3:15 PM - QN01.16.02
Emergence of an Antiferromagnetic Mott Insulating Phase in Hexagonal π-Conjugated Covalent Organic Frameworks
Hong Li1,Simil Thomas1,Jean-Luc Bredas1
Georgia Institute of Technology1
With rapid advances in the synthesis and characterization of two-dimensional (2D) π-conjugated organic covalent frameworks (COFs), the search for 2D COF-based materials that can display –like graphene– a Dirac cone at the Fermi level, is attracting much interest. Radical-carrying carbon-based hexagonal COFs, due to their similarity to graphene, are natural choice. While there are recent theoretical reports 1-3 of Dirac-cone electronic structures in such 2D COFs, the chemical, structural, and electronic stabilities of these systems have not been fully addressed.
Here, we discuss a series of 2D COFs consisting of three radical-carrying building blocks and various linkers, and investigate their relative stabilities in different electronic configurations and geometrical structures, including closed-shell semimetal and semiconducting electronic configurations, and open-shell ferromagnetic and antiferromagnetic configurations. Density functional theory (DFT) calculations are carried out at the global-hybrid PBE0 level to optimize the geometric structures and determine the electronic band structures and to estimate the Hubbard on-site repulsion parameter U and inter-site electronic coupling t. In contrast to the conclusions of earlier studies 1-3 (which either did not consider spin-polarized configurations or attributed the presence of magnetically ordered phases to a symmetry lowering of the COF lattice geometry from hexagonal to trigonal), we find that the most stable phase of these 2D COFs is in fact an antiferromagnetic (AFM) Mott insulating phase with the same lattice symmetry as in the semimetal (SM) phase.
To rationalize the appearance of the AFM phase, the systems can be cast as “effective graphene lattices” 4 and described in the context of the standard Hubbard model. Importantly, earlier Quantum Monte Carlo (QMC) studies of a half-filled honeycomb lattice, based on the Hubbard model, have revealed a rich phase diagram spanning from nonmagnetic semimetal to spin-liquid and to insulating antiferromagnet (AFM), as a function of the U/t ratio.4 The QMC investigations 4 indicate that the insulating AFM phase is the most stable when U/t ≥ 4.3, while the nonmagnetic semimetal phase appears when U/t ≤ 3.5 (as is the case in graphene), and a disordered spin-liquid phase is predicted in the intermediate U/t range (3.5 ≤ U/t ≤ 4.3). As a function of the nature of the building blocks and linkers, the U/t ratios in our 2D COFs evolve between ca. 16 and 6 (with U estimated to be in the 2.2-1.3 eV range and t, in the 0.1- 0.2 eV), which places all our 2D COFs on the AFM side of the phase diagram. Interestingly, 2D COFs with a U/t ratio approaching 6, appear close to the boundary between the antiferromagnetic and spin-liquid phases. Further molecular design, aimed at increasing the electronic coupling t and decreasing the on-site repulsion U, can thus be expected to push the U/t ratio onto the spin-liquid phase and even the semimetal phase.
1. Adjizian, J.-J.; Briddon, P.; Humbert, B.; Duvail, J.-L.; Wagner, P.; Adda, C.; Ewels, C., Nat. Commun. 2014, 5, 5842.
2. Alcón, I.; Viñes, F.; Moreira, I. d. P. R.; Bromley, S. T., Nat. Commun. 2017, 8 (1), 1957.
3. Jing, Y.; Heine, T., J. Am. Chem. Soc. 2018. DOI: 10.1021/jacs.8b09900
4. Meng, Z. Y.; Lang, T. C.; Wessel, S.; Assaad, F. F.; Muramatsu, A., Nature 2010, 464, 847.