Collective All-Carbon Magnetism in Triangulene Dimers

Triangular zigzag nanographenes, such as triangulene and its pi-extended homologues, have received widespread attention as organic nanomagnets for molecular spintronics, and may serve as building blocks for high-spin networks with long-range magnetic order - of immense fundamental and technological relevance. As a first step toward these lines, we present the on-surface synthesis and a proof-of-principle experimental study of magnetism in covalently bonded triangulene dimers. On-surface reactions of rationally-designed precursor molecules on Au(111) lead to the selective formation of triangulene dimers in which the triangulene units are either directly connected through their minority sublattice atoms, or are separated via a 1,4-phenylene spacer. The chemical structures of the dimers have been characterized by bond-resolved scanning tunneling microscopy. Scanning tunneling spectroscopy and inelastic electron tunneling spectroscopy measurements reveal collective singlet-triplet spin excitations in the dimers, demonstrating efficient inter-triangulene magnetic coupling.


Introduction
The fusion of benzenoid rings in a triangular fashion leads to the generation of triangular zigzag nanographenes (TZNGs) for which no Kekulé valence structures can be drawn without leaving unpaired electrons. [1] The underlying basis for the non-Kekulé structure of TZNGs is an inherent sublattice imbalance in the bipartite honeycomb lattice such that the simultaneous pairing of all pz-electrons into π-bonds is impossible (Scheme 1). [2][3][4] Application of Ovchinnikov's rule [5,6] predicts an increasing ground state total spin quantum number S with increasing size of TZNGs. Derivatives of phenalenyl [7] (three fused rings, S = 1/2) and triangulene [8,9] (six fused rings, S = 1) have been obtained in solution, and their magnetic ground states have been confirmed by electron paramagnetic resonance spectroscopy. In the last three years, unsubstituted triangulene [10] and its larger homologues, [11,12] that is, πextended [4]-and [5]-triangulene containing ten and fifteen fused rings, with S = 3/2 and 2, respectively, have been obtained on metal and insulator surfaces, and their electronic structures have been elucidated at submolecular resolution using scanning tunneling microscopy and spectroscopy (STM and STS). A range of applications have been envisaged for TZNGs in molecular electronics and spintronics such as spin filters, [13,14] qubits for quantum information processing [15] and electrically-controllable magnetic switches. [16,17] Given their high-spin ground states, interesting fundamental and technological prospects lie in the construction of one-dimensional chains and two-dimensional networks incorporating TZNGs as building blocks-such as the discovery of elusive quantum states of matter [18] and room temperature long-range magnetic ordering. [19][20][21] With the advent of on-surface synthesis as a chemical toolbox, [22] fabrication of extended TZNG nanostructures seems feasible on metal surfaces, given the proper chemical precursor design. Scheme 1 illustrates the versatility of TZNG nanostructures. Connecting two triangulene units directly through their minority sublattice carbon atoms does not produce a net sublattice imbalance in the structure, and is thus expected to yield an S = 0 ground state as per Ovchinnikov's rule, which could either correspond to an open-shell singlet or a non-magnetic, closed-shell ground state. Introduction of an organic spacer in the structure serves to not only tune the magnetic coupling between the triangulene units, but also modify the magnetic correlations, leading to high-or low-spin ground states. As shown in Scheme 1, while separation of two triangulene units by a 1,4-phenylene spacer is expected to result in an S = 0 ground state, separation through a 1,3-phenylene spacer generates a net sublattice imbalance in the structure, and therefore should result in an S > 0 ground state. Therefore, a range of nanoarchitectures based on TZNGs can be conceived with tunable coupling strengths and magnetic ground states. Scheme 1. Tunability of magnetic coupling and synthetic route toward triangulene dimers. a) Chemical structure of triangulene with the carbon atoms of the two interpenetrating triangular sublattices highlighted with blue and red filled circles (left). NA and NB denote the number of carbon atoms in the A and B sublattices, respectively. Triangulene exhibits a sublattice imbalance of two, with the majority sublattice atoms located at the zigzag edges. Direct coupling of two triangulene units through their minority sublattice atoms leads to no sublattice imbalance in the dimer (right). b) Schematic showing triangulene dimers with a 1,4-phenylene (left) and 1,3-phenylene (right) spacers. The dimer with 1,3-phenylene spacer contains a net sublattice imbalance of four in the structure. c) Synthetic route toward triangulene dimers reported in this work.

