First-principle study has been conducted using the full potential linearized augmented plane wave plus local orbital method (FPLAPW + LO) within the scope of density functional theory with generalized gradient approximation (GGA) and Generalized Gradient Approximation plus Hubbard parameters U (GGA + U) as exchange correlation potentials to study the mechanical, structural, electronic and magnetic properties of two spinels type structure compounds MgX₂O₄ (X = Fe and Co). The structural parameters evaluated from the solution of equation of state with GGA are consistent with experiment. For the calculation of electronic as well as magnetic properties of these compounds, we have used the GGA + U formalism to treat the d state of transition metals Fe and Co more efficiently. Moreover, the crystal fields splitting for both of the compounds are also explored. The electronic band structure and density of states predicts the half metallic/metallic nature of MgFe₂O₄ and MgCo₂O₄, respectively. The spin polarized total magnetic moments of the compounds under investigation reveal the ferromagnetic behavior of these compounds. Moreover, the elastic properties of these compounds are also calculated with GGA and compared with available calculations. These compounds are founds to be elastically stable and ductile in nature. Half metallic/metallic ferromagnetic nature of MgFe₂O₄ and MgCo₂O₄, respectively, predicts the important of these spinels in spintronic devices.

在密度泛函理论的范围内使用全势线性增强平面波加局部轨道方法 (FPLAPW + LO) 进行了第一性原理研究，具有广义梯度近似 (GGA) 和广义梯度近似加哈伯德参数 U (GGA + U) ) 作为交换相关电位来研究两种尖晶石型结构化合物 MgX ₂ O ₄的机械、结构、电子和磁性能(X = Fe 和 Co)。用GGA解状态方程得到的结构参数与实验一致。为了计算这些化合物的电子和磁性能，我们使用 GGA + U 形式更有效地处理过渡金属 Fe 和 Co 的 d 态。此外，还探索了两种化合物的晶体场分裂。电子能带结构和态密度预测了 MgFe ₂ O ₄和 MgCo ₂ O ₄的半金属/金属性质， 分别。所研究化合物的自旋极化总磁矩揭示了这些化合物的铁磁行为。此外，这些化合物的弹性性能也用 GGA 计算并与可用计算进行比较。发现这些化合物在性质上是弹性稳定和可延展的。MgFe ₂ O ₄和MgCo ₂ O _{4 的}半金属/金属铁磁性质分别预测了这些尖晶石在自旋电子器件中的重要性。