Coexistence of Dirac Fermions and Magnons in a Layered Two-Dimensional Semiquinoid Metal-Organic Framework

Low-dimensional magnetism lies at the heart of numerous novel phenomena in condensed matter physics, including high-Tc superconductivity, topological quantum spin liquids, and quantum criticality. Central to designing quantum magnets is understanding and manipulating the delicate interplay between spin and orbital motions of an electron, and their coupling to the lattice. Typically, magnetic states are controlled and fine-tuned by strain, light, gating, proximity and moiré heterostructuring, however, many of these external perturbations are hard to implement within fabricated devices. Metal-organic frameworks provide a new route to overcome this challenge by building new magnetic materials with programmable intrinsic properties. By combining DFT and DMRG approaches, we find the two-dimensional metal-semiquinoid framework to host a host a rich landscape of electronic and magnetic properties for various 3d transition metals, including Dirac semimetals and flat band magnetic insulators, along with Dirac-like and nodal-ring spin excitations. Multiple compounds exhibit the coexistence of Dirac fermions and magnons, thereby providing a unique platform to examine non-trivial fermion-magnon coupled band topologies.