🔬 mesoscale physics

Vibrational excitations in magnetic triangular nanographenes

This study demonstrates that inelastic excitations observed in the spin S = 1/2 phenalenyl radical on Au(111) via inelastic electron tunneling spectroscopy are of vibrational rather than magnetic origin, as confirmed by spatial intensity analysis and theoretical simulations.

Original authors: Nils Krane, Elia Turco, Annika Bernhardt, Michal Juríček, Roman Fasel, Pascal Ruffieux

Published 2026-10-02

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CC BY 4.0

Original authors: Nils Krane, Elia Turco, Annika Bernhardt, Michal Juríček, Roman Fasel, Pascal 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

In the microscopic world of carbon-based materials, scientists are increasingly interested in tiny, flat structures that behave like magnets. These structures, known as nanographenes, are made of carbon atoms arranged in specific geometric patterns. Some of these patterns create an imbalance that leaves the molecule with a "spin," a fundamental magnetic property that makes the molecule act like a tiny compass needle. Researchers are eager to study these magnetic spins because they could one day serve as the building blocks for powerful new computers or sensors. To see these spins in action, scientists use a technique called inelastic electron tunneling spectroscopy. This method involves hovering an incredibly sharp metal tip just above a molecule and sending a stream of electrons through it. By measuring how the electrical current changes as the voltage increases, researchers can detect when an electron has given up a tiny bit of energy to excite the molecule. Usually, this energy jump reveals that the molecule's magnetic spin has flipped to a higher state. However, there is a catch: the molecule can also vibrate, and these vibrations can cause the exact same energy jumps in the electrical signal. Distinguishing between a magnetic flip and a mechanical shake is essential, yet difficult, because both look identical on a standard energy graph.

A team of researchers at the Swiss Federal Laboratories for Materials Science and Technology and the University of Zurich set out to solve this puzzle using a specific carbon molecule called the phenalenyl radical. This molecule is the smallest member of a family of triangular carbon shapes and possesses a single unpaired electron, giving it a magnetic spin of one-half. The scientists placed this molecule on a gold surface and used their microscope to map out exactly where the energy jumps occurred. They found that while the magnetic signal was strongest at the edges of the triangle, the mysterious energy steps appeared most clearly in the very center of the molecule. This spatial difference was the key. If the steps were caused by the magnetic spin flipping, they should have been strongest where the magnetic electron was most accessible, which is at the edges. Instead, the fact that the steps were brightest in the center suggested that the molecule was not flipping its spin, but rather shaking in a specific way.

To confirm this, the researchers turned to computer simulations based on the laws of quantum mechanics. They modeled how the phenalenyl molecule would vibrate and calculated how those vibrations would interact with the electrons from the microscope tip. The simulations predicted that three specific out-of-plane vibrations—where the outer carbon atoms move up and down like a drum skin—would create strong signals right in the center of the molecule. One of these vibrations had an energy of 35.4 millielectronvolts, and two others were paired at 20.0 millielectronvolts. The computer models showed that these movements broke the symmetry of the molecule's electronic cloud in a way that allowed electrons to tunnel through the center, creating the exact pattern the scientists observed in their experiments. The match between the real-world measurements and the theoretical predictions was so precise that the researchers could definitively rule out magnetic excitations as the cause of the steps.

The study demonstrates that what looks like a magnetic signal on a graph can actually be a mechanical vibration, depending entirely on where the microscope tip is placed. By mapping the location of these signals, the team proved that the steps at 35.4 millielectronvolts and 20.0 millielectronvolts were caused by the molecule vibrating, not by its spin changing. This distinction is vital for anyone trying to study the magnetic properties of these tiny carbon structures. If a researcher does not know how to tell the difference between a spin flip and a vibration, they might mistake a harmless shake for a complex magnetic event. The work provides a clear method for identifying these vibrational modes, ensuring that future experiments on carbon-based magnets are based on accurate interpretations of the data.

Technical Summary: Vibrational Excitations in Magnetic Triangular Nanographenes

Problem Statement
Inelastic electron tunneling spectroscopy (IETS) is a standard technique in scanning tunneling microscopy (STM) used to probe excited states in nanostructures, particularly the magnetic properties of complex spin systems. However, a significant challenge arises because inelastic steps in differential conductance ( $dI/dV$ ) spectra can originate from either magnetic spin excitations or vibrational mode excitations. Distinguishing between these two mechanisms is critical when investigating magnetic ground and excited states, as misattribution can lead to incorrect conclusions about spin systems. This is particularly relevant for open-shell nanographenes (NGs), such as zigzag-edged triangular NGs ([n]triangulenes), which are promising platforms for entangled spin systems due to their weak spin-orbit and hyperfine coupling.

