  Recent discovery of superconducting (SC) ternary iron selenides has block
antiferromagentic (AFM) long range order. Many experiments show possible
mesoscopic phase separation of the superconductivity and antiferromagnetism,
while the 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
due to the proximity effect within a phase separation scenario. We use a
two-orbital model to study the proximity effect on a layer of 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
semi-quantitatively. The suppression of the magnetic moment due to the SC
proximity effect is found to be more pronounced in the d-wave superconductivity
and may be enhanced by the frustrated structure of the block AFM state.
