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Orbital Symmetry of Kondo State in Adsorbed FePc Molecules on the Au(110) Metal Surface Pierluigi Gargiani, Maria Grazia Betti, Amina Taleb-Ibrahimi, Patrick Le Fevre, and Silvio Modesti J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b07805 • Publication Date (Web): 02 Dec 2016 Downloaded from http://pubs.acs.org on December 5, 2016

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The Journal of Physical Chemistry

Orbital Symmetry of Kondo State in Adsorbed FePc Molecules on the Au(110) Metal Surface Pierluigi Gargiani,∗,†,‡ Maria Grazia Betti,† Amina Taleb Ibrahimi,¶ Patrick Le Fèvre,¶ and Silvio Modesti§,k †Dipartimento di Fisica, Universit` a di Roma “La Sapienza”, Piazzale A. Moro 5, I-00185 Roma, Italy ‡ALBA Synchrotron Light Source, E-08290 Cerdanyola del Vallés, Barcelona, Spain ¶Synchrotron SOLEIL, L’Orme des Merisiers, Saint-Aubin, BP 48, 91192 Gif-sur-Yvette, France §Dipartimento di Fisica, Universit` a di Trieste, via Valerio 2, I-34100 Trieste, Italy kCNR-IOM TASC, S.S. 14, km 163.5, I-34149 Trieste, Italy E-mail: [email protected] Phone: +34935924391

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Abstract The Kondo ground state can arise in surface supported organometallic systems, such as the 3d transition metal phthalocyanines, as a result of the hybridization of the 3d localized orbitals with the underlying metal substrate electrons. Low-temperature Scanning Tunneling Spectroscopy can identify the Kondo states as a zero-bias anomaly in the differential conductance curves, often localized in close proximity with the 3d metal center. However the information on the symmetry of the Kondo state, on the exact shape of the spectral function and on the magnetic state is generally missing from the experimental data. We apply complementary techniques, i.e. scanning tunneling spectroscopy, resonant photoemission spectroscopy and x-ray magnetic circular dichroism, to identify the Kondo state, the orbital symmetry and the magnetic moment of Fe-Phthalocyanine chains formed by two structural phases with increasing molecular density: first ×5 and at higher coverage ×7 FePc ordered chain structures assembled on the Au(110) surface. The experimental data suggest the presence of a Kondo state only in the ×5 phase, at lower molecular density, with a Kondo temperature of about 60 K, having parent states with the dxz , dyz symmetry, that cancels the magnetic moment of the molecules at low temperatures.

Introduction The Kondo effect may arise from the coupling of a non-zero spin localized state of an atom, a molecule or a nanostructure with a Fermi sea through the spin-flip scattering and generates a spin-zero many-body state below a Kondo temperature TK with a resonance in the density of states at the Fermi level. 1,2 When the localized unpaired spins form an array - the Kondo lattice - the coupling between the spins and the periodicity adds to the Kondo screening of the itinerant electrons and may give rise to the rich physics of the “heavy fermions” below a coherence temperature T ∗ . 1 Up to now, the experimental method used to investigate the Kondo state of atoms and molecules adsorbed on metal surfaces with high spatial resolution

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is Scanning Tunneling Spectroscopy (STS). Often this technique does not provide a direct picture of the peaks of density of states of Kondo systems due to the quantum interference between the tunneling channels (from the tip to the localized state and from the tip to the delocalized states of the conduction electrons) 3–7 that generate a Fano-like lineshape with an enhanced contribution of the delocalized states to the Kondo peak. On the other hand photoemission spectral density better describes the electronic states involved in the Kondo state although results on molecular systems are rare, 8 because of the low surface density of adsorbed Kondo centers. Photoemission spectroscopy may provide complementary information on the Kondo state of metal-organic adsorbates with respect to STS, because it can pinpoint the contribution of the localized states to the Kondo state by exploiting the resonant effects and it can unveil the symmetry of the state by applying the selection rules. Resonant photoemission occurs when a core-electron excitation is degenerate with continuum excitations and causes a photon-energy dependent enhancement of specific localized states. 9 It has been already used to detect a Kondo-like peak in the photoemission spectra of adsorbed Ce atoms. 10 The information gathered by local probe approaches and resonant photoemission can be further complemented exploiting the chemical selectivity and magnetic sensitivity of X-ray Magnetic Circular Dichroism (XMCD) in order to elucidate the magnetic response of the adsorbed molecules metal-centers coupled with the conduction electrons. Here we apply these techniques to a paradigmatic organometallic system: FePc chains assembled along the Au(110) reconstructed channels. 11,12 The molecule-substrate interplay induces a self-templating effect of the metal surface, driving the self-assembly of planar molecular from 1D chains to long range ordered reconstructed structures: i. e. a compact single layer (SL) that has a ×7 periodicity with respect to the substrate, with two FePc chains per unit cell spaced by 1.4 nm, and a more open ×5 phase (at about 50% of the compact SL coverage) with adjacent FePc chains separated by one row of Au atoms 11,12 as shown in the inset of Fig.1 left and right panels respectively. The magnetic state of isolated FePc molecules is controlled by the Fe 3d states in the

