Spin and Charge Control of Topological End States in Chiral Graphene Nanoribbons on a 2D Ferromagnet

Abstract

Tailor‐made graphene nanostructures can exhibit symmetry‐protected topological boundary states that host localized spin‐1/2 magnetic moments at half filling. However, one frequently observes charge transfer on coinage metal substrates, which results in closed‐shell configurations. Using low‐temperature scanning tunneling spectroscopy, it is demonstrated here that pristine topologically nontrivial chiral graphene nanoribbons synthesized directly on the ferromagnet GdAu₂ can either maintain a charge‐neutral diradical state, or convert to a singly anionic doublet. As an underlying mechanism, both a work function and an exchange field modulated by the moiré‐induced superstructure are identified, as corroborated by Kelvin probe force microscopy and spin‐flip spectroscopy. The joint electrostatic and magnetic interactions allow reversibly switching between the three spin multiplicities by atomic manipulation. An effective Hubbard dimer model is introduced that unifies the effects of local electrostatic gating, electron–electron correlation, hybridization and an exchange field to outline the phase diagram of accessible spin states. These results establish a platform for the local control of π‐radicals adsorbed on metallic substrates.

Chiral graphene nanoribbons on a ferromagnetic gadolinium‐gold surface alloy display tunable spin and charge states at their termini. Atomic work function variations and exchange fields enabe transitions between singlet, doublet, and triplet configurations. Scanning tunneling spectroscopy and a minimal Hubbard model reveal how local fields control π‐radicals adsorbed on magnetic substrates.

1. Introduction

Despite its many remarkable properties, graphene is intrinsically diamagnetic in bulk form. Yet, in finite geometries, local magnetic moments can emerge due to the alignment of unpaired p _z electrons along boundaries.^{[ 1} , ^{2 ]} These so‐called nanographenes can be synthesized from specifically designed precursors via on‐surface synthesis (OSS) on catalyzing noble metals under ultra‐high vacuum conditions.^{[ 3} , ^{4 ]} Open‐shell configurations can occur in such nanostructures as a consequence of several mechanisms: a net sublattice imbalance,^{[ 5} , ^{6 ]} as is the case in triangulene‐based nanographenes,^{[ 7} , ⁸ , ⁹ , ¹⁰ , ¹¹ , ¹² , ^{13 ]} topological frustration,^{[ 14} , ¹⁵ , ^{16 ]} or bulk‐boundary correspondence, characteristic of topological order.^{[ 17} , ¹⁸ , ^{19 ]}

The latter is at play in chiral graphene nanoribbons (chGNRs), whose translation vector (m, n) lies between the primitive armchair and zigzag directions, as indicated in Figure  1a.^{[ 20} , ²¹ , ²² , ^{23 ]} Due to their finite width w, the electronic bands formed along their chiral edges overlap and introduce a spectral gap which can be engineered to be nontrivial by appropriate choice of (m, n, w).^{[ 24 ]} In these special cases, two zero‐energy modes confined to the two termini emerge in finite‐length chGNRs. Due to their single occupancy at half filling, the resulting radical system can be considered an interacting pair of electron spins. Given the intrinsically balanced sublattices, Lieb's theorem^{[ 5 ]} predicts these symmetry‐protected topological end states (SPTES) to align antiferromagnetically to form an overall S = 0 singlet state.^{[ 24 ]}

Figure 1.

Characterization of (3, 2, 8)‐chGNRs on GdAu₂. a) The chemical structure of two conjugated precursor units, and a scheme of the competing interactions between topological end states and the ferromagnetic surface in longer ribbons. b) STM scan of chGNRs on GdAu₂ (0.4 V, 1 nA, 15 × 15 nm²). c,d) Differential conductance spectra of two 7 PU chGNRs in different adsorption positions. Insets show tip positions where spectra were recorded. Outsets show high‐resolution spectra of the split Kondo feature in a narrow energy range at a closer tip separation. The nanoribbon in (c) is in a fully neutral charge state, with two screened radical moments, while (d) exists in a singly anionic doublet configuration. Reference spectra recorded on bare GdAu₂ are shown in gray (see Figure S5 for complementary reference spectra). All spectra have been normalized to the stabilization conductance G _S = 1.7 nS in (c) and 2.5 nS in (d). The trace recorded on the right terminus in (d) has been scaled by the indicated factor and downshifted by 2G _S.

