The pressure effects on the antiferromagentic orders in iron-based ladder compounds CsFe2Se3 and BaFe2S3 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 CsFe2Se3 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 BaFe2S3, undergoes a quantum phase transition where an abrupt increase of Néel temperature by more than 50% occurs at about 1 GPa, accompanied by a jump in the ordered moment. With its spin structure unchanged, BaFe2S3 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.PACS numbers: 74.25. Ha, The antiferromagnetic (AF) phase adjacent to superconductivity (SC) is so richly faceted that its microscopic origin still eludes a unified description. Significant variation of the ordered magnetic moment and the underlying degree of electron correlations lie at the heart of the heated dispute [1][2][3]. The static AF phase in the parent compounds has roughly two categories: stripe magnetism and block magnetism. The former includes the single stripe in LaFeAsO, BaFe 2 As 2 , NaFeAs, and double stripe in FeTe [4]. Spin block order was found in the vacancy-ordered K 2 Fe 4 Se 5 (245) [5]. These materials all have a plane of Fe square lattice once deemed indispensable for the occurence of SC. The recent successful induction of SC by pressure in the ladder compound BaFe 2 S 3 [6,7] has introduced a quasi-one dimensional structural motif for the studies of iron-based superconductors and a parallel to the quasi-1D cuprates [8]. As if the layers of the superconducting Fe square lattice were sliced up and staggered, the AFe 2 X 3 (A = K, Rb, Cs or Ba and X = Chalcogens) compounds consist of ladders of two-leg Fechains with edge-sharing tetrahedra of anions (Se or S) surrounding each Fe site, as shown in Figure 1(a). The reduced dimensionality leads to modified bandwidth [9], Fermi surface topology, and provides a rare insight into critical open issues such as the nature of the AF order.Both stripe-and block-types of AF orders are hosted by the Fe-ladder compounds. BaFe 2 S 3 and CsFe 2 Se 3 , with the CsCu 2 Cl 3 type structure (Cmcm space group), have the stripe AF order where the ferromagnetic (FM) spin pairs on the same ladder rung correlate antiferromagnetically along the leg direction. The ordered moment lies in the rung-direction in BaFe 2 S 3 (Fig.1(b)) [6] and the leg-direction in CsFe 2 Se 3 (Fig.1(c)) [10]. In BaFe 2 Se 3 , the distorted FeSe 4 tetrahedron lose the Ccentering and result in the lowered symmetry P nma [11]. The magnetic structure consists of blocks of 4 FM spins forming alternating AF pattern along the leg direction [12]. The magnetic excitations in BaFe 2 Se 3 fits the description of localized spins and...