[Paper Review] Polarization switching mechanism in HfO$_2$ from first-principles lattice mode analysis

Yubo Qi, Sobhit Singh+1 more|arXiv (Cornell University)|Aug 28, 2021

Ferroelectric and Negative Capacitance Devices6 citations

TL;DR

This study reveals that polarization switching in HfO₂ is governed by coupled polar (Γ₁₅ᶻ) and anti-polar (X₂⁻) lattice modes, where reversal of the nonpolar X₂⁻ mode imposes a high energy barrier incompatible with electric field control. The analysis explains sluggish domain wall motion and the impossibility of electric-field-induced transformation from the anti-polar Pbca phase to the polar Pca2₁ phase.

ABSTRACT

In this work, we carry out first-principles calculations and lattice mode analysis to investigate the polarization switching mechanism in HfO$_2$. Because the stability of the polar orthorhombic $Pca2_1$ phase of HfO$_2$ arises from a trilinear coupling, polarization switching requires the flipping of not only the polar $Γ_{15}^Z$ mode, but also at least one zone-boundary anti-polar mode. The coupling between the polar and anti-polar modes thus leads to substantial differences among different polarization switching paths. Specifically, our lattice-mode-coupling analysis shows that paths in which the $X_2^-$ mode is reversed involve a large activation energy, which because the $X_2^-$ mode is nonpolar cannot be directly overcome by applying an electric field. Our results show that the anti-polar $Pbca$ phase, whose structure is locally quite similar to that of the $Pca2_1$ phase, similarly cannot be transformed to this phase by an electric field as this would require local reversal of the $X_2^-$ mode pattern. Moreover, for the domain wall structure most widely considered, propagation also requires the reversal of the $X_2^-$ mode, leading to a much larger activation energy compared with that for the propagation of domain wall structures with a single sign for the $X_2^-$ mode. Finally, these first-principles results for domain wall propagation in HfO$_2$ have implications to many experimental observations, such as sluggish domain wall motion and robust ferroelectricity in thin films, and lattice mode analysis deepens our understanding of these distinctive properties of ferroelectric HfO$_2$.

Motivation & Objective

• To understand the intrinsic polarization switching mechanism in HfO₂ beyond empirical observations.
• To resolve the contradiction between observed robust ferroelectricity and sluggish domain wall motion in thin films.
• To determine why the anti-polar Pbca phase cannot be switched to the polar Pca2₁ phase by an electric field.
• To identify the role of lattice mode coupling in determining activation energies for different switching paths.
• To explain the energetic differences between domain wall propagation paths based on X₂⁻ mode sign consistency.

Proposed method

• First-principles density functional theory (DFT) calculations were performed to model the electronic and structural properties of HfO₂ polymorphs.
• Lattice mode analysis was used to decompose atomic distortions into symmetry-adapted normal modes, identifying Γ₁₅ᶻ (polar) and X₂⁻ (anti-polar) modes.
• Trilinear coupling between the Γ₁₅ᶻ and X₂⁻ modes was analyzed to determine the stability and switching pathways of the polar Pca2₁ phase.
• The nudged elastic band (NEB) method was applied to compute minimum energy pathways for domain wall propagation between different polarization variants.
• The sign of the X₂⁻ mode amplitude in adjacent unit cells was used to classify domain wall types into two categories: consistent or sign-reversing.
• Energy barriers for switching and domain wall motion were quantified by comparing transition state energies to initial and final states.

Experimental results

Research questions

• RQ1 What is the role of anti-polar X₂⁻ lattice modes in polarization switching of HfO₂?
• RQ2 Why is the anti-polar Pbca phase not transformable to the polar Pca2₁ phase via an electric field?
• RQ3 How does the sign of the X₂⁻ mode affect the activation energy for domain wall propagation?
• RQ4 Why is domain wall motion in HfO₂ significantly slower than in conventional perovskite ferroelectrics?
• RQ5 What determines the energetic preference among different polarization switching paths in HfO₂?

Key findings

• Polarization switching in HfO₂ requires simultaneous reversal of both the polar Γ₁₅ᶻ mode and at least one anti-polar X₂⁻ mode.
• The X₂⁻ mode cannot be directly reversed by an electric field due to its nonpolar nature, leading to a high activation barrier.
• Domain wall propagation with consistent X₂⁻ mode sign (Type I) has a low activation energy of 0.12 eV/cell, while sign-reversing walls (Type III/IV) require 0.57–1.02 eV/cell.
• The highest-energy transition state for sign-reversing domain walls corresponds to a high-energy t-like structure with a sharp sign change in X₂⁻ mode pattern.
• The anti-polar Pbca phase cannot be switched to the polar Pca2₁ phase by an electric field because it requires reversal of the X₂⁻ mode with opposite signs in neighboring cells.
• The high activation energy for domain wall motion in the most widely studied structure (with X₂⁻ sign reversal) explains the experimentally observed sluggish domain wall dynamics.