Unraveling the orbital physics in a canonical orbital system KCuF$_3$

TL;DR

This study investigates orbital excitations in KCuF$_3$, revealing localized high-energy orbitons and dispersive magnetic excitations, suggesting orbiton dispersion is below detection limits and highlighting the role of Jahn-Teller effects.

Contribution

It provides experimental evidence of localized orbitons and dispersive magnetic excitations in KCuF$_3$, reconciling orbital physics with Jahn-Teller effects.

Findings

High-energy peaks are from localized $dd$ orbital excitations.

Low-energy excitations show clear dispersion matching two-spinon continuum.

Orbiton dispersion likely below current detection limits.

Abstract

We explore the existence of the collective orbital excitations, orbitons, in the canonical orbital system KCuF$_3$. Using the Cu $L_3$-edge resonant inelastic X-ray scattering we show that the non-dispersive high-energy peaks result from the Cu$^{2+}$ $dd$ orbital excitations. These high-energy modes show good agreement with the {\it ab-initio} quantum chemistry calculation based on a single cluster, indicating that the $dd$ excitations are highly localized. At the same time, the low-energy excitations present clear dispersion. They match extremely well with the two-spinon continuum following the comparison with Mueller Ansatz calculations. The localized $dd$ excitations and the observation of the strongly dispersive magnetic excitations suggest that orbiton dispersion is below the resolution detection limit. Our results can reconcile with the strong {\it local} Jahn-Teller effect in KCuF$_3$, which predominantly drives orbital ordering.