Theory of intermolecular exchange in coupled spin-1/2 nanographenes

TL;DR

This paper investigates the microscopic mechanisms behind intermolecular exchange in open-shell nanographenes, revealing three contributing processes and their dependence on Coulomb interactions, with implications for magnetic properties of coupled spin systems.

Contribution

It identifies and analyzes three distinct exchange mechanisms in coupled nanographenes, including Coulomb-driven superexchange, and computes their effects using advanced multi-configurational methods.

Findings

Coulomb-driven superexchange can be ferromagnetic or antiferromagnetic.

Three exchange mechanisms are identified: Hund's ferromagnetic, superexchange, and Coulomb-driven superexchange.

The study uses multi-configurational methods to quantify exchange energies in phenalenyl triangulenes.

Abstract

Open-shell nanographenes can be covalently bonded and still preserve their local moments, forming interacting spins lattices. In the case of benzenoid nanographenes, the Ovchinnikov-Lieb rules anticipate the spin of the ground state of the superstructure, and thereby the sign of the intermolecular exchange. Here we address the underlying microscopic mechanisms for intermolecular exchange in this type of system. We find that, in general, three different mechanisms contribute. First, Hund's ferromagnetic exchange that promotes ferromagnetic interactions of electrons in overlapping orbitals. Second, superexchange driven by intermolecular hybridization, identical to Anderson kinetic exchange, which is a decreasing function of the Hubbard-$U$ energy scale, and is always antiferromagnetic. Third, a Coulomb-driven superexchange, that increases as a function of $U$, and involves virtual excitation of excited molecular orbitals that are extended over the entire structure. We find that Coulomb-driven superexchange can be either ferro or antiferromagnetic, accounting for Ovchinnikov-Lieb rules. We compute these exchange energies for the case of coupled $S=1/2$ phenalenyl triangulenes, using multi-configurational methods both with Hubbard and extended Hubbard models, thereby addressing the influence of long-range Coulomb interactions on the exchange interactions.