Competing phases and domain structures of ferroelectric perovskites: the benefit of epitaxial (110) growth

TL;DR

This paper addresses how epitaxial (110) strain modulates phase stability and domain structures in ferroelectric perovskites, a regime less explored than (001) growth. It employs a first-principles based effective Hamiltonian within coarse-grained molecular dynamics to map strain–temperature phase diagrams for BaTiO$_3$, KNbO$_3$, and PbTiO$_3$. The study reveals a rich landscape of metastable nanoscale domains and heterophases under (110) strain, including layer-by-layer and side-by-side walls in BaTiO$_3$ and KNbO$_3$ and antiferroelectric-like, superdomain patterns in PbTiO$_3$, with domain stability strongly influenced by thermal history. These findings suggest new routes for reconfigurable nanoscale ferroelectric devices and enhanced functional responses.

Abstract

Strain and domain engineering offer powerful routes to control phase and domain stability in ferroelectric thin films. While most studies have focused on (100)-oriented growth, the impact of lower-symmetry orientations remains underexplored. We address this gap in knowledge with first-principles based molecular dynamics simulation for the example of prototypical ferroelectric perovskites under (110) strain. Epitaxial (110) strains may indeed outperform the widely studied (100) orientation, as even modest strain values stabilize a diverse set of metastable nanoscale states with potential high functional tunability. In this regime, the films exhibit multidomain configurations with domain wall normal oriented along the clamped in-plane or the relaxed out-of-plane directions and heterophases in BaTiO$_3$ and KNbO$_3$. Besides, complex superdomain patterns and antiferroelectric-like domains are observed in PbTiO$_3$. These metastable nanoscale configurations may allow for large reversible responses.

Figures (12)

• Figure 1: (a) Unit cell of the ABO$_3$ perovksite structure (A (green): Pb, Ba, K; B (blue): Ti, Nb; O (red)) with alternating O$_2^{4-}$ and A-B-O$^{4+}$ (orange) (110) planes. (b) The elastic boundary conditions illustrated on a (110) plane. The lattice is relaxed along the growth direction, i.e., [110], and the lattice constants along [001] and [1$\bar{1}$0] are clamped to $(1+\eta)a_0$ and $(1+\eta)\sqrt{2}a_0$, respectively, where $\eta$ is the external strain and $a_0$ is the reference lattice parameter taken from the paraelectric cubic phase directly above the ferroelectric transition temperature.
• Figure 2: Possible polarization directions relative to the [110] growth direction. (a) Under compressive strain one polarization component is along (110), i.e., O phase, and with increasing magnitude of $P_{[{001}]}$ or $P_{[{1\bar{1}0}]}$ M$_\text{B}$ and M$_\text{C}$ phases bridge towards R and T phases, respectively. (b) Under tensile strain, the in-plane polarization can rotate between T and and R phase via phase M$_\text{A}$. An example of possible Tri phases with finite $P_{[{001}]}$, $P_{[{110}]}$, and $P_{[{1\bar{1}0}]}$ are shown in gray arrows.
• Figure 3: Phase diagram of BaTiO$_3$ under epitaxial (110) strain. The bulk $T_{\text{c}}$ as predicted by our model of 280 K, 140 K, and 80 K for C to T ($T_{c}^{C-T}$), T to O ($T_{c}^{T-O}$), and O to R phase ($T_{c}^{O-R}$) are given as reference (right). Observed phases and domain structures are color-coded as: paraelectric (gray), T (${[00a]}$, yellow), M$_\text{A}$ (${[\pm b\mp ba]}$, green), O (${[aa0]}$, red), M$_\text{C}$ (${[ab0]}$ or ${[ba0]}$, purple), M$_\text{B}$ (${[aa\pm b]}$, orange), and triclinic (Tri) phases with two different domain structures (white with and without hatches, see text).
• Figure 4: Collection of metastable domain structures found under (110) strain for BaTiO$_3$: (a)--(e) structures observed for BaTiO$_3$ during cooling, cf. Fig. \ref{['fig:bto_phase']}, (f) heterophase phase found during heating of BaTiO$_3$ from the single domain M$_\text{A}$ phase. For each structure, the polarization projected on $P_{[{110}]}$, $P_{[{1\bar{1}0}]}$, and $P_{[{001}]}$ direction is shown (rows, color bar: right). Arrows indicate the polarization of domains projected on the corresponding surface planes. The same configurations are found for KNbO$_3$ for different conditions.
• Figure 5: Energy as a function of strain $\Delta$E($\eta$) of BaTiO$_3$ at (a) 45 K and (b) 200 K for possible charge-neutral multidomain configurations (solid curves), single domain states (sg, dotted lines), or heterophases (dashed lines), with $P_{[{110}]}$ and $P_{[{001}]}$ (red), $P_{[{1\bar{1}0}]}$ and $P_{[{001}]}$ (blue), with $P_{[{110}]}$, $P_{[{001}]}$, and $P_{[{1\bar{1}0}]}$ (black), or with only $P_{[{110}]}$ (pink). Markers indicate the domain wall normal: layer-by-layer [110] (triangles), [1$\bar{1}$0] (circles), [001] (crosses), as well as [001]- and [1$\bar{1}$0]-walls (diamonds). Stars or pluses refer to heterophase that has a coexisting O phase distorted slightly away from the [1$\bar{1}$0] direction, see Fig. \ref{['fig:bto_multi']} (f), or from the [110] direction, respectively. At large compressive or tensile strain, the Tri phase with [110]-walls (black triangles) or with [001] and [1$\bar{1}$0] (black diamonds) becomes the single domain O phase (pink dotted curve) or multidomain M$_\text{A}$ phase (blue crosses) observed upon cooling via continuous reversible polarization rotation, respectively.