First-principles calculations of density functional theory (DFT) using the generalized gradient approximation (GGA) and generalized gradient approximation with the Hubbard U (GGA + U) for the exchange-correlation energy functional are used to investigate the structural, electronic, and magnetic properties of the spinel system $C{d}_{x}N{i}_{1-x}F{e}_2{O}_4$ in the range $0\le x\le 1$. High-temperature series expansions (HTSE) combined with the Padé approximants (PA) method and mean field theory (MFT) are applied to the $C{d}_{x}N{i}_{1-x}F{e}_2{O}_4$ systems. The lattice parameter and magnetic moment of Fe and Ni ions increase when Cd content x increases. Density of States (DOS) calculations show that the $C{d}_{x}N{i}_{1-x}F{e}_2{O}_4$ has a semiconductor behaviour. The obtained theoretical results show that the Curie temperature decreases with x. These obtained results are in agreement with experimental ones.

使用广义梯度近似（GGA）和使用Hubbard U（GGA + U）进行交换相关能量泛函的广义​​梯度近似对密度泛函理论（DFT）进行第一性原理计算，以研究结构，电子和磁性尖晶石系统的性质 $C{d}_Xñ{\mathrm{一世}}_{\mathrm{1个}-X}F{Ë}_2{Ø}_4$ 范围中 $0\le X\le \mathrm{1个}$。高温序列展开（HTSE）与Padé近似值（PA）方法和平均场论（MFT）结合使用$C{d}_Xñ{\mathrm{一世}}_{\mathrm{1个}-X}F{Ë}_2{Ø}_4$系统。当Cd含量x增加时，Fe和Ni离子的晶格参数和磁矩增加。状态密度（DOS）计算表明$C{d}_Xñ{\mathrm{一世}}_{\mathrm{1个}-X}F{Ë}_2{Ø}_4$具有半导体行为。获得的理论结果表明，居里温度随x降低。这些结果与实验结果一致。