Polarization switching in ferroelectric <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>HfO</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math> from first-principles lattice mode analysis

Abstract

In this paper, we introduce a first-principles-based lattice mode analysis method to investigate the competition between different polarization switching paths in ${\mathrm{HfO}}_{2}$. Because the stability of the polar orthorhombic $Pca{2}_{1}$ phase of ${\mathrm{HfO}}_{2}$ arises from a trilinear coupling, polarization switching requires the flipping of not only the polar ${\mathrm{\ensuremath{\Gamma}}}_{15}^{Z}$ mode, but also at least one zone-boundary antipolar mode. This means that each polarization state has multiple variants, leading to multiple possible switching paths connecting up- and down-polarized states, which can be systemically enumerated within this framework for efficient identification of the optimal switching path. Our lattice mode analysis also explains why the activation energy of propagation of the most widely studied domain-wall structure in ${\mathrm{HfO}}_{2}$, which requires the reversal of the ${X}_{2}^{\ensuremath{-}}$ mode, is much larger than that of propagation of domain-wall structures with a uniform sign for the ${X}_{2}^{\ensuremath{-}}$ mode. This approach deepens our understanding of distinctive properties of ferroelectric ${\mathrm{HfO}}_{2}$ related to polarization switching and domain-wall motion, including sluggish domain-wall motion, robust ferroelectricity in thin films, and the observation that the antipolar $Pbca$ phase can hardly be transformed to the ferroelectric $Pca{2}_{1}$ phase by an electric field. Our mode analysis method can be more generally applied to any improper or hybrid improper ferroelectric, in which polarization switching requires changes of nonpolar distortions, for systematic and efficient prediction of optimal switching paths and estimation of coercive fields.

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