludes that Pmc2_1 becomes thermodynamically more favorable around room temperature. This is load-bearing for the claim of accessible FiE. Please provide a quantitative error estimate, cross-check with another method (e.g., the deep-learning potential cited as Ref. [43]), or soften the thermodynamic claim to 'competitive metastable state'.
  2. [Fig. 3(a) inset and text on kinetic accessibility] The paper asserts that the Pbam-to-Pmc2_1 transition is 'barrier-free' and 'kinetically easily accessible' based on the direct group-subgroup relation and shared fourfold periodicity. A group-subgroup relation does not guarantee a barrier-free path; continuous symmetry-allowed transitions can still be first-order with a finite nucleation barrier. No nudged-elastic-band calculation, Landau energy profile along the transition path, or explicit kinetic model is provided. Since the argument that Pmc2_1 can compete with the Ima2 ground state relies on this kinetic accessibility, please either compute the barrier or replace 'barrier-free' with a more cautious statement.
  3. [Fig. 4(d-g) and iDPC evidence] The experimental identification of Pmc2_1 is based on asymmetric oxygen-chain rippling measured from an iDPC image near a chemically intermixed PZO/SRO interface, and from regions with Pb vacancies in the single crystal. The rippling angles are reported without error bars, and no simulated iDPC images of alternative local distortions (e.g., Pbam with inhomogeneous strain, defect-induced tilt patterns, or interface polarity effects) are compared. The sentence 'provides definitive structural evidence supporting the presence of the Pmc2_1-like FiE state' is stronger than the data support. Please quantify the rippling amplitude with uncertainties, and test against plausible alternative structural models in the same local environment.
minor comments (4)
  1. [Throughout] Some arrow symbols in the abstract and body appear garbled (e.g., the polarization pattern symbols). Please ensure the typesetting of the 'up-up-down-down' pattern is consistent and correct.
  2. [Introduction and Fig. 1] The notation 'Sym.δ Pb' and 'Asym.∆ O' is clear in the figure, but the main text would benefit from a one-sentence definition of δ and ∆ as displacement and ripple variables, respectively.
  3. [Section on Landau model] Equations (1)-(3) give the coupling terms symbolically, but the actual Landau polynomial is only in the Supplementary Material. A sample free-energy expression with fitted coefficient values in the main text would help readers assess the competition described in Fig. 2.
  4. [Fig. 2(b)] The label 'QΓ4−=0' is not defined in the caption; specify that it is the order-parameter amplitude of the polar mode.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central Pmc21 ferrielectricity claim rests on symmetry analysis and direct DFT relaxations, while the Landau model is explicitly fitted and labeled as such.

full rationale

The paper's main derivation—that adding an M2+ in-phase octahedral tilt to the Pbam phase of PbZrO3 lifts the symmetry constraint and produces polar Pmc21 with uncompensated ↑↑↓↓ dipoles—is established through group-theoretic mode analysis and direct first-principles structural relaxations, not through a quantity fitted to the conclusion. The Landau couplings in Fig. 2 are explicitly fitted to DFT enthalpy data (the caption states that symbols are first-principles results while curves and contour map are derived from the fitted Landau model), and the paper does not present those curves as independent predictions; they are an interpretive summary of the DFT energies. The stability of Pmc21 under pressure is obtained from relaxed DFT structures, phonon dispersions, and QHA free energies, and the approximate exclusion of imaginary Pbam modes is openly attributed to an external study with the caveat 'although approximate, this approach captures the essential trends [13]'. Thus any weakness in the finite-temperature ordering is a numerical/approximation risk, not an input-output identity. Self-citations (e.g., refs. 43, 45, 60) are contextual—used for kinetic barriers, earlier observations, or suggested applications—and are not load-bearing reductions of the central mechanism. No fitted parameter is renamed as a prediction, and no equation reduces to its own input by construction. The experimental STEM/iDPC evidence is used as corroboration, not as a circularly defined verification. Overall, the derivation chain is self-contained against first-principles calculations and external references.

