Orbital-symmetry effects on magnetic exchange in open-shell nanographenes

Collective Magnetism of Spin Coronoid via On-Surface Synthesis

Polyradicals obtained from open-shell coronoids hold promise for applications in spintronics and quantum technologies due to the strong interactions between spins in fully fused cyclic systems. Coronoid synthesis has long been considered difficult due to the cyclization of nanographene. It becomes an immense challenge to synthesize open-shell coronoids since radicals appear only when the macrocycle size exceeds a critical value. Here we present an open-shell coronoid with six radicals achieved through an on-surface synthesis. This spin coronoid displays a collective spin state arising from both the nearest-neighbor exchange interaction and the next-nearest-neighbor exchange interaction of six unpaired π electrons along the conjugation pathways. The characterization of the spin excitation from the ground state to the excited state was carried out by using inelastic electron tunneling spectroscopy. Additionally, we show that the spin coronoid can be utilized as a nanoscale platform to achieve short antiferromagnetic spin-1/2 Heisenberg chains through tip manipulation. Our findings present a design strategy for creating coronoids with polyradicals, which could provide inspiration for fabrication of open-shell coronoid or cyclic spintronic systems.

A Route toward the On-Surface Synthesis of Organic Ferromagnetic Quantum Spin Chains

Engineering sublattice imbalance is an intuitive way to induce high-spin ground states in bipartite polycyclic conjugated hydrocarbons (PCHs). Such molecules can be employed as building blocks of quantum spin chains, which are outstanding platforms to study fundamental models in quantum magnetism. This is exemplified by recent reports on the bottom-up synthesis of antiferromagnetic spin chains that provided insights into paradigmatic quantum phenomena such as fractionalization. In contrast to antiferromagnetism, demonstration of ferromagnetic coupling between PCHs has been scarce. Previous attempts in this direction were limited by the formation of nonbenzenoid rings leading to spin quenching or the use of spacer motifs that weaken the magnitude of ferromagnetic exchange. Here, we demonstrate the on-surface synthesis of short ferromagnetic spin chains based on dibenzotriangulene, a triplet PCH. Our synthetic strategy centers on the concept of achieving a direct (without spacer motifs) majority-minority sublattice coupling between adjacent molecules. This leads to a global sublattice imbalance in spin chains scaling with the chain length and therefore a ferromagnetic ground state with a strong intermolecular ferromagnetic exchange. Through scanning probe measurements and quantum chemical calculations, we analyze the electronic and magnetic properties of ferromagnetic dimers and trimers of dibenzotriangulene and confirm their quintet and septet ground states, respectively, with an intermolecular ferromagnetic exchange of 7 meV. Furthermore, we elucidate the role of sublattice coupling on magnetism through complementary experiments on antiferromagnetic dibenzotriangulene dimers with majority-majority and minority-minority sublattice couplings. We expect our study to provide impetus for the design of organic ferromagnetic materials.

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, π ${\pi }$ -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 spinS = 1 ${S = 1}$ . By combining in-solution synthesis of rationally designed molecular precursors with on-surface synthesis, we successfully achieve covalently bondedS = 2 ${S = 2}$ triangulene dimers andS = 3 ${S = 3}$ 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 largerS = 3 ${S = 3}$ 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.

Atomically Precise Control of Topological State Hybridization in Conjugated Polymers

Realization of topological quantum states in carbon nanostructures has recently emerged as a promising platform for hosting highly coherent and controllable quantum dot spin qubits. However, their adjustable manipulation remains elusive. Here, we report the atomically accurate control of the hybridization level of topologically protected quantum edge states emerging from topological interfaces in bottom-up-fabricated π-conjugated polymers. Our investigation employed a combination of low-temperature scanning tunneling microscopy and spectroscopy, along with high-resolution atomic force microscopy, to effectively modify the hybridization level of neighboring edge states by the selective dehydrogenation reaction of molecular units in a pentacene-based polymer and demonstrate their reversible character. Density functional theory, tight binding, and complete active space calculations for the Hubbard model were employed to support our findings, revealing that the extent of orbital overlap between the topological edge states can be finely tuned based on the geometry and electronic bandgap of the interconnecting region. These results demonstrate the utility of topological edge states as components for designing complex quantum arrangements for advanced electronic devices.

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.

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.

