Electron Spin Resonance of Single Molecules and Magnetic Interaction through Ligands

Electron spin resonance (ESR) spectroscopy is a crucial tool to determine the chemical structure of materials. ESR spectra measured in molecular systems, however, are established on large ensembles of spins and usually require complicated structural analysis. Recently, scanning tunneling microscopy (STM) combined with ESR has been proven as a powerful tool to image and coherently control individual atomic spins on surfaces. Here, we extend this technique to demonstrate ESR on single organic molecules - iron phthalocyanine (FePc) - and investigate the magnetic interactions between a molecular spin and either another molecular or atomic spin. We show that the molecular spin density is not only localized at the central Fe atom, but also distributed to the outer ligands, yielding a strongly anisotropic exchange coupling. Our work opens the door for using molecules in nanoscale ESR studies and promises tuning magnetic interactions between non-localized spins via tailoring ligand field symmetry and strength, which is essential for developing molecule-based spintronic devices. between this simple model and the experimental data by comparing the simulated contour lines with those measured data points, revealing the anisotropy of exchange interaction with a molecular spin. These results highlight that the ligands play a crucial role in molecular spin-spin interactions. Exchange FePc-TiB pairs with different TiB-ligand distance. a, c, e, STM pairs connection of


Introduction (Main)
Chemical engineering and fabrication of single molecular spins at the nanoscale is of vital importance in molecule-based quantum devices. 1 To detect and drive single molecular spins, there have been various approaches such as optical detection of diluted molecular spins [2][3][4] , magnetic resonance force microscopy 5 , nitrogen-vacancy magnetometry 6 , and break junction-based molecular devices [7][8][9] . Nevertheless, these systems may be subject to imbedding the molecule in a solid-state host and lack the flexibility to locate and access individual spins or harness intra-and inter-molecular spin-spin interactions.
The conventional electron spin resonance (ESR) studies on chemical ensembles 10 have not been reported to date, besides early attempts at room temperature and in ambient condition 17 . Molecules often have non-trivial spin distribution owing to the conjoint ligands 18 , giving the unique opportunity to harness the spin distribution on the ligands for engineering spinspin interaction with atomic resolution. 3 Metal phthalocyanines with various substitutional central metal atoms have been extensively employed as model systems in many-body quantum physics 18,19 and spin-dependent transport 20 .
Here, we report a system of spin-1/2 molecules, iron phthalocyanine (FePc) on bilayer magnesium oxide (MgO) grown atop an Ag(100) surface. We perform ESR on individual FePc molecules and characterize the effects of ligand orientations on spin-spin interactions in FePc-FePc dimers and FePc-titanium atom (Ti) dimers. DFT calculations show that the spin density spreads to the outer molecular ligands. Our result highlights the role of non-localized spins in the transfer of magnetic interactions, which can be crucial for fabricating molecular devices 21 .

