First-principles approach based on density functional theory was applied to investigate the structural, elastic, phonon dynamics, thermodynamics, electronic, and magnetic properties of GeNaZ (where Z = Ca, Sr and Ba) ternary Heusler alloys. The Perdew-Burke-Ernzerhof generalized gradient approximation (GGA) and the modified Becke-Johnson (mBJ-GGA) were used for the exchange-correlation energy and potential. The GeNaZ ternary Heusler alloys were found to be half-metallic and stable in the ferromagnetic α phase. The alloys were found to satisfy the criteria for dynamic and elastic stabilities. Thus, they are dynamically and elastically stable. The calculated spin-polarized electronic band structure and density of states using GGA (mBJ-GGA) reveal that the minority spin channel has metallic character and the majority spin channel having an electronic band gap of 0.26 (0.59), 0.39 (0.66), and 0.08 (0.33) eV for the GeNaCa, GeNaSr, and GeNaBa ternary Heusler alloys, respectively. The considered alloys all result in a stable ferromagnetic half-metallic ground state structure with a magnetic moment of 1 μ_B/cell. The density of states and the spin-charge density of these alloys show that the magnetization originates primarily from the 4p states of the Ge atoms. The GeNaZ ternary Heusler alloys do not have any magnetic elements, and their induced magnetism makes them very promising materials for spintronic devices.

应用基于密度泛函理论的第一性原理方法研究GeNaZ（其中Z = Ca，Sr和Ba）三元Heusler合金的结构，弹性，声子动力学，热力学，电子和磁性。Perdew-Burke-Ernzerhof广义梯度近似（GGA）和改进的Becke-Johnson（mBJ-GGA）用于交换相关能量和势。发现GeNaZ三元Heusler合金是半金属且在铁磁α中稳定相。发现该合金满足动态和弹性稳定性的标准。因此，它们是动态和弹性稳定的。使用GGA（mBJ-GGA）计算出的自旋极化电子带结构和态密度表明，少数自旋通道具有金属特性，而多数自旋通道的电子带隙为0.26（0.59），0.39（0.66）和GeNaCa，GeNaSr和GeNaBa三元Heusler合金分别为0.08（0.33）eV。所考虑的合金所有结果与1μ的磁矩稳定铁磁半金属基态结构_乙/细胞。这些合金的态密度和自旋电荷密度表明，磁化强度主要来自4 p。锗原子的状态。GeNaZ三元Heusler合金没有任何磁性元素，其感应磁性使其成为自旋电子器件非常有希望的材料。