Carbon-based nanostructures as a versatile platform for tunableπ-magnetism

Observation of SOMO-HOMO Inversion in a Neutral Polycyclic Conjugated Hydrocarbon

We report the generation of a nonbenzenoid polycyclic conjugated hydrocarbon, which consists of a biphenyl moiety substituted by indenyl units at the 4,4' positions, on ultrathin sodium chloride films by tip-induced chemistry. Single-molecule characterization by scanning tunneling and atomic force microscopy reveals an open-shell biradical ground state with a peculiar electronic configuration wherein the singly occupied molecular orbitals (SOMOs) are lower in energy than the highest occupied molecular orbital (HOMO).

Regioselective On-Surface Synthesis of [3]Triangulene Graphene Nanoribbons

The integration of low-energy states into bottom-up engineered graphene nanoribbons (GNRs) is a robust strategy for realizing materials with tailored electronic band structure for nanoelectronics. Low-energy zero-modes (ZMs) can be introduced into nanographenes (NGs) by creating an imbalance between the two sublattices of graphene. This phenomenon is exemplified by the family of [n]triangulenes (n ∈ N ). Here, we demonstrate the synthesis of [3]triangulene-GNRs, a regioregular one-dimensional (1D) chain of [3]triangulenes linked by five-membered rings. Hybridization between ZMs on adjacent [3]triangulenes leads to the emergence of a narrow band gap, Eg,exp ∼ 0.7 eV, and topological end states that are experimentally verified using scanning tunneling spectroscopy. Tight-binding and first-principles density functional theory calculations within the local density approximation corroborate our experimental observations. Our synthetic design takes advantage of a selective on-surface head-to-tail coupling of monomer building blocks enabling the regioselective synthesis of [3]triangulene-GNRs. Detailed ab initio theory provides insights into the mechanism of on-surface radical polymerization, revealing the pivotal role of Au-C bond formation/breakage in driving selectivity.

Delocalized spin states at zigzag termini of armchair graphene nanoribbon

Using scanning tunneling microscopy and spectroscopy we demonstrate a revival of magnetism in 7-armchair nanoribbon by unpassivated atoms at the termini. Namely, a pair of intense Kondo resonances emerges at the peripheries of zigzag terminus revealing the many-body screening effects of local magnetic moments. Although Kondo resonance originates from a missing local orbital, it extends to a distance of 2.5 nm along the edge of the ribbon. The results are complemented by density functional theory calculations which suggest a possible coupling between Kondo states despite screening effects of substrate electrons. These findings indicate a possibility to restore intrinsic magnetic ordering in graphene nanoribbon without major structural modifications.

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.

Tunable Magnetic Coupling in Graphene Nanoribbon Quantum Dots

Carbon-based quantum dots (QDs) enable flexible manipulation of electronic behavior at the nanoscale, but controlling their magnetic properties requires atomically precise structural control. While magnetism is observed in organic molecules and graphene nanoribbons (GNRs), GNR precursors enabling bottom-up fabrication of QDs with various spin ground states have not yet been reported. Here the development of a new GNR precursor that results in magnetic QD structures embedded in semiconducting GNRs is reported. Inserting one such molecule into the GNR backbone and graphitizing it results in a QD region hosting one unpaired electron. QDs composed of two precursor molecules exhibit nonmagnetic, antiferromagnetic, or antiferromagnetic ground states, depending on the structural details that determine the coupling behavior of the spins originating from each molecule. The synthesis of these QDs and the emergence of localized states are demonstrated through high-resolution atomic force microscopy (HR-AFM), scanning tunneling microscopy (STM) imaging, and spectroscopy, and the relationship between QD atomic structure and magnetic properties is uncovered. GNR QDs provide a useful platform for controlling the spin-degree of freedom in carbon-based nanostructures.

Highly entangled polyradical nanographene with coexisting strong correlation and topological frustration

Open-shell nanographenes exhibit unconventional π-magnetism arising from topological frustration or strong electron-electron interaction. However, conventional design approaches are typically limited to a single magnetic origin, which can restrict the number of correlated spins or the type of magnetic ordering in open-shell nanographenes. Here we present a design strategy that combines topological frustration and electron-electron interactions to fabricate a large fully fused 'butterfly'-shaped tetraradical nanographene on Au(111). We employ bond-resolved scanning tunnelling microscopy and spin-excitation spectroscopy to resolve the molecular backbone and reveal the strongly correlated open-shell character, respectively. This nanographene contains four unpaired electrons with both ferromagnetic and anti-ferromagnetic interactions, harbouring a many-body singlet ground state and strong multi-spin entanglement, which is well described by many-body calculations. Furthermore, we study the magnetic properties and spin states in the nanographene using a nickelocene magnetic probe. The ability to imprint and characterize many-body strongly correlated spins in polyradical nanographenes paves the way for future advancements in quantum information technologies.

