Role of strong correlation and spin-orbit coupling in $\textrm{LuB}_{4}$: a first principle study

The recent observation of magnetization plateaus in rare-earth metallic tetraborides has drawn a lot of attention to this class of materials. In this work, we investigate the electronic structure of one such canonical system $\textrm{LuB}_{4}$, using first-principle density functional theory, together with strong Coulomb correlation and spin-orbit coupling (SOC) effects. The electronic band structures show that $\textrm{LuB}_{4}$ is a non-magnetic correlated metal with completely filled $4f$ shell. The projected density of states (DOS) shows a continuum at the Fermi level (FL), arising mainly from hybridized Lu $d$ and B $p$ orbitals, along with some discrete peaks, well separated from the continuum. These peaks arise mainly due to core-level Lu $s$, $p$ and $4f$ atomic orbitals. Upon inclusion of SOC, the discrete peak arising due to Lu $p$ is split into two peaks with $j = 1/2$, $j = 3/2$ while the peak arising due to Lu $4f$ orbitals splits into two peaks with $j = 5/2$ and $j = 7/2$. These peaks will give rise to multiplet structure in core level X-ray photo-emission spectroscopy. Inclusion of strong correlation effects pushes the Lu $4f$ peak away from the FL while the qualitative features remain intact.