Results and Discussion
Toward the synthesis of 1, a submonolayer coverage of 3 was deposited on a Au(111) surface held at room temperature, and annealed to 300 °C to promote oxidative cyclization of the methyl groups. STM imaging of the surface after the annealing step revealed isolated dumbbell-shaped molecules and covalently bonded oligomers ( Figure 1a). Figure 1b presents a high-resolution STM image of an individual molecule, which shows characteristic lobed signatures in the local density of states (LDOS). We conducted ultrahigh-resolution STM imaging with a carbon monoxide-functionalized tip [27,28] to obtain the bond-resolved structure of the molecule, which confirmed the successful formation of 1 (Figure 1c and Supporting Information, Figure S1). The synthesis of 2 was conducted in a similar manner. STM imaging after a 300 °C annealing step of a Au(111) surface with pre-deposited 4 revealed isolated molecules similar in appearance to 1 (Figures 1d,e), and ultrahigh-resolution STM imaging confirmed the successful formation of 2 ( Figure 1f).   Figure 2 shows the electronic and magnetic structures of triangulene and the dimers 1 and 2 at successively more refined levels of theory. We start by analyzing the three systems in the nearest neighbor tight-binding (TB) model, which disregards any electron-electron interaction. The salient features in the TB energy spectra correspond to two and four non-bonding zero-energy states (ZESs) for triangulene [2,29]  The lowest-energy MFH solution corresponds to an antiferromagnetic order between the triangulene units of 1 and 2, leading to an S = 0 open-shell singlet ground state, in agreement with Ovchinnikov's rule. In the case of a single triangulene molecule, the magnetic ground state has been found to be an open-shell triplet (S = 1), which is approximately 500 meV lower in energy than the closed-shell first excited state. [30] Accordingly, 1 and 2 may be considered as weakly-coupled Heisenberg spin-1 dimers, since the effective exchange coupling between the triangulene units, Jeff, can be assumed to be much smaller than the strong ferromagnetic coupling within the triangulene using the exact diagonalization in the complete active space (CAS) formed by six electrons in six single-particle states-that is, the four non-bonding states, along with the HOMO−1 and LUMO+1 states, where HOMO and LUMO refer to the highest occupied and the lowest unoccupied molecular orbitals, respectively (see Supporting Information for method details). The Hubbard model is known to give results in line with those of advanced quantum chemistry methods. [30] The exact diagonalization of CAS (6,6)   This confirms the detection of the spin-split frontier molecular orbitals of both species, and their Coulomb gaps approximately equal 1.65 eV. dI/dV spectroscopy on 1 in the vicinity of the Fermi energy reveals conductance steps symmetric around zero bias (Figure 3c, blue curve), which is indicative of an inelastic excitation. [31] Given the open-shell singlet ground state and the open-shell triplet first excited state of 1, we ascribe the inelastic excitations to singlet-triplet (S = 0 to S = 1) spin excitation, which obeys the IETS spin selection rule that dictates ΔS = 0, ±1 for magnetic excitations (Supporting Information, Note S2). The excitation threshold, extracted from a fit to the experimental IETS spectrum with an antiferromagnetic spin-1 Heisenberg dimer model, [32] is ±14 mV, and provides a direct experimental measure of the Jeff (or, the singlet-triplet gap) of 1 (Figure 3c, red curve and Supporting Information, Figure S2). Similarly, dI/dV spectroscopy on 2 also presents singlet-triplet spin excitations

Conclusion
In summary, we have demonstrated the on-surface synthesis of triangulene dimers with and without a 1,4-phenylene spacer. The magnetic ground states of both dimers are predicted to be the open-shell singlet, with the first and second excited states being the open-shell triplet and quintet, respectively. In accordance with theoretical predictions, we experimentally detect singlet-triplet spin excitations, whose strength can be tuned with the spatial separation between the triangulene units. Our results prove that TZNGs on metal surfaces retain their high-spin magnetic ground states, and can efficiently couple to give rise to collective magnetism. Given the large exchange interaction of 14 meV and the presumably small magnetic anisotropy in triangulene dimers due to the weak spinorbit coupling in carbon, our findings should pave the way for fabrication of magnetic TZNG networks, providing a platform to explore emergent quantum phases and realize technologically relevant magnetic materials.

Table of Contents graphical abstract:
On-surface synthesis of covalently bonded triangulene dimers with or without a 1,4-phenylene spacer is achieved on Au(111). Scanning tunneling spectroscopy measurements reveal collective magnetism in the dimers in the form of singlet-triplet spin excitations, demonstrating efficient and tunable inter-triangulene magnetic coupling.