The localized magnetic character of SPTES in graphene nanoribbons has so far eluded experimental observation due to work function mismatches between graphene and common substrates.^{[ 9 ]} For instance, on the electronegative surface Au(111), chGNRs undergo significant cationic charge transfer,^{[ 24 ]} while more electropositive supports like Ag(111), Ag(100), and MgO/Ag(100) give highly anionic states.^{[ 25} , ^{26 ]} In these cases, both SPTES are fully (de)populated, leading to a nonmagnetic closed‐shell state. Rare earth‐gold intermetallic layers grown on Au(111) surfaces^{[ 27} , ²⁸ , ^{29 ]} have been shown to be a suitable strategy for lowering the work function of the parent crystal while maintaining its catalytic activity for on‐surface synthesis.^{[ 30} , ³¹ , ^{32 ]}

We demonstrate here that topological chGNRs can retain charge neutrality on GdAu₂ due to an almost ideally matched work function, allowing us to sense the spin localized at each terminus using scanning tunneling spectroscopy. The ferromagnetic ordering in GdAu₂ at low temperatures additionally enables us to explore the competing exchange interactions between polyradical boundary states and an in‐plane magnetization.^{[ 32} , ³³ , ^{34 ]} To this end, we spectroscopically probe the sizable exchange field imposed by the substrate onto π‐radicals and study its effect on the molecular spin multiplicity of chGNRs. Spin‐flip spectroscopy and many‐body modeling confirm magnetic coupling to GdAu₂ can dominate over the intramolecular exchange between SPTES. By this mechanism, large exchange fields can induce unusual high‐spin ground states in adsorbed polyradical nanographenes such as chGNRs.

The unique surface structure stemming from the epitaxial relation between the GdAu₂ overlayer and Au(111)^{[ 27 ]} opens further possibilities of controlling spin. We find that the exchange field acting on each terminus of a chGNR depends on its adsorption position, allowing us to tune or even suppress it entirely by reversible lateral manipulation of individual ribbons across the moiré‐induced superstructure. In addition, GdAu₂ also exhibits small variations in its local work function, which can modify the electron occupancy of the SPTES. By repositioning the chGNRs, we access configurations in which an extra electron is transferred into one of the end states, effectively achieving electrostatic gating via controlled molecular manipulation. Even when one of the SPTES radicals is paired and thus lacks of intramolecular exchange, the remaining doublet remains oriented by its magnetic coupling to the substrate.

2. Results and Discussion

The GdAu₂ substrate was prepared under ultra‐high vacuum conditions by exposing the pristine surface of a Au(111) single crystal to an atomic gadolinium beam at elevated temperatures (see Experimental Section and Supporting Information for details). The relaxation of the GdAu₂ surface over the Au(111) bulk appears with a characteristic superstructure in STM images (Figure 1b, see non‐contact atomic force microscopy image in Figure S8, Supporting Information), composed of triangular features (white triangles in Figure 1b) arranged in a hexagonal lattice with spacing of ∼ 4 nm.^{[ 28 ]}

We subsequently deposited a brominated tetrakisanthracene organic precursor (3,2‐DBQA, see ref. [24]) known to form (3, 2, 8)‐chGNRs. Following their synthesis on the GdAu₂ substrate, scanning tunneling microscopy (STM) images resolve chiral graphene nanoribbons with varying lengths L reaching up to more than 10 precursor units (PU), generally oriented along the high‐symmetry directions of the underlying superstructure, as seen in Figure 1b. Bond‐resolved noncontact atomic force microscopy (AFM)^{[ 35 ]} (shown in Figure S9, Supporting Information) confirms their defect‐free chemical structure.

To investigate the charge and spin ground state of the synthesized chGNRs, we explored their local density of states using scanning tunneling spectroscopy (see Figure S6 in Supporting Information for a length dependent study). As shown in Figure 1c for the case of a 7 PU long chGNR, differential conductance tunneling spectra recorded on each of the two termini respectively reveal a sharp zero‐bias feature, whereas measurements on the chiral edge only show the faint onsets of characteristic edge band local density of states (LDOS). We attribute the former features to Kondo resonances arising from the independent screening of each π‐radical by conduction electrons. Their emergence indicates a charge‐neutral, half‐filled chGNR, as corroborated by the symmetric position of the Fermi level within the ∼200 meV wide band gap. This spectral features contrast with the broader unoccupied states reported for the same chGNRs on Au(111),^{[ 24 ]} evidencing a doubly cationic ground state on that substrate. High‐resolution spectra of the zero‐bias feature often reveal a small splitting. As we discuss below, this split is indicative of a Kondo effect in the presence of an exchange field originating from the ferromagnetic substrate.^{[ 31} , ³⁶ , ³⁷ , ³⁸ , ^{39 ]}

