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Based on a hybrid interlayer coupling mechanism, we study the coexistence ofsuperconductivity (SC) and antiferromagnetism (AFM) in trilayer cuprates. Byintroducing an interlayer magnetic scattering term, we solve the multilayer$t{-}J$ model with Josephson coupling under the framework of Gutzwillerprojection. We show that both the SC and AFM orders in the multilayered systemare enhanced and the range of AFM order is extended. The layer configuration ofd-wave pairing gap and AFM order further plays an essential role in determiningthe interlayer magnetic and superconducting coupling phase diagram of suchmultilayered systems. Abrupt phase transitions between correlated statescarrying distinct configurational symmetries are unveiled by tuning the dopinglevel and/or the tunneling strengths.

Coexistence of Enhanced Superconductivity and Antiferromagnetism: Possible Correlated Phase Transitions in Trilayer High-Tc Cuprates