Organic altermagnets based in two-dimensional nanographene frameworks

Abstract: Altermagnetism stands as a third type of collinear magnetic order, whose band structure combines a net zero magnetization with a non-relativistic spin-splitting caused by a broken time reversal symmetry. So far, the strategy to design platforms displaying altermagnetism has relied mostly on inorganic crystals with d-metals as spin centers, where a representative example is the two-dimensional square lattice with antiparallel D2h magnetic blocks related by a pi/2 rotation. Despite the fact that there is no strong requirement for the magnetic atoms to be metals, the construction of an altermagnetic framework with light elements like carbon is challenging due to symmetric constrictions. We show how it is possible to overcome this by including non-alternant rings in pi-conjugated nanographenes. More specifically, dibenzo[ef,kl]heptalene, an S = 1 pi-conjugated hydrocarbon consisting of a graph of two fused heptagons and hexagons, represents a suitable building block for an altermagnetic 2D crystal. In this work, we confirm this hypothesis with DFT calculations of the spin polarized band structure, presenting a spin compensated ground state with broken time reversal symmetry, and a d-wave symmetry of the first valence and conduction bands. Consistent results are obtained for covalent organic frameworks based on dibenzo[ef,kl]heptalene units connected by linkers, paving the way for the realization of organic altermagnetic materials.