The ferrite nanoparticles of Ni_0.5Cu_0.2Cd_0.3Fe_2-zAl_zO₄ (0.00 ≤ z ≤ 0.075 with step 0.015) were synthesized with popular sol–gel method and their physical, magnetic and electrical transport characteristics have been analysed. The X-ray diffraction pattern confirms the precise single-phase spinel structure for every composition as justified by the Rietveld refinement analysis. The Field emission scanning electron microscopy (FESEM) technique reveals surface morphology of the synthesized sample at nanoscale. The FESEM image shows the nanosized (99–46 nm) ferrites with narrow size distribution occupying spherical shapes. To illustrate magnetic characteristics, vibrating sample magnetometer and the law of approach to saturation has been used to analyse (M–H) data in saturation region in order to extract the hysteresis parameters. The intrinsic saturation magnetization (M_s) as well as magnetic moment are found to increase with Al³⁺ substitution up to z = 0.03. The dielectric properties (real and imaginary part, loss tangent (tanδ) and ac conductivity (σ_ac) were measured with frequency at room temperature. Both tanδ and σ_ac were decreased with Al content showing potentiality for high-frequency applications. Complex impedance studies disclose the increase of grain resistance and grain boundary resistance with increasing Al content. Modulus spectroscopy study shows the dynamics of conduction mechanism in the synthesized ferrite nanoparticles.

Ni _0.5 Cu _0.2 Cd _0.3 Fe _2-z Al _z O ₄ (0.00 ≤  z ≤ 0.075 步长 0.015) 是用流行的溶胶-凝胶法合成的，并分析了它们的物理、磁和电传输特性。X 射线衍射图证实了每种成分的精确单相尖晶石结构，正如 Rietveld 精修分析所证明的那样。场发射扫描电子显微镜 (FESEM) 技术揭示了合成样品的纳米级表面形态。FESEM 图像显示纳米尺寸 (99–46 nm) 铁氧体，其尺寸分布较窄，呈球形。为了说明磁特性，使用振动样品磁力计和趋近饱和定律来分析饱和区的（M-H）数据，以提取磁滞参数。固有饱和磁化强度 ( M _s) 以及磁矩随着 Al ³⁺取代增加到z  = 0.03。介电性能（实部和虚部、损耗角正切 (tan δ ) 和交流电导率 ( σ _ac ) 在室温下随频率测量。tan δ和σ _ac均随着 Al 含量的增加而降低，显示出高频应用的潜力。复杂阻抗研究揭示了晶粒电阻和晶界电阻随着铝含量的增加而增加。模量光谱研究显示了合成铁氧体纳米粒子中导电机制的动力学。