Assumptions & free parameters 1 free parameters · 6 assumptions · 0 invented entities

No new particles, forces, or conserved quantities are introduced; Pmc2_1 is a crystallographic phase and M2+/S1 are standard phonon modes. The key unstated inputs are listed as axioms above; the only fitted parameters are the Landau coefficients.

free parameters (1)
  • Landau polynomial coefficients (quadratic, cubic, quartic terms for M2+, S1, Γ4- and their couplings) = Not given in main text; in Supplementary S5
    Fitted to first-principles enthalpy-vs-mode-amplitude data at 10 GPa; they drive the dual-pathway picture and polarization sign-switch shown in Fig. 2(b–d).
assumptions (6)
  • domain assumption DFT with PBEsol and norm-conserving pseudopotentials reliably ranks competing PbZrO3 phases at the meV/f.u. level.
    Underlies all enthalpy and free-energy differences (Figs. 2–3); no experimental calibration of this error bar is given.
  • domain assumption Quasi-harmonic approximation with imaginary Pbam phonon modes excluded captures the finite-temperature free-energy ordering.
    Used for Fig. 3(b); the paper states the exclusion is 'approximate, although... captures essential trends'.
  • ad hoc to paper The six modes R5-, S2, Σ2, M2+, S1, Γ4- are sufficient to describe the Pmc2_1 energy landscape and polarization.
    Landau model truncates to these modes; omitted modes could modify fitted coefficients and coupling signs.
  • domain assumption Lattice contraction (pressure, epitaxial strain, Pb vacancies) promotes the M2+ tilt and hence Pmc2_1.
    Connects the experimental observations (interface, Pb-vacancy-containing crystal) to the theoretical stabilization mechanism.
  • ad hoc to paper Group-subgroup connection and shared fourfold periodicity imply a barrier-free Pbam→Pmc2_1 kinetic pathway.
    The 'kinetically easily accessible' claim rests on this; no explicit energy barrier calculation is shown.
  • ad hoc to paper The STEM/iDPC images from near an intermixed interface and defect-containing crystal are representative of the Pmc2_1 phase.
    Experimental identification is 'Pmc2_1-like'; alternative local distortions from intermixing or Pb vacancies are not excluded.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Tilt-driven ferrielectricity in PbZrO$_3$." pith.science (2026). https://pith.science/paper/ZVHEGSQ4

@misc{pith2026260727752,
  author       = {Pith},
  title        = {Pith review of: Tilt-driven ferrielectricity in PbZrO$_3$},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZVHEGSQ4}},
  note         = {Machine review of arXiv:2607.27752}
}
abstract

We reveal a tilt-driven mechanism for ferrielectricity in prototypical antiferroelectric PbZrO$_3$. Specifically, introducing an additional octahedral tilt into the antiferroelectric $Pbam$ phase breaks the symmetry constraint that enforces equal antiparallel dipoles, converting the compensated ``$\uparrow \uparrow \downarrow \downarrow$'' nonpolar configuration into an uncompensated ``$\uparrow \uparrow \downarrow \downarrow$'' polar $Pmc2_1$ phase. First-principles calculations show that the $Pmc2_1$ phase becomes stabilized under lattice contraction and gains increasing free-energy advantage over competing phases at finite temperatures. Atomic-scale imaging directly confirms the presence of $Pmc2_1$-like structures in thin films and single crystals. This work identifies a symmetry-governed, kinetically easily accessible pathway to ferrielectricity and establishes a form of ``competitive'' improper ferroelectricity, with broad implications for antiferroelectrics.

Figures

Figures reproduced from arXiv: 2607.27752 by the authors.

