Decoding the Complexity of Ferroelectric Orthorhombic HfO2: A Unified Mode Expansion Approach

Abstract

The ferroelectricity in $\mathrm{HfO}_2$ thin films is widely attributed to the formation of a polar orthorhombic phase named OIII phase. However, the complexity of OIII phase originated from its low symmetry becomes an obstacle for studying ferroelectric properties of $\mathrm{HfO}_2$. Here, we developed a unified framework based on phonon mode expansion for studying ferroelectric $\mathrm{HfO}_2$. In this framework, phase structures, domain walls and switching paths of orthogonal crystal system can be studied from the same basis of mode analysis. The OIII phase and other orthogonal phases can be represented by the high-symmetry cubic phase with the excitation of cubic phonon modes, into which the complexity of orthogonal phases is faithfully coded. To present the capability of this mode expansion approach, we clarified the origin of orthorhombic stability from the energy functional of modes; enumerated inequivalent domain walls and calculated their stable criteria; and summarized all possible switching mechanisms. This unified framework can be used to simplify the study of domain wall structures and transition paths. Furthermore, it can provide a new perspective for ferroelectricity in $\mathrm{HfO}_2$ from phonon mode analysis.