Doping is a widely used method to tune physical properties of ferroelectric perovskites. Since doping can induce charges due to the substitution of certain elements, charge effects shall be considered in doped samples. To understand how charges can affect the system, we incorporate the dipole-charge interaction into our simulations, where the pinched hysteresis loops can well be reproduced. Two charge compensation models are proposed and numerically investigated to understand how lanthanum doping affect BaTiO$_{3}$'s ferroelectric phase transition temperature and hysteresis loop. The consequences of the two charge compensation models are compared and discussed.

中文翻译：

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供体掺杂钙钛矿铁电体中的电荷效应

掺杂是一种广泛使用的调整铁电钙钛矿物理性质的方法。由于掺杂会由于某些元素的取代而产生电荷，因此在掺杂样品中应考虑电荷效应。为了了解电荷如何影响系统，我们将偶极电荷相互作用纳入我们的模拟中，其中可以很好地再现收缩磁滞回线。提出并数值研究了两种电荷补偿模型，以了解镧掺杂如何影响 BaTiO$_{3}$ 的铁电相变温度和磁滞回线。比较和讨论了两种电荷补偿模型的结果。