Polarization, esp. of ferroelectrics, is conventionally described by ion distortions or ion positions, e.g. by Born effective charges, because of the complete entanglement of electron polarization with that of ions. We show that such description, which we call Born polarization, breaks partially down in the presence of field, owing to the incomplete entanglement of electron polarization with that of ions. Considering the deviation from Born polarization, we report a method that accurately calculates both macroscopic and unit-cell-by-unit-cell total polarization, of which correctness is demonstrated. This method is based on the global consistency of Born polarization PSi and provides simple analytical formulas to calculate total polarization PS and depolarization field using Psi, while Psi can be estimated from ion-positions. Therefore, the present method enables an experimental estimation of total polarization Ps under field. The present method reveals that Ps varies across ferroelectric/insulator far less than the conventional estimates Psi, which explains substantially reduced depolarization field and the absence of metallicity. In addition, vortex-like domains are discussed in view of the correction of depolarization field.

中文翻译：

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非出生有效电荷分解离子极化对应和准确极化

极化，特别是 通常，由于电子极化与离子的完全缠结，通常通过离子变形或离子位置（例如，玻恩有效电荷）来描述铁电层。我们表明，由于电子极化与离子的不完全缠结，这种称为“玻恩极化”的描述在电场存在下会部分分解。考虑到与Born极化的偏差，我们报告了一种可精确计算宏观和单位单元逐总极化的方法，该方法已证明了正确性。该方法基于Born极化PSi的整体一致性，并提供了简单的解析公式，可以使用Psi计算总极化PS和去极化场，而Psi可以从离子位置估算。因此，本方法使得能够对场下的总极化Ps进行实验估计。本方法揭示了在铁电体/绝缘体上的Ps变化远小于传统估计值Psi，这说明了去极化场大大减小并且没有金属性。另外，鉴于去极化场的校正，讨论了涡状区域。