The electronic structure and magnetism of LiFeOFeSe are investigated using the first-principle calculations. The ground state is Nel antiferromagnetic (AFM) Mott insulating state for Fe1 with localized magnetism in LiFeO layer and striped AFM metallic state for Fe2 with itinerant magnetism in FeSe layer, accompanied with a weak interlayer AFM coupling between Fe1 and Fe2 ions, resulting in a coexistence of localized and itinerant magnetism. Moreover, the layered LiFeO is found to be more than an insulating block layer but responsible for enhanced AFM correlation in FeSe layer through the interlayer magnetic coupling. The interplay between the magnetisms of Fe1 and Fe2 introduces a control mechanism for spin fluctuations associated with superconductivity in iron-based superconductors.

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