Figure 1
Figure 1. FIG. 1. Symmetry-based mechanism of tilt-driven FiE in [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Thermodynamic stability and kinetic accessibility [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. FIG. 4. Experimental evidence of [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

60 extracted references · 1 canonical work pages

  1. [43]

    Finite- temperature properties of the antiferroelectric perovskite PbZrO3 from a deep-learning interatomic potential

    Huazhang Zhang, Hao-Cheng Thong, Louis Bastogne, Churen Gui, Xu He, and Philippe Ghosez. Finite- temperature properties of the antiferroelectric perovskite PbZrO3 from a deep-learning interatomic potential. Phys. Rev. B, 110:054109, 2024

    2024

  2. [1]

    C. Kittel. Theory of antiferroelectric crystals.Physical Review, 82:729–732, 1951

    1951

  3. [2]

    Rabe.Antiferroelectricity in Oxides: A Reex- amination

    Karin M. Rabe.Antiferroelectricity in Oxides: A Reex- amination. In Functional Metal Oxides (eds S.B. Ogale, T.V. Venkatesan and M.G. Blamire), pages 221–244. John Wiley & Sons, Ltd., 2013

    2013

  4. [3]

    Oxford University Press, 1977

    M E Lines and A M Glass.Principles and Applications of Ferroelectrics and Related Materials. Oxford University Press, 1977

    1977

  5. [4]

    A mod- ern perspective on antiferroelectrics.Nature Materials, 25(4):557–565, 2026

    Gustau Catalan, Alexei Gruverman, Jorge Íñiguez González, Dennis Meier, and Morgan Trassin. A mod- ern perspective on antiferroelectrics.Nature Materials, 25(4):557–565, 2026

    2026

  6. [5]

    Sawaguchi, H

    E. Sawaguchi, H. Maniwa, and S. Hoshino. Antifer- roelectric structure of lead zirconate.Physical Review, 83(5):1078–1078, 1951

    1951

  7. [6]

    Whatmore

    D.L.Corker, A.M.Glazer, J.Dec, K.Roleder, andR.W. Whatmore. A re-investigation of the crystal structure of the perovskitePbZrO 3 by X-ray and neutron diffraction. Acta Crystallographica Section B, 53(1):135–142, 1997

    1997

  8. [7]

    A. K. Tagantsev, K. Vaideeswaran, S. B. Vakhrushev, A. V. Filimonov, R. G. Burkovsky, A. Shaganov, D. An- dronikova, A. I. Rudskoy, A. Q. R. Baron, H. Uchiyama, D. Chernyshov, A. Bosak, Z. Ujma, K. Roleder, A. Ma- jchrowski, J. H. Ko, and N. Setter. The origin of an- tiferroelectricity inPbZrO 3.Nature Communications, 4(1):2229, 2013

    2013

Show all 60 references
  1. [8]

    Ideal anti- ferroelectricity with large digital electrostrain inPbZrO3 epitaxial thin films.Nature Communications, 16(1):4263, 2025

    Yangyang Si, Ningbo Fan, Yongqi Dong, Zhen Ye, Shiqing Deng, Yijie Li, Chao Zhou, Qibin Zeng, Lu You, Yimei Zhu, Zhenlin Luo, Sujit Das, Laurent Bellaiche, Bin Xu, Huajun Liu, and Zuhuang Chen. Ideal anti- ferroelectricity with large digital electrostrain inPbZrO3 epitaxial th...

    2025

  2. [9]

    Weak fer- roelectricity in antiferroelectric lead zirconate.Physical Review B, 51(5):2651–2655, 1995

    Xunhu Dai, Jie-Fang Li, and Dwight Viehland. Weak fer- roelectricity in antiferroelectric lead zirconate.Physical Review B, 51(5):2651–2655, 1995

    1995

  3. [10]

    Coexistence of ferroelectricity and anti- ferroelectricity in epitaxialPbZrO 3 films with different orientations.Journal of Applied Physics, 103(2):024101, 2008

    Lucian Pintilie, Ksenia Boldyreva, Marin Alexe, and Di- etrich Hesse. Coexistence of ferroelectricity and anti- ferroelectricity in epitaxialPbZrO 3 films with different orientations.Journal of Applied Physics, 103(2):024101, 2008

    2008

  4. [11]

    Ferroelectric phase transitions in epitaxial anti- ferroelectricPbZrO 3 thin films.Applied Physics Reviews, 10(2):021405, 2023

    Pauline Dufour, Thomas Maroutian, Maxime Vallet, Kinnary Patel, André Chanthbouala, Charlotte Jacque- mont, Lluis Yedra, Vincent Humbert, Florian Godel, Bin Xu, Sergey Prosandeev, Laurent Bellaiche, Mojca Otoničar, Stéphane Fusil, Brahim Dkhil, and Vincent Garcia. Ferroelectri...