Designer Spin Models in Tunable Two-Dimensional Nanographene Lattices

Motivated by recent experimental breakthroughs, we propose a strategy for designing two-dimensional spin-lattices with competing interactions that lead to nontrivial emergent quantum states. We consider S = 1/2 nanographenes with C3 symmetry as building blocks, and we leverage the potential to control both the sign and the strength of exchange with first neighbors to build a family of spin models. Specifically, we consider the case of a Heisenberg model in a triangle-decorated honeycomb lattice with competing ferromagnetic and antiferromagnetic interactions whose ratio can be varied in a wide range. On the basis of the exact diagonalization of both Fermionic and spin models, we predict a quantum phase transition between a valence bond crystal of spin singlets with triplon excitations living in a Kagomé lattice and a Néel phase of effective S = 3/2 in the limit of dominant ferromagnetic interactions.

Topological Structure Realized in Cove-Edged Graphene Nanoribbons via Incorporation of Periodic Pentagon Rings

Cove-edged zigzag graphene nanoribbons are predicted to show metallic, topological, or trivial semiconducting band structures, which are precisely determined by their cove offset positions at both edges as well as the ribbon width. However, due to the challenge of introducing coves into zigzag-edged graphene nanoribbons, only a few cove-edged graphene nanoribbons with trivial semiconducting bandgaps have been realized experimentally. Here, we report that the topological band structure can be realized in cove-edged graphene nanoribbons by embedding periodic pentagon rings on the cove edges through on-surface synthesis. Upon noncontact atomic force microscopy and scanning tunneling spectroscopy measurements, the chemical and electronic structures of cove-edged graphene nanoribbons with periodic pentagon rings have been characterized for different lengths. Combined with theoretical calculations, we find that upon inducing periodic pentagon rings the cove-edged graphene nanoribbons exhibit nontrivial topological structures. Our results provide insights for the design and understanding of the topological character in cove-edged graphene nanoribbons.

Atomic-Limit Mott Insulator in [4]Triangulene Frameworks

Triangulene, one unique class of zigzag-edged triangular graphene molecules, has attracted tremendous research interest. In this work, as an ultimate phase of the Mott insulator, we present the realization of the atomic-limit Mott insulator in experimentally synthesized [4]triangulene frameworks ([4]-TGFs) from first-principles calculations. The frontier molecular orbitals of the nonmagnetic [4]triangulene consist of three coupled corner modes. After the isolated [4]triangulene is assembled into [4]-TGF, one special enantiomorphic flat band is created through the coupling of these corner modes, which is identified to be a second-order topological insulator with half-filled topological corner states at the Fermi level. Moreover, [4]-TGF prefers an antiferromagnetic ground state under Hubbard interactions, which further splits these metallic zero-energy states into an atomic-limit Mott insulator with spin-polarized corners. Since the fractional filling of topological corner states is a smoking-gun signature of higher-order topology, our results demonstrate a universal approach to explore the atomic-limit Mott insulators in higher-order topological materials.

Cycl[2,2,4]azine-embedded non-alternant nanographenes containing fused antiaromatic azepine ring

The development of non-alternant nanographenes has attracted considerable attention due to their unique photophysical properties. Herein, we reported a novel aza-doped, non-alternant nanographene (NG) 1 by embedding the cycl[2,2,4]azine unit into the benzenoid NG framework. Single-crystal X-ray diffractometry suggests saddle or twisted nonplanar geometry of the entire backbone of 1 and coplanar conformation of the cycl[2,2,4]azine unit. DFT calculation together with solid structure indicates that NG 1 possesses significant local antiaromaticity in the azepine ring. By oxidative process or trifluoroacetic acid treatment, this nanographene can transform into a mono-radical cation, which was confirmed by UV/Vis absorption, 1H NMR, and electron paramagnetic resonance (EPR) spectroscopy. The antiaromaticity/aromaticity switching of the azepine ring on 1˙+ from 1 enables the high stability of this radical cation, which remained intact for over 1 day. Due to the electron-donating nature of the nitrogen and the unique electronic structure, NG 1 exhibits strong electron-donating properties, as proved by the intermolecular charge transfer towards C60 with a high association constant. Furthermore, selective modification of NG 1 was accomplished by Vilsmeier reaction, and the derivatives 7 and 8 with substituted benzophenone were obtained. The photophysical and electronic properties can be tuned by the introduction of different electronic groups in benzophenone.