Orbital order in classical models of transition-metal compounds

TL;DR

This paper investigates classical orbital models of transition-metal compounds, revealing that they exhibit long-range order at low temperatures through an 'order by disorder' mechanism, implying similar ordering in quantum counterparts.

Contribution

It demonstrates the presence of orbital ordering in classical models and suggests quantum models likely share this ordering despite spin order absence.

Findings

Classical orbital models show long-range order at low temperatures.

Order by disorder mechanism drives the orbital ordering.

Quantum models are expected to exhibit similar orbital order.

Abstract

We study the classical 120-degree and related orbital models. These are the classical limits of quantum models which describe the interactions among orbitals of transition-metal compounds. We demonstrate that at low temperatures these models exhibit a long-range order which arises via an "order by disorder" mechanism. This strongly indicates that there is orbital ordering in the quantum version of these models, notwithstanding recent rigorous results on the absence of spin order in these systems.