Heusler, Weyl and Berry

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.