Methodology
The authors investigated the smallest member of the [n]triangulene family, the phenalenyl radical (spin $S = 1/2$ ), adsorbed on an Au(111) surface. The study employed the following experimental and theoretical approaches:

Sample Preparation: Hydrogen-passivated 1H-phenalene was deposited onto an atomically clean Au(111) substrate under ultrahigh vacuum. The molecule was subsequently deprotonated via tip-induced manipulation to generate the phenalenyl radical.
Experimental Characterization: Low-temperature STM ( $T = 4.5$ K) was used to acquire $dI/dV$ spectra at various positions across the molecule. To map the spatial distribution of inelastic features, constant-height $dI/dV$ maps were recorded at bias voltages just above and below the energy thresholds of observed steps. These maps were subtracted to isolate the intensity of specific inelastic channels.
Theoretical Simulation: Density Functional Theory (DFT) calculations (Gaussian 16, B3LYP/6-311g(d,p)) were performed for a gas-phase molecule to model vibrational modes. The tunneling probability for off-resonant vibrational excitation was simulated using Bardeen's tunneling theory. This involved calculating the change in the molecular wavefunction ( $\delta\Psi_{m,k}$ ) upon perturbing the structure by the root mean square displacement of specific vibrational modes ( $\delta Q_k$ ).

Key Results

Spectral Features: $dI/dV$ spectra taken at the edges of the phenalenyl radical displayed a strong Kondo resonance (indicative of the screened unpaired spin). In contrast, spectra taken near the molecular center showed a suppressed Kondo peak but revealed distinct inelastic steps symmetric around zero bias at $\pm 22.5$ mV and $\pm 35$ mV.
Spatial Distribution Analysis: The spatial intensity of the inelastic steps differed fundamentally from the Kondo resonance. The Kondo signal was strongest at the edges (where tunneling into the singly occupied molecular orbital, SOMO, is maximized) and vanished at the center due to destructive interference. Conversely, the inelastic steps were strongest at the center of the molecule and faded toward the edges. This spatial mismatch ruled out spin excitations as the origin, as spin excitations require tunneling through the SOMO.
Vibrational Assignment: DFT simulations identified three low-energy vibrational modes ( $k=1, 2, 4$ $k = 1, 2, 4$ ) with significant electron-phonon coupling:
- Modes $k=1$ and $k=2$ are degenerate ( $E \approx 20.0$ meV) and exhibit intensity in the intermediate region between the center and the edge.
- Mode $k=4$ ( $E \approx 35.4$ meV) is localized in the center of the molecule.
- All three modes involve out-of-plane motion of the six outer carbon atoms. The displacement symmetry of mode $k=4$ matches the phase of the SOMO, breaking the symmetry that causes destructive interference in the elastic channel and thereby enabling high tunneling probability at the molecular center.
Experimental Validation: The experimentally derived spatial maps of the inelastic step intensities (obtained via map subtraction) showed excellent agreement with the simulated spatial distributions of the vibrational modes. The maps confirmed that the steps at $\pm 35$ mV correspond to the central mode ( $k=4$ ), while the $\pm 22.5$ mV features correspond to the degenerate modes ( $k=1, 2$ ).

Significance and Claims
The paper demonstrates a robust method for identifying and distinguishing vibrational excitations from magnetic spin excitations in IETS measurements of magnetic nanographenes. By combining spatial mapping of inelastic tunneling probabilities with ab-initio DFT simulations, the authors successfully assigned specific spectral features to distinct vibrational modes.

The authors claim that this work highlights the necessity of verifying the spatial distribution of IETS signals to avoid misinterpreting vibrational features as magnetic excitations. Furthermore, understanding the spatial distribution of electron-phonon coupling is presented as crucial for selecting appropriate tip positions when investigating the magnetic properties of nanographenes, ensuring that vibrational background does not obscure or mimic magnetic signals. The study confirms that for the phenalenyl radical on Au(111), the observed inelastic features are purely vibrational in origin.

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