Abstract
Lieb lattice has been extensively studied to realize ferromagnetism due to its exotic flat band. However, its material realization has remained elusive; so far only artificial Lieb lattices have been made experimentally. Here, based on first-principles and tight-binding calculations, we discover that a recently synthesized two-dimensional sp2 carbon-conjugated covalent-organic framework (sp2c-COF) represents a material realization of a Lieb-like lattice. The observed ferromagnetism upon doping arises from a Dirac (valence) band in a non-ideal Lieb lattice with strong electronic inhomogeneity (EI) rather than the topological flat band in an ideal Lieb lattice. The EI, as characterized with a large on-site energy difference and a strong dimerization interaction between the corner and edge-center ligands, quenches the kinetic energy of the usual dispersive Dirac band, subjecting to an instability against spin polarization. We predict an even higher spin density for monolayer sp2c-COF to accommodate a higher doping concentration with reduced interlayer interaction.
Highlights
Lieb lattice has been extensively studied to realize ferromagnetism due to its exotic flat band
On the other hand, achieving ferromagnetism in organic materials has been an active subject for both fundamental interests in organic magnetism and practical applications as permanent magnets supplementary to their inorganic counterparts[12,13,14]
Based on density functional theory (DFT) calculation and tight-binding (TB) modeling, we discover that the sp2c-covalent-organic frameworks (COFs) represents a kind of Lieb lattice (Lieb-3) with “ideally” one flat band sitting between Dirac bands, arising from the edge-center and corner states, respectively
Summary
Lieb lattice has been extensively studied to realize ferromagnetism due to its exotic flat band. Based on density functional theory (DFT) calculation and tight-binding (TB) modeling, we discover that the sp2c-COF represents a kind of Lieb lattice (Lieb-3) with “ideally” one flat band sitting between Dirac bands, arising from the edge-center and corner states, respectively.
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