Due to the time reversal symmetry breaking or spin-valley coupling, there are intrinsic valley splittings in two-dimensional magnetic materials, which are closely related to the symmetry and magnetic order. Based on MnPTe monolayers with different symmetries, we present an understanding of direction dependent spin/valley splitting and anomalous Hall conductivity from the perspective of orbital interactions. Unlike T-MnPTe with central inversion symmetry, in-plane magnetization leads to further non-degeneracy of valley electrons of H–MnPTe, and the splitted valley states are spin polarized, which is perpendicular to the in-plane magnetization direction. The model and first-principle calculations consistently indicate that the splitting of the valley states is almost proportional to sinθ, which originates from the difference in spin-up and spin-down interactions introduced by the breaking of spatial inversion symmetry. Regardless of spin degeneracy, non-zero anomalous Hall conductivity occurs with out-of-plane magnetization, and this direction dependent anomalous Hall effect is caused by mirror symmetry breaking from the neighboring Te atoms and spin-orbit coupling. Magnetization direction is an important means of regulating valley/spin splittings and anomalous Hall effect, which has certain significance for realizing spin or valley polarized Hall effect and the research of spintronic or valleytronic devices.

中文翻译：

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反铁磁单层 MnPTe3 的对称性和磁方向依赖的自旋/谷分裂和反常霍尔电导率

由于时间反演对称性破缺或自旋谷耦合，二维磁性材料存在固有的谷分裂，这与对称性和磁序密切相关。基于具有不同对称性的MnPTe单层，我们从轨道相互作用的角度提出了对方向依赖的自旋/谷分裂和反常霍尔电导率的理解。与具有中心反演对称性的T-MnPTe不同，面内磁化导致H-MnPTe的谷电子进一步非简并，并且分裂的谷态是自旋极化的，其垂直于面内磁化方向。模型和第一原理计算一致表明，谷态的分裂几乎与sinθ成正比，这源于空间反演对称性破缺引入的自旋向上和自旋向下相互作用的差异。无论自旋简并度如何，面外磁化都会产生非零反常霍尔电导率，这种方向相关的反常霍尔效应是由相邻 Te 原子的镜面对称性破坏和自旋轨道耦合引起的。磁化方向是调控谷/自旋分裂和反常霍尔效应的重要手段，对于实现自旋或谷极化霍尔效应以及自旋电子或谷电子器件的研究具有一定意义。