In this paper, effect of Gd³⁺ was investigated on structural, magnetic, and dielectric properties of Mn_0.5Zn_0.5Gd_xFe_2−xO₄(x = 0, 0.025, 0.050, 0.075, and 0.1) nanoparticles prepared by facile coprecipitation method. X-ray diffraction (XRD) studies confirmed the single cubic spinel phase for all the samples and showed that lattice parameter (a_exp) was found to increase from 8.414 to 8.446 Å with the substitution of Gd³⁺ ions due to their larger ionic radii than the replaced Fe³⁺ ions. Shape and size of developed nanoparticles were studied using transmission electron microscopy (TEM) and found that particle size decreased from 31.06 to 21.12 nm for x = 0–0.1. Magnetic properties showed that maximum magnetization decreased from 39.21 to 23.59 emu/g, and Curie temperature decreased from 192 to 176 °C with increase in x from 0 to 0.1 due to weakening of superexchange interaction. Dielectric parameters like dielectric constant (ε′ and ε″), dielectric loss (tanδ), AC conductivity (σ_ac), and impedance (Z′ and Z″) as a function of frequency and composition were analyzed and discussed. It was found that ε′, ε″, σ_ac, and tanδ values decreased with Gd substitution, which has been explained based on Maxwell-Wagner theory and hopping mechanism of electrons between Fe³⁺ and Fe²⁺ ions at octahedral sites. Nyquist plots for all the developed compositions showed single semi-circular arc which indicate the dominant effect of grain boundaries.

中文翻译：

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Mn 0.5 Zn 0.5 Gd x Fe 2-x O 4（x = 0、0.025、0.050、0.075和0.1）的结构，热磁和介电性能

在本文中，研究了Gd ³⁺对通过方便制备的Mn _0.5 Zn _0.5 Gd _x Fe _{2− x} O ₄（x = 0、0.025、0.050、0.075和0.1）纳米粒子的结构，磁性和介电性能的影响。共沉淀法。X射线衍射（XRD）研究证实对于所有样品的单一立方尖晶石相，并表明，晶格参数（一个_EXP）被发现增加从8.414到8.446埃以Gd的置换³⁺离子由于其较大离子半径比被替换的Fe ³⁺离子。使用透射电子显微镜（TEM）研究了已开发纳米颗粒的形状和尺寸，发现对于x = 0-0.1 ，颗粒尺寸从31.06 nm减小到21.12 nm 。磁性能显示，由于超交换相互作用的减弱，最大x磁化强度从39.21降低至23.59 emu / g，居里温度从192降低至176°C，x值从0升高至0.1。介电参数，如介电常数（ε'和ε“ ），介电损耗（tanδ δ），AC电导率（σ _AC）和阻抗（Z'和Z”）作为频率和成分的函数进行了分析和讨论。据发现，ε'，ε“，σ_交流和TaN δ值以Gd替代，这已经说明基于麦克斯韦-瓦格纳理论和跳频的Fe之间的电子机构降低³⁺和Fe ²⁺在八面体位置的离子。所有已开发成分的奈奎斯特图均显示单个半圆弧，这表明晶界占主导地位。