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D4h symmetry: five Fe 3d orbitals transform as a1g (dz2 ), b1g (dx2 +y2 ), eg (dxz+zy ) and b2g (dxy ). 13 These orbitals, hybridized with the organic states, contain six electrons that fill the b2g orbital leaving one hole in the eg and a1g orbitals respectively and the higher energy b1g state completely empty, resulting in a S=1 ground state of the free molecule. The interaction of FePc with the Au(110) causes a strong rehybridization of the out of plane molecular states with the substrate. 14 The FePc single layer in the ordered ×7 structure is still magnetic, as indicated by X-ray Magnetic Circular Dichroism (XMCD), 14 even if with a reduced magnetic moment with respect to the FePc thin films 14,15 or FePc single layer adsorbed on weakly interacting substrates. 16

Experimental section Photoemission experiments were carried out at the CASSIOPEE beamline at Soleil synchrotron radiation storage ring. The photoemitted electrons were analyzed with a R4000 Scienta analyzer with an overall energy resolution of 18 meV at 60 eV photon energy. The photon energy polarization was linear with the electric field vector either parallel or perpendicular to the incidence plane (p and s-polarization respectively). The photon beam impinging angle was 45◦ degree from the sample surface. The sample was azimuthally oriented with the plane of incidence parallel to the [1-10] direction, collinear with the molecular chains. The spectra were recorded with the substrate at a base temperature of 8 K. Temperature dependent photoemission spectra were collected warming the sample up to room temperature. The sample preparation is described in ref. 11 STS spectra were obtained by measuring the differential conductance dI/dV on various parts of the FePc molecule with an Au tip by the lock-in technique with a bias voltage modulation < 7 mVpp and a tunneling current < 100 pA at 5 K. The XMCD experiment was performed at ESRF-ID08 beamline and the experimental conditions are reported in ref. 14

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Results and discussion

Figure 1: STS spectra of FePc molecules on Au(110) in the ×5 (left panel) and in the ×7 (right panel) phase measured at T=5 K. An arbitrary offset has been added to the curves of spectra 1 and 2 for the sake of clarity, namely 1.0 and 0.5 arb. units to left panel, 1.0 and 0.2 arb. units in the right panel. The spectra measured on top of the center - the Fe atom-(1), at about 0.2 nm from the center (2) and on the organic periphery of the molecule (3). The arrow in the left panel points to the zero bias anomaly present only at about 0.2 nm from the center. The insets show the STM topographic images of the ×5 and ×7 phases and the points where the STS spectra were acquired.

Scanning tunneling spectroscopy A selected set of tunneling spectra measured on FePc molecules in the ×5 and ×7 phases at T=5K on the Fe atom at the center of the molecule (spectrum 1), at about 0.2 nm from the

