目前所發(fā)現(xiàn)的大多數(shù)二維鐵磁半導(dǎo)體材料的居里溫度遠低于室溫，限制了其實際的應(yīng)用。而居里溫度與材料的磁交換相互作用強度有關(guān)，尋找合適的方法調(diào)控材料的磁交換相互作用顯得尤為重要。

來自南開大學(xué)電子信息與光學(xué)工程學(xué)院的邵斌副教授、左旭教授團隊，該研究通過元素替換的方法，調(diào)控p-d軌道之間的能量，提高軌道耦合的共價性，從而增強材料的磁交換相互作用強度，提高材料的居里溫度。他們基于第一性原理計算和緊束縛理論，分析了影響材料磁交換相互作用強度的主要因素，發(fā)現(xiàn)對于具有八面體晶體場的半導(dǎo)體材料，降低陰離子p軌道與金屬e_g軌道的能量差，可以顯著提高材料的磁交換相互作用。

作者通過對鉻硫?qū)冫u素化合物（CrXY）單層的研究，發(fā)現(xiàn)材料初始的三重旋轉(zhuǎn)對稱性引起的p-d軌道之間電子的交換極化作用，使得材料在鐵磁態(tài)的能量是最低的?；诰o束縛理論構(gòu)建的哈密頓量矩陣，通過downfolding原理將高維條件的哈密頓量投影至低維的有效哈密頓量，得到的磁交換相互作用的具體形式表明，p-d軌道的能量差對磁交換相互作用強度有著重要的影響。當使用S/Se替換O離子時，會顯著地降低p-e_g軌道的能量差，從而增強CrSY/CrSeY單層的鐵磁耦合強度，使得材料的居里溫度提高至室溫附近。

該研究闡明了軌道能量差引起的共價性對于材料的磁交換相互作用的重要性，這為調(diào)控鐵磁半導(dǎo)體材料的居里溫度提供了可行性的思路。相關(guān)論文近期發(fā)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及其翻譯

Enhancing ferromagnetic coupling in CrXY (X = O, S, Se; Y = Cl, Br, I) monolayers by turning the covalent character of Cr-X bonds (通過調(diào)控Cr-X鍵的共價性增強CrXY（X = O、S、Se；Y = Cl、Br、I）單層的鐵磁耦合)

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.

摘要基于第一原理計算，我們探究了空間群為Pm1的1T相CrCl₂結(jié)構(gòu)的鉻硫?qū)冫u素化合物CrXY（X = O，S，Se；Y = Cl，Br，I）單層的電子性質(zhì)和磁性質(zhì)。除了CrOI單層，所有的CrXY單層都是穩(wěn)定的鐵磁半導(dǎo)體。計算結(jié)果顯示，材料中的鐵磁耦合是由Cr原子的e_g軌道和陰離子的p軌道在三重旋轉(zhuǎn)對稱性下的超交換過程所貢獻的。在該情況下，鐵磁耦合強度可通過調(diào)節(jié)Cr-X鍵的特性來增強，即，通過減小雜化軌道之間的能量差來增強Cr-X鍵的共價性。我們以CrOY為例子，證明通過用S/Se來替換O離子，材料的居里溫度（T_c）幾乎增加了三倍，其中CrSeI單層的T_c可以達到334 K。這些單層鐵磁材料的高穩(wěn)定性和高居里溫度表明其可被合成并應(yīng)用于二維自旋電子器件。