🔬 mesoscale physics

Exchange interactions and intermolecular hybridization in a spin-1/2 nanographene dimer

This paper reports the synthesis and characterization of a phenalenyl dimer, demonstrating through inelastic electron tunneling spectroscopy and theoretical analysis that interphenalenyl exchange interactions and third-neighbor orbital hybridization govern its spin-1/2 singlet-triplet excitations, which are significantly renormalized by the underlying metal substrate.

Original authors: N. Krane, E. Turco, A. Bernhardt, D. Jacob, G. Gandus, D. Passerone, M. Luisier, M. Juríček, R. Fasel, J. Fernández-Rossier, P. Ruffieux

Published 2026-10-02

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CC BY 4.0

Original authors: N. Krane, E. Turco, A. Bernhardt, D. Jacob, G. Gandus, D. Passerone, M. Luisier, M. Juríček, R. Fasel, J. Fernández-Rossier, P. Ruffieux

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

At the frontier of materials science, researchers are learning to build electronic devices atom by atom, crafting structures that behave not just as conductors or insulators, but as tiny magnets. Central to this effort are molecules known as radicals, which possess an unpaired electron. In the world of quantum physics, this single unpaired electron acts like a tiny compass needle, carrying a property called spin. When scientists can arrange these magnetic molecules into precise patterns, they create artificial lattices that could one day serve as the foundation for quantum computers or ultra-sensitive sensors. However, controlling how these magnetic needles interact with one another is difficult. They must be close enough to talk to each other, yet isolated enough that the noisy environment of the metal surface they sit on does not drown out their delicate magnetic signals. Understanding exactly how these molecules exchange energy and influence each other is the essential first step toward turning these theoretical possibilities into reality.

In a recent study, a team of researchers from Switzerland, Spain, and Portugal took a significant step forward by creating and examining a simple pair of these magnetic molecules. They focused on a triangular carbon structure called phenalenyl, which naturally hosts a single unpaired electron, making it a spin-1/2 system. While individual phenalenyl molecules are highly reactive and difficult to handle, the team managed to join two of them together to form a dimer, which they named diphenalenyl. To study this fragile structure without destroying it, they employed a clever two-step strategy. First, they synthesized a stable precursor molecule in a liquid solution. Then, using a scanning tunneling microscope—a device with a tip so sharp it can manipulate individual atoms—they placed this precursor onto a gold surface and carefully removed specific hydrogen atoms to activate the molecule, turning it into the desired magnetic dimer.

The researchers then probed the magnetic behavior of these dimers using a technique called inelastic electron tunneling spectroscopy. This method involves measuring how electrons jump across the molecule as the voltage is slowly increased. When an electron has just the right amount of energy to flip the spin of the molecule, it leaves a distinct signature in the data. The team observed these signatures clearly, identifying a jump in energy that corresponds to the molecule switching from a calm, paired state to an excited, unpaired state. This confirmed that the two magnetic centers within the dimer were indeed interacting, locking their spins in an antiparallel arrangement, a state known as a singlet.

A crucial part of the experiment involved comparing how the molecule behaved on a bare gold surface versus on a thin, insulating layer of salt placed over the gold. On the bare gold, the energy required to flip the spin was measured at 41 milli-electron volts. When the salt layer was added, acting as a buffer to isolate the molecule from the metal, this energy requirement rose to 48 milli-electron volts. This difference revealed that the gold surface was actively influencing the molecule's magnetic properties, effectively lowering the energy needed for the spin flip through a process of electronic screening. The salt layer, by blocking this interaction, allowed the molecule to display its intrinsic magnetic strength.

Beyond the energy levels, the researchers discovered a fascinating asymmetry in how the molecule responded to electrical current. Depending on the direction of the voltage and the exact position of the microscope tip, the strength of the magnetic signal varied in a predictable way. Through detailed computer simulations, they traced this behavior to the specific way the electrons in the two triangular halves of the molecule overlapped. Because of the unique geometry of the phenalenyl units, the electrons could not hop directly between the closest points of the two triangles. Instead, they had to take a longer path, jumping to a third neighbor to connect the two halves. This specific type of connection, which the researchers identified as third-neighbor hopping, was essential for the magnetic exchange to occur.

The study concludes that diphenalenyl is a robust system where two magnetic spins are strongly coupled, yet their interaction is highly sensitive to their environment. The work provides a clear blueprint for how to build larger networks of these magnetic molecules. By understanding how the substrate changes the energy of the spin flips and how the specific shape of the molecule dictates the path of electron exchange, scientists can now design more complex structures. These findings lay the groundwork for future efforts to construct larger, organized arrays of magnetic spins, bringing the vision of carbon-based quantum technologies closer to reality.

