【DFT+TB】南开的邵斌和左旭教授也用狸猫换了太子：结果居里温度…

目前所发现的大多数二维铁磁半导体材料的居里温度远低于室温，限制了其实际的应用。而居里温度与材料的磁交换相互作用强度有关，寻找合适的方法调控材料的磁交换相互作用显得尤为重要。

来自南开大学电子信息与光学工程学院的邵斌副教授、左旭教授团队，该研究通过元素替换的方法，调控p-d轨道之间的能量，提高轨道耦合的共价性，从而增强材料的磁交换相互作用强度，提高材料的居里温度。他们基于第一性原理计算和紧束缚理论，分析了影响材料磁交换相互作用强度的主要因素，发现对于具有八面体晶体场的半导体材料，降低阴离子p轨道与金属e_g轨道的能量差，可以显著提高材料的磁交换相互作用。

作者通过对铬硫属卤素化合物（CrXY）单层的研究，发现材料初始的三重旋转对称性引起的p-d轨道之间电子的交换极化作用，使得材料在铁磁态的能量是最低的。基于紧束缚理论构建的哈密顿量矩阵，通过downfolding原理将高维条件的哈密顿量投影至低维的有效哈密顿量，得到的磁交换相互作用的具体形式表明，p-d轨道的能量差对磁交换相互作用强度有着重要的影响。当使用S/Se替换O离子时，会显著地降低p-e_g轨道的能量差，从而增强CrSY/CrSeY单层的铁磁耦合强度，使得材料的居里温度提高至室温附近。

该研究阐明了轨道能量差引起的共价性对于材料的磁交换相互作用的重要性，这为调控铁磁半导体材料的居里温度提供了可行性的思路。相关论文近期发布于npj Computational Materials 9: 56 (2023)。

Editorial Summary

The Curie temperature of most of the two-dimensional ferromagnetic semiconductor materials found so far is far below room temperature, which limits their practical applications. And the Curie temperature is related to the strength of the magnetic exchange interactions of the materials, it is particularly important to find a suitable method to tune the magnetic exchange interactions of the materials.

Here, the energy between p-d orbitals is tuned by elemental substitution to improve the covalency of the orbital coupling, which enhances the strength of the magnetic exchange interaction and increases the Curie temperature of the material. A team led by Assoc. Prof. Bin Shao and Prof. Xu Zuo from the College of Electronic Information and Optical Engineering, Nankai University, based on first-principles calculations and tight-binding theory, analyzed the main factors affecting the strength of magnetic exchange interactions of materials and found that for semiconductor materials with octahedral crystal fields, reducing the energy difference between the anion p orbitals and the metal e_g orbitals can significantly improve the magnetic exchange interactions of materials. By the research of CrXY monolayers, a chromium-sulfur halogen compound, the authors found that the exchange polarization of electrons between p-dorbitals caused by the initial triple rotational symmetry of the material makes the material the lowest energy in the ferromagnetic state. Based on the Hamiltonian matrix constructed by the tight-binding theory, the specific form of the magnetic exchange interaction can be obtained by projecting the Hamiltonian of the high-dimensional condition to the effective Hamiltonian of the lower dimension through the downfolding principle, showing that the energy difference of the p-d orbitals has an important effect on the strength of the magnetic exchange interaction. When S/Se is used to replace the O ions, the energy difference of the p-e_g orbitals is significantly reduced, which enhances the ferromagnetic coupling strength of the CrSY/CrSeY monolayer and enables the material to increase its Curie temperature to near room temperature. 

Their research elucidates the importance of covalency due to orbital energy differences for the magnetic exchange interactions of the material, which provides a feasible idea for regulating the Curie temperature of ferromagnetic semiconductor materials. This article was recently published in npj Computational Materials 9: 56 (2023).

Fig. 7 Specific heat capacity and Curie temperature of CrXY monolayers. 

原文Abstract及其翻译

Enhancing ferromagnetic coupling in CrXY (X = O, S, Se; Y = Cl, Br, I) monolayers by turning the covalent character of Cr-X bonds (通过调控Cr-X键的共价性增强CrXY（X = O、S、Se；Y = Cl、Br、I）单层的铁磁耦合)

Haoran Zhu, Bin Shao & Xu Zuo

Abstract On the basis of first-principles calculations, we investigate the electronic and magnetic properties of 1T phase chromium sulfide halide CrXY (X = O, S, Se; Y = Cl, Br, I) monolayers in CrCl₂structure with the Pm1 space group. Except for the CrOI monolayer, all CrXY monolayers are stable and ferromagnetic semiconductors. Our results show that the ferromagnetic coupling is dominated by the kinetic exchange between the empty e_g-orbital of Cr atoms and the p-orbital of anions under the three-fold rotational symmetry. In this context, the coupling strength allows for being greatly enhanced by turning the nature of Cr-X bonds, i.e., increasing the covalent contribution of the bonds by minimizing the energy difference of the coupled orbitals. As we illustrate for the example of CrOY, the Curie temperature (T_c) is nearly tripled by substituting O by S/Se ion, eventually reaching the highest Tc in CrSeI monolayer (334 K). The high stabilities and Curie temperature manifest these monolayer ferromagnetic materials feasible for synthesis and applicable to 2D spintronic devices.

摘要基于第一原理计算，我们探究了空间群为Pm1的1T相CrCl₂结构的铬硫属卤素化合物CrXY（X = O，S，Se；Y = Cl，Br，I）单层的电子性质和磁性质。除了CrOI单层，所有的CrXY单层都是稳定的铁磁半导体。计算结果显示，材料中的铁磁耦合是由Cr原子的e_g轨道和阴离子的p轨道在三重旋转对称性下的超交换过程所贡献的。在该情况下，铁磁耦合强度可通过调节Cr-X键的特性来增强，即，通过减小杂化轨道之间的能量差来增强Cr-X键的共价性。我们以CrOY为例子，证明通过用S/Se来替换O离子，材料的居里温度（T_c）几乎增加了三倍，其中CrSeI单层的T_c可以达到334 K。这些单层铁磁材料的高稳定性和高居里温度表明其可被合成并应用于二维自旋电子器件。