Metamagnetic transition and anomalous Hall effect in Mn-based kagomé magnets RMn6Ge6(R=Tb−Lu)

We investigate electrical transport and magnetic properties of the single-crystalline, Mn-based kagom\'e magnets $R{\mathrm{Mn}}_{6}{\mathrm{Ge}}_{6}$ ($R$=Tb-Lu). The compounds mostly feature a series of magnetic orderings of $R$ and Mn moments at different temperatures and metamagnetic transition (MMT) under an external magnetic field. We classify the MMT into three types, i.e., from skewed spiral to a structure containing decoupled $R$ and Mn moments, from antiferromagnetic to flat spiral Mn moments, and from flat spiral to a ferrimagnetic state of $R$ and Mn moments. The former two induce a small anomalous Hall effect (AHE), whereas the latter gives rise to a large one. We conclude that ferromagnetic ordered Mn moments in the kagom\'e lattice lead to a significant AHE, while other magnetic structures of $R$ and Mn moments do not. The AHE in ${\mathrm{TbMn}}_{6}{\mathrm{Ge}}_{6}$ generally has an intrinsic origin, while no clear sign of intrinsic AHE is found in other compounds.