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

Problem Statement
Phenalenyl is a triangular nanographene radical hosting an unpaired electron with spin $S = 1/2$ . While its open-shell nature is theoretically expected to persist in covalently bonded networks, experimental investigation has been hindered by the high chemical reactivity of radical species. Understanding the exchange interactions between phenalenyl units, both with each other and with conductive substrates, is a prerequisite for utilizing these molecules as building blocks for artificial spin lattices, quantum simulators, or spin qubits. Specifically, there is a need to characterize the singlet-triplet excitation energies and the role of intermolecular hybridization in such dimers, as well as to quantify how substrate coupling renormalizes these magnetic properties.

Methodology
The study employs a hybrid approach combining in-solution synthesis with on-surface activation and characterization.

Synthesis: A 2H-diphenalenyl precursor (a closed-shell hydro-precursor) was synthesized via a nine-step sequence starting from naphthalene. This precursor was deposited onto Au(111) surfaces, both bare and covered with a monolayer of NaCl.
Activation: The target diphenalenyl diradical was generated in situ using a Scanning Tunneling Microscope (STM) tip to induce selective dehydrogenation of the sp³ carbon atoms via voltage pulses.
Characterization: The resulting molecules were characterized using non-contact Atomic Force Microscopy (nc-AFM) to confirm structural transformation and Scanning Tunneling Spectroscopy (STS), specifically Inelastic Electron Tunneling Spectroscopy (IETS), to probe electronic and magnetic properties. Measurements were performed on both Au(111) and the decoupling NaCl monolayer.
Theoretical Modeling: The experimental data were interpreted using a combination of Tight-Binding (TB) calculations within the Mean-Field Hubbard (MFH) approximation, Density Functional Theory (DFT), and a generalized many-body Hubbard model. The latter included long-range Coulomb interactions and was solved using the One-Crossing Approximation (OCA) for an Anderson impurity model to account for substrate coupling and Kondo effects.

Key Contributions and Results

Synthesis and Structural Confirmation: The authors successfully synthesized the diphenalenyl dimer and activated it on a surface. nc-AFM and STM imaging confirmed the transition from the precursor to the open-shell diradical, revealing distinct lobes and nodal planes characteristic of the activated molecule.
Observation of Singlet-Triplet Excitations: IETS measurements revealed inelastic steps corresponding to spin excitations.
- On Au(111), the excitation energy was measured at 41 meV.
- On the NaCl/Au(111) decoupled surface, the excitation energy increased to 48 meV.
- These steps are identified as transitions from an $S=0$ singlet ground state to an $S=1$ triplet excited state, consistent with Ovchinnikov's rule and Lieb's theorem for coupled $S=1/2$ spins.
Substrate Renormalization: The ~7 meV difference in excitation energy is attributed to the interaction with the substrate. Theoretical analysis indicates that the metallic Au(111) surface screens Coulomb interactions (reducing the effective Hubbard $U$ ) and induces Kondo exchange, which renormalizes the excitation energy downward compared to the decoupled NaCl case. The linewidth of the steps is also significantly broader on Au(111) due to coupling with conduction electrons.
Intermolecular Hybridization and Third-Neighbor Hopping: A distinct position-dependent asymmetry in the height of the inelastic steps was observed.
- Spectra taken at the center of the dimer showed a larger step at negative bias.
- Spectra taken at the outer lobes showed different asymmetries depending on the substrate.
- Theoretical modeling revealed that the zero-modes of the phenalenyl units have null weight at the binding site, preventing first-neighbor hopping. Instead, intermolecular hybridization is driven by third-neighbor hopping ( $t_3$ ). This hybridization is essential for activating kinetic interphenalenyl exchange. The observed bias asymmetry is explained by the spatial distribution of the HOMO and LUMO wavefunctions: at the center of the molecule, the LUMO wavefunction vanishes, causing the Local Density of States (LDOS) to be dominated by the HOMO spectral function, which exhibits a larger step at negative bias.
Orbital Assignment: The study mapped the Singly Occupied Molecular Orbitals (SOMOs) and Singly Unoccupied Molecular Orbitals (SUMOs), identifying them at -0.6 V and +1.1 V, respectively. Theoretical spectral functions confirmed that the bias asymmetry arises from the proximity of ion resonances and the specific spatial distribution of the HOMO and LUMO wavefunctions, where the HOMO and LUMO contribute with opposite asymmetries to the step heights.

Significance
The paper establishes a foundational step toward the bottom-up synthesis of spin- $1/2$ lattices using phenalenyl units. By demonstrating that the singlet-triplet exchange interaction can be tuned and measured via substrate engineering (using NaCl as a decoupling layer), the work highlights the critical role of substrate-induced renormalization in open-shell nanographenes. Furthermore, the identification of third-neighbor hopping as the driver for intermolecular hybridization in this system provides a necessary correction to simplified models of graphene-based radicals. These findings offer a pathway for engineering electronic phases with topological order and robust quantum information processing platforms, provided that exchange interactions can be precisely controlled.

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