    2023

  5. [12]

    Epitaxial strain stabilization of a ferro- electric phase inPbZrO 3 thin films.Physical Review B, 84(5):054112, 2011

    Ayan Roy Chaudhuri, Miryam Arredondo, Angelika Häh- nel, Alessio Morelli, Michael Becker, Marin Alexe, and Ionela Vrejoiu. Epitaxial strain stabilization of a ferro- electric phase inPbZrO 3 thin films.Physical Review B, 84(5):054112, 2011

    2011

  6. [13]

    On the possibility thatPbZrO3 not be antiferroelectric.npj Computational Materials, 7(1):196, 2021

    Hugo Aramberri, Claudio Cazorla, Massimiliano Stengel, and Jorge Íñiguez. On the possibility thatPbZrO3 not be antiferroelectric.npj Computational Materials, 7(1):196, 2021

    2021

  7. [14]

    Cairney, Jordi Arbiol, and Gustau Catalan

    Ying Liu, Ranming Niu, Andrzej Majchrowski, Krystian Roleder, Kumara Cordero-Edwards, Julie M. Cairney, Jordi Arbiol, and Gustau Catalan. Translational bound- aries as incipient ferrielectric domains in antiferroelectric PbZrO3.Physical Review Letters, 130(21):216801, 2023

    2023

  8. [15]

    Ferrielec- tricity in the archetypal antiferroelectric,PbZrO3.Ad- vanced Materials, 35(3):2206541, 2023

    Yulian Yao, Aaron Naden, Mengkun Tian, Sergey Lisenkov, Zachary Beller, Amit Kumar, Josh Kacher, Inna Ponomareva, and Nazanin Bassiri-Gharb. Ferrielec- tricity in the archetypal antiferroelectric,PbZrO3.Ad- vanced Materials, 35(3):2206541, 2023

    2023

  9. [16]

    Antiferroelectric thin films embedded with ferroelectric switching loop for giant negative elec- trocaloric effect.Science Advances, 12(27):eaed5447, 2026

    PeipeiSu, JianchuChen, JunningLi, JinbinWang, Zhen- zhong Yang, Yongshuai Ge, Ke Qu, Xiangli Zhong, and Gaokuo Zhong. Antiferroelectric thin films embedded with ferroelectric switching loop for giant negative elec- trocaloric effect.Science Advances, 12(27):eaed5447, 2026

    2026

  10. [17]

    Uncompensated polarization in incom- mensurate modulations of perovskite antiferroelectrics

    Tao Ma, Zhongming Fan, Bin Xu, Tae-Hoon Kim, Ping Lu, Laurent Bellaiche, Matthew J Kramer, Xiaoli Tan, and Lin Zhou. Uncompensated polarization in incom- mensurate modulations of perovskite antiferroelectrics. Physical Review Letters, 123(21):217602, 2019

    2019

  11. [18]

    Unveiling the ferrielec- tric nature ofPbZrO 3-based antiferroelectric materials

    Zhengqian Fu, Xuefeng Chen, Zhenqin Li, Tengfei Hu, Linlin Zhang, Ping Lu, Shujun Zhang, Genshui Wang, Xianlin Dong, and Fangfang Xu. Unveiling the ferrielec- tric nature ofPbZrO 3-based antiferroelectric materials. Nature Communications, 11(1):3809, 2020

    2020

  12. [19]

    Atomic insight into the successive an- tiferroelectric–ferroelectric phase transition in antiferro- electric oxides.Nano Letters, 23(4):1522–1529, 2023

    Ru-Jian Jiang, Yi Cao, Wan-Rong Geng, Mei-Xiong Zhu, Yun-Long Tang, Yin-Lian Zhu, Yujia Wang, Fenghui Gong, Su-Zhen Liu, Yu-Ting Chen, Jiaqi Liu, Nan Liu, Jing-Hui Wang, Xiao-Dong Lv, Shuang-Jie Chen, and Xiu-Liang Ma. Atomic insight into the successive an- tiferroelectric–fer...

