Origin of the orbital and spin orderings in rare-earth titanates

TL;DR

This paper reveals that in rare-earth titanates, subtle lattice distortions, rather than Jahn-Teller effects, drive the orbital and spin orderings, explaining their magnetic phase transitions.

Contribution

The study demonstrates that antipolar lattice motions induce effective Jahn-Teller-like distortions, providing a new understanding of orbital and spin orderings in titanates beyond traditional Jahn-Teller mechanisms.

Findings

Jahn-Teller distortion is negligible in titanates.

Antipolar motions produce effective Jahn-Teller-like effects.

Orbital and spin orders are driven by lattice distortions, not Jahn-Teller effects.

Abstract

Rare-earth titanates RTiO$_3$ are Mott insulators displaying a rich physical behavior, featuring most notably orbital and spin orders in their ground state. The origin of their ferromagnetic to antiferromagnetic transition as a function of the size of the rare-earth however remains debated. Here we show on the basis of symmetry analysis and first-principles calculations that although rare-earth titanates are nominally Jahn-Teller active, the Jahn-Teller distortion is negligible and irrelevant for the description of the ground state properties. At the same time, we demonstrate that the combination of two antipolar motions produces an effective Jahn-Teller-like motion which is the key of the varying spin-orbital orders appearing in titanates. Thus, titanates are prototypical examples illustrating how a subtle interplay between several lattice distortions commonly appearing in perovskites can produce orbital orderings and insulating phases irrespective of proper Jahn-Teller motions.