Academic Articles & Supplements

Stress-Induced Ferroelectricity in Hafnia Core-Shell Nanoparticles

Eugene Eliseev, Anna Morozovska

Author

Eugene Eliseev, Anna Morozovska

Title

Stress-Induced Ferroelectricity in Hafnia Core-Shell Nanoparticles

Description

Supplement to the paper, archived at https://doi.org/10.48550/arXiv.2602.09262 (arXiv:2602.09262)

Stress-Induced Ferroelectricity in Hafnia Core-Shell Nanoparticles

Eugene A. Eliseev and Anna N. Morozovska

In contrast to thin films of hafnia

(

HfO

), where the appearance of switchable ferroelectric polarization can be induced by strain or defect engineering, reliable methods for controlling ferroelectricity are absent in

HfO

nanoparticles. Direct experimental observations of ferroelectric hysteresis and ferroelectric domains in these nanoparticles are also absent. To the best of our knowledge, stress-induced ferroelectric states in the

HfO

nanoparticles have not been explored. In this work, we study the influence of chemical stress on phase diagrams, dielectric and polar properties of spherical

HfO

core-shell nanoparticles using a Landau-Ginzburg-Devonshire free energy functional that includes trilinear and biquadratic couplings involving polar, antipolar, and nonpolar order parameters. The ferroelectric phase exhibits reentrant behavior as a function of nanoparticle size, such that the spontaneous polarization exists only within a limited range of core radii

𝑅

, namely

min

max

The minimal critical radius

min

is primarily determined by the size dependence of the depolarization field and correlation effects. The maximal critical radius

max

is primarily determined by the size dependence of chemical stresses induced by the elastic defects in the shell.

Functions and parameters

color-maps


fundamental constans and global parameters


material constans (local parameters)


definition

Minimization function


Table transformations functions


Physical properties and phase diagrams vs.
(
R
c
,n
) at
W
s
=-10
3
Å

(*SetDirectory["C:\\Users\\user\\OneDrive\\Робочий стіл\\work2026\\HfO2_nano\\Data_figures"]*)

In[]:=

(*LGDnano[slct_,R_,ni_,optns...]*)

Preliminary phase diagrams


ε
e
=3


ε
e
=30


ε
e
=300


Cite this as: Eugene Eliseev, Anna Morozovska, "Stress-Induced Ferroelectricity in Hafnia Core-Shell Nanoparticles" from the Notebook Archive (2026), https://notebookarchive.org/2026-03-6gx3be5

Stress-Induced Ferroelectricity in Hafnia Core-Shell Nanoparticles

Functions and parameters

color-maps

fundamental constans and global parameters

material constans (local parameters)

definition

Minimization function

Table transformations functions

Physical properties and phase diagrams vs. (Rc,n) at Ws=-10 3Å

Preliminary phase diagrams

εe=3

εe=30

εe=300

color-maps


fundamental constans and global parameters


material constans (local parameters)


Minimization function


Table transformations functions


Physical properties and phase diagrams vs.
(
R
c
,n
) at
W
s
=-10
3
Å

Preliminary phase diagrams


ε
e
=3


ε
e
=30


ε
e
=300
