  Kagome magnet has been found to be a fertile ground for the search of exotic
quantum states in condensed matter. Arising from the unusual geometry, the
quantum interactions in the kagome lattice give rise to various quantum states,
including the Chern-gapped Dirac fermion, Weyl fermion, flat band and van Hove
singularity. Here we review recent advances in the study of the R166 kagome
magnet (RT6E6, R = rare earths; T = transition metals; and E = Sn, Ge, etc.)
whose crystal structure highlights the transition-metal-based kagome lattice
and rare-earth sublattice. Compared with other kagome magnets, the R166 family
owns the particularly strong interplays between the d electrons on the kagome
site and the localized f electrons on the rare-earth site. In the form of
spin-orbital coupling, exchange interaction and many-body effect, the quantum
interactions play an essential role in the Berry curvature field in both the
reciprocal and real spaces of R166 family. We discuss the spectroscopic and
transport visualization of the topological electrons hosted in the Mn kagome
layer of RMn6Sn6 and the various topological effects due to the quantum
interactions, including the Chern-gap opening, the exchange-biased effect, the
topological Hall effect and the emergent inductance. We hope this work serves
as a guide for future explorations of quantum magnets.
