Topological Chern bands for electrons and magnons realized in one Kagome ferromagnet: CoCu₃(OH)₆Cl₂

We study the topological electron bands and spinon bands in the ferromagnetic phase of CoCu₃(OH)₆Cl₂. The Cu ions with fractional valence and magnetic moments form a 3D trigonal crystal stacked from 2D Kagome layers. A t-J model with spin-orbit coupling is constructed from the hybridized Wannier orbitals and studied using the Schwinger bosons to calculate the spinon bands. The Chern numbers of the electron and spinon bands reveal their nontrivial topological properties and implications on the spintronic transport properties are discussed. Our work provides an example for the study of interactions between two topological systems and sheds light on the understanding of correlated electrons in magnetic topological materials.