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center close to the pyrrole ring (spectrum 2) and on the periphery of the molecule (spectrum 3) is shown in Fig.1 left and right panels respectively. The Fermi level corresponds to zero bias. A sharp feature at the Fermi level EF - a dip about 30 meV wide pointed out by the arrow - is present in the spectra measured 0.2 nm from the center in the ×5 phase only (spectrum 2). The dip at 0 bias is a weak feature on a large background. The intensity of this dominating background decreases rapidly moving away from the center of the molecule. For these reasons, the dip does not produce features in the dI/dV map at zero bias in contrast to the case of other systems where the sharp zero bias feature dominate the background. 17 At least two molecular states are present near EF in both the ×5 and ×7 phases: one (A) about 75 meV below EF and localized on the central Fe atom (spectrum 1), the other (B) about 200 meV below EF and localized on the periphery (spectrum 3). The spectrum measured at 0.2 nm from the molecular center (spectrum 2) shows a peak A′ at the same energy of peak A but narrower. In contrast to the ×5 phase, no sharp structure at the Fermi level is observed in any part of the molecule in the ×7 phase (Fig.1 right panel). It is worth noting the reduced width of peak A on the central Fe atom in the ×7 phase (spectrum 1, Fig.1 right panel). A detailed analysis of the density of states by means of DFT calculations and photoemission spectroscopy has been already presented in refs. 11,14,18 We attribute peak A, that has maximum intensity on top of the exact center of the molecule, to a state resulting from the hybridization of the Fe a1g (dz2 ) orbital - half filled in the free molecule - with the substrate. Most of the peak A is below EF in agreement with the almost complete filling of the a1g orbital as the result of the interaction with the substrate as reported by DFT calculations. 11,14,18 In both the ×5 and ×7 phases the DFT calculations results report an a1g hybridization with the Au d states leading to the formation of a broad density of states peak close to the Fermi level 11,18 with its center at about 50 to 70 meV below EF , in good qualitative agreement with the STS data for the peak A. The narrowing observed in the ×7 phase suggests a lower hybridization of the molecular states with the Au states continuum.

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Broad peaks measured by STS close to the Fermi level and comparable to the features A and A’, have been observed in MPcs adsorbed on metal surfaces such as FePc/Au(111) 19 and MnPc/Ag(100) 20 and have been attributed to Kondo states with TK well above 100 K. The only way to prove the Kondo nature of an STS peak is to measure its temperature and/or magnetic field dependence. If a peak has a width similar to that of our A peak, i.e. ≥150 meV, the magnetic fields necessary to modify appreciably its shape are too large to be obtained in a laboratory and the temperatures at which the peak should broaden - several hundred kelvin - cause the desorption or the decomposition of the adsorbed layer. For these reasons the possible Kondo nature of the A peak cannot be proved. The A peak could be thus rationalized as an hybridization state arising from the interaction of the of the FePc a1g (dz2 ) with the substrate. The peak B, absent at the center and intense at the periphery, is attributed to a state mostly localized on the organic part of the molecule also in agreement with previous reports 11,12,18 showing the presence in this energy range and locations of hybridization states related to the a1u molecular orbital interacting with Au d states. It is worth noting that the Fe adsorption site both in the ×5 and ×7 configurations is on-top of an Au atomic row, with little surface free energy difference between an atomic on-top and an atomic bridge adsorption configurations as previously reported in Refs. 11,12 In particular in the ×5 symmetry phase the FePc molecules assemble in chains along the [1-10] Au(110) surface direction inside ×5 Au reconstructed channels, with each chain separated by an Au atomic row. 11 The ×7 phase is formed when a further molecular chain is adsorbed on the Au row separating the ×5 molecular chains, leading to a further substrate reconstruction, as can be evinced comparing the STM images in the inset in Fig.1. 12 The sharp STS dip present only in the ×5 phase is observed at a distance of about 0.2 nm away from the center of the molecule. The presence of the narrow structure far from the Fe center suggests a parent state characterized by a nodal plane normal to the molecule surface, excluding the a1g (dz2 ) orbital state. Similar dips at the Fermi level have been observed on FePc on Au(111) 19,21 and have been attributed to a Kondo state. This resemblance suggests

