# Orbiton-magnon interplay in the spin-orbital polarons of KCuF3 and LaMnO3

## TL;DR

This paper develops a quasi-analytical model showing that in KCuF3 and LaMnO3, hole propagation involves both orbiton and magnon excitations, with orbitons playing a dominant role, providing insights relevant for photoemission experiments.

## Contribution

It introduces a variational Green's function approach to analyze spin-orbital interactions, highlighting the dominant role of orbitons in hole propagation within these materials.

## Key findings

- Orbitons dominate hole propagation spectra.
- Magnons alone do not produce a full quasiparticle band.
- Qualitative scenario for photoemission in LaMnO3 is proposed.

## Abstract

We present a quasi-analytical solution of a spin-orbital model of KCuF$_{3}$, using the variational method for Green's functions. By analyzing the spectra for different partial bosonic compositions as well as the full solution, we show that hole propagation needs both orbiton and magnon excitations to develop, but the orbitons dominate the picture. We further elucidate the role of the different bosons by analyzing the self-energies for simplified models, establishing that because of the nature of the spin-orbital ground state, magnons alone do not produce a full quasiparticle band, in contrast to orbitons. Finally, using the electron-hole transformation between the $e_g$ states of KCuF$_3$ and LaMnO$_3$ we suggest the qualitative scenario for photoemission experiments in LaMnO$_3$.