LAUSR

The electronic structure of ${\mathrm{BaFe}}_{2}{X}_{3}$ ($X$ = S and Se) and ${\mathrm{CsFe}}_{2}{\mathrm{Se}}_{3}$ 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 ${\mathrm{BaFe}}_{2}{X}_{3}$ exhibit two components, indicating that itinerant and localized Fe $3d$ sites coexist. Substantial x-ray linear dichroism is observed in polarization dependent spectra, indicating the existence of orbital order or fluctuation in the Fe ladder even above the N\'eel temperature ${T}_{\mathrm{N}}$. Direct exchange interaction along the legs of the Fe ladder stabilizes the orbital and antiferromagnetic orders in ${\mathrm{BaFe}}_{2}{\mathrm{S}}_{3}$, while the ferromagnetic molecular orbitals are realized between the rungs in ${\mathrm{CsFe}}_{2}{\mathrm{Se}}_{3}$.