Lattice Distortion and Magnetic Ground State of YTiO$_3$ and LaTiO$_3$

TL;DR

This paper investigates how lattice distortions influence the magnetic ground states of YTiO$_3$ and LaTiO$_3$, emphasizing the importance of considering multiple interactions beyond simple approximations.

Contribution

It introduces an accurate tight-binding parametrization of the $t_{2g}$ electronic structure and highlights the necessity of going beyond Hartree-Fock to understand these compounds.

Findings

Lattice distortions significantly affect the magnetic ground states.

Standard Hartree-Fock approximation is insufficient for these materials.

All relevant interactions must be treated on equal footing.

Abstract

Effects of lattice distortion on the magnetic ground state of YTiO$_3$ and LaiO$_3$ are investigated on the basis accurate tight-binding parametrization of the $t_{2g}$ electronic structure extracted from the local-density approximation. The complexity of these compounds is related with the fact that the $t_{2g}$-level splitting, caused by lattice distortions, is comparable with the energies of superexchange and spin-orbit interactions. Therefore, all these interactions are equally important and should be treated on an equal footing. The Hartree-Fock approximation fails to provide a coherent description simultaneously for YTiO$_3$ and LaTiO$_3$, and it is essential to go beyond.