Re-entrant Ferroelectricity in Nanosized Hafnia-Zirconia: Landau-type Theory
Author
Eugene Eliseev, Anna Morozovska
Title
Re-entrant Ferroelectricity in Nanosized Hafnia-Zirconia: Landau-type Theory
Description
Supplement to the paper, archived at https://doi.org/10.48550/arXiv.2601.06267 (arXiv:2601.06267)
Category
Academic Articles & Supplements
Keywords
ferroelectric hafnia, Landau model, thin epitaxial films, nanoislands
URL
http://www.notebookarchive.org/2026-01-60qfsh4/
DOI
https://notebookarchive.org/2026-01-60qfsh4
Date Added
2026-01-13
Date Last Modified
2026-01-13
File Size
0.52 megabytes
Supplements
Rights
CC BY 4.0
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Supplement to the paper, Anna N. Morozovska, Eugene A. Eliseev, Sergei V. Kalinin, Maksym V. Strikha, “Sizes of Ferroelectricity Appearance and Disappearence in Nanosized Hafnia-Zirconia:Landau-type Theory.”
archived at
https://arxiv.org/abs/2601.06267 (arXiv:2601.06267)
archived at
https://arxiv.org/abs/2601.06267 (arXiv:2601.06267)
Re-entrant Ferroelectricity in Nanosized
Hafnia-Zirconia: Landau-type Theory
Re-entrant Ferroelectricity in Nanosized
Hafnia-Zirconia: Landau-type Theory
Hafnia-Zirconia: Landau-type Theory
Eugene A. Eliseev and Anna N. Morozovska
The distinctive feature of nanoscale hafnia-zirconia are the critical sizes of ferroelectricity
appearance, whereas the critical sizes of ferroelectricity disappearance exist
in other ferroelectrics. Using the Landau-Ginzburg-Devonshire free energy
functional with higher powers, trilinear and biquadratic couplings of polar,
nonpolar and antipolar order parameters, we calculated analytically the
strain-dependent critical sizes of the ferroelectricity appearance and
disappearance, analyzed how the size effect and mismatch strains influence the
phase diagrams and polarization switching barrier in epitaxial HfO2 thin films
and nano-islands with the out-of-plane spontaneous polarization. We have shown
that the critical thickness/height of out-of-plane spontaneous polarization
disappearance is determined by the size dependence of the depolarization field
and correlation effects. The critical thickness/height of the ferroelectricity
appearance is determined by the size dependence of the effective mismatch
strain considering possible appearance of misfit dislocations and lateral
relaxion of strains.
appearance, whereas the critical sizes of ferroelectricity disappearance exist
in other ferroelectrics. Using the Landau-Ginzburg-Devonshire free energy
functional with higher powers, trilinear and biquadratic couplings of polar,
nonpolar and antipolar order parameters, we calculated analytically the
strain-dependent critical sizes of the ferroelectricity appearance and
disappearance, analyzed how the size effect and mismatch strains influence the
phase diagrams and polarization switching barrier in epitaxial HfO2 thin films
and nano-islands with the out-of-plane spontaneous polarization. We have shown
that the critical thickness/height of out-of-plane spontaneous polarization
disappearance is determined by the size dependence of the depolarization field
and correlation effects. The critical thickness/height of the ferroelectricity
appearance is determined by the size dependence of the effective mismatch
strain considering possible appearance of misfit dislocations and lateral
relaxion of strains.
Determination of bulk parameters of Landau-Ginsburg-Devonshire model for compound
HfO
2
different LGD free energy as a function of dimensionlessorderparametersQΓ3,QY2andQY4
different LGD free energy as a function of
dimensionlessorderparameters,and
Q
Γ3
Q
Y2
Q
Y4
Free energy dependence on order parameters, calculated by Delodovici et al.
Free energy dependence on order parameters, calculated by Delodovici et al.
Fit of Delodovici et al. data with different LGD functionals
Fit of Delodovici et al. data with different LGD functionals
LGD parameters and their dependence on strain
LGD parameters and their dependence on strain
strain dependence of b200 (β200)
strain dependence of b200
()
β
200
strain dependence of g111 (γ111)
strain dependence of g111
()
γ
111
LGD parameters in “real” physical coordinates
LGD parameters in “real” physical coordinates
Phase diagrams of multiferroics: thin films and islands
mmm
symmetry
Functions and parameters
Functions and parameters
color-maps
color-maps
fundamental constans and global parameters
fundamental constans and global parameters
material constans (local parameters)
material constans (local parameters)
definition
definition
tests of function LGDmmm
tests of function LGDmmm
Phase diagrams for thin films (2R>>h)
Phase diagrams for thin films (2R>>h)
(*SetDirectory["C:\\Users\\user\\OneDrive\\Робочий стіл\\work2025\\DFT_HZO_LGD_Yunseok-Kim\\figures"]*)
um-h phase diagrams: λ=0.1 nm
u
m
um-h phase diagrams: λ=20 pm
u
m
um-h phase diagrams: λ=0 nm
u
m
Phase diagrams for islands (R~h) at λ=0.2 Å
Phase diagrams for islands (R~h) at λ=0.2 Å
um-h phase diagrams: “cake” h=0.4*R
u
m
um-h phase diagrams: “pill” with h=R
u
m
um-h phase diagrams: “cans” with h=2R
u
m
Free energy maps
Free energy maps
Films with different λ
Films with different λ
Islands with different radius for h=10 nm
Islands with different radius for h=10 nm
Cite this as: Eugene Eliseev, Anna Morozovska, "Re-entrant Ferroelectricity in Nanosized Hafnia-Zirconia: Landau-type Theory" from the Notebook Archive (2026), https://notebookarchive.org/2026-01-60qfsh4
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