On-Surface Synthesis of a Radical 2D Supramolecular Organic Framework

The design of supramolecular organic radical cages and frameworks is one of the main challenges in supramolecular chemistry. Their interesting material properties and wide applications make them very promising for (photo)redox catalysis, sensors, or host-guest spin-spin interactions. However, the high reactivity of radical organic systems makes the design of such supramolecular radical assemblies challenging. Here, we report the on-surface synthesis of a purely organic supramolecular radical framework on Au(111), by combining supramolecular and on-surface chemistry. We employ a tripodal precursor, functionalized with 7-azaindole groups that, catalyzed by a single gold atom on the surface, forms a radical molecular product constituted by a π-extended fluoradene-based radical core. The radical products self-assemble through hydrogen bonding, leading to extended 2D domains ordered in a Kagome-honeycomb lattice. This approach demonstrates the potential of on-surface synthesis for developing 2D supramolecular radical organic chemistry.

Five-Membered Rings Create Off-Zero Modes in Nanographene

The low-energy electronic structure of nanographenes can be tuned through zero-energy π-electron states, typically referred to as zero-modes. Customizable electronic and magnetic structures have been engineered by coupling zero-modes through exchange and hybridization interactions. Manipulation of the energy of such states, however, has not yet received significant attention. We find that attaching a five-membered ring to a zigzag edge hosting a zero-mode perturbs the energy of that mode and turns it into an off-zero mode: a localized state with a distinctive electron-accepting character. Whereas the end states of typical 7-atom-wide armchair graphene nanoribbons (7-AGNRs) lose their electrons when physisorbed on Au(111) (due to its high work function), converting them into off-zero modes by introducing cyclopentadienyl five-membered rings allows them to retain their single-electron occupation. This approach enables the magnetic properties of 7-AGNR end states to be explored using scanning tunneling microscopy (STM) on a gold substrate. We find a gradual decrease of the magnetic coupling between off-zero mode end states as a function of GNR length, and evolution from a more closed-shell to a more open-shell ground state.

Length-Dependent Magnetic Evolution of Anthenes on Au(111)

Nanographenes with zigzag edges, for example, anthenes, exhibit a unique nonbonding π-electron state, which can be described as a spin-polarized edge state that yields specific magnetic ground state. However, prior researches on the magnetism of anthenes with varying lengths on a surface is lacking. This study systematically fabricated anthenes with inherent zigzag carbon atoms of different lengths ranging from bisanthene to hexanthene. Their magnetic evolution on the Au(111) surface was analyzed through bond-resolved scanning probe techniques and density functional theory calculations. The analyses revealed a transition in magnetic properties associated with the length of the anthenes, arising from the imbalance between hybridization energy and the Coulomb repulsion between valence electrons. With the increasing length of the anthenes, the ground state transforms gradually from a closed-shell to an antiferromagnetic open-shell singlet, exhibiting a weak exchange coupling of 4 meV and a charge transfer-induced doublet. Therefore, this study formulated a chemically tunable platform to explore size-dependent π magnetism at the atomic scale, providing a framework for research in organic spintronics.

Emergence of π-Magnetism in Fused Aza-Triangulenes: Symmetry and Charge Transfer Effects

On-surface synthesis has paved the way toward the fabrication and characterization of conjugated carbon-based molecular materials that exhibit π-magnetism such as triangulenes. Aza-triangulene, a nitrogen-substituted derivative, was recently shown to display rich on-surface chemistry, offering an ideal platform to investigate structure-property relations regarding spin-selective charge transfer and magnetic fingerprints. Herein, we study electronic changes upon fusion of single molecules into larger dimeric derivatives. We show that the closed-shell structure of aza-triangulene on Ag(111) leads to closed-shell dimers covalently coupled through sterically accessible carbon atoms. Meanwhile, its open-shell structure on Au(111) leads to coupling via atoms displaying a high spin density, resulting in symmetric or asymmetric products. Interestingly, whereas all dimers on Au(111) exhibit similar charge transfer properties, only asymmetric ones show magnetic fingerprints due to spin-selective charge transfer. These results expose clear relationships among molecular symmetry, charge transfer, and spin states of π-conjugated carbon-based nanostructures.

