Symmetry mediated tunable molecular magnetism on a 2D material

The induction of unconventional superconductivity by twisting two layers of graphene a small angle was groundbreaking1, and since then has attracted widespread attention to novel phenomena caused by lattice or angle mismatch between two-dimensional (2D) materials2. While many studies address the influence of angle mismatch between layered 2D materials3-5 , the impact of the absorption alignment on the physical properties of planar molecules on 2D substrates has not been studied in detail. Using scanning probe microscopy (SPM) we show that individual cobalt phthalocyanine (CoPc) molecules adsorbed on the layered superconductor 2H-NbSe2 change drastically their charge and spin state when the symmetry axes of the molecule and the substrate are twisted with respect to each other. The CoPc changes from an effective spin-1/2 as found in gas-phase6 to a molecule with non-magnetic ground-state. On the latter we observe a singlet-triplet transition originating from an antiferromagnetic interaction between the central-ion spin and a distributed magnetic moment on the molecular ligands. Because the Ising superconductor 2H-NbSe2 lacks inversion symmetry and has large spin-orbit coupling7 this intramolecular magnetic exchange has significant non-collinear Dzyaloshinskii-Moriya (DM)8, 9 contribution.

interaction between the central-ion spin and a distributed magnetic moment on the molecular ligands. Because the Ising superconductor 2H-NbSe 2 lacks inversion symmetry and has large spin-orbit coupling 7 this intramolecular magnetic exchange has significant noncollinear DzyaloshinskiiMoriya (DM) 8,9 contribution.
Symmetry as a fundamental concept enables to classify properties of molecules and materials such as their optical activity, electronic bandstructure, or vibration modes 10 . The molecular symmetry can be changed without modifying its structure by adsorbing the molecule on a sample with a dissimilar point-group. In particular, low dimensional 2D materials are potentially interesting as platforms because of their intrinsic slowly decaying long-range interactions and the resulting extended coherence 11 . Especially the surface of H phase transition metal dichalcogenides (TMDs) provide broken in-plane inversion symmetry and significant spin-orbit coupling induced by the central 4d metal ions. These properties together are key for introducing non-collinear magnetism via antisymmetric DM exchange interactions in adsorbed magnetic systems 12 .
We choose CoPc, a highly symmetric metal-organic complex with flat adsorption geometry, on superconducting 2H-NbSe 2 to explore the influence of symmetry on the magnetic properties of metal-organic molecules by means of SPM. We find two stable adsorption sites of the molecules (Fig. 1a, c) which differ in their in-plane orientation: The molecule is either aligned or twisted by 15˝with respect to the main surface directions (Fig. 1d, f). Constant-height SPM images also show slight differences in the topographic appearance of the two types hinting to a distinction between their electronic structures. At first glance both types of CoPc molecules have retained their cross-2 like appearance, however, a closer inspection reveals that the topography of the molecules has only mirror symmetry.
We can rationalize the observation of the two differently adsorbed CoPc molecules by noticing that the difference between C 3v symmetry of the surface and C 4v symmetry of the molecules completely breaks all nontrivial rotational symmetries letting the mirror symmetries the only retaining ones of the system (for details see SOM). Therefore, to reach maximum symmetry, one of the three σ v mirror planes of the sample can be either aligned to one of the two σ v or the two σ d mirror planes of the CoPc molecules, resulting naturally in the two different adsorption geometries with 15˝rotational difference. Those molecules in which the σ v of the sample is aligned with their σ d have magnetic properties similar to CoPc in the gas phase with an effective spin S " 1{2 that originates from an unpaired electron at the central Co 2`i on 13 . We label these molecules CoPc d .
Contrarily, molecules in which the σ v of the sample and of the molecule are aligned couple stronger to the substrate and enable charge transfer between the molecular orbitals and the sample. We label these molecules as CoPc v .
We now characterize in detail the magnetic state of CoPc d by dI{dV spectroscopy using a Pb-coated SC tip with an effective gap of ∆ T « 1.15 meV (for details see methods). Placing the tip of our SPM over the bare sample we observe a gap of˘p∆ S`∆T q due to SC -SC tunneling between tip and sample (∆ S « 1.3 meV) while we measure a pair of peaks at «˘1.8 meV on the molecule (Fig. 2a, b). These peaks originate from the scattering of Cooper pairs at the unscreened magnetic moment of the CoPc d molecule leading to a pair of Yu-Shiba-Rusinov (YSR) states within the SC gap of the surface [14][15][16][17] . We find good agreement with the measured data when simulating these YSR states using a scattering model in which the impurity is treated in classical approximation with an effective magnetic moment of 1 2 πρ S J S S "´0.60˘0.02 and where J S is the coupling strength between the Co 2`i on and the sample, ρ S is the density of electron states of the sample in the normal conducting phase, and S is the effective spin of the central ion (for details see SOM) 18 . The asymmetric intensity between the peaks at positive and negative bias indicates that particle-hole symmetry is broken which we account for by an additional Coulomb scattering of πρ S U " 0.28˘0.02.
