Thermal stability of nano-scale ferroelectric domains by molecular dynamics modeling

TL;DR

The paper investigates how thermal fluctuations limit the stability of ultra-dense ferroelectric domain walls in BaTiO$_3$ by combining atomistic core-shell MD and a coarse-grained effective Hamiltonian MD. It demonstrates that domain-wall fluctuations can roughen walls and nucleate bridging segments, causing spontaneous collapse of nano-sized reversed domains well below the Curie temperature, thereby setting a lower bound on domain spacing and maximum wall density. The authors develop and compare methods to quantify domain-wall width $d_{ ext{DW}}$ and energy $\Delta E^*_{ ext{DW}}$, reveal temperature-dependent trends in $P_z$ and wall energy, and construct an energy-landscape picture of domain switching that emphasizes the role of charged interfaces and wall-area changes. The findings have implications for nanoelectronic devices relying on dense domain-wall networks and suggest strategies such as pinning to stabilize high-density walls, with broader relevance to ferroelectric perovskites beyond BaTiO$_3$.

Abstract

Ultra-dense domain walls are increasingly important for many devices but their microscopic properties are so far not fully understood. Here we use molecular dynamic simulations to study the domain wall stability in the prototypical ferroelectric BaTiO3 combining core-shell pair potentials and a coarse-grained effective Hamiltonian. We transfer the discussion of the field-driven nucleation and motion of domain walls to thermally induced modifications of the wall without an external driving force. Our simulations show that domain wall dynamics and stability depend crucially on microscopic thermal fluctuations. Enhanced fluctuations at domain walls may result in the formation of critical nuclei for the permanent shift of the domain wall. If two domain walls are close - put in other words, when domains are small - thermal fluctuations can be sufficient to bring domain walls into contact and lead to the annihilation of small domains. This is even true well below the Curie temperature and when domain walls are initially as far apart as 6 unit cells. Such small domains are, thus, not stable and limit the maximum achievable domain wall density in nanoelectronic devices.

Figures (14)

• Figure 1: Illustration of the modeled degrees of freedoms. (a) Atomistic core-shell model for BaTiO3: Each ion is modeled by one positively charged core and one negatively charged shell particle with small mass which are connected by a spring. (b) Coarse-grained effective Hamiltonian: the atomic degrees of freedom per formula unit are mapped on the local dipole moment $\bm{u}_i$, i.e., the local polarization $\bm{P}_i$, and the local strain $\bm{w}_{i}$ which is internally optimized during each time step. (c) Exemplary simulation cell with 48 x 48 x 48 and a small reversal domain of 3 thickness. For simplicity, each unit cell is shown as one dot and only the z-component of each $\bm{P}_i$ is color coded (red = positive; blue = negative).
• Figure 2: Polarization profiles across 180° DWs. (a) Comparison between Ba-centered and Ti-centered walls at 0 from the atomistic core-shell model. Insets give the corresponding domain wall energies. (b) Comparison at different temperatures $\Delta T$ for both models.
• Figure 3: Local polarization evolution and collapse of small domains from the atomistic simulation. (a) 3D representation of the full system; (b) only cells with negative polarization are shown; (c) top view (along $z$-direction) with column-wise averages of the polarization as the background color. In this scenario the initial thickness is 3 at $\Delta T = \qty{-26}{\kelvin}$. Each dot represents one unit cell color coded by its polarization $P_z$. Chains of switched dipoles form in both domains and disappear spontaneously on a sub-picosecond timescale. In addition to these fluctuations, the polarization pattern in the negative domain changes with time and vanishes after few tens of picoseconds.
• Figure 4: Collapse of nano-sized domains with width $d= \qty{4}{\uc}$ at $\Delta T = \qty{-13}{\kelvin}$. (a) Representative course of the fraction of positively polarized unit cells in the full simulation cell over time. Switching starts at 15 and is complete at 60. (b) Snapshots of the layers L1 - L4 inside the small domain and its adjacent layers L0 & L5 at 7.2. (c) Correlation between layers inside the small domain of (b). (d) - (f) Different scenarios of collapsing domains.
• Figure 5: Collection of representative scenarios of the time-evolution of polarization in the reversed domain. The normalized polarization per layer $P_z$/ $P_s$ is shown for the $H^{\text{eff}}$ -model at $\Delta T = \qty{-26}{\kelvin}$.