The temperature, doping concentration, size, and magnetic field dependences of the real part of the dielectric function ϵ′ for Fe and Er ion‐doped BaTiO₃bulk and nanoparticles—are calculated using microscopic models and the Green's function technique. The Fe ions substitute the Ti ions and cause a tensile strain. The maximum value of ϵ′ and the ferroelectric phase transition temperature T_C decrease with increasing the Fe doping concentration. Moreover, ϵ′ decreases with decreasing particle size and increases with increasing an external magnetic field. The latter is an evidence for a strong magnetodielectric effect. By substituting the Ba with Er ions, there appears a strong compressive strain. It causes an increase in the maximum of ϵ′ and T_C with increasing the Er ion concentration.

中文翻译：

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过渡金属和稀土掺杂的多铁性BaTiO3纳米粒子的介电性能

温度，掺杂浓度，尺寸和电介质函数的实部的磁场依存性ε '为Fe和铒离子掺杂的BaTiO ₃ 散装和纳米粒子使用微观模型和格林函数技术计算。Fe离子替代Ti离子并引起拉伸应变。的最大值ε '和铁电相变温度Ť _Ç减少与增加的Fe掺杂浓度。而且ϵ'随着粒径的减小而减小，而随着外部磁场的增大而增大。后者是强磁电效应的证据。通过用Er离子代替Ba，会出现很强的压缩应变。随着Er离子浓度的增加，导致最大的ϵ '和T _C的增加。