    2023

  13. [20]

    Room-temperature stabilizing strongly competing ferrielectric and antiferroelectric phases inPbZrO 3 by strain-mediated phase separation.Nature Communica- tions, 15(1):3438, 2024

    Ziyi Yu, Ningbo Fan, Zhengqian Fu, Biao He, Shiguang Yan, Henghui Cai, Xuefeng Chen, Linlin Zhang, Yuanyuan Zhang, Bin Xu, Genshui Wang, and Fangfang Xu. Room-temperature stabilizing strongly competing ferrielectric and antiferroelectric phases inPbZrO 3 by strain-mediated pha...

    2024

  14. [21]

    Burkovsky, Georgiy A

    Roman G. Burkovsky, Georgiy A. Lityagin, Alexander E. Ganzha, Alexander F. Vakulenko, Ran Gao, Arvind Das- gupta, Bin Xu, Alexey V. Filimonov, and Lane W. Mar- tin. Field-induced heterophase state inPbZrO 3 thin films.Physical Review B, 105(12):125409, 2022

    2022

  15. [22]

    Tuning of polar domain bound- aries in nonpolar perovskite.Advanced Materials, 35(11):2207665, 2023

    Zheyi An, Hiroko Yokota, Kyomaru Kurihara, No- 7 zomu Hasegawa, Pavel Marton, Anthony Michael Glazer, Yoshiaki Uesu, Wei Ren, Zuo-Guang Ye, Marek Paś- ciak, and Nan Zhang. Tuning of polar domain bound- aries in nonpolar perovskite.Advanced Materials, 35(11):2207665, 2023

    2023

  16. [23]

    Improper ferroelec- tricity in perovskite oxide artificial superlattices.Nature, 452(7188):732–736, 2008

    Eric Bousquet, Matthew Dawber, Nicolas Stucki, Céline Lichtensteiger, Patrick Hermet, Stefano Gariglio, Jean- Marc Triscone, and Philippe Ghosez. Improper ferroelec- tricity in perovskite oxide artificial superlattices.Nature, 452(7188):732–736, 2008

    2008

  17. [24]

    Benedek and Craig J

    Nicole A. Benedek and Craig J. Fennie. Hybrid im- proper ferroelectricity: A mechanism for controllable polarization-magnetization coupling.Physical Review Letters, 106(10):107204, 2011

    2011

  18. [25]

    see Supplemental Material, which includes Refs. [13, 26– 42], for method details, extended theoretical analyses including phase stability and Landau modeling, supple- mentary experimental data, and discussions on the gen- erality of the mechanism

  19. [26]

    Verstraete, Joao Abreu, Guillaume E

    Matthieu J. Verstraete, Joao Abreu, Guillaume E. Alle- mand, Bernard Amadon, Gabriel Antonius, Maryam Az- izi, Lucas Baguet, Clémentine Barat, Louis Bastogne, Romuald Béjaud, Jean-Michel Beuken, Jordan Bieder, Augustin Blanchet, Francois Bottin, Johann Bouchet, Julien Bouquiau...

