Orbital ordering and frustrations

TL;DR

This paper explores the origins of orbital ordering and frustration in transition metal compounds, analyzing how lattice geometry influences ground states like orbital liquids and ordered phases.

Contribution

It provides a detailed discussion of the mechanisms behind orbital frustration and potential ground states in cubic and triangular lattice systems.

Findings

Frustration arises from exchange interactions in orbitally degenerate systems.

Possible ground states include disordered orbital liquids and order-from-disorder phases.

Lattice geometry critically influences the nature of orbital ordering.

Abstract

An orbital ordering occurs in many transition metal compounds with Jahn-Teller ions and plays an important role in these materials. At the same time, exchange interactions in orbitally degenerate systems are inherently frustrated, even in materials with simple crystal lattices. We discuss the origin of this frustration, considering in detail materials with a cubic and triangular lattice of transition metal ions. We also discuss possible types of ground states of such systems, e.g., disordered orbital liquids and ordering due to the order-from-disorder mechanism.