Heusler compounds are a large family of binary, ternary, and quaternary compounds that exhibit a wide range of properties of both fundamental and potential technological interest. The extensive tunability of the Heusler compounds through chemical substitutions and structural motifs makes the family especially interesting. In this article we highlight recent major developments in the field of Heusler compounds and put these in the historical context. The evolution of the Heusler compounds can be described by four major periods of research. In the latest period, Heusler 4.0 has led to the observation of a variety of properties derived from topology that includes topological metals with Weyl and Dirac points; a variety of noncollinear spin textures, including the very recent observation of skyrmions at room temperature; and giant anomalous Hall effects in antiferromagnetic Heuslers with triangular magnetic structures. Here we give a comprehensive overview of these major achievements and set research into Heusler materials within the context of recent emerging trends in condensed matter physics

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A comprehensive study of the total energy of manganese-rich Heusler compounds using density functional theory is presented. Starting from a large set of cubic parent systems, the response to tetragonal distortions is studied in detail. We single out the systems that remain cubic from those that most likely become tetragonal. The driving force of the tetragonal distortion and its effect on the magnetic properties, especially where they deviate from the Slater-Pauling rule, as well as the trends in the Curie temperatures, are highlighted. By means of partial densities of states, the electronic structural changes reveal the microscopic origin of the observed trends. We focus our attention on the magnetocrystalline anisotropy and find astonishingly high values for tetragonal Heusler compounds containing heavy transition metals accompanied by low magnetic moments, which indicates that these materials are promising candidates for spin-transfer-torque magnetization-switching applications