Academic Articles & Supplements

"Flexo-phonons" and "Flexo-ferrons" in Van der Waals ferroelectric CuInP2S6

Anna Morozovska, Eugene Eliseev

Author

Anna Morozovska, Eugene Eliseev

Title

"Flexo-phonons" and "Flexo-ferrons" in Van der Waals ferroelectric CuInP2S6

Description

code used to perform numerical and analytical calculations, presented in ArXive publication https://doi.org/10.48550/arXiv.2503.06305

“Flexo-phonons” and “Flexo-ferrons” in Van der Waals ferroelectrics
CuIn
P
2
S
6

[Anna N. Morozovska, Eugene Eliseev, Oleksiy V. Bereznikov, Mykola Ye. Yelisieiev, Guo-Dong Zhao, Yujie Zhu, Venkatraman Gopalan, Long-Qing Chen, Jia-Mian Hu, and Yulian M. Vysochanskii. “” Flexo-phonons” and” Flexo-ferrons” in Van der Waals ferroelectrics.” arXiv preprint arXiv:2503.06305 (2025).]

Anna N. Morozovska and Eugene A. Eliseev

The contribution of flexoelectric coupling to the long-range order parameter fluctuations in ferroics can be critically important to the ferron dispersion and related polar, pyroelectric and electrocaloric properties. Here we calculate analytically the dispersion relations of soft optic and acoustic “flexo-phonons” and “flexo-ferrons” by incorporating the flexoelectric coupling, damping, and higher elastic gradients in the Landau-Ginzburg-Devonshire free energy functional using the van der Waals uniaxial ferrielectric CuInP2S6 as an example. We analyze the changes in the flexo-phonon and flexo-ferron spectra arising from the appearance of spatially modulated phases induced by the flexoelectric coupling. We show that the free energy landscape of CuInP2S6 determines the specific features of its phonon spectra and ferron dispersion. We also discuss the contributions of optic and acoustic flexo-ferrons to the pyroelectric and electrocaloric responses of CuInP2S6 at low temperatures.

Function “Ferron3D” definition


Figures

(*options*)

In[]:=

PropF={Γ0.0,M->0.01

-9

,μ->4.*

-14

,v3333->3.*

-9

,z333->1.*

};

Dispersion curves of
Γ
ω
A
and
Γ
ω
O
for
f
55
=const
(Figure 1)


Dispersion curves of
Γ
ω
A
and
Γ
ω
O
for
Γ=const
(Figure 2)


Dispersion contours of
Re(
ω
A
)
and
Im(
ω
A
)
for
Γ=0
(Figure 3)


Dispersion curves of
δP
A
and
δP
O
(Figure 4)


figures for ΔP vs T at different
f
55
and zero field (Figure 5a)


figure for ΔΠ vs T at different
f
55
and zero field (Figure 5b)


figures for ΔP and ΔΠ vs E at different
f
55
(Figure 5c and 5d)


contours for ΔP vs E and
f
55
at T=10K ( Figure 6a)


contours for ΔΠ vs E and
f
55
at T=10K (Figure 6b)


integrands vs ω at room temperature (Suplementary Figure A1)


Different contributions to ΔΠ vs T at different
f
55
and zero field (Figure A3)


Different contributions to ΔP vs T at different
f
55
(estimation purposes )


Cite this as: Anna Morozovska, Eugene Eliseev, ""Flexo-phonons" and "Flexo-ferrons" in Van der Waals ferroelectric CuInP2S6" from the Notebook Archive (2025), https://notebookarchive.org/2025-03-8a3v8ii

“Flexo-phonons” and “Flexo-ferrons” in Van der Waals ferroelectrics CuInP2S6

Function “Ferron3D” definition

Figures

Dispersion curves of ΓωA and ΓωO for f55=const (Figure 1)

Dispersion curves of ΓωA and ΓωO for Γ=const (Figure 2)

Dispersion contours of Re(ωA) and Im(ωA) for Γ=0 (Figure 3)

Dispersion curves of δPA and δPO (Figure 4)

figures for ΔP vs T at different f55 and zero field (Figure 5a)

figure for ΔΠ vs T at different f55 and zero field (Figure 5b)

figures for ΔP and ΔΠ vs E at different f55 (Figure 5c and 5d)

contours for ΔP vs E and f55 at T=10K ( Figure 6a)

contours for ΔΠ vs E and f55 at T=10K (Figure 6b)

integrands vs ω at room temperature (Suplementary Figure A1)

Different contributions to ΔΠ vs T at different f55 and zero field (Figure A3)

Different contributions to ΔP vs T at different f55 (estimation purposes )