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the presence of a Kondo state also for the ×5 phase of FePc on Au(110), with peak A′ as its possible parent state. A fit of the dip with the Kondo lineshape given by Frota 22,23 (see Supplementary Material S3) provides a half-width at half-maximum (HWHM) of 20±4 meV and a Wilson Kondo temperature TK of about 60 K (HWHM= 0.45 · ΓK = 3.7kB TK from Refs. 22,23 ). This is an estimate of the Kondo temperature introducing an analytical lineshape valid for isolated Kondo impurities. This approximation is supported by the localization of the dip at a distance of about 0.2 nm from the molecule center and absent between the FePc molecules. If a Kondo lattice is formed, for example by O2 on Au(110), the presence of a dip can be also detected between the molecules. 24 For this reason, we assume that lattice effects can be neglected for the purpose of this paper. We do not observe the zero bias dip in the spectra measured at 300 K, well above the estimated Kondo temperature, in agreement with the expected temperature dependence of a Kondo peak. A more detailed study of the temperature dependence of the zero bias feature has been done by photoemission experiments (see below). A dip, instead of the expected Kondo peak in the density of states, is often found in the STS spectra of adsorbate Kondo states and it is generally attributed to a Fano-like lineshape arising from the interference of a tunneling channel from the tip to the substrate trough a localized state, and the direct tunneling channel from the tip to the substrate states. When the second channel, the direct tip-substrate tunneling, dominates a dip is expected in the STS spectra in contrast to the impurity localized states peak at the Fermi level. According to the simplified-model calculations of Ref. 5 this feature is caused by a dip in the density of states of the delocalized electrons around the impurity. A more rigorous treatment of the Kondo lineshape requires methods that reliably combine ab initio DFT calculations with many-body techniques that have been only recently attempted, and their results are not always in good agreement with the experiment in particular for more complex systems. 19,20,25 The unit cell of our system is too complex for coupled ab initio and many-body calculations of the Kondo STS spectra, thus a discussion of the exact lineshape of the feature at EF is out of the scope

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of this work.

Resonant photoemission and polarization dependence

FePc/Au(110) hν=60 eV, s pol.

a)

FePc/Au(110) x5

b)

s pol. hv=40 eV hv=60 eV hv=70 eV hv=80 eV

Coverage: 0.3 SL 0.5 SL 1.0 SL

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hν=40 eV

hν=60 eV

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p pol. s pol. hv

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]

01

[110] [0

-0.4 -0.3 -0.2 -0.1 0.0 -0.4 -0.3 -0.2 -0.1 0.0 E-EF (eV) E-EF (eV) Figure 2: a) Coverage dependence of the photoemission spectra close to EF at 60 eV in s-polarization; b) Photon energy dependence of the spectra at T=8K in s-polarization c) d) s and p-polarized spectra measured off-resonance (hν=40 eV) and on-resonance (hν=60 eV) at a coverage of 0.5 SL at T=8K. The experimental geometry of the s and p-type polarization is reported in the inset. The spectra where integrated by ±15◦ around the normal in the [001] direction. The angular resolved spectra at Γ present the same polarization and photon energy dependence of the feature at EF . All the spectra have been normalized at the same intensity at -0.4 eV. A confirmation of the presence and of the symmetry of the Kondo state can be obtained from the photoemission data at normal emission. We report in Fig.2a the photoemission 9



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spectral density close to the Fermi level measured at T=8K for the FePc/Au(110) at increasing molecular coverage, namely 0.3 single layers (SL) corresponding to a 60% complete ×5 phase, 0.5 SL associated to the ×5 phase and 1.0 SL associated to the ×7 phase. The spectra are collected at 60 eV photon energy with the plane of incidence parallel to the molecular chains with the electric field of the incoming linearly-polarized photons perpendicular to the plane of incidence (s-polarization geometry). A peak at the Fermi level is visible at 0.3 SL coverage, becoming dominant in the ×5 phase (0.5 SL), while being completely washed out at the completion of the ×7 symmetry phase. In order to verify if this peak is localized on Fe central atoms, we measured the photon energy dependence of the spectra with photon energies ranging from hν=20 to hν=80 eV (Fig.2b), finding the maximum photoemission intensity at the Fermi level at about hν=60 eV, close to the binding energy of the Fe 3p levels (54-57 eV). The enhancement of the spectral density at EF by approximately a factor 2 at hν=60 eV cannot be explained by the calculated Fe 3d photoionization cross section, that has a broad maximum at 45 eV, or by photoionization cross section of C, N and Au, 26 but it is consistent with a resonant photoemission mechanism at the Fe 3p threshold and, accordingly, with a spectral density related to Fe-localized states. The observed resonant enhancement at the 3p threshold is similar to that measured on Fe oxides compounds. 27,28 Moreover a similar 3d resonant-enhancement of the spectral density close to the Fermi level was already observed for a monolayer of FePc adsorbed on Ag(111) exploiting 2p-3d resonant transitions and it was ascribed to a charge-transfer between the molecular 3d open-shell and the substrate. 29 A similar approach has been employed to enhance the resonant peak at the Fermi level and to measure the full valence electron spectral function of Ce isolated ad-atoms adsorbed on Rh(111) at a coverage of 0.003 monolayer. 10 In the case of FePc/Au(110) the equivalent Fe surface coverage is 4% and 6% for the ×5 and ×7 phase respectively, thus allowing a sufficient signal in a resonant photoemission process to measure the Kondo peak at the Fermi level. The polarization-dependendent photoemission selection rules can be exploited in order to

