Topological states of matter in two-dimensional (2D) system, especially those combined with magnetism have received special attention currently, because of their new physics and the potential applications in spintronics and nanoscale. At present, realizing multiple topological phases in a single 2D Magnetic material and studying their potential entanglement still face great challenges. Here, we predict a novel 2D topological material namely monolayer EuO₂, which can realize multiple types of topological states, namely, type-I Weyl point (WP), type-II WP, critical-type WP, and Quantum anomalous Hall (QAH) effect. Specifically, Without considering Spin-orbit coupling (SOC), these Weyl points perfectly possess the 100% spin-polarization because monolayer EuO₂ is a half metal phase with huge spin-related energy gap as large as 6.2 eV. Remarkably, With considering SOC, the topological states in monolayer EuO₂ can be tuned by direction of magnetization. Under out-plane magnetization, monolayer EuO₂ can realize the QAH effect with single chiral edge state occurring inside the energy gap. Under in-plane magnetization, the system can remain 2D Weyl states at special directions. In other in-plane magnetization, the system shows the in-plane QAH effect with the Chern number of −1 or 1. Therefore, Our work promotes the realization of tunable topological phase in 2D half metals.

二维（2D）系统中的物质拓扑状态，尤其是与磁性相结合的拓扑状态，由于其新的物理性质以及在自旋电子学和纳米尺度中的潜在应用，目前受到了特别的关注。目前，在单个2D磁性材料中实现多个拓扑阶段并研究其潜在纠缠仍然面临巨大挑战。在这里，我们预测一种新颖的二维拓扑材料，即单层EuO ₂，它可以实现多种类型的拓扑状态，即I型Weyl点（WP），II型WP，临界型WP和量子异常霍尔（QAH） ） 影响。具体而言，由于单层EuO ₂，这些Weyl点在不考虑自旋轨道耦合（SOC）的情况下完全拥有100％自旋极化是半金属相，具有与自旋相关的巨大能隙，最大能隙为6.2 eV。值得注意的是，考虑到SOC，可以通过磁化方向来调整单层EuO _2中的拓扑状态。在面外磁化作用下，单层EuO ₂可以在能隙内发生单手性边缘状态，从而实现QAH效应。在面内磁化下，系统可以在特定方向上保持2维Weyl状态。在其他面内磁化中，系统显示的Chern数为-1或1的面内QAH效应。因此，我们的工作促进了二维半金属中可调谐拓扑相的实现。