Anatomy of linear and nonlinear intermolecular exchange in S = 1 nanographene

Abstract

Nanographene triangulenes with an S = 1 ground state have been used as building blocks of topological antiferromagnetic Haldane spin chains. Using inelastic electron spectroscopy, it was found that the intermolecular exchange was described by the bilinear-biquadratic Hamiltonian. Starting from a Hubbard model, we analytically derive these effective spin interactions using perturbation theory, up to fourth order. For chains with more than two units, other interactions arise that entail second neighbor linear and three-site nonlinear exchange. We discuss the extension to general S = 1 molecules and give numerical results for the strength of the nonlinear exchange for several nanographenes.