Anharmonic stabilization of ferrielectricity in ${\mathrm{CuInP}}_{2}{\mathrm{Se}}_{6}$

Open Access

Anharmonic stabilization of ferrielectricity in ${CuInP}_{2} {Se}_{6}$

Nikhil Sivadas, Peter Doak, and P. Ganesh

Phys. Rev. Research 4, 013094 – Published 4 February 2022

Abstract

Using first-principles calculations and group-theory-based models, we study the stabilization of ferrielectricity (FiE) in ${CuInP}_{2} {Se}_{6}$ . We find that the FiE ground state is stabilized by a large anharmonic coupling between the polar mode and a fully symmetric Raman-active mode. Our results open possibilities for controlling the single-step switching barrier for polarization by tuning the Raman-active mode. We discuss the implications of our findings in the context of designing next-generation optoelectronic devices that can overcome the voltage-time dilemma.

Received 15 June 2021
Revised 10 December 2021
Accepted 11 December 2021

DOI:https://doi.org/10.1103/PhysRevResearch.4.013094

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Anharmonic lattice dynamics Ferroelectricity Quantum criticality Structural order parameter

2-dimensional systems

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Nikhil Sivadas^1,*, Peter Doak^1,2, and P. Ganesh^1,†

¹Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
²Computational Science and Engineering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA

^*sivadasn@ornl.gov
^†ganeshp@ornl.gov

Article Text

Click to Expand

Supplemental Material

Click to Expand

References

Click to Expand

Issue

Vol. 4, Iss. 1 — February - April 2022

Subject Areas

Condensed Matter Physics

Reuse & Permissions

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
The crystal structure and the atomic distortions in the paraelectric (PE) and ferrielectric (FiE) phases of ${CuInP}_{2} {Se}_{6}$ (CIPSe). (a) The top view and (b) the side view of the PE phase ( $P \bar{3} 1 c$ ) with one of the inversion center labeled (“ $\times$ ”). (c) The top view and (d) the side view of the FiE phase ( $P 31 c$ ). The Se-Se bonds are shown only as visual aid for the modes involving the Se atoms. The FiE phase can be decomposed into six polar symmetry adapted modes (SAMs) and four fully symmetric SAMs that transform as the $Γ_{2}^{-}$ and $Γ_{1}^{+}$ irreducible representation (irrep) of $P \bar{3} 1 c$ , respectively. The arrows represent the local distortions. All the arrows have the same amplitude. (e) The displacement of the Cu atom towards the top trigonal ${Se}_{t}$ plane ( $Γ_{2}^{-} [A_{3}]$ ). (f) The expansion (contraction) of the trigonal ${Se}_{t}$ ( ${Se}_{b}$ ) planes ( $Γ_{2}^{-} [A_{1}]$ ), and (g) the in-phase rotation of the ${Se}_{t}$ and ${Se}_{b}$ planes about the Cu atoms ( $Γ_{2}^{-} [A_{2}]$ ). (h) The out-of-plane expansion of the Se sub-layers ( $Γ_{1}^{+} [A_{3}]$ ), (i) an in-plane expansion of the trigonal Se planes ( $Γ_{1}^{+} [A_{1}]$ ), and (j) the out-of-phase rotation of the ${Se}_{t}$ planes and the ${Se}_{b}$ planes ( $Γ_{1}^{+} [A_{2}]$ ) about the Cu atoms.
Reuse & Permissions
Figure 2
The decomposition of the total polarization as a function of the fractional amplitude of the fully symmetric mode ( $Q_{Γ_{1}^{+}}$ ) and the polar mode ( $Q_{Γ_{2}^{-}}$ ). The polar mode creates most of the polarization. The fully symmetric mode on its own does not carry any dipole moment.
Reuse & Permissions
Figure 3
The energy as a function of the atom-projected polar mode ( $Q_{Γ_{2}^{-}}$ ). The energy as a function of the full polar mode that is unstable (black), and the component of the mode involving the displacement of only the Cu atoms (blue), the In atoms (orange), and both Cu and In atoms (red). The energy gain from only the polar modes is small.
Reuse & Permissions
Figure 4
The anharmonic energy surface. (a) The total energy (meV/f.u. atom), (b) the electronic-structure contribution from the valance electrons (eV/f.u. atom), and (c) the contribution from the ion-ion electrostatic interaction (eV/f.u. atom), as a function of the fractional amplitude of the fully symmetric mode ( $Q_{Γ_{1}^{+}}$ ) and the polar mode ( $Q_{Γ_{2}^{-}}$ ). The scale of the latter is the same as that in Fig. 3. All the reported energies are relative to the fully relaxed PE phase ( $P \bar{3} 1 c$ ).
Reuse & Permissions
Figure 5
The total energy as a function of the fractional amplitude of the distortion from the PE phase to the FiE phase, for different value of biaxial strain ( $ε_{x^{2} + y^{2}}$ ). Results for tensile strains of $2 %$ (blue), $1 %$ (black), the unstrained case (red), and compressive strain of $1 %$ (green), and $2 %$ (magenta) are reported. The energy difference can be enhanced or suppressed by the application of an in-plane strain.
Reuse & Permissions

Physical Review Research

Anharmonic stabilization of ferrielectricity in CuInP2Se6

Nikhil Sivadas, Peter Doak, and P. Ganesh

Phys. Rev. Research 4, 013094 – Published 4 February 2022

Abstract

Physics Subject Headings (PhySH)

Authors & Affiliations

Article Text

Supplemental Material

References

Issue

Subject Areas

Authorization Required

Other Options

Download & Share

Images

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Reuse & Permissions

Log In

Search

Article Lookup

Paste a citation or DOI

Enter a citation

Anharmonic stabilization of ferrielectricity in ${CuInP}_{2} {Se}_{6}$