Phenomenological description of bright domain walls in ferroelectric-antiferroelectric layered chalcogenides

Anna N. Morozovska, Eugene A. Eliseev, Kyle Kelley, Yulian M. Vysochanskii, Sergei V. Kalinin, and Petro Maksymovych

Phys. Rev. B 102, 174108 – Published 17 November 2020

Abstract

Recently, a layered ferroelectric $CuIn P_{2} {Se}_{6}$ was shown to exhibit domain walls with locally enhanced piezoresponse—a striking departure from the observations of nominally zero piezoresponse in most ferroelectrics. Although it was proposed that such “bright” domain walls are phase boundaries between ferri- and antiferroelectrically ordered regions of the materials, the physical mechanisms behind the existence and response of these boundaries remain to be understood. Here, using Landau-Ginzburg-Devonshire phenomenology combined with a four sublattices model, we describe quantitatively the bright-contrast and dark-contrast domain boundaries between the antiferroelectric, ferroelectric, or ferrielectric long-range-ordered phases in a layered ferroelectric-antiferroelectric ferroics, such as $CuIn P_{2} {(S_{1 - y} {Se}_{y})}_{6}$ .

Received 15 September 2020
Accepted 2 November 2020

DOI:https://doi.org/10.1103/PhysRevB.102.174108

Physics Subject Headings (PhySH)

Antiferroelectricity Ferroelectric domains Ferroelectricity Structural order parameter

Chalcogenides

Landau-Ginzburg theory Piezoresponse force microscopy Scanning probe microscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Anna N. Morozovska ^1,*, Eugene A. Eliseev ², Kyle Kelley³, Yulian M. Vysochanskii ⁴, Sergei V. Kalinin^3,†, and Petro Maksymovych^3,‡

¹Institute of Physics, National Academy of Sciences of Ukraine, 46 prospect Nauky, 03028 Kyiv, Ukraine
²Institute for Problems of Materials Science, National Academy of Sciences of Ukraine, Krjijanovskogo 3, 03142 Kyiv, Ukraine
³The Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
⁴Institute of Solid State Physics and Chemistry, Uzhhorod University, 88000 Uzhhorod, Ukraine

^*Corresponding author: anna.n.morozovska@gmail.com
^†Corresponding author: sergei2@ornl.gov
^‡Corresponding author: maksymovychp@ornl.gov

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Issue

Vol. 102, Iss. 17 — 1 November 2020

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Images

Figure 1
Atomic structures of $CuIn P_{2} {(S_{1 - y} {Se}_{y})}_{6}$ , obtained by DFT, where the small yellow and blue, small and bigger violet balls are S (or Se) and Cu atoms, P, and In atoms, respectively. The structure is recalculated using DFT data from Ref. [31], which is Open Access under a Creative Commons Attribution 4.0 International License [42]. Here the spatial structure is modified; red and blue arrows inside the atomic groups illustrate the polarization direction for different types of atomic displacements $U^{(m)}$ in the quasihomogeneous ferroelectric (or ferrielectric) FE state (a), and three types of antiferroelectric states: AFE1 (b), AFE2 (c), and AFE3 (d). The orientation of the crystallographic axes $a$ , $b$ , and $c$ is shown at the bottom of each plot.
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Figure 2
The free energy (9) as a function of order-parameter components $p_{1}$ and $p_{2}$ for different values of the AFE-FE coupling constant $χ$ : (a) $χ = - 0.4$ , (b) $χ = 0$ , (c) $χ = 0.4$ , (d) $χ = 1$ , and (e) $χ = 4$ . Curie temperatures change parameter $ε = - 0.5$ for the top line, $ε = 0$ for the middle line, and $ε = + 0.5$ for the bottom line. Red color denotes zero energy, while violet color is its minimal value in relative units. Capital letters O and $T_{a, p}$ denote orthorhombic and tetragonal spatially homogeneous phases, respectively.
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Figure 3
Color map of order parameters $a$ (a) and $p$ (b) in coordinates χ and ε. Color bar on the right represents the color code for the both order parameters.
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Figure 4
Distributions of the FE and AFE order parameters, $p$ (blue curves) and $a$ (red curves), respectively. Plots (a) and (b) illustrate the profiles of $a$ and $p$ at the domain wall in FE and AFE phases, corresponding to $ε_{0} = - \frac{1}{4}$ and $ε_{0} = + \frac{1}{4}$ , respectively. Plots (c) and (d) show the profiles of $a$ and $p$ at the boundaries between FE and AFE phases, induced by the function $ε (x) = ε_{0} [tanh (\frac{x + x_{0}}{L_{d}}) - 1 - tanh (\frac{x - x_{0}}{L_{d}})]$ . The difference between (c) and (d) is in the initial distribution of the order parameters and AFE region width. Other parameters: $ε_{0} = 0.25$ , $L_{d} = 10$ nm, $x_{0} = 40$ nm (c) or 80 nm (d), $χ = 1$ , $g = 4 n m^{2}$ . Solid curves in all plots are calculated by FEM. Dashed curves in plots (a) and (d) are calculated from Eqs. (11a) and (11b) with fitting parameters listed in the text. Dotted vertical lines in plots (c) and (d) denote the points where $ε \approx 0$ .
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Figure 5
Local piezoresponse (in arbitrary units) at $CuIn P_{2} {Se}_{6}$ (a) and ${Cu}_{1 - x} In P_{2} S_{6}$ (b) surfaces. Red and blue diamonds are PFM data [31] measured at 140 K in ultrahigh vacuum for $CuIn P_{2} {Se}_{6}$ and that of $CuIn P_{2} S_{6}$ at room temperature in controlled environment. Solid dark red and blue curves are fitted by Eq. (13a) with parameters provided in the text. Black arrows point to the regions of the bright (a) and dark (b) domain walls. Line profiles of piezoresponses (a),(b) were measured along the white dashed lines, crossing domain boundaries in inset to plots (a) and (b), respectively. Color insets are adapted from [31] using Open Access under a Creative Commons Attribution 4.0 International License [43].
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