Broken-symmetry magnetic phases in two-dimensional triangulene crystals

TL;DR

This paper develops a comprehensive theoretical framework for understanding magnetic phases in two-dimensional triangulene crystals, combining Hubbard and DFT calculations, and confirms predictions with experimental observations and spin wave analysis.

Contribution

It introduces a combined Hubbard and DFT approach to predict magnetic phases in triangulene crystals, including the effects of symmetry and flat bands, and validates these with spin wave spectra and experimental data.

Findings

Centrosymmetric crystals exhibit antiferromagnetic phases.

Non-centrosymmetric crystals show ferrimagnetic phases.

Spin wave spectra agree with Heisenberg model predictions.

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 non-centrosymmetric triangulene crystals. In all cases, DFT and mean-field Hubbard model predict the emergence of broken-symmetry antiferromagnetic (ferrimagnetic) phases for the centrosymmetric (non-centrosymmetric) crystals. This includes the special case of the [4,4]triangulene crystal, whose non-interacting 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 N\'eel 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 multi-configuration 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.