Exotic 4f Correlated Electronic States of Ferromagnetic Kondo Lattice Compounds ReRh$_6$Ge$_4$ (Re=Ce, Ho, Er, Tm)

TL;DR

This study uses density functional theory to explore the electronic and magnetic properties of ReRh$_6$Ge$_4$ compounds, revealing a crossover from localized to itinerant 4f electrons and predicting magnetic easy axes.

Contribution

It provides the first theoretical predictions of magnetic easy axes and electronic structure details for ReRh$_6$Ge$_4$ compounds, highlighting the 4f electron crossover.

Findings

CeRh$_6$Ge$_4$ has in-plane magnetic easy axis.

TmRh$_6$Ge$_4$ has c-axis magnetic easy axis.

A localized to itinerant 4f electron crossover occurs across the series.

Abstract

CeRh$_6$Ge$_4$ stands out as the first stoichiometric metallic compound with a ferromagnetic quantum critical point, thereby garnering significant attention. Ferromagnetic Kondo lattice compounds ReRh$_6$Ge$_4$ (Re=Ce, Ho, Er, Tm) have been systematically investigated with density functional theory incorporating Coulomb interaction U and spin-orbital coupling. We determined the magnetic easy axis of CeRh$_6$Ge$_4$ is within the ab plane, which is in agreement with previous magnetization measurements conducted under external magnetic field and muSR experiments. We also predicted the magnetic easy axes for the other three compounds. For TmRh$_6$Ge$_4$, the magnetic easy axis aligns along the c axis, thus preserving the $C_3$ rotational symmetry of the c axis. Especially, there are triply degenerate nodal points along the $\Gamma-A$ direction in the band structure including spin-orbital coupling. A possible localized to itinerant crossover is revealed as $4f$ electrons increase from CeRh$_6$Ge$_4$ to TmRh$_6$Ge$_4$. Specifically, the $4f$ electrons of TmRh$_6$Ge$_4$ contribute to the formation of a large Fermi surface, indicating their participation in the conduction process. Conversely, the $4f$ electrons in HoRh$_6$Ge$_4$, ErRh$_6$Ge$_4$ and CeRh$_6$Ge$_4$ remain localized, which result in smaller Fermi surfaces for these compounds. These theoretical investigations on electronic structure and magnetic properties shed deep insight into the unique nature of $4f$ electrons, providing critical predictions for subsequent experimental studies.