We observe a second class of otherwise identical chGNRs in different adsorption positions. For instance, in Figure 1d, a (split) Kondo feature is encountered only at one of the termini, whereas the other displays a much broader (>100 mV) resonance well below the Fermi level. We assign this second feature to a doubly populated SPTES, which implies an anionic net charge q = −e. In a single‐particle picture, the surplus electron here resides within the left terminus and pairs with its π‐radical, forming the HOMO. Negative charge accumulation is consistent with the Fermi level now residing closer toward the conduction band, which remains localized along the chiral edge. As confirmed by mean‐field Hubbard model (MFH) calculations shown in the Supporting Information, this species forms a S = 1/2 ground state, which we refer to as the charged doublet.

Further insight into the origin of two coexisting charge states is gained by repeated manipulation of a single chGNR into several adsorption positions with the STM tip. For instance, the 7 PU chGNR presented in Figure  2a,b, in its original orientation, shows a split Kondo resonance on terminus T1, and a doubly occupied SPTES on T2. When dragged and rotated slightly, the molecule becomes charge‐neutral, with split Kondo resonances on both termini (Figure 2c). After repositioning by a few nanometers, an excess electron is gained by T1, now displaying a HOMO, whereas the local moment of T2 remains (Figure 2d). In the final position (Figure 2e), a pair of zero‐bias peaks with no resolved splitting is restored, again indicating perfect half‐filling.

Figure 2.

Controlling the spin multiplicity of a 7 PU chGNR on GdAu₂. a) By lateral manipulation of the same molecule into four different positions, we observe the excess charge of terminus T2 (b) transferring to T1 (d). Due to the narrower bias range, the HOMO here appears as a broad step instead of the peak seen in Figure 1d. Therefore, charged doublets in panels b and d are consistent with that in Figure 1d, but with inelastic gaps of different widths. The intermediate neutral case is realized in (c), with a particularly large exchange field B _eff on T2. In the last position (e), Kondo coupling dominates B _eff on either termini, and the zero‐bias resonance is restored. Fits of the inelastic tunneling theory (b–d) and Frota lineshapes (e) are shown in gray. All spectra have been normalized to the stabilization conductance G _S = 10 and 30 nS for T1 and T2 in (b), 100 nS in (c,e) and 30 nS in (d). The highest occupied molecular orbital (HOMO) resonances in (b,e) have been downscaled by the indicated factor, and all traces on T1 shifted up by 0.7G _S for better comparison.

The reversible orientation‐dependent switching between the anionic and neutral charge states suggests a varying degree of electrostatic interaction with GdAu₂. To explore its local character, we map the local contact potential difference (LCPD) across the superstructure using Kelvin probe force microscopy (KPFM). As seen in Figure  3a, the triangular moiré minima possess a decreased LCPD compared to the rest of the unit cell by approximately 80 mV (Figure S10 in Supporting Information compares individual KPFM spectra), indicating a locally smaller substrate work function,^{[ 40 ]} and hence an electron‐donating character.^{[ 29 ]} These regions act as a local gating potential^{[ 41 ]} that can increase the electron occupation depending on the proximity of the chGNR to one or various triangular features. As shown in Figure S7 (Supporting Information), small changes in position of a chGNR within the superstructure can lead to variations in the occupancy of one or both SPTES.

Figure 3.

Visualizing the localized charging effect with constant‐height KPFM. a) A map of LCPD recorded over bare GdAu₂ reveals a decreased local work function in the triangular moiré minima by tens of meV (oscillation amplitude 50 pm, 5 × 5 nm², tip height set at 0.2 V and 2 nA on a moiré maximum). b) STM image of a chGNR, which exhibits a doubly occupied orbital on terminus T1, lying close to a moiré minimum (0.5 V, 1 nA, 9 × 4.5 nm²). The apparent height of both termini is similar. c) Map of LCPD (color scale in mV) measured over the chGNR shown in (b) (oscillation amplitude 50 pm, 9 × 4.5 nm², tip height set at 0.5 V and 1 nA on the center of the molecule, then approached by 50 pm). The T1 SPTES shows a localized increase of ∼ 70 mV LCPD with respect to T2, consistent with a single excess electron residing in T1 (giving a higher local work function), and a 100 mV LCPD surplus over the chGNR bulk and chiral edges.

