Magnetic topological semimetals (TSMs) are topological quantum materials with broken time-reversal symmetry (TRS) and isolated nodal points or lines near the Fermi level. Their topological properties would typically reveal from the bulk-edge correspondence principle as nontrivial surface states such as Fermi arcs or drumhead states, etc. Depending on the degeneracies and distribution of the nodes in the crystal momentum space, TSMs are usually classified into Weyl semimetals (WSMs), Dirac semimetals (DSMs), nodal-line semimetals (NLSMs), triple-point semimetals (TPSMs), etc. In this review article, we present the recent advances of magnetic TSMs from a computational perspective. We first review the early predicted magnetic WSMs such as pyrochlore iridates and HgCr₂Se₄, as well as the recently proposed Heusler, Kagome layers, and honeycomb lattice WSMs. Then we discuss the recent developments of magnetic DSMs, especially CuMnAs in Type-III and EuCd₂As₂ in Type-IV magnetic space groups (MSGs). Then we introduce some magnetic NLSMs that are robust against spin–orbit coupling (SOC), namely Fe₃GeTe₂ and LaCl (LaBr). Finally, we discuss the prospects of magnetic TSMs and the interesting directions for future research.

磁性拓扑半金属（TSM）是拓扑量子材料，具有打破的时间反转对称性（TRS）和孤立的结点或费米能级附近的线。它们的拓扑特性通常会从体边缘对应原理中揭示为非平凡的表面状态，例如费米弧或鼓面状态等。根据晶体动量空间中节点的简并性和分布，TSM通常分为Weyl半金属（ WSMs，狄拉克半金属（DSMs），节点线半金属（NLSMs），三点半金属（TPSMs）等。在这篇综述文章中，我们从计算的角度介绍了磁性TSM的最新进展。我们首先回顾早期预测的磁性WSM，例如烧绿石伊利酸盐和HgCr ₂ Se _4。，以及最近提出的Heusler层，Kagome层和蜂窝晶格WSM。然后，我们讨论了磁性DSM的最新发展，特别是III型的CuMnAs和IV型磁性空间群（MSG）中的EuCd ₂ As ₂。然后，我们介绍一些对自旋轨道耦合（SOC）具有鲁棒性的磁性NLSM，即Fe ₃ GeTe ₂和LaCl（LaBr）。最后，我们讨论了磁性TSM的前景以及未来研究的有趣方向。