Not yet reviewed by Pith; the record is open.

The interplay of magnetism and topology opens up the possibility for exotic linear response effects, such as the anomalous Hall effect and the anomalous Nernst effect, which can be strongly enhanced by designing a strong Berry curvature in the electronic structure. It is even possible to utilize this to create a quantum anomalous Hall state at high temperatures by reducing the dimensionality. Magnetic Heusler compounds are a promising class of materials for this purpose because they grow in thin films, have a high Curie temperature, and their electronic structure hosts strong topological features. Here, we provide a comprehensive study of the intrinsic anomalous transport for magnetic cubic full Heusler compounds and we illustrate that several Heusler compounds outperform the best so far reported materials. The results reveal the importance of symmetries, especially mirror planes, in combination with magnetism for giant anomalous Hall and Nernst effects, which should be valid in general for linear responses (spin Hall effect, spin orbital torque, etc.) dominated by intrinsic contributions.