Enhancement of antiferromagnetic correlations below superconducting transition temperature in bilayer superconductors

Motivated by the recent experiment in multilayered cuprate superconductors reporting the enhancement of antiferromagnetic order below the superconducting transition temperature, we study the proximity effect of the antiferromagnetic correlation in a bilayer system and also examine the possibility of a coexistence of antiferromagnetic order and superconductivity. We present the result of mean field theory that is consistent with the experiment and supports the proximity effect picture.