Results and discussion
Individual FePc molecules, Fe, and Ti atoms were deposited subsequently onto a two monolayers (ML) MgO surface on Ag(100) substrate and all measurements were performed at a temperature of 2 K in a commercial STM with vector magnetic fields. The molecules and atoms are well isolated from each other at a low coverage and can be distinguished readily by their topographical appearance, as shown in Fig. 1a. Individual FePc molecules appear as a cross-like shape and lattice analysis indicates that the central Fe atom of the molecule sits atop an oxygen atom of MgO. The molecular axes are rotated by approximately 27° with respect to the underlying oxygen rows (inset of Fig. 1a). The Ti atoms in our experiment are mainly found on oxygen-oxygen bridge sites (marked as TiB) and appear taller than the Fe atoms atop the oxygen-site 22,23 .
Previous studies have reported that FePc possesses a spin S = 1 in bulk and on several surfaces 24,25 . Surprisingly, our differential conductance (dI/dV) spectra measured on well-isolated FePc molecules on a MgO surface show a clear conductance maximum, reminiscent of the Kondo effect at zero bias when no magnetic field is applied, suggesting the FePc spin being S = 1/2 4 ( Supplementary Fig. S1). This agrees with our DFT calculations, suggesting that an electron is transferred from the Ag substrate to the dz 2 orbital of FePc and the molecular spin becomes S = 1/2. The spin density of a negatively charged FePc (referred as FePc throughout this paper) is plotted in Fig. 1b, indicating that the spin distributes mainly on the central Fe atom and partially extends along the ligands 19 . Further analysis of the frontier orbital indicates that it consists of about 90% dz 2 and 10% contributions from the ligands (Supplementary Information Section 8).
We performed ESR on individual FePc molecules using rf frequency sweeps 12,14 at a fixed external magnetic field (Fig. 1c). The external magnetic field sets the Zeeman splitting of the FePc spin and the two Zeeman states of FePc spin (labeled as |0⟩ and |1⟩) can be coherently driven when the frequency of the applied oscillating electric field rf matches the Larmor frequency (inset of Fig. 1c). The spin Hamiltonian of a single FePc spin system can be written as: where is the magnetic moment of FePc. is the spin operator and the total magnetic field which sets the Zeeman splitting is a sum of external magnetic field ( ex ) and tip field ( tip ): = ex + tip . When we apply an external magnetic field along the out-of-plane (z) direction, we simplify the external magnetic field and tip field as z and tip . The resonance frequency 0 corresponding to the transition between |0⟩ and |1⟩ states is determined by As shown in Fig. 1c S2). Such deviation may stem from the spin occupied orbital configuration. These results imply that the magnetic moment of FePc on MgO is nearly isotropic having spin-1/2 and the tip field can be utilized as a local magnetic field addressing an individual spin.  Fig. 2b and e. For each dimer, the splitting between two adjacent ESR peaks appears to be independent of the tip field, implying the splitting is purely associated with the intermolecular coupling while the intensity of each peak evolves differently as the tip field varies ( Fig. 2c and f).
Moreover, the ESR splitting on (3,4) and (0, 5) configurations is different although the centercenter distance of the configurations is the same, which we will discuss later.
In order to understand the ESR spectra quantitatively, we utilize a Hamiltonian model of the two-spin system including exchange and dipolar coupling 28,29 between two FePc molecules: Here, the subscripts 1, 2 represent the two FePc spins in a dimer. The one under the tip is denoted as 1 whose Zeeman energy is set by both external magnetic field and tip field. The 1 and 2 are the magnetic moment of each FePc. The first two terms describe the Zeeman energy of a dimer system. Both FePc spins align with the external magnetic field direction since both molecules are spin-1/2 . The third and last term represent intermolecular exchange and dipolar coupling with the energy constant and , respectively. ̂ is the unit distance vector connecting the centers of two FePc spins. is given by 0 1 2 3 , where 0 is the vacuum permeability. The presence of and makes the quantum eigenstates deviate from the four pure Zeeman product states |00⟩, |01⟩, |10⟩ and |11⟩, giving rise to singlet-triplet states. While |00⟩ and |11⟩ remain as the eigenstates of 12 , the other two eigenstates become superpositions of the two Zeeman states |01⟩ and |10⟩ as defined below: where indicates the relative weight of |01⟩, |10⟩ component in the | −⟩ and | +⟩ states 22,28 and equals to +√ 2 + 2 , in which = 2( 1 − 2 ) ex + 2 1 tip and = − 2 (1 − 3 cos 2 ). is the angle between ̂ and FePc spin orientation.  its Fe center by an angle of with respect to the (2, 1) lattice direction. The center-center distance remains unchanged during such a rotation while the minimal ligand-ligand distance min (defined 11 as the nearest distance between two hydrogen atoms in the benzene rings as shown in Fig. 3c) changes accordingly. The variation in min when changes in (3,4) and (5, 0) configuration is exhibited in the inset of Fig. 3b. We note a small difference in the min of (3, 4) and (5, 0) dimers when they are in optimized configurations (i.e. = 0°). We then calculated the energy difference between ferromagnetic ( FM ) and antiferromagnetic coupling ( AFM ), the value of which equals to 1 2 for a two spin-1/2 system 30 , as a function of min (Fig. 3b). The calculated | FM − AFM | obeys an exponential decay (∝ exp (− min / )) as min increases, which can be attributed to an exchange interaction through the molecular ligands. We extract a characteristic decay length of = 0.0345 nm, which is similar to the length scale of exchange coupling in other molecular system 31 .
The calculated decreases as min gets larger in optimized (3,4), (0, 5) and (2, 5) dimer configurations, consistent with the trend observed in our experiments (Fig. 3d). Besides, we found a few dimers whose ligand-ligand distance ( Supplementary Fig. S7) deviated significantly from the optimized dimer configurations. The exchange coupling energy was significantly larger at equal center-center distance but shorter ligand-ligand distances. This result indicates that the molecular spin-spin coupling can be engineered via tuning inter-ligand symmetry. To sense the spin distribution on the molecular ligands in greater detail, we substituted a spin-1/2 TiB atom for a FePc molecule and measured the exchange coupling energy in FePc-TiB pairs.
While FePc-FePc dimers prefer to arrange only in a few configurations as mentioned above, the 13 relative spatial position of a TiB atom with respect to a FePc molecule can be controlled with atomic precision using atom manipulation. Here, the TiB atom is considered as a point magnet based on previous studies 28,29 and our DFT calculations ( Supplementary Fig. S10). We applied only z field for measuring FePc-TiB pairs in order to be able to ignore the angular dependence of the dipolar interaction. The measured exchange coupling energy is thus merely its component along the outof-plane direction, simplified as .  15 To map the anisotropic spin distribution of the FePc molecules, we measured of a total of 14 FePc-TiB pairs and observed a drastic decay of as both Fe-TiB distance ( ) and ligand-TiB distance ( ) increases (Supplementary Fig. S8). Figure 5  Upper panel: simulated spatial exchange coupling energy map by using a sum of two exponential terms representing -dependence and -dependence, respectively. The frequency range is set as 3,000 MHz (upper limit) and 5 MHz (lower limit). 17 We have demonstrated single-molecule ESR by driving the spin of an individual FePc molecule on a surface. ESR-STM measurements on molecular dimers and molecule-metal atom pairs enable us to investigate the crucial role of the molecular ligands on the exchange coupling between molecules. Here, we found that the magnetic exchange interaction with a molecule shows strong anisotropy, emphasizing the important role of ligands for the transfer of spin-polarization in molecular systems. Our work extends ESR-STM from single atoms to a much larger class of matter -magnetic molecules. This allows synthetic chemistry to design the spin properties through engineering the ligand field and symmetry. Moreover, our work suggests molecules as a potential platform to investigate magnetic interactions with non-localized spins, which has brought intensive interest in the field of metal-organic-networks and is essential for developing molecule-based spintronic and quantum information devices 32 .

