Anomalous Hall effect in a two sub-lattice ferrimagnet.

The anomalous Hall effect (AHE) is a characteristic of ferromagnets where a finite Hall effect proportional to the magnetization appears in zero external magnetic field. It is now known that the AHE can also arise in non-collinear and non-coplanar antiferromagnets due to spin chirality and in materials consisting of topologically non-trivial electronic structure such as Weyl semimetals. Here we will present the observation of an anomalous Hall effect in a hexagonal ferrimagnet TbMn₆Sn₆ consisting of two spin sub-lattices due to Mn and Tb ordering. Both spin sublattices order simultaneously above room temperature and show a spin reorientation below 310 K from the basal plane towards c-axis. The AHE that is observed at temperatures well below the spin reorientation temperature does not follow the underlying net magnetization, indicating the formation of a non-coplanar or complex chiral spins textures