Quantum interactions in topological R166 kagome magnet

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 thedelectrons on the kagome site and the localizedfelectrons 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 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 RMn₆Sn₆and 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.