Broken-symmetry magnetic phases in two-dimensional triangulene crystals

Abstract

We provide a comprehensive theory of magnetic phases in two-dimensional triangulene crystals, using both Hubbard model and density functional theory (DFT) calculations. We consider centrosymmetric and noncentrosymmetric triangulene crystals. In all cases DFT and the mean-field Hubbard model predict the emergence of broken-symmetry antiferromagnetic (ferrimagnetic) phases for the centrosymmetric (noncentrosymmetric) crystals. This includes the special case of the [4,4]triangulene crystal, whose noninteracting energy bands feature a gap with flat valence and conduction bands. We show how the lack of contrast between the local density of states of these bands, recently measured via scanning tunneling spectroscopy, is a natural consequence of a broken-symmetry Néel state that blocks intermolecular hybridization. Using random phase approximation, we also compute the spin wave spectrum of these crystals, including the recently synthesized [4,4]triangulene crystal. The results are in excellent agreement with the predictions of a Heisenberg spin model derived from multiconfiguration calculations for the unit cell. We conclude that experimental results are compatible with an antiferromagnetically ordered phase where each triangulene retains the spin predicted for the isolated species.