The quasi-one-dimensional spin ladder compounds, BaFe$_2$S$_3$ and BaFe$_2$Se$_3$, are investigated by infrared spectroscopy and density functional theory (DFT) calculations. We observe strong anisotropic electronic properties and an optical gap in the leg direction that is gradually filled above the antiferromagnetic (afm) ordering temperature, turning the systems into a metallic phase. Combining the optical data with the DFT calculations we associate the optical gap feature with the $p$-$d$ transition that appears only in the afm ordered state. Hence, the insulating ground state along the leg direction is attributed to Slater physics rather than Mott-type correlations.
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