Lattice Distortion and Magnetism of 3d-$t_{2g}$ Perovskite Oxides

TL;DR

This study uses first-principles calculations to understand how lattice distortions influence the magnetic properties of certain $t_{2g}$ perovskite oxides, revealing the importance of electron correlations and structural effects.

Contribution

It introduces a new downfolding method and combines multiple theoretical approaches to accurately model the magnetic structures of $t_{2g}$ perovskite oxides.

Findings

Crystal distortion constrains orbital states, favoring observed magnetic structures.

Correlation effects improve agreement with experimental magnetic data.

Failed to reproduce LaTiO$_3$'s magnetic ground state with current approximations.

Abstract

Several puzzling aspects of interplay of the experimental lattice distortion and the the magnetic properties of four narrow $t_{2g}$-band perovskite oxides (YTiO$_3$, LaTiO$_3$, YVO$_3$, and LaVO$_3$) are clarified using results of first-principles electronic structure calculations. First, we derive parameters of the effective Hubbard-type Hamiltonian for the isolated $t_{2g}$ bands using newly developed downfolding method for the kinetic-energy part and a hybrid approach, based on the combination of the random-phase approximation and the constraint local-density approximation, for the screened Coulomb interaction part. Then, we solve the obtained Hamiltonian using a number of techniques, including the mean-field Hartree-Fock (HF) approximation, the second-order perturbation theory for the correlation energy, and a variational superexchange theory. Even though the crystal-field splitting is not particularly large to quench the orbital degrees of freedom, the crystal distortion imposes a severe constraint on the form of the possible orbital states, which favor the formation of the experimentally observed magnetic structures in YTiO$_3$, YVO$_$, and LaVO$_3$ even at the HF level. Beyond the HF approximation, the correlations effects systematically improve the agreement with the experimental data. Using the same type of approximations we could not reproduce the correct magnetic ground state of LaTiO$_3$. However, we expect that the situation may change by systematically improving the level of approximations for dealing with the correlation effects.