Correlation Energies in Distorted 3d-$t_{2g}$ Perovskite Oxides

TL;DR

This study evaluates how correlation energies influence magnetic stability in distorted 3d-$t_{2g}$ perovskite oxides using first-principles derived Hamiltonians and compares different correlation approximation methods.

Contribution

It introduces and compares two approximation methods for correlation energy calculations, improving understanding of magnetic structure stabilization in these materials.

Findings

Correlation effects improve agreement with experimental magnetic structures.

Nonlocal correlations stabilize certain magnetic states.

Local correlations are stronger at less distorted sites.

Abstract

Using an effective low-energy Hamiltonian derived from the first-principles electronic structure calculations for the narrow $t_{2g}$ bands of YTiO$_3$, LaTiO$_3$, YVO$_3$, and LaVO$_3$, we evaluate the contributions of the correlation energy ($E_C$) to the stability of different magnetic structures, which can be realized in these distorted perovskite oxides. We consider two approximations for $E_C$, which are based on the regular perturbation theory expansion around a nondegenerate Hartree-Fock ground state. One is the second order of perturbation theory, which allows us to compare the effects of local and nonlocal correlations. Another one is the local $t$-matrix approach, which allows us to treat some higher-order contributions to $E_C$. The correlation effects systematically improve the agreement with the experimental data and additionally stabilize the experimentally observed $G$- and $C$-type antiferromagnetic (AFM) structures in YVO$_3$ and LaVO$_3$, though the absolute magnitude of the stabilization energy is sensitive to the level of approximations and somewhat smaller in the $t$-matrix method. The nonlocal correlations additionally stabilize the ferromagnetic ground state in YTiO$_3$ and the $C$-type AFM ground state in LaVO$_3$. Amongst two inequivalent transition-metal sites in the monoclinic structure, the local correlations are stronger at the sites with the least distorted environment. Limitations of the regular perturbation-theory expansion for LaTiO$_3$ are also discussed.