Ferroelectric Properties and Topological Polar Textures of PbTiO$_3$ from a Second-Principles Open-Source Interatomic Potential

TL;DR

This work addresses the need for scalable, accurate atomistic modeling of PbTiO3 to study ferroelectric phase transitions, domain walls, and topological textures. It introduces an open-source second-principles interatomic potential trained on extensive DFT data and validated against first-principles results, enabling large-scale simulations with high fidelity. The model captures finite-temperature phase behavior, phonon softening, and complex domain-wall and topological textures, including Bloch skyrmions, skyrmioniums, and related structures, and reveals Ising lines in 180-degree walls. By providing open data and code, the work facilitates exploration of ferroelectric phenomena and potential device applications that require scales beyond conventional DFT.

Abstract

We introduce an open-source, fully atomistic second-principles interatomic potential for lead titanate (PbTiO3), a benchmark ferroelectric material known for its strong polarization and hightemperature phase transitions. While density functional theory excels at capturing atomic-scale behavior, it remains computationally prohibitive for large-scale simulations required to explore complex phenomena. Our model addresses this limitation by accurately reproducing key properties of PbTiO3, including domain wall dynamics and different topological textures formation, which are known as key features to next-generation memory and energy-efficient technologies. Validated against DFT data, the model remains predictive across a wide range of conditions. It offers an accessible and efficient framework for high-accuracy large-scale simulations, allowing deeper insights into PbTiO3 and its potential applications.

Figures (6)

• Figure 1: Validation against DFT of the interatomic potential for PbTiO$_\mathrm{3}$. (a) Comparison between model and DFT energies, as predicted for the structures contained in the training set. The inset shows the distribution of the amplitude of absolute error made by the model. (b) Comparison between DFT and model energies for different (meta)-stable phases, as consistently relaxed within each approach. (c) Comparison between DFT and model cumulative total phonon density of states in the tetragonal $P4mm$ ground state. The inset shows the comparison between DFT and model contributions to the cumulative phonon density of states individually for each type of atoms. (d) Comparison between DFT and model distortion amplitudes for different meta- and stable phases, as consistently relaxed within each approach.
• Figure 2: Ferroelectric $P4mm$ to paralectric $Pm\mathrm{\bar{3}}m$ phase transition of PbTiO$_\mathrm{3}$ in temperature as predicted by the interatomic potential . (a) Evolution of the spontaneous polarization (normalized with the polarization $P_0 = 1.1$ C/m$^2$ at 0 K) with temperature, in comparison with the results of Refs Wojdel2013liu2013reinterpretationwu2023modulardawber2007tailoringwang2023finite. The orange dashed curve shows a critical exponent fit of $n=0.28$. (b) Evolution of the homogeneous strains with temperature, in comparison with the results of Refs Wojdel2013xie2022ab. Note that the data of Ref. Wojdel2013 with a negative pressure of -14 GPa have been shifted to align with our strain at $T_c$
• Figure 3: Temperature-dependent phonon dispersion curves of PbTiO$_\mathrm{3}$. (a) Temperature-dependent phonon dispersion in the cubic phase above $T_c$ ($T_c$ stands for critical temperature of the simulation considering $4\times 4\times 4$ supercell). (b) Mode softenings at $\Gamma$ (polar modes) and $R$ (antiferrodistortive modes). (c) Temperature-dependent phonon dispersion curves in the tetragonal phase at $T_{exp}=300\ K$ in a $4\times 4\times 4$ supercell, compared with experimental data from Refs tomeno2006latticefontana1991raman.
• Figure 4: Characterization of 180$^\circ$ Bloch DW in tetragonal PbTiO$_\mathrm{3}$. (a) Polarization profile of $P \parallel [100]$ ($P_x$) (purple) and $P \parallel [010]$ ($P_y$) (orange) in a 180$^\circ$ domain structure. (b) Results of NEB calculations illustrating the domain wall energy evolution along the transition from a Bloch DW to two distinct monodomain configurations: one with the final polarization aligned parallel to the original domain polarization and the other with the final polarization oriented perpendicular to the original domain polarization. Both NEB paths are compared to DFT calculations. (c) Evolution of the energy when DW approach each other and its fit with exponential and power laws. (d) Polarization profile in x-z plane highlighting the appearance of Ising lines within DW.
• Figure 5: Skyrmion, skyrmionium, target-skyrmion and skyrmion bag in PbTiO$_\mathrm{3}$. (a) Sketch of a Bloch skyrmion. (b) Sketch of a skyrmionium constructed using $180^{\circ}$ domains. (c) Relaxed Bloch skyrmion using a $20\times 20\times 1$ supercell, starting from the configuration of panel (a). (d) Relaxed Bloch skyrmionium using a $32\times 32\times 1$ supercell, starting from the configuration of panel (b). (e) Results of a NEB calculation along the path between the skyrmion and monodomain states using a $20\times 20\times 1$ supercell. (f) Relaxed Bloch target-skyrmion using a $41\times 41\times 1$ supercell. (g) Relaxed Bloch skyrmion bag using a $40\times 40\times 1$ supercell.