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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 ofx-ray absorption and resonant inelastic x-ray scattering spectroscopy. Thex-ray absorption spectra at the Fe L edges for BaFe$_2X_3$ exhibit twocomponents, indicating that itinerant and localized Fe 3$d$ sites coexist.Substantial x-ray linear dichroism (XLD) is observed in polarization dependentspectra, indicating the existence of orbital order or fluctuation in theFe-ladder even above the N\'{e}el temperature $T_N$. Direct exchangeinteraction along the legs of the Fe-ladder stabilizes the orbital andantiferromagnetic orders in BaFe$_2$S$_3$, while the ferromagnetic molecularorbitals are realized between the rungs in CsFe$_2$Se$_3$.

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