    2025

  20. [27]

    Perdew, Adrienn Ruzsinszky, Gábor I

    John P. Perdew, Adrienn Ruzsinszky, Gábor I. Csonka, Oleg A. Vydrov, Gustavo E. Scuseria, Lucian A. Con- stantin, Xiaolan Zhou, and Kieron Burke. Restoring the density-gradientexpansionforexchangeinsolidsandsur- faces.Physical Review Letters, 100:136406, 2008

    2008

  21. [28]

    D. R. Hamann, M. Schlüter, and C. Chiang. Norm- conserving pseudopotentials.Physical Review Letters, 43(20):1494–1497, 1979

    1979

  22. [29]

    D. R. Hamann. Optimized norm-conserving vanderbilt pseudopotentials.Physical Review B, 88(8):085117, 2013

    2013

  23. [30]

    van Setten, M

    M.J. van Setten, M. Giantomassi, E. Bousquet, M.J. Ver- straete, D.R. Hamann, X. Gonze, and G.-M. Rignanese. The PseudoDojo: Training and grading a 85 element optimized norm-conserving pseudopotential table.Com- puter Physics Communications, 226:39–54, 2018

    2018

  24. [31]

    BrantonJ.Campbell, HaroldT.Stokes, DavidE.Tanner, and Dorian M. Hatch. ISODISPLACE: A web-based tool for exploring structural distortions.Journal of Applied Crystallography, 39(4):607–614, 2006

    2006

  25. [32]

    Hatch and Harold T

    Dorian M. Hatch and Harold T. Stokes. INVARIANTS: program for obtaining a list of invariant polynomials of the order-parameter components associated with ir- reducible representations of a space group.Journal of Applied Crystallography, 36:951–952, 2003

    2003

  26. [33]

    Xavier Gonze and Changyol Lee. Dynamical matrices, Born effective charges, dielectric permittivity tensors, and interatomic force constants from density-functional perturbation theory.Physical Review B, 55(16):10355– 10368, 1997

    1997

  27. [34]

    First-principles phonon calculations of thermal ex- pansion in Ti3SiC2, Ti3AlC2, and Ti3GeC2.Phys

    Atsushi Togo, Laurent Chaput, Isao Tanaka, and Gilles Hug. First-principles phonon calculations of thermal ex- pansion in Ti3SiC2, Ti3AlC2, and Ti3GeC2.Phys. Rev. B, 81:174301, 2010

    2010

  28. [35]

    Hÿtch, E

    M.J. Hÿtch, E. Snoeck, and R. Kilaas. Quantitative mea- surement of displacement and strain fields from hrem mi- crographs.Ultramicroscopy, 74(3):131–146, 1998

    1998

  29. [36]

    Atomap: A new software tool for the automated analysis of atomic resolution im- ages using two-dimensional gaussian fitting.Advanced Structural and Chemical Imaging, 3(1):9, 2017

    Magnus Nord, Per Erik Vullum, Ian MacLaren, Thomas Tybell, and Randi Holmestad. Atomap: A new software tool for the automated analysis of atomic resolution im- ages using two-dimensional gaussian fitting.Advanced Structural and Chemical Imaging, 3(1):9, 2017

    2017

  30. [37]

    Tilt- driven antiferroelectricity inPbZrO 3.Physical Review Materials, 7(7):L071401, 2023

    Konstantin Shapovalov and Massimiliano Stengel. Tilt- driven antiferroelectricity inPbZrO 3.Physical Review Materials, 7(7):L071401, 2023

    2023

  31. [38]

    Baker, M

    J.S. Baker, M. Paściak, J.K. Shenton, P. Vales-Castro, B. Xu, J. Hlinka, P. Márton, R.G. Burkovsky, G. Cata- lan, A.M. Glazer, and D.R. Bowler. A re-examination of antiferroelectricPbZrO 3 andPbHfO 3: An 80-atom P namstructure. arXiv: 2102.08856

    arXiv

  32. [39]

    A graph neural network for the era of large atomistic models.npj Computational Materials, 2026

    Duo Zhang, Anyang Peng, Chun Cai, Wentao Li, Yuan- chang Zhou, Jinzhe Zeng, Mingyu Guo, Chengqian Zhang, Bowen Li, Hong Jiang, Tong Zhu, Weile Jia, Lin- feng Zhang, and Han Wang. A graph neural network for the era of large atomistic models.npj Computational Materials, 2026. DO...

