Realization of nontrivial band topology in condensed matter systems is of great interest in recent years. Using first-principles calculations and symmetry analysis, we propose an exotic topological phase with tunable ferromagnetic Weyl fermions in a half-metallic oxide CrP₂O₇. In the absence of spin–orbit coupling (SOC), we reveal that CrP₂O₇ possesses a hybrid nodal ring. When SOC is present, the spin-rotation symmetry is broken. As a result, the hybrid nodal ring shrinks to discrete nodal points and forms different types of Weyl points. The Fermi arcs projected on the (100) surface are clearly visible, which can contribute to the experimental study for the topological properties of CrP₂O₇. In addition, the calculated quasiparticle interference patterns are also highly desirable for the experimental study of CrP₂O₇. Our findings provide a good candidate of ferromagnetic Weyl semimetals, and are expected to realize related topological applications with their attracted features.

近年来，在凝聚态系统中实现非平凡的频带拓扑引起了人们的极大兴趣。使用第一性原理计算和对称性分析，我们提出了一种在半金属氧化物CrP ₂ O _7中具有可调谐铁磁Weyl费米子的奇异拓扑相。在没有自旋轨道耦合（SOC）的情况下，我们发现CrP ₂ O ₇具有杂化的节环。当存在SOC时，自旋旋转对称性被破坏。结果，混合节点环收缩到离散的节点并形成不同类型的Weyl点。投射在（100）表面上的费米弧清晰可见，这有助于对CrP ₂ O ₇的拓扑特性进行实验研究。另外，对于CrP ₂ O ₇的实验研究，计算出的准粒子干涉图也是非常理想的。我们的发现为铁磁Weyl半金属提供了很好的候选者，并有望以其吸引人的特征实现相关的拓扑应用。