Exotic 4f-Correlated Electronic States of Ferromagnetic Kondo-Lattice Compounds ReRh6Ge4 (Re = Ce, Ho, Er, Tm).

As the first metallic compound proposed to exhibit a ferromagnetic quantum critical point, CeRh6Ge4 has garnered significant attention. We investigate the ferromagnetic Kondo lattice compounds ReRh6Ge4 (Re = Ce, Ho, Er, Tm) systematically using density functional theory including Coulomb interaction corrections (DFT+U) and spin-orbit coupling. Our results indicate that the magnetic easy axis of CeRh6Ge4 lies within the ab plane, consistent with prior magnetization measurements under external magnetic fields and μSR experiments. We also predict the magnetic easy axes for the other three compounds. For TmRh6Ge4, the easy axis is along the c axis, thereby preserving the C 3v rotational symmetry about the c axis. Notably, in the band structure including spin-orbit coupling, triply degenerate nodes exist along the Γ-A direction. Within our DFT+U calculations, we observe a possible trend from localized to more itinerant 4f behavior as the number of 4f electrons increases from CeRh6Ge4 to TmRh6Ge4. The 4f electrons exhibit some itinerant character under conditions that are neither empty, full, nor half-filled. These localized-itinerant 4f electrons are the primary reason for the formation of the ferromagnetic ground state in our calculations. Density of states and Fermi surface calculations show that the 4f electrons in TmRh6Ge4 contribute to the formation of a large Fermi surface, indicating their participation in the conduction process. Conversely, the 4f electrons in HoRh6Ge4, ErRh6Ge4, and CeRh6Ge4 remain largely localized, resulting in smaller Fermi surfaces for these compounds. These theoretical investigations provide deep insights into the unique nature of 4f electrons and offer key predictions for subsequent experimental studies.