We calculated the frequency-dependent dielectric response (electric susceptibility) of layered ferroelectric–dielectric junction, biased by the time-dependent harmonic voltage with single frequency \(\omega \). Working point is stabilized, by the charge boundary condition between the layers, in the region with negative electric capacitance. The static susceptibility \(\chi _0\) is negative and the relative dielectric constant \(\epsilon _r\) is smaller than 1, clearly indicating the opposite direction of electric field and polarization in the ferroelectric layer due to the negative electric capacitance. At finite frequencies, this sign is preserved in real part of susceptibility which gains the frequency dependence. Also, frequency-dependent imaginary part arises due to the phase shift between electric field and polarization. The type of that frequency dependence in linear regime is the so-called relaxation (Debye) response, i.e., \(\chi '(\omega )=\chi _0/(1+(\tau \omega )^2)\) and \(\chi ''(\omega )=\chi _0\tau \omega /(1+(\tau \omega )^2)\), where \(\tau \) is the polarization switching time characteristic to ferroelectric material. In particular, we modeled the junction of ferroelectric BaTiO\(_3\) and dielectric Al\(_2\)O\(_3\), taking the experimental values of material parameters, and addressed the role of nonlinearity with respect to result of the linear response theory.

中文翻译：

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具有负电容的铁电介质结的频率相关介电响应

我们计算了层状铁电-介电结的频率相关介电响应（电磁化率），其受单一频率\（\ omega \）随时间变化的谐波电压的影响。通过层之间的电荷边界条件，在具有负电容的区域中使工作点稳定。静态磁化率\（\ chi _0 \）为负，相对介电常数\（\ epsilon _r \）小于1，清楚地表明由于负电容，铁电层中电场和极化的方向相反。在有限的频率下，该符号保留在磁化率的实际部分中，从而获得了频率依赖性。同样，由于电场和极化之间的相移，出现了频率相关的虚部。线性状态下这种频率依赖性的类型是所谓的弛豫（Debye）响应，即\（\ chi'（\ omega）= \ chi _0 /（1 +（\ tau \ omega）^ 2）\）和\（\ chi``（\ omega）= \ chi _0 \ tau \ omega /（1 +（\ tau \ omega ^^ 2）\），其中\（\ tau \）是铁电材料的极化切换时间特性。特别是，我们利用材料参数的实验值对铁电BaTiO \（_ 3 \）和电介质Al \（_ 2 \） O \（_ 3 \）的结进行了建模，并针对非线性结果对非线性的作用进行了研究。线性响应理论。