KPFM has also been applied to map charge distribution down to the intramolecular level.^{[ 42} , ⁴³ , ⁴⁴ , ⁴⁵ , ^{46 ]} Here, we sense the spatial extent of the excess electron residing in terminus T1 of the charged doublet chGNR shown in Figure 3b (Figure S11 in Supporting Information). The KPFM image (Figure 3c) reveals two key features. For one, the pillow effect the molecule has on GdAu₂ results in a decreased work function (∼−100 meV) in a wide perimeter around its boundary.^{[ 47 ]} Second, we note a sharp increase in LCPD in the upper section of T1, which we assign to the expected negative charge density. Terminus T2, with a singly occupied SPTES, exhibits no such feature (see Figure S12 in Supporting Information for complementary details). Remarkably, the electrostatic potential emanating from T1 is large enough to negate both the pillow effect, and the smaller work function of the moiré minimum underneath.

As shown in Figure 2, the magnitude of the inelastic gap associated with the split Kondo feature approaches 20 meV, an energy scale well beyond the conventional Zeeman effect. Rather than originating from stray fields, such splittings arise from spin‐dependent Kondo hybridization with the ferromagnetic substrate, which gives an effective field B _eff that scales with both the substrate's electron density and spin polarization.^{[ 36} , ⁴⁸ , ^{49 ]} For example, on terminus T2 in Figure 2c, the fit of a third‐order inelastic tunneling model,^{[ 50 ]} assuming a free electron g‐factor, yields a value for B _eff as large as 84 T.

The exchange field varies with the adsorption position. It often even differs significantly in magnitude between termini, hinting at a modulation of the magnetic coupling with the substrate on a similar length scale to the variations in work function reported above. Presumably, π‐radicals interact with Gd^{3 +} 4f moments via an indirect exchange mechanism mediated by hybridization of Gd 5d with the Au s and p bands, which has already been suggested as the coupling mechanism responsible for the in‐plane magnetic order in GdAu₂.^{[ 33 ]} The resulting conduction electron polarization was shown to exhibit a texture congruent to the moiré‐induced superstructure, consistent with our observations.^{[ 32} , ^{34 ]}

In the absence of B _eff, intramolecular Coulomb repulsion promotes antiferromagnetic alignment between π‐radicals in charge‐neutral chGNRs, particularly for short lengths where SPTES significantly overlap. When interfaced with GdAu₂, each terminus couples via an addtional exchange interaction to the magnetic surface. We describe these competing effects using two key parameters: an intramolecular spin‐spin interaction J > 0, favoring antiferromagnetic alignment, and an effective substrate‐induced magnetic field B _eff, here assumed identical at both termini for simplicity but without loss of generality.

In our experiment, the interplay between J and B _eff determines the ground‐state spin configuration of chGNRs. If J >B _eff, the singlet ground state would be stable. If instead B _eff>J, a triplet state becomes energetically favorable, characterized by parallel alignment of both radical spins with the substrate magnetization. In both cases, spin‐flip excitations would be the spectral manifestation observed in the experiments if both J and B _eff are larger than the energy scale of Kondo fluctuations, i.e. $|g{\mu }_{\mathrm{B}}{B}_{\mathrm{eff}}|,|J|>k_{\mathrm{B}}{T}_{\mathrm{K}}$.

However, our measurements suggest that intramolecular exchange J plays only a secondary role as a magnetic interaction in our experiments. In ribbons with lengths L ⩾ 5 PU, proper repositioning on the substrate can consistently restore a zero‐bias resonance with no resolved splitting (e.g., in Figure 2 or in Figure S7, Supporting Information). This observation indicates that J/k _B must be smaller than the Kondo temperature T _K, which we estimate at approximately 32 K for the terminus labeled T2 in Figure 2d.^{[ 51 ]} The triplet state, on the other hand, is stable against these fluctuations if $|g{\mu }_{\mathrm{B}}{B}_{\mathrm{eff}}|>k_{\mathrm{B}}{T}_{\mathrm{K}},J$. Thus, the existence of site‐dependent inelastic gaps over the ends of chGNRs evidences that the SPTES behave length independent (i.e. J < k _B T _K) and that the built‐in surface exchange field aligns and effectively protects the π‐radical moments from conduction electron scattering‐induced relaxation. ^{[ 52 ]}

