Magnetic structure and spin wave excitations in the Kagome magnet LuMn$_{6}$Sn$_{6}$

We present a study of the magnetic structure and spin wave excitations in the metallic Kagome magnet LuMn$_{6}$Sn$_{6}$ using neutron diffraction and inelastic neutron scattering. This material, characterized by strong magnetic frustration due to competing interactions between Kagome layers, exhibits a complex magnetic phase diagram with coplanar and non-coplanar spin configurations over a wide range of temperatures and magnetic fields. Neutron diffraction reveals a series of magnetic phase transitions between coplanar and non-coplanar spin arrangements. Additionally, inelastic neutron scattering uncovers distinct spin wave excitations tied to these configurations, offering key insights into the spin dynamics and exchange interactions. By correlating these magnetic structures with transport measurements, we find that the anomalous Hall effect (AHE) is present in both spin configurations. Surprisingly, the coplanar phase, which retains PT symmetry and is not expected to exhibit an AHE, displays a larger effect than the non-coplanar phase, suggesting additional mechanisms beyond the intrinsic AHE in this material. This work provides a comprehensive view of how magnetic frustration in Kagome lattices influences both the magnetic structure and the resulting electronic transport properties, offering new insights into topological magnetism.