The first-principles approach based on density functional theory (DFT) and the full-potential linearized augmented plane-wave method were employed to investigate the structural, elastic, electronic and magnetic properties of Na[Formula: see text]NO ([Formula: see text], Sr and Ba) quaternary half-Heusler alloys. The generalized gradient approximation (GGA) as parameterized by Perdew, Burke and Ernzerhof (PBE) and the modified Becke–Johnson exchange potential were used. As far as we know, we present our results which for the first time quantitatively account for the electronic structures and magnetic properties of Na[Formula: see text]NO ([Formula: see text], Sr and Ba) quaternary half-Heusler alloys. From the total energy calculation using three possible atomic configurations ([Formula: see text], [Formula: see text] and [Formula: see text]), it is found that the Na[Formula: see text]NO ([Formula: see text], Sr and Ba) quaternary half-Heusler alloys are more stable in the ferromagnetic [Formula: see text]-phase. From our estimated elastic constants [Formula: see text], it is found that all the considered Heusler alloys are mechanically stable in the [Formula: see text]-phase. We have also investigated the robustness of the half-metallicity with respect to the variation of lattice constants in these alloys. We have found that these alloys are half-metallic ferromagnets (HMFs) with a magnetic moment of 2[Formula: see text][Formula: see text] per formula unit at their equilibrium volumes. The spin-polarized electronic band structure and density of states of these quaternary half-Heusler alloys calculated by GGA (mBJ-GGA) show that the minority spin channels have metallic nature and the majority spin channels have a semiconductor character with half-metallic gaps of 0.49[Formula: see text]eV (2.17[Formula: see text]eV), 0.72[Formula: see text]eV (2.28[Formula: see text]eV) and 0.96[Formula: see text]eV (2.22[Formula: see text]eV) for NaCaNO, NaSrNO and NaBaNO quaternary half-Heusler alloys, respectively. Analysis of the density of states and the spin charge density of these quaternary alloys indicates that their magnetic moments mainly originate from the strong spin-polarization of 2[Formula: see text] states of N atoms and O atoms.

中文翻译：

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新型半金属铁磁四元-赫斯勒合金NaXNO (X=Ca, Sr, Ba)的第一性原理研究

采用基于密度泛函理论 (DFT) 的第一性原理方法和全势线性化增强平面波方法研究 Na [公式：见正文]NO ([公式：见正文], Sr 和 Ba) 四元半赫斯勒合金。使用由 Perdew、Burke 和 Ernzerhof (PBE) 参数化的广义梯度近似 (GGA) 和改进的 Becke-Johnson 交换势。据我们所知，我们首次展示了我们的结果，该结果首次定量解释了 Na[公式：见正文]NO（[公式：见正文]，Sr 和 Ba）四元半赫斯勒合金的电子结构和磁性. 从使用三种可能的原子配置（[公式：见文本]、[公式：见文本]和[公式：见文本]）的总能量计算，发现Na[分子式：见文字]NO（[分子式：见文字]，Sr和Ba）四元半赫斯勒合金在铁磁[分子式：见文字]相中更稳定。从我们估计的弹性常数 [公式：见文本]，发现所有考虑的 Heusler 合金在 [公式：见文本] 相中是机械稳定的。我们还研究了半金属性对这些合金中晶格常数变化的稳健性。我们发现这些合金是半金属铁磁体 (HMF)，在其平衡体积下，每个公式单位的磁矩为 2[公式：见正文][公式：见正文]。由 GGA (mBJ-GGA) 计算的这些四元半赫斯勒合金的自旋极化电子能带结构和态密度表明，少数自旋通道具有金属性质，大多数自旋通道具有半金属间隙为0.49[公式：见文]eV（2.17[公式：见文]eV），0.72[公式：见文]eV（2.28[公式：见文]eV）和0.96[公式：见文]eV（2.22[公式：见正文]eV) 分别用于 NaCaNO、NaSrNO 和 NaBaNO 四元半赫斯勒合金。分析这些四元合金的态密度和自旋电荷密度表明，它们的磁矩主要来源于N原子和O原子的2[公式：见正文]态的强自旋极化。见文]eV（2.17[公式：见文]eV）、0.72[公式：见文]eV（2.28[公式：见文]eV）和0.96[公式：见文]eV（2.22[公式：见文] eV) 分别用于 NaCaNO、NaSrNO 和 NaBaNO 四元半赫斯勒合金。分析这些四元合金的态密度和自旋电荷密度表明，它们的磁矩主要来源于N原子和O原子的2[公式：见正文]态的强自旋极化。见文]eV（2.17[公式：见文]eV）、0.72[公式：见文]eV（2.28[公式：见文]eV）和0.96[公式：见文]eV（2.22[公式：见文] eV) 分别用于 NaCaNO、NaSrNO 和 NaBaNO 四元半赫斯勒合金。分析这些四元合金的态密度和自旋电荷密度表明，它们的磁矩主要来源于N原子和O原子的2[公式：见正文]态的强自旋极化。