An asymmetric Hubbard dimer model: To rationalize the intricate interplay between these interactions and the observed spin and charge states, we map our experimental system onto a modified Hubbard dimer model. In this model, each dimer site represents one SPTES, spatially distributed across multiple graphene lattice sites, as illustrated in Figure  4a.^{[ 2} , ^{53 ]} In such simplified description of the system, differences in local orbital energies at each terminus account for local charging, whereas the global magnetic field mimics the uniform exchange coupling to the GdAu₂ substrate. The resulting Hamiltonian, expressed in second quantization, reads:

$$\begin{array}{c}\widehat{\mathcal{H}}=-t\sum _{\sigma }\left({\widehat{c}}_{\mathrm{T}1,\sigma }^{†}{\widehat{c}}_{\mathrm{T}2,\sigma }+\mathrm{h}.\mathrm{c}.\right)+U_{\mathrm{eff}}\sum _i{\widehat{n}}_{i\uparrow }{\widehat{n}}_{i\downarrow }\\ +\sum _i\sum _{\sigma }{\epsilon }_i{\widehat{n}}_{i\sigma }+g{\mu }_{\mathrm{B}}{B}_{\mathrm{eff}}\sum _i\left({\widehat{n}}_{i\uparrow }-{\widehat{n}}_{i\downarrow }\right)\end{array}$$ (1)

Figure 4.

Predicting the chGNR spin multiplicity from the Hubbard dimer model. a) Two sites T1 and T2, representing SPTES under an exchange field B _eff, experience Coulomb repulsions U _eff and are coupled by a hopping amplitude t, both obtained from tight‐binding theory of (3, 2, 8)‐chGNRs with varying length. T1 is additionally gated by a local potential. The system adapts a many‐body ground state $|N,m_s⟩$ depending on the parameters. b) Ground‐state transition from two‐particle states toward the charged doublet $|3,\pm 1/2⟩$ with Δϕ. c) Spin level scheme of the singlet‐triplet transition at a critical value of B _eff. Only one component of $|2,0⟩$ is shown. d) The chGNR phase diagram, here at L = 7, exhibits two critical points in Δϕ and B _eff. Color denotes the total spin projection S _z /ℏ. e) Δϕ^c and $B_{\mathrm{eff}}^{\mathrm{c}}$ as a function of length. The intramolecular exchange $J=|g{\mu }_{\mathrm{B}}{B}_{\mathrm{eff}}^{\mathrm{c}}|\sim 4t^2/U_{\mathrm{eff}}$ falls rapidly, while the critical gating potential approaches −U _eff/2.

Here, the first two terms correspond to the conventional Hubbard dimer, with i, being the site indices T1 and T2, a hopping amplitude t representing length‐dependent hybridization between SPTES, and an effective Coulomb repulsion U _eff among end‐localized π‐electrons of spin σ. The site‐specific energies ε _i and the Zeeman effect enter as additional diagonal elements, for which we set g = −2. To connect the former to the local variations in the substrate work function, we introduce a gating potential Δϕ acting only on T1, such that ε_T1 = −U _eff/2 + Δϕ. Conversely, T2 is assumed to be perfectly matched to the electrostatic background by setting ε_T2 = −U _eff/2. As such, half filling – with one electron occupying each site – is most stable at Δϕ = 0. At Δϕ < 0, negative charge transfer into T1 is favored, consistent with a locally decreased work function. A generalized treatment, with entirely asymmetric parameters, is given in the Supporting Information.

The validity of this dimer approximation is justified by a full MFH description of chGNRs (Supporting Information), holding true for small to intermediate on‐site Coulomb repulsion (U _H < 3 eV) and charge states from −2e to +2e. Within these parameter ranges, the spin‐polarized active space is effectively restricted to the isolated SPTES, which remain energetically separated from the quantized edge‐localized bands. Such a reduced active space agrees with the experimental observation of zero‐bias Kondo resonances localized at the chGNR termini (shown as Figure S2, Supporting Information).

