The pressure effects on the antiferromagentic orders in iron-based ladder compounds CsFe$_2$Se$_3$ and BaFe$_2$S$_3$ have been studied using neutron diffraction. With identical crystal structure and similar magnetic structures, the two compounds exhibit highly contrasting magnetic behaviors under moderate external pressures. In CsFe$_2$Se$_3$ the ladders are brought much closer to each other by pressure, but the stripe-type magnetic order shows no observable change. In contrast, the stripe order in BaFe$_2$S$_3$, undergoes a quantum phase transition where an abrupt increase of N$acute{e}$el temperature by more than 50$%$ occurs at about 1 GPa, accompanied by a jump in the ordered moment. With its spin structure unchanged, BaFe$_2$S$_3$ enters an enhanced magnetic phase that bears the characteristics of an orbital selective Mott phase, which is the true neighbor of superconductivity emerging at higher pressures.
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