Sample preparation and STM/STS measurements. STM measurements were performed with a Scienta
Omicron low-temperature LT-STM operating at 4.5 K and base pressure below 5×10 -11 mbar. Au(111) single crystal surfaces were prepared by Ar + sputtering and annealing cycles. Precursor molecules 3 and 4 were contained in quartz crucibles and deposited at 483 and 530 K, respectively, from a home-built evaporator on Au(111) held at room temperature. STM images and dI/dV maps were acquired in constant-current mode. Unless noted otherwise, gold-coated tungsten tips were used for imaging and spectroscopy. Indicated tunneling biases are provided with respect to the sample. dI/dV and IETS spectra, and dI/dV maps were acquired with a lock-in amplifier operating at a frequency of 860 Hz. Lock-in modulation voltages (root mean square amplitude, Vrms) for each measurement is provided in the respective figure captions. The fitting of dI/dV and IETS spectra to extract the spin excitation thresholds were performed using a code developed by Markus Ternes. [1] Ultra-high resolution STM images were acquired with carbon monoxide-functionalized tips, where the molecules are scanned in a constant-height mode, and the current channel is displayed. Open feedback parameters, and subsequent tip approach distances (Δz) for each measurement is provided in the respective figure captions. Carbon monoxide molecules were deposited on Au(111) at a maximum sample temperature of 13 K. The data shown in this study were processed and analyzed with WaveMetrics Igor Pro or WSxM software. [2] 1.2. Tight binding calculations of the electronic structure. The tight-binding calculations of 1 and 2 have been performed by numerically solving the mean-field Hubbard Hamiltonian with nearest neighbor hopping: Here, , † and , denote the spin selective ( ∈ {↑, ↓} with � ∈ {↓, ↑}) creation and annihilation operator at neighboring sites and , is the nearest neighbor hopping parameter (with = 2.7 eV used), is the on-site Coulomb repulsion, , is the number operator and 〈 , 〉 is the mean occupation number at site α. Orbital electron densities, , of the th -eigenstate with energy have been simulated from the corresponding state vector , , by: where denotes the atomic site index, and 2 denotes the Slater 2pz orbital for carbon.

Complete Active Space (CAS) calculations.
The CAS method, described by Ortiz et al., [3] can be broken down in the following steps: 1. Solution of the one-orbital tight-binding model for a given structure and choice of hopping parameters. This yields a single particle spectrum and a set of molecular orbitals.

2.
Representation of the Hubbard model in the basis of molecular orbitals.
3. Choice of active space orbitals. In our calculations we include the four non-bonding zero-energy states and the lowest energy pair of finite-energy states above and below the non-bonding states (that is, HOMO−1 and LUMO+1).

Construction of the many-body configurations for six electrons in six orbitals.
The number of configurations is 6 (12) = � 12 6 � = 924. 5. Construction of the many-body matrix Hamiltonian, obtained by the representation of the Hubbard model in this basis. S3 6. Diagonalization of the many-body matrix and analysis of energy spectrum degeneracies, that permit to identify the multiplets.

Solution synthesis.
Unless otherwise noted, all starting chemical materials were purchased from Sigma Aldrich, TCI, ABCR, and other chemical providers. All starting materials were used as received without further purification. The solution chemical reactions, unless otherwise mentioned, were conducted under air-and moisture-free conditions using a sealed Schlenk system under argon atmosphere, because of handling air-and moisturesensitive chemical substances. The reaction progress was monitored by thin layer chromatography (TLC), containing silica-coated aluminum plates and fluorescence marker F254 (silica 60, F254, Merck). If necessary, crude reaction products were purified by preparative silica gel chromatography (particle size: 40-63 µm, VWR Chemicals) and recycling gel permeation chromatography (rGPC). rGPC was carried out on JAI HPLC LC 9110 II NEXT instrument with fraction collector FC-3310, and in series connected GPC columns 2H and 1H with chloroform (HPLC grade) as eluent. For structural characterization, proton and carbon nuclear magnetic resonance spectra ( 1 H and 13 C-NMR, respectively) were recorded at room temperature (296 K) on a BRUKER AC 300 P NMR instrument, operating at 300 MHz for 1 H-NMR and 75 MHz for 13

S6
Note S1: Solution of the Heisenberg dimer model. The energy spectrum for a Heisenberg dimer Hamiltonian where is the exchange coupling between the spins and and correspond to the individual spin operators, can be obtained using the following trick. We define the total spin operator We use the fact that the spectrum of 2 = . is ( + 1), where are the integer/half integer numbers that cover the range | 1 − 2 |, … , 1 + 2 . We now write The spectrum of the first two operators on the right hand side of equation (S5) is 1,2 ( 1,2 + 1). Therefore, we can For triangulene, 1 = 2 = 1, and can thus take three values, that is, = 0, = 1 and = 2. The energies of the three spin states are given by: For > 0 (that is, antiferromagnetic coupling between the triangulenes), the ground state has = 0, and we have ( ) − (0) = ( /2) ( + 1), which yields the excitation energies as also obtained through the CAS(6,6) method.