Exact diagonalization yields solutions we label as $|N,S_z/\hslash ⟩$, where N = 2, 3 are the occupancies found in our experiment, and S _z the total spin projection. These are, in general, entangled combinations of single‐particle states such as ${\widehat{c}}_{\mathrm{T}1\uparrow }^{†}{\widehat{c}}_{\mathrm{T}2\downarrow }^{†}|0⟩$ sketched in Figure 2. Depending on Δϕ, B _eff and t, five many‐body solutions can constitute the ground state. At half filling (N = 2), the system may reside either in a neutral singlet state $|2,0⟩$ or in one of the triplet states $|2,\pm 1⟩$. For sufficiently long chGNRs, such that U _eff ≫ t, the singlet approximately consists in a superposition of two singly occupied SPTES – an open‐shell configuration. The triplet states $|2,\pm 1⟩$ represent ferromagnetically aligned SPTES, and become non‐degenerate under the exchange field^{[ 54 ]}. For N = 3, we identify the charged doublet $|3,\pm 1/2⟩$, also split by B _eff. Its energetic separation from the two‐electron states is primarily given by the energy gain associated to T1 via the local gating potential.

To assess the magnetic ground state of the chGNRs in our experiment using the Hubbard dimer, we calculate effective parameters from a tight‐binding description of the full π‐lattice over a range of lengths L (see Supporting Information for further details). The dimer hopping amplitude is extracted from the small hybridization gap between SPTES, which amounts to 2t, and decays exponentially with their separation. The effective repulsion U _eff is computed from the self‐overlap integral over each SPTES multiplied by U _H = 3 eV, and bears only a small correction due to confinement at short L. The nanoribbon length thereby directly controls the ratio U _eff/t, key measure of electron localization. The parameters obtained are validated by the experimental observation of J < k _B T _K for L ⩾ 5 PU.

The ground‐state phase diagram spanned by the parameters Δϕ and B _eff is shown in Figure 4d, where we set L = 7 PU. Along the vertical axis, we identify the critical point Δϕ^c, which marks the boundary between neutral singlet and charged doublet ground states. Its origin is most apparent by considering the occupation energy levels as depicted in Figure 4b: the required double population of T1 becomes favorable only for Δϕ < −U _eff/2. If Δϕ is strong, these solutions simply correspond to doubly occupancy of T1, and one unpaired electron on T2.

Similarly, $B_{\mathrm{eff}}^{\mathrm{c}}$ marks the transition between singlet and triplet states. As exemplified by the spin level scheme in Figure 4c drawn for a single‐particle state, spin down (up) levels in the composition of $|2,0⟩$ are shifted down (up) in energy by B _eff > 0, resulting in the triplet solution $|2,-1⟩$ lying below the singlet $|2,0⟩$. Due to hybridization, the magnitudes of $B_{\mathrm{eff}}^{\mathrm{c}}$ and Δϕ^c generally depend on U _eff/t, and thereby on L. For instance, increasing the length from 3 to 9 PU, U _eff/t rises from 28 to 1013. Consequently, the critical field $B_{\mathrm{eff}}^{\mathrm{c}}$ decreases from 35 T to below 1 mT, as displayed in Figure 4e. If Δϕ is negligible, the description simplifies to a Heisenberg‐coupled spin dimer in the limit of large L, with a singlet‐triplet gap amounting to $J=|g{\mu }_{\mathrm{B}}{B}_{\mathrm{eff}}^{\mathrm{c}}|=4t^2/U_{\mathrm{eff}}$.^{[ 2} , ⁵³ , ^{55 ]}

Based on the small magnetic coupling between termini, we deduce that the neutral 7 PU‐chGNR in Figure 2c resides in a stable triplet ground state, as the exchange field extracted from the inelastic gap exceeds both $B_{\mathrm{eff}}^{\mathrm{c}}\sim 30\mathrm{mT}$ and the Kondo energy by far. The observed spin‐flip excitations are then from the triplet to the singlet configuration. Due to the localized nature of the SPTES, this change in equilibrium magnetic configuration does not significantly modify the remaining molecular orbitals (as shown in Figure S13, Supporting Information).

Conversely, as is apparent in Figure 4e, the critical gating potential Δϕ^c is only weakly length‐dependent and tends to a constant value of −U _eff/2 = −48 meV for L > 5 PU. In this limit, the hybridization t becomes insignificant, and Δϕ must only overcome Coulomb repulsion to doubly occupy the left site. The decreased work function detected within the moiré minima of GdAu₂ of 80 meV is therefore sufficient in magnitude to induce the charged doublet state observed in our experiments, for all nanoribbon lengths.

