Cd_1 − xMn_xFe₂O₄ (x = 0, 0.25, 0.5, 0.75, 1) spinel ferrite nanoparticle samples were synthesized using a flash auto-combustion technique and analyzed using X-ray diffraction (XRD), scanning electron microscopy (SEM), and Fourier-transform infrared spectroscopy (FTIR). The inspection of dielectric and magnetic properties of the prepared ferrites was carried out by using broadband dielectric spectroscopy (BDS) and vibration sample magnetometer (VSM) measurements, respectively. X-ray diffraction analysis verified the formation of the main cubic phase with space group Fd3m and a decrease in lattice constants with the increase in Mn-content. FTIR study revealed the two characteristic absorption bands of spinel ferrites and their dependence on Mn-content was investigated and explained. Elastic moduli, bulk modulus, rigidity modulus, Young modulus, and calculated Debye temperature have been studied and found to decrease with the increase in Mn-content. SEM analysis revealed nanoparticles agglomeration of uniform grains with increasing in the average grain size as Mn-content increased. The VSM measurements showed an increase in saturation magnetization accompanied by a decrease in coercivity as Mn-content increased. Dielectric investigations showed very high values of permittivity and dielectric loss at lower frequencies (between 10⁵ and 10⁶ @ 0.1 Hz according to the manganese content) reflecting the combination of exchange of electrons between ferrous and ferric ions and ions’ transport. The ac-conductivity showed a plateau that yields the dc-conductivity at lower frequencies followed by a characteristic frequency at which it tends out to follow a power law. The relation between these two parameters confirms the empirical BNN-relation.

Cd _{1 − x} Mn _x Fe ₂ O ₄(x = 0, 0.25, 0.5, 0.75, 1) 尖晶石铁氧体纳米颗粒样品使用快速自动燃烧技术合成，并使用 X 射线衍射 (XRD)、扫描电子显微镜 (SEM) 和傅里叶变换红外光谱进行分析(FTIR)。通过使用宽带介电光谱（BDS）和振动样品磁强计（VSM）测量分别对制备的铁氧体的介电和磁性能进行检查。X 射线衍射分析证实了具有空间群 Fd3m 的主立方相的形成，并且随着 Mn 含量的增加，晶格常数降低。FTIR 研究揭示了尖晶石铁氧体的两个特征吸收带，并研究并解释了它们对 Mn 含量的依赖性。弹性模量、体积模量、刚性模量、杨氏模量、研究了计算的德拜温度，发现随着 Mn 含量的增加而降低。SEM 分析表明，随着 Mn 含量的增加，均匀晶粒的纳米颗粒团聚，平均晶粒尺寸增加。VSM 测量表明，随着 Mn 含量的增加，饱和磁化强度增加，同时矫顽力降低。介电研究表明，在较低频率（10⁵和 10 ⁶ @ 0.1 Hz（根据锰含量）反映了亚铁和三价铁离子之间的电子交换和离子传输的组合。交流电导率显示出一个平台，在较低频率下产生直流电导率，然后是特征频率，在该频率下它倾向于遵循幂律。这两个参数之间的关系证实了经验 BNN 关系。