Exchange Interactions and Intermolecular Hybridization in a Spin-1/2 Nanographene Dimer

Phenalenyl is a radical nanographene with a triangular shape hosting an unpaired electron with spin S = 1/2. The open-shell nature of the phenalenyl is expected to be retained in covalently bonded networks. As a first step, we report synthesis of the phenalenyl dimer by combining in-solution synthesis and on-surface activation and its characterization on Au(111) and on a NaCl decoupling layer by means of inelastic electron tunneling spectroscopy (IETS). IETS shows inelastic steps that are identified as singlet-triplet excitation arising from interphenalenyl exchange. Spin excitation energies with and without the NaCl decoupling layer are 48 and 41 meV, respectively, indicating significant renormalization due to exchange with Au(111) electrons. Furthermore, third-neighbor hopping-induced interphenalenyl hybridization is fundamental to explaining the position-dependent bias asymmetry of the inelastic steps and activation of kinetic interphenalenyl exchange. Our results pave the way for bottom-up synthesis of S = 1/2 spin-lattices with large exchange interactions.

Synthesis of a Porous [14]Annulene Graphene Nanoribbon and a Porous [30]Annulene Graphene Nanosheet on Metal Surfaces

The electrical and mechanical properties of graphene-based materials can be tuned by the introduction of nanopores, which are sensitively related to the size, morphology, density, and location of nanopores. The synthesis of low-dimensional graphene nanostructures containing well-defined nonplanar nanopores has been challenging due to the intrinsic steric hindrance. Herein, we report the selective synthesis of one-dimensional (1D) graphene nanoribbons (GNRs) containing periodic nonplanar [14]annulene pores on Ag(111) and two-dimensional (2D) porous graphene nanosheet containing periodic nonplanar [30]annulene pores on Au(111), starting from a same precursor. The formation of distinct products on the two substrates originates from the different thermodynamics and kinetics of coupling reactions. The reaction mechanisms were confirmed by a series of control experiments, and the appropriate thermodynamic and kinetic parameters for optimizing the reaction pathways were proposed. In addition, the combined scanning tunneling spectroscopy (STS) and density functional theory (DFT) calculations revealed the electronic structures of porous graphene structures, demonstrating the impact of nonplanar pores on the π-conjugation of molecules.

Detecting the spin-polarization of edge states in graphene nanoribbons

Low dimensional carbon-based materials can show intrinsic magnetism associated to p-electrons in open-shell π-conjugated systems. Chemical design provides atomically precise control of the π-electron cloud, which makes them promising for nanoscale magnetic devices. However, direct verification of their spatially resolved spin-moment remains elusive. Here, we report the spin-polarization of chiral graphene nanoribbons (one-dimensional strips of graphene with alternating zig-zag and arm-chair boundaries), obtained by means of spin-polarized scanning tunnelling microscopy. We extract the energy-dependent spin-moment distribution of spatially extended edge states with π-orbital character, thus beyond localized magnetic moments at radical or defective carbon sites. Guided by mean-field Hubbard calculations, we demonstrate that electron correlations are responsible for the spin-splitting of the electronic structure. Our versatile platform utilizes a ferromagnetic substrate that stabilizes the organic magnetic moments against thermal and quantum fluctuations, while being fully compatible with on-surface synthesis of the rapidly growing class of nanographenes.

On-Surface Synthesis and Characterization of a High-Spin Aza-[5]-Triangulene

Triangulenes are a class of open-shell triangular graphene flakes with total spin increasing with their size. In the last years, on-surface-synthesis strategies have permitted fabricating and engineering triangulenes of various sizes and structures with atomic precision. However, direct proof of the increasing total spin with their size remains elusive. In this work, we report the combined in-solution and on-surface synthesis of a large nitrogen-doped triangulene (aza-[5]-triangulene) on a Au(111) surface, and the detection of its high-spin ground state. Bond-resolved scanning tunneling microscopy images uncovered radical states distributed along the zigzag edges, which were detected as weak zero-bias resonances in scanning tunneling spectra. These spectral features reveal the partial Kondo screening of a high-spin state. Through a combination of several simulation tools, we find that the observed distribution of radical states is explained by a quintet ground state (S=2), instead of the quartet state (S=3/2) expected for the neutral species. This confirms that electron transfer to the metal substrate raises the spin of the ground state. We further provide a qualitative description of the change of (anti)aromaticity introduced by N-substitution, and its role in the charge stabilization on a surface, resulting in an S=2 aza-triangulene on Au(111).

