A cluster calculation investigation of A- and B-sites-ordered perovskite oxide CaCu₃Fe₂Os₂O₁₂

Taking the quadruple perovskite oxide CaCu_3Fe_2Os_2O_12 as an example, by performing both experimental sum rules and theoretical configuration interaction cluster calculations, we have investigated the spin and orbital configurations of all the transition metal cations, Cu, Fe, and Os, as well as their local microscopic physical parameters of crystal field, spin-orbit coupling (SOC), Coulomb potential, and hybridization. Specifically, we found that Os^5+ (5d^3) with a half-filled t_\rm 2g orbital exhibits a large orbital moment on account of the mixing of t_\rm 2g and e_\rm g orbitals, which can be ascribed to the strong SOC of the 5d elements. On the other hand, SOC of the Cu^2+ (3d^9) is markedly reduced, but is still nonnegligible compared to the crystal field 10Dq, leading to a finite orbital moment of Cu^2+. This work provides a microscopic and element-selective perspective of the local environment of magnetic cations in complex compounds.