S7
Note S2: IETS spin selection rule. Here we elaborate on the origin of the = 0, ±1 spin selection rule for IETS. Our starting point is the assumption that the inelastic co-tunneling event is a spin conserving process when both the molecule and the tunneling electron are considered. Therefore, the initial and final total spin must be conserved, that is Now, the initial spin state of the tunneling electron and the molecule is the one obtained from combining the initial spin of the molecule and the = 1/2 for the electron Similarly, the final spin state is also expressed in terms of the final spin of the molecule and the = 1/2 for the electron Now, combining equations (S9)-(S11), we arrive at the condition which provides the selection rule for observing spin excitations in IETS. (2-(1,3-Dioxolan-2-yl)phenyl(4-bromo-2,6-dimethylphenyl)methanol (7): Commercially available 5-bromo-2iodo-m-xylene (6) (3.5 g, 11.2 mmol, 1.0 eq.) was dissolved in 45 ml dry tetrahydrofuran (THF) and cooled to -78 °C. A solution of n-butyl lithium (n-BuLi) in hexane (1.6 M, 7.7 ml, 12.3 mmol, 2.2 eq.) was added dropwise under argon atmosphere and the reaction was maintained at -78 °C for 1 hour. Separately, 2-(1,3-dioxolan-2yl)benzaldehyde (5) (1.0 g, 5.6 mmol, 1.0 eq.), synthesized according to literature procedure, [4] was dissolved in 5 ml dry THF and added under argon atmosphere to the reaction mixture via syringe. The resulting mixture was allowed to warm up gradually to room temperature and the reaction mixture stirred until completion. The reaction mixture was quenched with an aqueous solution of ammonium chloride (NH4Cl), extracted three times with ethyl acetate (EA), and the combined organic layer was washed with brine and dried over magnesium sulfate (MgSO4).
The solvent excess was removed by evaporation and the crude compound was purified by silica gel chromatography using EA/iso-hexane 1:3 as eluent to afford 7 as white solid (800 mg, 39 %).

2-((4-Bromo-2,6-dimethylphenyl)(methoxy)methyl)benzaldehyde (9):
Compound 8 (200.0 mg, 0.5 mmol, 1.0 eq.) was dissolved in a mixture of 6 ml THF and 6 ml 10 % aqueous hydrochloric acid (HCl). The mixture was stirred at room temperature for 5 hours and then neutralized by adding a diluted, aqueous solution of sodium bicarbonate (NaHCO3). After extraction with EA three times, the combined organic phase was washed with brine and dried over MgSO4. The excess of organic solvent was evaporated under reduced pressure and compound 9 was obtained as yellow sticky oil, which has been directly used for the next reaction step without further purification. washed with brine and dried over MgSO4. The crude target was purified by silica gel chromatography using DCM/iso-hexane 1:9 as eluent to afford 11 as light yellow solid (250 mg, 47 %).  and stirred at room temperature for 30 minutes under glove box conditions. Afterwards, 9-(4-bromo-2,6-dimethylphenyl)anthracene (11) (10.0 mg, 28.0 µmol, 2.0 eq.) was added in one portion and the mixture was stirred at room temperature overnight. Afterwards, the reaction mixture was quenched with water and was extracted three times with DCM. The combined organic layer was washed with brine and dried over MgSO4. After removing the solvent excess under reduced pressure, the crude compound was purified by silica gel chromatography using DCM/iso-hexane 1:9 as eluent to afford title compound 3 as light yellow solid (6 mg, 77 %).  (EtOH), 1 ml water (H2O) and 1 ml toluene has been prepared and intensively purged with argon for at least 15 minutes. Meanwhile, compound 11 (37.0 mg, 0.2 mmol, 1.0 eq.), commercially available 1,4-phenylenediboronic acid (12) (201.0 mg, 0.5 mmol, 2.5 eq.) and potassium carbonate (K2CO3) (277.0 mg, 2.0 mmol, 9.0 eq.) have been added. At last, tetrakis(triphenylphosphine)palladium(0) (Pd(PPh3)4) (15.0 mg, 0.01 mmol, 0.06 eq.) was quickly added in one portion and reaction mixture was heated to 110 °C overnight. After cooling down to room temperature the reaction mixture was extracted three times with DCM, washed with brine and dried over MgSO4.
The crude material was purified by silica column chromatography using DCM/iso-hexane 1:9 as eluent to afford 4 as dark yellow solid (50 mg, 35 %). Further purification by rGPC afford 4 as yellow solid.