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

Open-shell nanographenes appear as promising candidates for future applications in spintronics and quantum technologies. A critical aspect to realize this potential is to design and control the magnetic exchange. Here, we reveal the effects of frontier orbital symmetries on the magnetic coupling in diradical nanographenes through scanning probe microscope measurements and different levels of theoretical calculations. In these open-shell nanographenes, the exchange energy exhibits a remarkable variation between 20 and 160 meV. Theoretical calculations reveal that frontier orbital symmetries play a key role in affecting the magnetic coupling on such a large scale. Moreover, a triradical nanographene is demonstrated for investigating the magnetic interaction among three unpaired electrons with unequal magnetic exchange, in agreement with Heisenberg spin model calculations. Our results provide insights into both theoretical design and experimental realization of nanographene materials with different exchange interactions through tuning the orbital symmetry, potentially useful for realizing magnetically operable graphene-based nanomaterials.

Triangle Counting Rule: An Approach to Forecast the Magnetic Properties of Benzenoid Polycyclic Hydrocarbons

Open-shell benzenoid polycyclic hydrocarbons (BPHs) are promising materials for future quantum applications. However, the search for and realization of open-shell BPHs with desired properties is a challenging task due to the gigantic chemical space of BPHs, requiring new strategies for both theoretical understanding and experimental advancement. In this work, by building a structure database of BPHs through graphical enumeration, performing data-driven analysis, and combining tight-binding and mean-field Hubbard calculations, we discovered that the number of the internal vertices of the BPH graphs is closely correlated to their open-shell characters. We further established a simple rule, the triangle counting rule, to predict the magnetic ground states of BPHs. These findings not only provide a database of open-shell BPHs, but also extend the well-known Lieb's theorem and Ovchinnikov's rule and provide a straightforward method for designing open-shell carbon nanostructures. These insights may aid in the exploration of emerging quantum phases and the development of magnetic carbon materials for technology applications.

Steering On-Surface Reactions by Kinetic and Thermodynamic Strategies

On-surface synthesis has emerged as a powerful tool to fabricate various functional low-dimensional nanostructures with atomic precision, thus becoming a promising platform for the preparation of next-generation semiconductive, magnetic, and topological nanodevices. With the aid of scanning tunneling microscopy/spectroscopy and noncontact atomic force microscopy, both the chemical structures and physical properties of the obtained products can be well characterized. A major challenge in this field is how to efficiently steer reaction pathways and improve the yield/quality of products. To address this problem, in recent years various kinetic and thermodynamic strategies have been successfully employed to control on-surface reactions. In this Perspective, we discuss these strategies in view of basic reaction steps on surfaces, including molecular adsorption, diffusion, and reaction. We hope this Perspective will help readers to deepen the understanding of the mechanisms of on-surface reactions and rationally design reaction procedures for the fabrication of high-quality functional nanomaterials on surfaces.

Steering Large Magnetic Exchange Coupling in Nanographenes near the Closed-Shell to Open-Shell Transition

The design of open-shell carbon-based nanomaterials is at the vanguard of materials science, steered by their beneficial magnetic properties like weaker spin-orbit coupling than that of transition metal atoms and larger spin delocalization, which are of potential relevance for future spintronics and quantum technologies. A key parameter in magnetic materials is the magnetic exchange coupling (MEC) between unpaired spins, which should be large enough to allow device operation at practical temperatures. In this work, we theoretically and experimentally explore three distinct families of nanographenes (NGs) (A, B, and C) featuring majority zigzag peripheries. Through many-body calculations, we identify a transition from a closed-shell ground state to an open-shell ground state upon an increase of the molecular size. Our predictions indicate that the largest MEC for open-shell NGs occurs in proximity to the transition between closed-shell and open-shell states. Such predictions are corroborated by the on-surface syntheses and structural, electronic, and magnetic characterizations of three NGs (A[3,5], B[4,5], and C[4,3]), which are the smallest open-shell systems in their respective chemical families and are thus located the closest to the transition boundary. Notably, two of the NGs (B[4,5] and C[4,3]) feature record values of MEC (close to 200 meV) measured on the Au(111) surface. Our strategy for maximizing the MEC provides perspectives for designing carbon nanomaterials with robust magnetic ground states.