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Thermal and thermoelectric measurements are known as powerful tools touncover the physical properties of quantum materials due to their sensitivitytowards the scattering and chirality of heat carriers. We use these techniquesto confirm the presence of momentum and real-space topology in ScMn$_6$Sn$_6$.There is an unconventional dramatic increase in the Seebeck coefficient onentering the transverse conical spiral (TCS) below $T$ = 200 K suggesting anunusual scattering of heat carriers. In addition, the observed anomalousthermal Hall effect and the anomalous Nernst effect indicates non-zero Berrycurvature in $k$-space. Furthermore, we identify a significant topologicalcontribution to the thermal Hall and Nernst signals in the TCS phase revealingthe impacts of real-space Berry curvature. We discuss the presence oftopological thermal Hall effect and topological Nernst effect for the firsttime in the diverse HfFe$_6$Ge$_6$ family. This study illustrates theimportance of transverse thermal and thermoelectric measurements to investigatethe origin of topological transport in the non-coplanar magnetic phases in thisfamily of kagome metals.

Topological Nernst and topological thermal Hall effect in rare-earth kagome ScMn$_6$Sn$_6$