Diverse magnetic phase diagram and anomalous Hall effect in antiferromagnetic LuMn6Sn6

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 LuMn$_6$Sn$_6$. The Hall effect analysis in LuMn$_6$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. We show the importance of considering magnetoresistance anisotropy when estimating the anomalous and topological Hall effects. These shortcomings in current approaches in partitioning the Hall response necessitate new tools to interpret transport results in complex magnetic materials such as LuMn$_6$Sn$_6$.