The interactions between conduction electrons and magnetism can significantly enhance the Hall signal, a phenomenon known as the anomalous Hall effect (AHE). While the AHE is generally not expected in antiferromagnets, a large AHE is observed in certain antiferromagnets with noncollinear spin textures and nonvanishing Berry curvature. In this work, we present a rich temperature and magnetic phase diagram with eight distinct magnetic phases for the antiferromagnetic kagome compound ${\mathrm{LuMn}}_6{\mathrm{Sn}}_6$. The Hall effect analysis in ${\mathrm{LuMn}}_6{\mathrm{Sn}}_6$ reveals both intriguing physical phenomena and methodological challenges. In the coplanar canted antiferromagnetic phase, we observe an AHE, which likely originates from the intrinsic effects. At low temperatures, upon entering the ferromagnetic phase, the AHE sharply increases and exceeds the conventional limits expected from intrinsic mechanisms. We also demonstrate the limitations of standard experimental methods in extracting the topological contribution to the Hall effect data. In particular, we show that accounting for magnetoresistance anisotropy helps reduce spurious contribution that can mimic topological Hall signals, although it does not fully resolve it. These shortcomings in current approaches in partitioning the Hall response necessitate new tools to interpret transport results in complex magnetic materials such as ${\mathrm{LuMn}}_6{\mathrm{Sn}}_6$.

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• Anomalous Hall effect
• Magnetic phase transitions
• Magnetism
• Magnetotransport
• Phase diagrams
• Topological Hall effect
• Topological materials