STM-ESR setup
ESR measurements were performed in a commercial low-temperature STM (Unisoku, USM1300). A radio frequency (rf) microwave which was generated by a signal generator (Keysight, E8257D) was added to a DC voltage ( ) using a bias tee at the tip side. With this setup, an oscillating electric field rf was applied at the tunneling junction 33

Titanium atom manipulation
After titanium deposition, naturally formed FePc-TiB pairs were abundant. In addition, we were able to position TiB atom using atom manipulation and construct FePc-TiB pairs with various configurations. When the tunneling conductance was set as V ≈ 350 mV, I ≈ 2.2 nA, the TiB atom under the tip could follow the tip movement and be positioned at desired sites. In contrast, controllable manipulation of FePc molecule rarely occurs under our manipulation parameters.

DFT calculations
All density functional theory (DFT) calculations were performed using Quantum Espresso (version 6.5) which implements DFT using plane waves and pseudopotentials 35,36 .
Pseudopotentials were chosen based on the SSSP library and the basis set was expanded using a kinetic cutoff of 40 Rydberg 37 . All pseudopotentials use the generalized gradient approximation of Perdew, Burke and Ernzerhof (PBE) and we treated van der Waals interaction using Grimme's D3 38,39 . 19 For single FePc, the calculation model includes 4 ML of silver capped by 2 ML of MgO exposing the (100) surface 40 . In z-direction, the cell is padded with 1.2 nm of vacuum. For FePc-FePc dimer, the cell was laterally expanded to accommodate both molecules and make sure that the separation of dimers and their periodic image is at least 5 times larger than the inter-dimer distance. The exchange coupling energy was calculated using the broken-symmetry approach introduced by Noodleman 30 . This approach maps the Kohn-Sham energies of the high-spin ( = 1 ) and the broken symmetry ( = 0 ) state to the diagonal elements of the Heisenberg Hamiltonian. More computational details can be found in Supplementary Information.

Supplementary information
(1) Kondo splitting in varied external magnetic fields.
(2) Extraction of FePc by using different methods and in different magnetic fields.
(3) Statistics on magnetic moment of different individual FePc molecules.
(4) Current-dependence ESR spectra of different FePc-FePc dimers and statistics on coupling energy.
(5) ESR transitions in Heisenberg two-spin system with the tip field detuning effect.
(7) Fitting of as a function of TiB-Fe distance and TiB-ligand distance.