Orbital order and fluctuations in Mott insulators

TL;DR

This paper explores the mechanisms of orbital order and fluctuations in transition metal oxides, contrasting classical lattice-driven and quantum superexchange models, and discusses their impact on magnetic properties and correlations.

Contribution

It provides a comparative analysis of classical and quantum orbital behaviors in various oxides, highlighting the effects of lattice, superexchange, and spin-orbital coupling on magnetic states.

Findings

Lattice effects dominate in manganites like LaMnO3.

Quantum superexchange leads to frustrated orbital states in titanites and vanadates.

Spin-orbital coupling causes unusual magnetic correlations in layered cobaltates.

Abstract

Basic mechanisms controlling orbital order and orbital fluctuations in transition metal oxides are discussed. The lattice driven classical orbital picture, e.g. like in manganites LaMnO$_3$, is contrasted to the quantum behavior of orbitals in frustrated superexchange models as realised in pseudocubic titanites ATiO$_3$ and vanadates AVO$_3$. In YVO$_3$, the lattice and superexchange effects strongly compete -- this explains the extreme sensitivity of magnetic states to temperature and doping. Lifting the $t_{2g}$ orbital degeneracy by a relativistic spin-orbital coupling is considered on example of the layered cobaltates. We find that the spin-orbital mixing of low-energy states leads to unusual magnetic correlations in a triangular lattice of the CoO$_2$ parent compound. Finally, the magnetism of sodium-rich compounds Na$_{1-x}$CoO$_2$ is discussed in terms of a spin/orbital polaronic liquid.