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The recent discoveries of strikingly large zero-field Hall and Nernst effectsin antiferromagnets Mn$_3$$X$, ($X$ = Sn, Ge) have brought the study ofmagnetic topological states to the forefront of condensed matter research andtechnological innovation. These effects are considered fingerprints of Weylnodes residing near the Fermi energy, promoting Mn$_3$$X$, ($X$ = Sn, Ge) as afascinating platform to explore the elusive magnetic Weyl fermions. In thisreview, we provide recent updates on the insights drawn from experimental andtheoretical studies of Mn$_3$$X$, ($X$ = Sn, Ge) by combining previous reportswith our new, comprehensive set of transport measurements of high-qualityMn$_3$Sn and Mn$_3$Ge single crystals. In particular, we reportmagnetotransport signatures specific to chiral anomalies in Mn$_3$Ge and planarHall effect in Mn$_3$Sn, which have not yet been found in earlier studies. Theresults summarized here indicate the essential role of magnetic Weyl fermionsin producing the large transverse responses in the absence of magnetization.

Anomalous transport due to Weyl fermions in the chiral antiferromagnets Mn$_3$$X$, $X$ = Sn, Ge