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

The recent discoveries of strikingly large zero-field Hall and Nernst effects in antiferromagnets Mn$_3$$X$, ($X$ = Sn, Ge) have brought the study of magnetic topological states to the forefront of condensed matter research and technological innovation. These effects are considered fingerprints of Weyl nodes residing near the Fermi energy, promoting Mn$_3$$X$, ($X$ = Sn, Ge) as a fascinating platform to explore the elusive magnetic Weyl fermions. In this review, we provide recent updates on the insights drawn from experimental and theoretical studies of Mn$_3$$X$, ($X$ = Sn, Ge) by combining previous reports with our new, comprehensive set of transport measurements of high-quality Mn$_3$Sn and Mn$_3$Ge single crystals. In particular, we report magnetotransport signatures specific to chiral anomalies in Mn$_3$Ge and planar Hall effect in Mn$_3$Sn, which have not yet been found in earlier studies. The results summarized here indicate the essential role of magnetic Weyl fermions in producing the large transverse responses in the absence of magnetization.