    2026 doi

  33. [40]

    Thompson, H

    Aidan P. Thompson, H. Metin Aktulga, Richard Berger, Dan S. Bolintineanu, W. Michael Brown, Paul S. Crozier, Pieter J. in ’t Veld, Axel Kohlmeyer, Stan G. Moore, Trung Dac Nguyen, Ray Shan, Mark J. Stevens, Julien Tranchida, Christian Trott, and Steven J. Plimpton. Lammps - a ...

    2022

  34. [41]

    Johnston, Chiu C

    Karen E. Johnston, Chiu C. Tang, Julia E. Parker, Kevin S. Knight, Philip Lightfoot, and Sharon E. Ash- brook. The polar phase ofNaNbO 3: A combined study by powder diffraction, solid-state nmr, and first- principles calculations.Journal of the American Chemi- cal Society, 132...

    2010

  35. [42]

    Structural and dynamical phase transitions ofNaNbO3 from first-principles calculations.Physical Review Mate- rials, 7(2):024408, 2023

    Safari Amisi, Philippe Lambin, and Philippe Ghosez. Structural and dynamical phase transitions ofNaNbO3 from first-principles calculations.Physical Review Mate- rials, 7(2):024408, 2023

    2023

  36. [44]

    Hui Liu, Longlong Fan, Shengdong Sun, Kun Lin, Yang Ren, Xiaoli Tan, Xianran Xing, and Jun Chen. Electric- 8 field-induced structure and domain texture evolution inPbZrO 3-based antiferroelectric by in-situ high-energy synchrotron X-ray diffraction.Acta Materialia, 184:41– 49, 2020

    2020

  37. [45]

    Cair- ney, Xiaozhou Liao, Jordi Arbiol, and Gustau Catalan

    Ying Liu, Ranming Niu, Roger Uriach, David Pesquera, José Manuel Caicedo Roque, José Santiso, Julie M. Cair- ney, Xiaozhou Liao, Jordi Arbiol, and Gustau Catalan. Coexistence of ferroelectric and ferrielectric phases in ul- trathin antiferroelectricPbZrO 3 thin films.Microstru...

    2024

  38. [46]

    Bosch, and Sorin Lazar

    Ivan Lazić, Eric G.T. Bosch, and Sorin Lazar. Phase contrast stem for thin samples: Integrated differential phase contrast.Ultramicroscopy, 160:265–280, 2016

    2016

  39. [47]

    Moss, Peter Finkel, Xiao-Zhou Liao, and Julie M

    Ying Liu, Ran-Ming Niu, Scott D. Moss, Peter Finkel, Xiao-Zhou Liao, and Julie M. Cairney. Atomic coordi- nates and polarization map around a pair of12a[01¯1]dis- location cores produced by plastic deformation in relaxor ferroelectric PIN–PMN–PT.Journal of Applied Physics, 129...

    2021

  40. [48]

    Dunin-Borkowski, and Joachim Mayer

    Xian-Kui Wei, Chun-Lin Jia, Krystian Roleder, Rafal E. Dunin-Borkowski, and Joachim Mayer. In situ observa- tion of point-defect-induced unit-cell-wise energy storage pathway in antiferroelectricPbZrO 3.Advanced Func- tional Materials, 31(13):2008609, 2021

    2021

  41. [49]

    Selbach, Thomas Tybell, Mari-Ann Einarsrud, and Tor Grande

    Sverre M. Selbach, Thomas Tybell, Mari-Ann Einarsrud, and Tor Grande. PbO-deficientPbTiO3: Mass transport, structural effects and possibility for intrinsic screening of the ferroelectric polarization.Applied Physics Letters, 98(9):091912, 2011

    2011

  42. [50]

    S12 for details [25]

    This can also be understood as a consequence of theΓ- instability of theP bamphase which exhibits mixed char- acter when decomposed into the irreducible representa- tions of the cubic reference phase; see Fig. S12 for details [25]

  43. [51]