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get information on the symmetry of the Fe state involved in the interaction process. The lower panels of Fig.2c and d compare the spectra acquired off-resonance (40 eV right panel Fig.2c) and on-resonance (60 eV left panel Fig.2d) in normal emission for s and p-polarizations and the plane of incidence parallel to the molecular chains direction [1-10], as described in panel Fig.2c inset. The p-polarized spectra show a broad bump centered at about -0.15 eV with weak photon energy dependence, in sharp contrast with the s-polarized spectra that are flat off-resonance and strongly peaked at EF on-resonance. The polarization enhancement of the peak at EF is still visible at photon energies well above the Fe absorption edge (see Fig.2b and Supplementary Material S4). This indicates that the different resonance behavior of the s- and p-polarized spectra cannot be attributed to a simple polarization dependence of the absorption because this dependence may be strong only a few eV close to the absorption edge. Given the photoemission selection rules, 30 an even state with respect to the photoemission plane shows up in the p-polarized spectra and is absent on the s-polarized spectra at normal emission, and an odd state behaves in the opposite way. In this experiment geometry the photoemission plane at normal emission (the plane containing the photon beam and the normal to the surface, see inset in Fig.2c) is the (001) plane, that is a mirror plane of the Au(110) surface and it is almost a mirror plane for the FePc chains. 31 Therefore the FePc molecular orbitals can be written as a linear combination of an even and odd component with respect to the photoemission plane. Among the Fe-localized molecular orbitals the ones that may give rise to a Kondo resonance are the semi-occupied a1g (dz2 ) and eg (dxz+zy ) having spin different from zero. The a1g state (dz2 ), that is even with respect to the mirror planes of the free molecule, retains a dominant even component in the adsorbed configuration being almost symmetric with respect to rotations along the sample surface normal and thus to the mirror operation along the photoemission plane. The eg state (dxz+zy ) present an odd symmetry with respect to vertical molecular symmetry plane, retaining a larger odd component with respect to the photoemission plane. The polarization dependence of the

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resonant peak, that suggests its odd symmetry, is thus well described by a partially filled eg state contributing to the resonance in agreement with the STS deduction.

Temperature dependent photoemission a)

8K

b)

K

8K

25K Intensity (arb. units)

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K

25K

60K

K

100K

60K

300K

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-0.4

-0.3

300K

-0.2 -0.1 E-EF (eV)

-0.0

-0.4

-0.3

-0.2 -0.1 E-EF (eV)

-0.0

Figure 3: a) Temperature dependence of the photoemission spectra for the ×5 phase in s (red) and p-type (black) polarization, blue line are the Fermi-Dirac (FD, see supplementary info for details) functions including a linear background calculated at 8K and convoluted with a Gaussian of FWHM=18 meV; b) spectra obtained dividing the s-polarized spectra by the p-polarized ones after a normalization at 0.4 eV below EF . A proof of the Kondo origin of the peak at the Fermi level can be provided by the temperature dependence of the photoemission spectra. We report in Fig.3a the temperature evolution of the photoemission spectra close to the Fermi level. The spectral density difference measured with s and p-polarization decreases when the temperature rises, becoming very weak above about 100 K. The intensity decrease of the Fermi anomaly as a function of temperature (observed only in s-polarization) is in agreement with a Kondo resonance 12


