Orbital Ordering and Orbital Fluctuations in Transition Metal Oxides

TL;DR

This paper reviews magnetic interactions and orbital fluctuations in transition metal oxides, highlighting differences between $t_{2g}$ and $e_g$ systems, and discussing the conditions for orbital liquid states.

Contribution

It provides a comparative analysis of orbital ordering and fluctuations in $t_{2g}$ and $e_g$ systems within spin-orbital models, emphasizing the role of quantum fluctuations.

Findings

Dimerization tendency in $t_{2g}$ systems confirmed

Orbital liquid states are more prevalent in $t_{2g}$ systems

Orbital liquid states in manganites are doping-dependent

Abstract

We summarize some characteristic features of the frustrated magnetic interactions in spin-orbital models adequate for cubic transition metal oxides with orbital degeneracy. A generic tendency towards dimerization, found already in the degenerate Hubbard model, is confirmed for $t_{2g}$ but not for $e_g$ systems. In the $t_{2g}$ case the quantum orbital fluctuations are more pronounced and contribute to a stronger competition between different magnetic and orbital states. Therefore the orbital liquid states exist in some undoped $t_{2g}$ systems, while in the manganites such states can be triggered only by doping.