It has been recently discovered that the superconducting (SC) ternary iron selenides have a block antiferromagnetic (AFM) long-range order. Many experiments show a possible mesoscopic phase separation of the superconductivity and antiferromagnetism, while a neutron experiment reveals a sizable suppression of magnetic moment due to the superconductivity, indicating a possible phase coexistence. Here we propose that the observed suppression of the magnetic moment may be explained by the proximity effect within a phase-separation scenario. We use a two-orbital model to study the proximity effect on a layer of the block AFM state induced by neighboring SC layers via an interlayer tunneling mechanism. We argue that the proximity effect in ternary Fe selenides should be large because of the large interlayer coupling and weak electron correlation. The result of our mean-field theory is compared with the neutron experiments semiquantitatively. The suppression of the magnetic moment due to the SC proximity effect is found to be more pronounced in d-wave superconductivity and may be enhanced by the frustrated structure of the block AFM state.
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