Tuning emergent magnetism in a Hund s impurity

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1 SUPPLEMENTARY INFORMATION DOI:.8/NNANO.5.9 Tuning emergent magnetism in a Hund s impurity A. A. Khajetoorians, M. Valentyuk, M. Steinbrecher, T. Schlenk, A. Shick, J. Kolorenc, A. I. Lichtenstein, T. O. Wehling, R. Wiesendanger, and J. Wiebe NATURE NANOTECHNOLOGY 5 Macmillan Publishers Limited. All rights reserved

2 DISTRIBUTION OF HYDROGENATED FE As reported in ref. for Ti atoms on hbn, H is dissociated, most likely by both the Pt surface and the Fe adatoms, resulting in atomic hydrogen adsorption on both the Pt() surface and the Fe adatoms. A typical area with prolonged exposure to H has a concentration of about -6% of atoms which are of FeH fcc,hcp type, whereas only % of atoms are of the FeH fcc,hcp type. The apparent height differences between all impurity types stated in the main manuscript were observed for all probed bias voltages up to V S = 5 mv, indicating they are most likely topographic in origin. Also, all impurity types remain round in geometry for all probed bias voltages, indicating that the hydrogen is most likely adsorbed on top, or below the Fe adatom. Moreover, FeH species can be laterally manipulated [] between hollow adsorption sites with typical manipulation parameters ( V S = mv, I t = na) while remaining hydrogenated. We also do not observe FeH without an occurrence of FeH. From all this we conclude, that FeH complexes contain a larger number of hydrogen atoms than the FeH complexes, and that, most probably, FeH contains only one hydrogen, and FeH contains two hydrogen atoms. Nevertheless, STM alone cannot discriminate between the number of hydrogen atoms which are bound to the Fe adatom and their bonding configuration, but our DFT calculations (see below) strongly support this conclusion. SIMULATED ISTS In order to extract the value of D for all Fe-hydrogen complexes in the effective spin model described in the main manuscript and in ref. [], we fit the ISTS using J = 5/. For FeH hcp, we fit the ISTS spectra only in that regime, where the Kondo effect is quenched, i.e. above B > T. The calculated magnetic field dependency of ISTS for the fitted D and g values for each Fehydrogen complex, assuming u = [], is plotted in Fig. S. The experimentally observed spin excitations can be fitted with different values of J, by adjusting D and J. In Fig. S, we plot the simulated spectra for Fe hcp and Fe fcc using three different values of J. For all Fe fcc impurities, the combination of B z and the out-of-plane easy axis, makes the differences in ISTS undiscernible without application of a transversal field which is not possible in our experimental setup. While only Fe fcc is plotted, the same trends are seen for FeH fcc and FeH fcc. For the hcp impurities, there are subtle differences in the low field regime, i.e. before the spin enters the J z = J ground 5 Macmillan Publishers Limited. All rights reserved

3 a b c fcc fcc fcc E (mv) FeH FeH Fe d e f hcp hcp hcp E (mv) FeH FeH Fe B (T) B (T) 6 5 B (T) Fig. S. Simulation of magnetic field dependency of ISTS for each Fe-hydrogen complex extracted from ĤJ, where (a) D =. mev, g =.8 (FeH fcc ), (b) D =. mev, g =.95 (FeH fcc ), (c) D =.9 mev, g =. (Fe fcc ), (d) D =. mev, g =. (FeH hcp ), (e) D =.5 mev, g =.9 (FeH hcp ), (f) D =. mev, g =. (Fe hcp ). state (B z < T). These variations originate from level crossings of J z states resulting from a combination of B z and an easy-plane magnetic anisotropy. The highest field transition (crossing point B z T), which is the level crossing to the maximum spin state J z = J, we refer to as the high spin transition. Various choices of J can be compensated with changes in D and g, in order to reproduce the experimentally observed zero-field spin excitation energy and high spin transition. However, none of the faint modulations in intensity which are visible in the simulated spectra below the high spin transition are observed in the experimental data for any case. Therefore, there are multiple choices of J which qualitatively reproduce the experimental data. 5 Macmillan Publishers Limited. All rights reserved

