Heusler compounds, initially discovered by Fritz Heusler more than a century ago, have grown into a family of more than 1,000 compounds, synthesized from combinations of more than 40 elements. Recently, by incorporating heavy elements that can give rise to strong spin–orbit coupling, non-trivial topological phases of matter, such as topological insulators, have been discovered in Heusler materials. Moreover, interplay between the symmetry, spin–orbit coupling and magnetic structure allows for the realization of a wide variety of topological phases through Berry curvature design. The topological properties of Heusler compounds can be manipulated by various external perturbations, resulting in exotic properties, such as the chiral anomaly and large anomalous, spin and topological Hall effects. In addition, the non-zero Berry curvature that arises as a result of non-collinear order gives rise to a non-zero anomalous Hall effect. Besides this k-space Berry curvature, Heusler compounds with non-collinear magnetic structures also possess real-space topological states in the form of magnetic antiskyrmions, which have not yet been observed in other materials. In this Review, we discuss Heusler compounds from a topological perspective and the connection between the topology and the symmetry properties, spin gapless semiconductors, magnetic compensated ferrimagnets, non-collinear order in ferromagnetic and antiferromagnetic Heusler compounds, the anomalous Hall effect and, finally, magnetic antiskyrmions. Together with the new topological viewpoint and the high tunability, novel physical properties and phenomena await discovery in Heusler compounds.

赫斯勒化合物最早是由Fritz Heusler于一个多世纪前发现的，现已成长为由40多种元素的组合合成的1,000多种化合物的家族。最近，通过掺入会引起强自旋-轨道耦合的重元素，在赫斯勒材料中发现了物质的非平凡拓扑相，例如拓扑绝缘体。此外，对称性，自旋轨道耦合和磁性结构之间的相互作用允许通过Berry曲率设计实现各种各样的拓扑阶段。Heusler化合物的拓扑特性可以通过各种外部扰动来操纵，从而产生奇异的特性，例如手性异常和大异常，自旋和拓扑霍尔效应。此外，由于非共线阶数而产生的非零贝里曲率会引起非零异常霍尔效应。除此以外具有非共线磁性结构的k-空间Berry曲率Heusler化合物还具有抗反离子形式的真实空间拓扑状态，这在其他材料中还没有观察到。在这篇综述中，我们从拓扑的角度讨论了赫斯勒化合物，以及拓扑与对称性之间的联系，自旋无隙半导体，磁补偿铁氧体，铁磁和反铁磁赫斯勒化合物的非共线顺序，反常霍尔效应，以及最后，磁性抗静电剂。伴随着新的拓扑学观点和高可调谐性，新的物理性质和现象在Heusler化合物中等待发现。