Role of spin-orbit coupling effects in rare-earth metallic tetra-borides: a first principle study

Abstract

Recent observation of magnetization plateau in rare-earth metallic tetra-borides, $\text {RB}_{4}$, have drawn lot of attention to this class of materials. In this article, using first principle electronic structure methods (DFT) implemented in Quantum Espresso (QE), we have studied hither-to neglected strong spin-orbit coupling (SOC) effects present in these systems on the electronic structure of these system in the non-magnetic ground state. The calculations were done under GGA and GGA+SO approximations. In the electronic band structure, strong SOC effect lifts degeneracy at various symmetry points. The projected density of states consists of 3 distinct spectral peaks well below the Fermi energy and separated from the continuum density of states around the Fermi energy. The discrete peaks arise due to rare-earth ${\varvec{s}}$, rare-earth ${\varvec{p}}$ + B ${\varvec{p}}$ and B ${\varvec{p}}$ while the continuum states around the Fermi level arises due to hybridized B ${\varvec{p}}$, rare-earth ${\varvec{p}}$ and ${\varvec{d}}$ orbitals. Upon inclusion of SOC the peak arising due to rare-earth p gets split into two peaks corresponding to ${\varvec{j}}={\textbf {0.5}}$ and ${\varvec{j}}={\textbf {1.5}}$ configurations. The splitting gap (${\varvec{\Delta }} {\varvec{E}}_{\text {gap}}$) between ${\varvec{j}}={\textbf {0.5}}$ and ${\varvec{j}}={\textbf {1.5}}$ manifold shows power law (${\varvec{\Delta }} {\varvec{E}}_{\text {gap}}\varvec{\propto } {\varvec{Z}}^{{\varvec{n}}}$, ${\varvec{Z}}$ is the atomic number of the rare-earth atom involved) behaviour with n =4.82. In case of $\text {LaB}_{4}$, in the presence of SOC, spin-split ${\textbf {4}}{\varvec{f}}$ orbitals contributes to density of states at the Fermi level while the density of states at the Fermi level largely remains unaffected for all other materials under consideration.

Graphic abstract