Giant anomalous Hall and Nernst conductivities in magnetic all-$d$ metal Heusler alloys

All-$d$ Heuslers are a category of novel compounds combining versatile functionalities such as caloric responses and spintronics with enhanced mechanical properties. Despite the promising transport properties (anomalous Hall (AHC) and anomalous Nernst (ANC) conductivities) shown in the conventional Co$_2$XY Heuslers with $p$-$d$ hybridization, the all-$d$ Heuslers with only $d$-$d$ hybridization open a new horizon to search for new candidates with outstanding transport properties. In this work, we evaluate the AHC and ANC for thermodynamically stable ferro/ferri-magnetic all-$d$-metal regular Heusler compounds based on high-throughput first-principles calculations. It is observed that quite a few materials exhibit giant AHCs and ANCs, such as cubic Re$_2$TaMn with an AHC of 2011 S/cm, and tetragonal Pt$_2$CrRh with an AHC of 1966 S/cm and an ANC of 7.50 A/mK. Comprehensive analysis on the electronic structure reveals that the high AHC can be attributed to the occurrence of the Weyl nodes or gapped nodal lines in the neighbourhood of the Fermi level. The correlations between such transport properties and the number of valence electrons are also thoroughly investigated, which provides a practical guidance to tailor AHC and ANC via chemical doping for transverse thermoelectric applications.