# Orbital order and fluctuations in the two-leg ladder materials BaFe$_2X_3$ ($X$ = S and Se) and CsFe$_2$Se$_3$

## TL;DR

This study investigates the electronic structure and orbital order in two-leg ladder iron-based materials BaFe$_2X_3$ ($X$ = S, Se) and CsFe$_2$Se$_3$ using x-ray spectroscopy, revealing coexistence of itinerant and localized electrons and distinct magnetic and orbital orders.

## Contribution

It provides new insights into the orbital order and fluctuations in Fe-ladder materials, highlighting the role of direct exchange interactions in stabilizing magnetic and orbital states.

## Key findings

- Coexistence of itinerant and localized Fe 3d electrons in BaFe$_2X_3$.
- Presence of orbital order or fluctuations above the N{é}el temperature.
- Different magnetic interactions stabilize orbital and magnetic orders in BaFe$_2$S$_3$ and CsFe$_2$Se$_3$.

## Abstract

The electronic structure of BaFe$_2X_3$ ($X$ = S and Se) and CsFe$_2$Se$_3$ in which two-leg ladders are formed by the Fe sites are studied by means of x-ray absorption and resonant inelastic x-ray scattering spectroscopy. The x-ray absorption spectra at the Fe L edges for BaFe$_2X_3$ exhibit two components, indicating that itinerant and localized Fe 3$d$ sites coexist. Substantial x-ray linear dichroism (XLD) is observed in polarization dependent spectra, indicating the existence of orbital order or fluctuation in the Fe-ladder even above the N\'{e}el temperature $T_N$. Direct exchange interaction along the legs of the Fe-ladder stabilizes the orbital and antiferromagnetic orders in BaFe$_2$S$_3$, while the ferromagnetic molecular orbitals are realized between the rungs in CsFe$_2$Se$_3$.