Control of Molecular Orbital Ordering Using a van der Waals Monolayer Ferroelectric

2D ferroelectric materials provide a promising platform for the electrical control of quantum states. In particular, due to their 2D nature, they are suitable for influencing the quantum states of deposited molecules via the proximity effect. Here, electrically controllable molecular states in phthalocyanine molecules adsorbed on monolayer ferroelectric material SnTe are reported. The strain and ferroelectric order in SnTe are found to create a transition between two distinct orbital orders in the adsorbed phthalocyanine molecules. By controlling the polarization of the ferroelectric domain using scanning tunneling microscopy (STM), it is successfully demonstrated that orbital order can be manipulated electrically. The results show how ferroelastic coupling in 2D systems allows for control of molecular states, providing a starting point for ferroelectrically switchable molecular orbital ordering and ultimately, electrical control of molecular magnetism.

orbital order can be manipulated electrically. Our results show how ferroelastic coupling in 2D systems allows control of molecular states, providing a starting point for ferroelectrically switchable molecular orbital ordering and ultimately, electrical control of molecular magnetism.
The use of electric fields is a powerful approach to manipulate molecular electronic states 1-7 , and consequently, optical properties, adsorption structures, vibrational frequencies, oxidation states and chemical reactivity 3, [8][9][10][11][12][13][14] . Being able to study these effects at the single molecule level would be very important for understanding the intimate interaction between molecules and their electrostatic environment. Yet, performing such an experiment in a well-controlled manner has proven to be extremely difficult and scanning tunneling microscopy (STM) has emerged as a leading technique in this challenging field [15][16][17] . In STM, a significant electric field is present between the STM tip and the sample surface, which will induce a Stark shift of the electronic states observed in the tunneling spectra 18,19 . By increasing the set-point tunneling current, the tip-sample distance decreases, leading to increasing electric field strength. Although this is a powerful experimental technique to study the effect of external electric fields on molecular electronic states, molecules are arXiv:2207.04245v2 [cond-mat.mtrl-sci] 22 Aug 2023 2 often required to be decoupled from a metallic substrate [20][21][22] , due to the strong perturbation of their electronic states by hybridization, charge transfer, and screening with the metal substrate 23,24 .
Finally, the tunneling current and electric field are linked and using high tunneling currents often leads to instabilities in the tip-molecule-sample junction.
We overcome these limitations by coupling single molecules with two-dimensional ferroelectric (2D-FE) materials as shown schematically in Fig. 1a with density-functional theory (DFT) calculations, which further support the effects caused by inplane electric fields on the FePc molecular states. Our study provides a well-defined, controllable platform for manipulation of molecular electronic states with an electric field, having also great potential for practical applications in molecular electronic and spintronic devices.
We first study the FE order of ultrathin SnTe monolayer grown by molecular beam epitaxy (MBE) on highly oriented pyrolytic graphite (HOPG) substrate (see Methods and Supporting Information Fig. S1).   when they are adsorbed on domain 1, 3, 5 (Fig. 2c). Furthermore, there are less intense features at around 1 V, which may come from further splitting of LUMO+1 peaks. We will discuss this in 6 more detail in Fig. 3. We can also visualize the changes from one ferroelectric domain to another across the boundary between the domains. This is shown in the line spectra on the molecules along the green arrow.

