Evolution of the Coulomb interactions in correlated transition-metal perovskite oxides from the constrained random phase approximation

Determining the strength of electronic correlations of correlated electrons plays important roles in accurately describing the electronic structures and physical properties of transition-metal (TM) perovskite oxides. Here, we study the evolution of electronic interaction parameters as a function of d-electron occupancy in an extended class of TM perovskite oxides ABO3 (A=Sr, Ca, and B=3d-5d TM elements) using the constrained random-phase-Approximation method adopting two distinct models: T2g-T2g and d-dp. For SrBO3 with B=Fe, Ru, and Ir, the t2g-T2g model faces critical challenges, as the low-energy Hamiltonian spanning t2g manifolds is ill-defined. The t2g-T2g model suggests that, for the early ABO3 series (B=d1-d3), the bare Coulomb interaction parameters V remain nearly constant due to the competition between extended t2g Wannier orbitals and bandwidth reduction. As the d-electron filling increases, both partially screened Coulomb interaction parameters U and fully screened Coulomb interaction parameters W decrease, which are attributed to enhanced eg-T2g and eg-p screenings. In contrast to the t2g-T2g model, the d-dp model effectively handles both early and late ABO3 perovskites and reveals different trends. Specifically, V varies inversely with the spreads of d orbitals. W reaches its minimum at the d3 occupancy due to an interplay between increasing d-orbital localization and increasing screening effects. An unusual trend is observed for U, with local maxima at both d1 and d4 occupations. This can be understood from two aspects: (1) the increasing full screening effects from d1 to d3 and (2) the strongest d-d and the weakest d-p screening effects near d4 for SrBO3. Our results underscore that the Coulomb interaction parameters not only depend on the choice of model frameworks, but also the interplay between the localization of d orbitals and screening strength, which are affected by d-orbital fillings and details of the band dispersion.