Magnetic field induced arrested state and observation of spontaneous anomalous Hall effect in TbMn$_6$Sn$_6$

The quasi two-dimensional kagome ferrimagnet TbMn$_6$Sn$_6$ is investigated for thermo-remanent magnetization and Hall effects. On cooling under a moderate magnetic field, the sample attains a magnetization value close to the saturation magnetization. Upon heating in a very small magnetic field, the sample continues to maintain the large value of magnetization, which eventually diminishes distinctly at around 200 K manifesting an ultrasharp jump. A similar feature is also observed in the Hall resistivity, which holds its saturation value when heated back in zero field after being field-cooled. The ultrasharp jump in magnetization is also get reflected in our Hall data. The observed data is exotic and can be rooted to the large anisotropy and the strong exchange interaction.