# Spectral properties of spin-orbital polarons as a fingerprint of orbital order

## TL;DR

This paper investigates the spectral properties of spin-orbital polarons in transition metal oxides with orbital order, revealing effects like orbital-magnetic polaron crossover and proposing experimental verification methods.

## Contribution

It develops an effective spin-orbital superexchange model for $e_g^3$ systems and uses a semi-analytical magnon expansion to analyze spectral features and orbital order effects.

## Key findings

- Orbital to magnetic polaron crossover identified.
- Coupling between orbital and magnetic order demonstrated.
- Orbital order influences one-dimensional quantum spin liquid behavior.

## Abstract

Transition metal oxides are a rich group of materials with very interesting physical properties that arise from the interplay of the charge, spin, orbital, and lattice degrees of freedom. One interesting consequence of this, encountered in systems with orbital degeneracy, is the coexistence of long range magnetic and orbital order, and the coupling between them. In this paper we develop and study an effective spin-orbital superexchange model for $e_g^3$ systems and use it to investigate the spectral properties of a charge (hole) injected into the system, which is relevant for photoemission spectroscopy. Using an accurate, semi-analytical, magnon expansion method, we gain insight into various physical aspects of these systems and demonstrate a number of subtle effects, such as orbital to magnetic polaron crossover, the coupling between orbital and magnetic order, as well as the orbital order driving the system towards one-dimensional quantum spin liquid behavior. Our calculations also suggest a potentially simple experimental verification of the character of the orbital order in the system, something that is not easily accessible through most experimental techniques.