Magnetic Phase Diagram of Two-dimensional Square Metal-Organic Frameworks under Electrostatic Gating*

Magnetism and magnetic phase transition induced by electrostatic gating of two-dimensional square metal-organic framework compounds was theoretically investigated. Results show that electrostatic gating can trigger phase transitions between homogeneous ferromagnetic and various spin-textured antiferromagnetic states. Hybridizations between transition-metal d-orbitals and conjugated π-orbitals in organic framework is evidenced by the electronic structure and Wannier function analysis. For compounds containing transition metal ions other than Mn, electronic structure around the Fermi energy is only slightly spin-splitted due to weak d-π hybridization and the magnetic interaction is of the Ruderman-Kittel-Kasuya-Yosida type. Mn-containing compounds exhibit strong d-π hybridization that drives spin-minority bands partially occupied, and the double-exchange model was adopted to understand the phase diagram in terms of carrier density.