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

Recent observation of magnetization plateau in rare-earth metallic tetra-borides, $$\text {RB}_{4}$$ 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 $${\varvec{s}}$$ s , rare-earth $${\varvec{p}}$$ p + B $${\varvec{p}}$$ p and B $${\varvec{p}}$$ p while the continuum states around the Fermi level arises due to hybridized B $${\varvec{p}}$$ p , rare-earth $${\varvec{p}}$$ p and $${\varvec{d}}$$ d orbitals. Upon inclusion of SOC the peak arising due to rare-earth p gets split into two peaks corresponding to $${\varvec{j}}={\textbf {0.5}}$$ j = 0.5 and $${\varvec{j}}={\textbf {1.5}}$$ j = 1.5 configurations. The splitting gap ( $${\varvec{\Delta }} {\varvec{E}}_{\text {gap}}$$ Δ E gap ) between $${\varvec{j}}={\textbf {0.5}}$$ j = 0.5 and $${\varvec{j}}={\textbf {1.5}}$$ j = 1.5 manifold shows power law ( $${\varvec{\Delta }} {\varvec{E}}_{\text {gap}}\varvec{\propto } {\varvec{Z}}^{{\varvec{n}}}$$ Δ E gap ∝ Z n , $${\varvec{Z}}$$ Z is the atomic number of the rare-earth atom involved) behaviour with n =4.82. In case of $$\text {LaB}_{4}$$ LaB 4 , in the presence of SOC, spin-split $${\textbf {4}}{\varvec{f}}$$ 4 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