Abstract A new equiatomic quarternary Heusler compound TiZrMnAl has been theoretically predicted. Two possible structural configurations are considered under the site preference rule and their equilibrium lattices have been derived. Electronic band structures identify TiZrMnAl compound as the spin gapless semiconductors in both two structure types. The total magnetic moments of TiZrMnAl are both equal to zero with the partial moments of Ti and Zr antiparallelly aligned to that of Mn. This integral value of total moment follows the Slater-Pauling rule in the form of Mt = Zt − 18, where Mt represents the total magnetic moment and Zt is the total number of valence electrons. The mechanical and dynamic stabilities of TiZrMnAl have also been validated and strong elastic anisotropy is further revealed with the calculated directional dependent Young’s modulus and shear modulus for both structures. Besides, the effect of random swap disorder between Ti and Zr atoms has been examined and it is found that through the whole swap range, TiZrMnAl maintains its fully compensated spin gapless semiconductivity, which is a very good property for possible applications in spintronic devices. Lastly, the uniform and tetragonal strains have been accessed and their effects on the electronic and magnetic properties have been studied. This systematic study can provide a comprehensive reference for the further development of Ti and Zr based quarternay Heusler compounds and even inspire other relative studies for the exploration of new spin gapless semiconductors.

中文翻译：

---

等原子四元赫斯勒材料 TiZrMnAl 中的完全自旋无间隙半导体

摘要 理论上预测了一种新的等原子四元赫斯勒化合物TiZrMnAl。在站点偏好规则下考虑了两种可能的结构配置，并推导出了它们的平衡点阵。电子能带结构将 TiZrMnAl 化合物识别为两种结构类型中的自旋无隙半导体。TiZrMnAl 的总磁矩均为零，Ti 和 Zr 的部分磁矩与 Mn 的部分磁矩反平行排列。该总磁矩的积分值遵循 Slater-Pauling 规则，形式为 Mt = Zt − 18，其中 Mt 代表总磁矩，Zt 是价电子的总数。TiZrMnAl 的机械和动态稳定性也得到了验证，并且通过计算两种结构的方向相关杨氏模量和剪切模量进一步揭示了强弹性各向异性。此外，还研究了 Ti 和 Zr 原子之间随机交换无序的影响，发现在整个交换范围内，TiZrMnAl 保持其完全补偿的自旋无间隙半导体，这对于自旋电子器件的可能应用来说是一个非常好的特性。最后，已经访问了均匀应变和四方应变，并研究了它们对电子和磁性的影响。