Hafnium dioxide $\left(\mathrm{Hf}{\mathrm{O}}_2\right)$ is a promising ferroelectric (FE) material for achieving high-density nonvolatile memory and neuromorphic computing due to its compatibility with the mainstream integrated circuit technology and the surprisingly enhanced ferroelectricity by reduced thickness. The FE switching dynamics is essential to the device performance, but the complexity of $\mathrm{Hf}{\mathrm{O}}_2$ atomic structure causes unknown of various FE switching paths and domain-wall configurations. Here, we demonstrate that its low-barrier paths and domain walls can be comprehensively found and understood from a perspective of topological symmetry. By discussing pseudochirality and equivalent transformation relations in a crystal with first principles and lattice modes, we classify and analyze 4 low-barrier FE switching paths and 93 irreducible topology domain-wall configurations in $\mathrm{Hf}{\mathrm{O}}_2$. The anisotropic switching mechanism is inferred based on the investigation for 12 types of ${180}^{\circ }\text{-side}$ domain walls. This methodology is expected to be generally applicable to displacive ferroelectrics with low unit-cell point-group symmetries and lay a foundation for mechanism study of the switching dynamics.

中文翻译：

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二氧化铪中铁电开关和畴壁的对称性

二氧化铪$\left(\mathrm{氢氟酸}{\mathrm{○}}_2\right)$由于其与主流集成电路技术的兼容性以及通过减小厚度而令人惊讶地增强了铁电性，它是一种很有前途的铁电（FE）材料，可用于实现高密度非易失性存储器和神经形态计算。FE 开关动态对于器件性能至关重要，但$\mathrm{氢氟酸}{\mathrm{○}}_2$原子结构导致各种有限元切换路径和畴壁配置的未知。在这里，我们证明了它的低势垒路径和畴壁可以从拓扑对称的角度全面发现和理解。通过讨论具有第一原理和晶格模式的晶体中的赝手性和等效变换关系，我们对 4 个低势垒有限元开关路径和 93 个不可约拓扑畴壁配置进行了分类和分析。$\mathrm{氢氟酸}{\mathrm{○}}_2$. 基于对 12 种类型的调查推断各向异性切换机制${180}^{\circ }\text{-边}$域墙。该方法有望普遍适用于具有低晶胞点群对称性的位移铁电体，并为开关动力学的机理研究奠定基础。