In order to follow the relation between polarization of an FE domain and a change in
We observe that in crossing the boundary between two domains (black arrow in the Fig. 3a), there is a discrete change in the dI/dV spectra (the FE domain boundary is indicated by the white dashed line in Fig. 3c ). In particular, we observe that the original LUMO and LUMO+1 peaks split and intensities are inverted once the direction of polarization changes. This is consistent with our observations on single molecules discussed above. It is important to note that this splitting is not related to where the molecules are located with respect to the underlying moiré pattern. In fact, the moiré pattern only periodically modulates the energy position of the conduction band of SnTe (see Fig. S4 in the SI). We have repeated the same experiment on different FePc islands and always observe the same behavior (see Fig. S6 in the SI). The main reason for this change is the Stark effect, which shifts and splits of molecular resonances due to the presence of an external electric field 30 . However, in our case, the electric field comes from the underlying FE substrate and it is not related to the electric field from the STM tip 16,17 . Under this electric field, the D 4h symmetry of FePc molecule is broken due to the coupling with ferroelectricity, and this further causes splitting of the partially occupied d xz and d yz levels of the FePc molecules as predicted by our DFT calculations (see detail below).
We have performed DFT calculations in order to understand the ground state and electronic properties of the FePc molecules in the presence of ferroelectricity from the SnTe substrate. The ground state of the isolated FePc molecule is a triplet S = 1 state, with the spin polarization mostly concentrated on the central Fe atom, as has been predicted before through DFT and Monte Carlo simulations 26,27,31 . The Fe 3d-electrons can also manifest the triplet state in different ways depending on the interaction with the substrate, and even a high spin quintuplet can be observed when FePc islands are deposited on a Cu surface 32,33 . Here we demonstrate that the triplet can also correspond to different spin configurations depending on the coupling of the FePc molecule with the ferroelectricity of the SnTe substrate. In our calculations, the different domains of the SnTe layer observed in the experiment were simulated by first fully relaxing the FePc+SnTe system, giving a lattice distortion of 2.5 %, and a second case was considered by increasing the distortion to 4% to model a strained system. Fig. 4a show that the D 4h tetragonal symmetry is slightly broken due to the coupling with ferroelectricity, and a subtle splitting of the partially occupied d xz and d yz levels is observed. Applying strain to the SnTe layer, hence increasing the coupling of the Fe states with the ferroelectricity, causes the promotion of one electron from the d z 2 to the d yz orbital. This where l x , l y , l z are the single particle angular momentum operators in the Fe d-manifold. The physical significance of the different terms can be understood as follows. The terms D and F account for the planar nature of the molecule, E for the four-fold rotational symmetry and G controls the induced breaking of rotational symmetry induced by the ferroelectric strained substrate. We first note that in the absence of strain in the sample, the two directions of the ferroelectric polarization would be equivalent due to the original C 4 symmetry of the substrate. In this scenario, ferroelectric polarizations rotated by 90 • must give rise to equivalent spectra due to symmetry, as depicted schematically in Fig. 4b. In contrast, in the presence of strain in the sample, two configurations with ferroelectric polarization rotated by 90 • will give rise to inequivalent electronic configurations, due to the explicit breaking of C 4 created by the strain. In this scenario, the two ferroelectric configurations will induce different values of |G| in the molecule, effectively allowing to control its state by the polarization of the underlying substrate. For small values of |G|, the crystal field gives rise to a spin density located in the d xz and d yz orbitals. Once the induced breaking driven by the strain ferroelectric surpasses a critical value, the term G drives an orbital ordering transition yielding a spin polarization located in the d z z and d xz orbitals. The schematic image in Fig. 4b shows the spin densities obtained through DFT around the Fe atom before and after the FePc undergoes the orbital transition. In particular, the symmetry breaking induced by G drives a splitting between the originally degenerate levels d xz and d yz , accounting for the orbital transition in the molecule. Fig. 4c shows that the orbital transition changes considerably the density of states of the Fe atom, mostly because the d z 2 orbital is partially occupied after the transition, explaining the different dI/dV spectra obtained when the FePc molecule is deposited in different domains. In conclusion, we have proposed a new platform for probing the effect of an electric field on molecular orbitals by coupling single molecules with a two-dimensional ferroelectric material, with the possibility to manipulate the molecular states by controlling the polarization of the FE domains.
In particular, we have demonstrated that under the presence of an intrinsic electric field from the underlying FE substrate, the orbital filling and degeneracy of d orbitals of a single FePc changes.
This provides a promising way to achieve nonvolatile switching of magnetism at the molecular scale by a 2D ferroelectric substrate and has great potential for practical applications in logic and spintronics devices. As we control the magnetism in a single molecule through the FE polarization, it is also a first step towards constructing artifical multiferroic states in molecule-2D materialhybrids. * kezilebieke.a.shawulienu@jyu.fi