    Roleder, G

    K. Roleder, G. Catalan, A. M. Glazer, J. S. Baker, J. H. Ko, F. H. Naqvi, S. B. Junaid, A. Majchrowski, Z. Trybuła, J. Zaręba, I. Lazar, D. Kajewski, J. Kop- erski, and A. Soszyński. Weak low-temperature po- larity in aPbZrO 3 single crystal.Physical Review B, 107(14):L140102, 2023

    2023

  44. [52]

    Zheyi An, Hiroko Yokota, Nan Zhang, Marek Paściak, Jan Fábry, Miloš Kopecký, Jiří Kub, Guanjie Zhang, A. M. Glazer, T. R. Welberry, Wei Ren, and Zuo- Guang Ye. Multiple structural components and their competition in the intermediate state of antiferroelectric Pb(Zr,Ti)O 3.Phys...

    2021

  45. [53]

    A study of struc- tural phase transitions in antiferroelectricPbZrO 3 by neutron diffraction.Journal of the Physical Society of Japan, 53(1):226–234, 1984

    Hideshi Fujishita and Sadao Hoshino. A study of struc- tural phase transitions in antiferroelectricPbZrO 3 by neutron diffraction.Journal of the Physical Society of Japan, 53(1):226–234, 1984

    1984

  46. [54]

    Modeling of ferro- electric oxide perovskites: From first to second principles

    Philippe Ghosez and Javier Junquera. Modeling of ferro- electric oxide perovskites: From first to second principles. Annual Review of Condensed Matter Physics, 13(1):325– 364, 2022

    2022

  47. [55]

    Benedek, James M

    Nicole A. Benedek, James M. Rondinelli, Hania Djani, Philippe Ghosez, and Philip Lightfoot. Understanding ferroelectricity in layered perovskites: New ideas and in- sights from theory and experiments.Dalton Transac- tions, 44(23):10543–10558, 2015

    2015

  48. [56]

    Omid Sayedaghaee, Jorge Íñiguez, and L

    Hao Tian, Xiao-Yu Kuang, Ai-Jie Mao, Yurong Yang, Hongjun Xiang, Changsong Xu, S. Omid Sayedaghaee, Jorge Íñiguez, and L. Bellaiche. Novel type of ferro- electricity in brownmillerite structures: A first-principles study.Physical Review Materials, 2(8):084402, 2018

    2018

  49. [57]

    Genetic algorithm prediction of pressure-induced multi- ferroicity in the perovskitePbCoO3.Physical Review B, 99(20):205104, 2019

    Feng Lou, Wei Luo, Junsheng Feng, and Hongjun Xiang. Genetic algorithm prediction of pressure-induced multi- ferroicity in the perovskitePbCoO3.Physical Review B, 99(20):205104, 2019

    2019

  50. [58]

    Antiferroelectrics for energy storage applications: A review.Advanced Mate- rials Technologies, 3(9):1800111, 2018

    Zhen Liu, Teng Lu, Jiaming Ye, Genshui Wang, Xianlin Dong, Ray Withers, and Yun Liu. Antiferroelectrics for energy storage applications: A review.Advanced Mate- rials Technologies, 3(9):1800111, 2018

    2018

  51. [59]

    Tun- able multi-level memory states in compositionally graded lead-free ferroelectric thin films.Advanced Materials, 38:e21967, 2026

    Jinyang Li, Suzhen Liu, Tao Wang, Zhongqi Ren, Cheng Gao, Fenghui Gong, Xiaodong Lv, Chen Su, Sujit Das, Hao Pan, Yunlong Tang, and Zuhuang Chen. Tun- able multi-level memory states in compositionally graded lead-free ferroelectric thin films.Advanced Materials, 38:e21967, 2026

    2026

  52. [60]

    Improper-proper ferroelectric competition as a mechanism for multistate polarisation and ferrielectric- like behaviour

    Cameron AM Scott, Finlay D Morrison, and Nicholas Bristowe. Improper-proper ferroelectric competition as a mechanism for multistate polarisation and ferrielectric- like behaviour. arXiv: 2510.02604

Pith tools

Reviewed August 1, 2026 · model on record in the stance chip above.