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

Abstract: 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 $AB$O$3$ ($A$=Sr, Ca, and $B$=3$d$-5$d$ TM elements) using the constrained random-phase-approximation method adopting two distinct models: $t{2g}$-$t_{2g}$ and $d$-$dp$. For Sr$B$O$3$ with $B$=Fe, Ru, and Ir, the $t{2g}$-$t_{2g}$ model faces critical challenges, as the low-energy Hamiltonian spanning $t_{2g}$ manifolds is ill-defined. The $t_{2g}$-$t_{2g}$ model suggests that, for early $AB$O$3$ series ($B$=$d^1$-$d^3$), the bare Coulomb interaction parameters $V$ remain nearly constant due to the competition between extended $t{2g}$ 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 $e_g$-$t_{2g}$ and $e_g$-$p$ screenings. In contrast to the $t_{2g}$-$t_{2g}$ model, the $d$-$dp$ model effectively handles both early and late $AB$O$_3$ perovskites and reveals different trends. Specifically, $V$ varies inversely with the spreads of $d$-orbitals. $W$ reaches its minimum at the $d^3$ 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 $d^1$ and $d^4$ occupations. This can be understood from two aspects: (1) the increasing full screening effects from $d^1$ to $d^3$ and (2) the strongest $d$-$d$ and the weakest $d$-$p$ screening effects near $d^4$ for Sr$B$O$_3$.