Abstract
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 single crytal neutron diffraction technique. 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
of 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 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 herald for superconductivity emerging at higher pressures.
