标题： 通过掺杂和应变调节Fe$_{5}$GeTe$_{2}$单层材料的磁各向异性 显示英文标题

标题： Tuning magnetic anisotropy in Fe$_{5}$GeTe$_{2}$ monolayer through doping and strain

摘要： 控制二维铁磁材料中的磁各向异性能（MAE）对于设计新型自旋电子器件至关重要。 使用第一性原理计算，我们系统地研究了单层 Fe$_5$GeTe$_2$ (F5GT) 在两种情况下的磁性：(I) Co 和 Ni 掺杂，以及 (II) 压缩和拉伸应变。 我们的结果表明，F5GT 单层表现出较弱的面内 MAE，可以通过 Co 掺杂显著增强。 此外，$1\%$的压缩应变会将磁易轴从面内切换到面外，而$4\%$的压缩应变可以进一步增强面外 MAE。 自旋-轨道耦合（SOC）矩阵分析表明，Co 掺杂 F5GT（Co-F5GT）中面内 MAE 的增强来源于 Te 的$ \left\langle {\it p}_{x} \left\vert L_z\right\vert {\it p}_{y} \right\rangle $和 Fe(2) 与 Fe(3) 的$ \left\langle {\it d}_{xy} \left\vert L_z\right\vert {\it d}_{x^2+y^2} \right\rangle $的变化。 压缩应变的影响主要归因于 Fe(1) 的$ \left\langle {\it d}_{xy} \left\vert L_z\right\vert {\it d}_{x^2+y^2} \right\rangle $的正贡献显著增加。 显示英文摘要

摘要： Controlling magnetic anisotropy energy (MAE) in two-dimensional (2D) ferromagnetic materials is crucial for designing novel spintronic devices. Using first-principles calculations, we systematically investigate the magnetic properties of monolayer Fe$_5$GeTe$_2$ (F5GT) under two scenarios: (I) Co and Ni doping, and (II) compressive and tensile strains. Our results show that the F5GT monolayer exhibits a weak in-plane MAE, which can be significantly enhanced by Co doping. Additionally, a $1\%$ compressive strain switches the magnetic easy axis from in-plane to out-of-plane, while $4\%$ compressive strain can further enhance the out-of-plane MAE. Spin-orbit coupling (SOC) matrix analysis reveals that the enhancement of in-plane MAE in Co-doped F5GT (Co-F5GT) arises from changes in $ \left\langle {\it p}_{x} \left\vert L_z\right\vert {\it p}_{y} \right\rangle $ of Te and $ \left\langle {\it d}_{xy} \left\vert L_z\right\vert {\it d}_{x^2+y^2} \right\rangle $ of Fe(2) and Fe(3). The effect of compressive strain is primarily attributed to a substantial increase in the positive contribution from $ \left\langle {\it d}_{xy} \left\vert L_z\right\vert {\it d}_{x^2+y^2} \right\rangle $ of Fe(1).