Beyond Spin Models in Orbitally Degenerate Open-Shell Nanographenes.

The study of open-shell nanographenes has relied on a paradigm where spins are the only low-energy degrees of freedom. Here we show that some nanographenes can host low-energy excitations that include strongly coupled spin and orbital degrees of freedom. The key ingredient is the existence of orbital degeneracy, as a consequence of leaving the benzenoid/half-filling scenario. We analyze the case of nitrogen-doped triangulenes, using both density-functional theory and Hubbard model multiconfigurational and random-phase approximation calculations. We find a rich interplay between orbital and spin degrees of freedom that confirms the need to go beyond the spin-only paradigm, opening a new avenue in this field of research.

Conformational Tuning of Magnetic Interactions in Coupled Nanographenes.

Phenalenyl (C13H9) is an open-shell spin-1/2 nanographene. Using scanning tunneling microscopy (STM) inelastic electron tunneling spectroscopy (IETS), covalently bonded phenalenyl dimers have been shown to feature conductance steps associated with singlet-triplet excitations of a spin-1/2 dimer with antiferromagnetic exchange. Here, we address the possibility of tuning the magnitude of the exchange interactions by varying the dihedral angle between the two molecules within a dimer. Theoretical methods ranging from density functional theory calculations to many-body model Hamiltonians solved within different levels of approximation are used to explain STM-IETS measurements of phenalenyl dimers on a hexagonal boron nitride (h-BN)/Rh(111) surface, which exhibit signatures of twisting. By means of first-principles calculations, we also propose strategies to induce sizable twist angles in surface-adsorbed phenalenyl dimers via functional groups, including a photoswitchable scheme. This work paves the way toward tuning magnetic couplings in carbon-based spin chains and two-dimensional lattices.

Magnetic Excitations in Ferromagnetically Coupled Spin-1 Nanographenes.

In the pursuit of high-spin building blocks for the formation of covalently bonded 1D or 2D materials with controlled magnetic interactions, $\pi$-electron magnetism offers an ideal framework to engineer ferromagnetic interactions between nanographenes. As a first step in this direction, we explore the spin properties of ferromagnetically coupled triangulenes -- triangular nanographenes with spin $S = 1$. By combining in-solution synthesis of rationally designed molecular precursors with on-surface synthesis, we successfully achieve covalently bonded $S = 2$ triangulene dimers and $S = 3$ trimers on Au(111). Starting with the triangulene dimer, we meticulously characterize its low-energy magnetic excitations using inelastic electron tunneling spectroscopy (IETS). IETS reveals conductance steps corresponding to a quintet-to-triplet excitation, and a zero-bias peak resulting from higher-order spin-spin scattering of the five-fold degenerate ferromagnetic ground state. The Heisenberg model captures the key parameters of inter-triangulene ferromagnetic exchange, and its successful extension to the larger $S = 3$ system validates the model's accuracy. We anticipate that incorporating ferromagnetically coupled building blocks into the repertoire of magnetic nanographenes will unlock new possibilities for designing carbon nanomaterials with complex magnetic ground states.

Observation of fractional edge excitations in nanographene spin chains.

Fractionalization is a phenomenon in which strong interactions in a quantum system drive the emergence of excitations with quantum numbers that are absent in the building blocks. Outstanding examples are excitations with charge e/3 in the fractional quantum Hall effect1,2, solitons in one-dimensional conducting polymers3,4 and Majorana states in topological superconductors5. Fractionalization is also predicted to manifest itself in low-dimensional quantum magnets, such as one-dimensional antiferromagnetic S = 1 chains. The fundamental features of this system are gapped excitations in the bulk6 and, remarkably, S = 1/2 edge states at the chain termini7-9, leading to a four-fold degenerate ground state that reflects the underlying symmetry-protected topological order10,11. Here, we use on-surface synthesis12 to fabricate one-dimensional spin chains that contain the S = 1 polycyclic aromatic hydrocarbon triangulene as the building block. Using scanning tunnelling microscopy and spectroscopy at 4.5 K, we probe length-dependent magnetic excitations at the atomic scale in both open-ended and cyclic spin chains, and directly observe gapped spin excitations and fractional edge states therein. Exact diagonalization calculations provide conclusive evidence that the spin chains are described by the S = 1 bilinear-biquadratic Hamiltonian in the Haldane symmetry-protected topological phase. Our results open a bottom-up approach to study strongly correlated phases in purely organic materials, with the potential for the realization of measurement-based quantum computation13.