From the Kondo temperature introduced above, a singlet ground state stabilized by intramolecular exchange as opposed to B _eff, namely J > k _B T _K,B _eff, could only occur for L ⩽ 3 PU (Figure S20, Supporting Information). Although in this limit the strong SPTES overlap could lead to a closed‐shell system,^{[ 24 ]} our experiments for a L = 3 PU shown in Figure S6 (Supporting Information) indicate that π‐radical state persist for this length, but the spin of the ground state is uncertain. Conversely, the (3,2,8)‐chGNRs with L > 4 PU behave rather length independent, with each SPTES governed by the local properties of the GdAu₂ superstructure, as mapped out in the Hubbard parameter space shown Figure S20 (Supporting Information).

3. Conclusion

In summary, we have investigated the charge and magnetic ground state of (3, 2, 8)‐chGNRs synthesized on GdAu₂ via on‐surface synthesis. These exhibit a topologically non‐trivial band structure, resulting in two SPTES localized at their termini, which constitute a pair of antiferromagnetically exchange‐coupled zero modes. Unlike conventional metallic substrates, GdAu₂ maintains the chGNRs in a charge‐neutral state, evidenced by the single occupancy of both end states, which we detect as two localized Kondo features in tunneling spectra. In some cases, we also encounter a negatively charged state, with a single excess electron hosted by one SPTES, locally quenching spin. Uniquely, the in‐plane magnetization of the rare‐earth alloy induces an additional exchange field B _eff that splits the Kondo resonances, providing a method to probe the local magnetic environment of the molecules. Interestingly, both the charge state and B _eff can vary depending on the adsorption position, as confirmed by reversible molecular manipulation. The former is ascribed to local work function variations on the order of ∼80 meV; similarly, the latter exhibits oscillations of up to several tens of Teslas. We attribute both effects to the superstructure formed by the topmost atomic layer of GdAu₂.

Using an asymmetric Hubbard dimer model, we show that the substrate‐induced magnetic coupling can overcome the intrinsic exchange between end states, promoting a transition to a triplet ground state, where both spins at the termini are forced to lie parallel. The same model also shows the observed singly anionic state in terms of local electrostatic gating to be compatible with the work function modulation found in our experiment. The pronounced susceptibility of nanographene zero modes to minute electrostatic variations illustrates how surface work‐function engineering can be exploited to access alternative charge configurations, potentially associated with emergent magnetic phenomena.^{[ 26} , ^{31 ]} Overall, our findings establish GdAu₂ as a powerful platform for preserving and controlling the spin states of open‐shell graphene nanostructures.

4. Experimental Section

A pristine Au(111) surface was obtained by repeated Ne‐ion bombardment (1.5 keV, 10⁻⁵ mbar) and annealing cycles () of a polished single crystal. GdAu₂ was then prepared by exposing the same surface held at to Gd vapor from an electron‐beam heated tungsten crucible under ultra‐high vacuum. (3, 2, 8)‐chGNRs were produced by the same on‐surface reaction described previously^{[ 24 ]} for which a (3,2)‐DBQA organic precursor was evaporated from a Knudsen cell at onto the room‐temperature GdAu₂ surface, and then annealed to for 20 min and for 10 min to induce stepwise Ullmann coupling and cyclodehydrogenation, respectively. STM, AFM and KPFM measurements were realized at low temperatures (∼5 K) under ultra‐high vacuum using a qPlus force sensor^{[ 56 ]} with a PtIr tip, allowing for simultaneous STM and AFM measurements. Lock‐in detection of differential conductance spectra was performed by modulation of the tunneling bias on the order of 1 mV_pp. AFM and KPFM measurements were carried out in the frequency modulation mode.^{[ 57 ]} The qPlus force sensor had a resonance frequency f ₀ of ∼30.7 kHz, spring constant k of ∼1.8 kN/m, and quality factor Q between 20,000‐30,000. Unless noted otherwise, the force sensor was operated at an oscillation amplitude of 50 pm. In this small amplitude regime, the measured frequency shift is approximately proportional to the vertical gradient of the tip‐sample force. For bond‐resolved AFM imaging, carbon monoxide was dosed onto the cold sample from a leak valve and deliberately picked up with the tip.

Conflict of Interest

The authors declare no conflict of interest.

Supporting information

Supporting Information

Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.