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behaviour. 1 The shape of the peak close to the Fermi level can be better identified by dividing the s-polarized spectra by the p-polarized ones measured at the same temperature and photon energy. In this way we can eliminate the contribution coming from the Fermi-Dirac distribution and the even-parity states to highlight the peak at the Fermi level. To avoid artifacts due to the energy misalignment between the two spectra, changes in the photon energy were kept less than 0.5 meV by maintaining the same monochromator settings during the whole set of measurements (see also Supplementary Material S1 for a detailed discussion of the normalization procedure). The results (fig.3b) show that the extra peak, present in s-polarization, has a prominent and narrow maximum at T=8 K with an HWHM of about 24±4 meV. At increasing temperature the peak at the Fermi level loses intensity and finally vanishes above 100 K. The width of the peak at T=8K and its temperature dependence is fully consistent with the approximate Kondo temperature of 60 K obtained by the STS data. The disappearance of the peak in the normalized spectra at high temperature rules out that this spectral enhancement at EF is simply caused by the tail of a DOS peak centred above EF and unrelated to a Kondo state. The absence of a Kondo feature of a1g (dz2 ) origin as deduced by STS and photoemission results may be explained by an hybridization so high that the electron-electron repulsion is overcome allowing the complete or almost-complete filling of the dz2 orbital and the loss of its magnetic moment, resulting in a quenching of the Kondo state. Other states such as the eg (dxz and dyz ), that are less hybridized with the substrate than the dz2 and contain an unpaired electron, may be the parent states of the Kondo peak with the symmetry observed by STS and photoemission. In this picture, because of the strong hybridization of the the dz2 state and of the Kondo screening of the eg states spins, the ×5 phase should not have a magnetic moment, in contrast to the ×7 phase where a magnetic dichroism has been measured. 14

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out-of-plane distributed 3d-like molecular states. The XMCD signal at B=5 T applied field is null within the noise level in the ×5 phase while a magnetic response is clearly detectable in the ×7 phase. At these field and temperature values we expect that a Kondo screening process can hinder the XMCD response of the FePc as previously suggested for a similar systems as CoPc adsorbed on Au(111). 32 Thus we ascribe the absence of the XMCD response in the ×5 phase as a result of the Kondo screening of the FePc unpaired spins, in agreement with the STS and photoemission results.

Conclusions The general picture provided by the three experimental techniques here employed on a paradigmatic highly ordered 2D molecular system, is accomplished comparing the two FePc structural phases with contrasting magnetic properties. The FePc ×5 phase has a dip in the tunneling spectra at EF , a peak in the s-polarized photoemission spectra close to the Fermi level and no magnetic dichroism. On the other hand, the ×7 phase, without STS dips or photoemission peaks at EF and presents magnetic dichroism. These results are fully consistent with the presence of a Kondo state on the ×5 phase, with eg symmetry parent state, as deduced by STS and polarization-dependent resonant photoemission, implying a quenching of the magnetic moment of the molecule. The lower hybridization of the Fe 3d-like states with the substrate electrons in the ×7 phase with respect to the ×5, testified by the sharper A and A′ peaks in STS (see Fig.1 right panel) and by the sharper XAS spectra in Fig.4, can strongly lower the Kondo temperature of the ×7 phase, well below T = 5 K, leaving the Kondo state undetected in the STS and XMCD experiment. As observed for FePc adsorbed on the Au(111) substrate, the Kondo state strongly depends on the different adsorption site symmetries and parent states. 19 Small changes in the hybridization between the Fe 3d molecular states and the substrate and in the symmetry of the binding site cause large variation in TK , 19 since this temperature depends exponentially

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on the coupling between localized and delocalized states. 1,3 The Au(110) corrugated reconstruction presents a stronger molecule substrate hybridization a lower molecule-substrate distance and a reduced steric interaction of the isoindole groups with the surface. 14 The strength of the interaction is reflected by the large width of peak A in the STS spectra that points to a strong hybridization of the dz2 orbital with the Au states, confirmed by the X-ray absorption spectroscopy (XAS) data and indicating a higher hybridization on the (110) 14 than on the (111) Au surface. 32 The consistency of the information obtained by STS, resonant photoemission and XMCD indicates that these complementary techniques can be reliably used to unravel the scenario of coupling process in Kondo systems, unveiling the spatial extension, the symmetry and orbital origin of the parent states and correlating the Kondo temperature to the interaction process with the underlying metallic states.

Supporting Information Available The following files are available free of charge. Photoemission spectra normalization procedure, experimental condition of XMCD experiment, fitting of the zero-bias peak according to Frota model and selected set of photoemission spectra across Fe 3p resonance.

Acknowledgement We thank the ID08 beamline staff at ESRF-Grenoble and the CASSIOPEE beamline staff at SOLEIL-Saint Aubin synchrotron radiation laboratories and E. Tosatti for useful discussions. This work is supported by the MIUR-PRIN project contract 20105ZZTSE and Sapienza University fundings.

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