In order to infer the spin of the CoPc d , we apply a magnetic field B ě 5 T perpendicular to the sample surface that is strong enough to suppress SC in tip and sample. Contrarily to the B " 0 data, we now observe split peaks around zero bias (Fig. 2c), typical for an S " 1{2 spin in the weak coupling Kondo regime where the Zeeman energy E Z " gµ B B is larger than the Kondo energy k B T K (µ B is the Bohr magneton and k B is the Boltzmann constant) 19 . The Kondo temperature T K is the characteristic temperature below which magnetic exchange interactions between the doublet state and the conduction electrons of the sample screen the local magnetic moment of the molecule forming a many-electron singlet state 20,21 . A linear regression of the peak splitting leads to a Landé g-factor of 1.54˘0.02, significantly smaller than the one for a free electron (Fig. 2d). The interception of the fit with the abscissa is not at the origin but at a B K " 0.67˘0.19 T. In linear approximation, B K is the minimal field strength necessary for splitting the Kondo singlet state and enables the estimation of Because the Kondo screening energy is much smaller than the Cooper pair binding energy of the sample, i. e. ∆ S " k B T K , the opening of the SC gap at B " 0 hinders Kondo screening by depleting the available electronic states at the Fermi energy, in perfect agreement with the appearance of the YSR-states 23 .
We now turn our interest towards the CoPc v molecules. On these molecules we detect strong spectroscopic features at |V | « 23´25 mV, but neither a Kondo peak close to zero bias nor YSR states inside the SC gap (Fig. 3a, b). Indeed, comparing the SC gap measured on the bare surface and on the molecule reveal no detectable difference at B " 0 ( Fig. 3b). In contrast to the observation on CoPc d , even at B-fields large enough to suppress SC, we observe only a flat and featureless spectrum suggesting that CoPc v is not S " 1{2, but has a non-magnetic ground-state  (Fig. 3g). In contrast, we observe a splitting in only two distinguishable excitations.
Remarkably, the excitations at lower absolute energy have about twice the intensity of the ones at higher absolute energy. This points to additional non-collinear interactions between both spins. To get a deeper understanding we model the excitation energy using the following Hamiltonian: Here, the first term accounts for the Zeeman energy with the B-field applied perpendicular to the surface in z-direction. The second and third terms account for the interaction between the two intramolecular spinsŜ i "`1 2σ  (Fig. 3d, f). The apparent visibility of only two transitions originates from an asymmetric shift of the triplet state energies so that even at high B-fields two of them can not be separated and overlay in the observed dI{dV spectra (Fig. 3h, i). This also clearly exclude that D ST has a significant out-of-plane component.
In contrast to the intermolecular interaction found in layers of CoPc 26 , here the main interaction between both spins on the CoPc v molecule is mediated by intramolecular superexchange and 6 varies only slightly (˘2.5%) with adsorption position on the charge-density-wave modulated 2H-NbSe 2 surface (see SOM). However, the significant DM coupling can not originate from within the flat molecule. Presumably it is due to interactions between the magnetic moments in the CoPc and the Nb d-orbitals of the 2H-NbSe 2 27, 28 resulting in an in-plane DM vector (Fig. 4a) 29 , in agreement with the experimental data.
To study the excitation of CoPc v in greater detail we take spectra on a grid of points covering one CoPc v molecule. At every point we determine J ST assuming a constant ratio | D ST |{J ST " 0.45 and the intensity of the inelastic conductance relative to the total conductance, A " σ inel. {pσ el.σ inel. q (Fig. 4b,c). The J ST map clearly reflects the 4-fold symmetry of the bare molecule (Fig. 4b).
The observed small variations of J ST with tip position are due to attractive mechanical forces exerted by the tip which bend the molecule and changes thereby the intramolecular magnetic coupling (see SOM).
In stark contrast to the J ST map, the A-map shows clear mirror symmetry along the σ v axes of molecule and surface, and a strong variation over the molecule with A ranging from. « 0.5´0.9.
This map describes the spatial distribution of the spin excitation intensity, which is correlated to the relative local density of states of the orbitals containing the unpaired spins 30 . Surprisingly, we detect large A not only on the central Co 2`i on but also on the phthalocyanine ring as two, c-shaped lobes symmetrically around the mirror plane, clearly marking this direction as the one in which