To gain insight into the spin-glass state of diluted magnetic semiconductors, we have examined the magnetic and electronic properties of ${\mathrm{Zn}}_{1-x}{\mathrm{Mn}}_x\mathrm{Te}$ using density-functional theory as well as performed magnetization measurements on the $x=0.43$ and 0.55 systems to demonstrate a clear spin-glass transition consistent with previous literature. Using a generalized gradient approximation, we investigate the electronic and magnetic properties for $x=0$, 0.075, 0.15, 0.25, and 0.50 doping levels using the magnetic moment of ${\mathrm{Mn}}^{2+}$ as guide for the dependence of the Hubbard onsite potential on the electronic structure. Simulations on both ferromagnetic (FM) and antiferromagnetic (AFM) configurations yield a distinct AFM ground-state preference, which is consistent with a zero-magnetic-moment spin-glass state. Here an onsite potential of up to 8 eV on the Mn $3d$ orbitals is needed to harden the magnetic moment toward $S=5/2$. From our analysis of the electronic structure evolution with doping and onsite potential, we confirm the semiconducting state of the Mn-doped ZnTe as well as show that the presence of Mn incorporated into the ZnTe matrix at the Zn lattice site produces magnetic interactions through the Te ions with a distinct Te-Mn $pd$-orbital hybridization. Furthermore, we show that this hybridization is activated with the Mn doping above 0.25 concentration, which corresponds to the doping level in which the spin-glass transition begins to rise. Therefore, it is likely that the coupling of $pd$-orbital hybridization of the Mn and Te $p$ orbitals is a precursor to the enhancement of the spin-glass transition temperature.

中文翻译：

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通过 Zn1−xMnxTe 中的 pd-轨道杂化提高自旋玻璃化转变温度

为了深入了解稀磁半导体的自旋玻璃态，我们研究了 ${锌}_{1-X}{锰}_X特$ 使用密度泛函理论以及对磁化强度进行测量 $X=0.43$和 0.55 系统，以证明与以前的文献一致的清晰的自旋玻璃化转变。使用广义梯度近似，我们研究了电子和磁性$X=0$, 0.075, 0.15, 0.25, 和 0.50 掺杂水平使用磁矩 ${锰}^{2+}$作为哈伯德现场电位对电子结构依赖性的指南。对铁磁 (FM) 和反铁磁 (AFM) 配置的模拟产生了明显的 AFM 基态偏好，这与零磁矩自旋玻璃态一致。这里 Mn 上的现场电位高达 8 eV$3d$ 需要轨道来硬化磁矩 $秒=5/2$. 根据我们对掺杂和现场电位的电子结构演变的分析，我们确认了 Mn 掺杂的 ZnTe 的半导体状态，并表明在 Zn 晶格位点处掺入 ZnTe 基质中的 Mn 的存在通过 Te 产生磁相互作用具有独特 Te-Mn 的离子$磷d$-轨道杂交。此外，我们表明这种杂化在 Mn 掺杂浓度高于 0.25 时被激活，这对应于自旋玻璃化转变开始上升的掺杂水平。因此，很可能是耦合$磷d$-Mn 和 Te 的轨道杂化 $磷$ 轨道是提高自旋玻璃化转变温度的前兆。