Half-Metallic Ferromagnetism in Radical-Bridged Metal-Organic Frameworks

Electrically conductive metal-organic frameworks (MOFs) are an emerging class of materials exhibiting not only tunable chemical functionality but also efficient charge carrier transport. Among them, radical-bridged Cu-based MOFs represent a specific category with intriguing magnetic properties. Here, based on density functional theory calculations, we systematically unravel the interplay between the electronic and magnetic properties of monolayers of two-dimensional (2D) MOFs consisting of Cu²⁺ ions and organic linkers made of deprotonated hexahydroxybenzene (HHB), 2,3,6,7,10,11-hexahydroxytriphenylene (HHTP), or 2,3,8,9,14,15-hexahydroxyltribenzocyclyne (HHTC). A number of spin configurations of the corresponding Cu₃(HHX)₂ MOFs, where X = B, TP, or TC, are examined. Importantly, the ferromagnetic state is found to be the most stable, followed by the up-up-down state and antiferromagnetic states, while the nonmagnetic state is the least stable. In the ferromagnetic state, the monolayers display half-metallic characteristics, with the densities of states across the Fermi level derived from one spin channel, while the other spin channel is semiconducting. More importantly, while the electronic states near the Fermi level are predominately derived from the organic linkers, the magnetic characteristics are associated with the contributions of both ligand radicals and unpaired Cu-3d electrons present in the MOF monolayer. Remarkably, the Fermi velocity in the gapless spin channel of the Cu₃(HHTC)₂ MOF is estimated to be 1.9 × 10⁵ m/s, which is about one-quarter that of graphene. The Dirac half-metallic features and high Fermi velocities of monolayers of Cu₃(HHX)₂ MOFs make them promising organic materials for electronic and spintronic applications.