4 Fe hcp Fe fcc J = 5/ 5 B (T) D =. mev g = T eff =.8 K D = -.9 mev g =. T eff = K J = J = / D =.8 mev g =. T eff =.8 K D = -.5 mev g =. T eff = K B (T) B (T) D =. mev g =.5 T eff =.8 K V (mv) D = -.8 mev g =. T eff = K V (mv) Fig. S. Simulation of magnetic field dependent ISTS for Fe hcp and Fe fcc for different vales of the effective spin J, D, and g. For a given J, D, and g were adjusted to give the same zero-field spin excitation, and to match the high spin transition for Fe hcp (B z T). Each colorplot contains the parameters used in the simulation. TRA MAGNETIC FIELD AND TEMPERATURE DEPENDENT FIT OF THE KONDO SPEC- For the temperature-dependent fit of the spectra presented in Fig. 5 of the main manuscript, we fit the temperature-dependent di /dv (V ) spectra to a Frota function which is defined as F(V ) = Im( iγ F ) [5] by variation of the parameter Γ i iγ F +V F. This leads to an excellent determination of the HWHM Γ of the resonance, considering Γ =.5Γ F [5, 6]. Here, the effect of 5 Macmillan Publishers Limited. All rights reserved

5 the q-factor, or so-called Fano lineshape, which can explain the weak asymmetry in di /dv with respect to zero bias [7], is neglected. It is important to note that the Frota function is strictly justified only for T << T K, but well fits the width of the spectral function in the whole temperature range as seen in Fig. 5a of the main manuscript text. Interestingly, trying to fit Γ(T ) of the HI to (/) (αk B T ) + (k B T K ) [8] with the usual choice of α = π leads to a poor fitting of the lineshape and unrealistic values of T K. Only when allowing α to vary, a reasonable fit is recovered (grey line in Fig.5 (c) of the main manuscript), however with a very large value of α = 5.. A similar value of α was needed to accurately describe the Γ(T ) dependence of a spin-/ Kondo molecule in the weak coupling regime [9]. This illustrates that the value of α varies largely from π in realistic Kondo systems. To extract (B z ), i.e. the splitting of the Kondo resonance in a magnetic field, we utilize a spin-/ Anderson-Appelbaum model in the weak coupling limit [9, ]. We consider a form of the conductance G(V ) = G + G (V ) + G (V ) as a function of bias voltage V, where G is a vertical offset resulting from an elastic term and G (V ) = K[S(S + ) + + ev M [γ( k B T ) + γ( ev )] () k B T G (V ) = G (V ) + G (V ) + G (V ) () G (V ) = KρJ[S(S + ) M + + ev M [γ( k B T G (V ) = KρJ[S(S + ) + M M γ( + ev k B T G (V ) = KρJ[S(S + ) + M M γ( ev k B T ) + γ( ev )]]F (V, T ) () k B T )]F (V + /e, T ) () )]F (V /e, T ) (5) where F (V, T ) = log ( E / (ev ) + (k B T ) ) was taken from ref. []. We also considered other forms of the function F (V, T ). All other parameters are described in ref. []. We chose E > mev, determined M from a Brillouin function, and the step function is γ(x) = (exp(x) x exp(x) )( exp(x)). We set S = /, and K = as for a spin-/ system the spin excitation intensity is independent of magnetic field. Therefore, we compare the ratio of G to G in our modeling. The fitting parameters are given by, by the effective temperature T, the exchange coupling term ρj, where ρ is the density of states of the substrate conduction electrons at E F and J the Kondo exchange coupling parameter, and by the g-factor. While the weak coupling spin-/ model strictly is not proper to correctly describe the Kondo effect in the Hund s impurity regime, it still can be used to extract the B z dependence of as 5 5 Macmillan Publishers Limited. All rights reserved

6 a first step and compared to spin-/ models in the weak coupling or strong coupling regime (NRG) []. STRUCTURAL AND GROUND STATE PROPERTIES OF FEH n COMPLEXES hcp fcc Fe FeH FeH Fe FeH FeH H position b a c b-b a-b a-c a a-c Fe height FeH n height Fe-H distance /.86.59/.96.59/ /.5 Table SI: Structural details of Fe hcp and Fe fcc configurations, as well as different hydrogenated configurations as obtained from relaxations in spin-polarized GGA of the substrate with a lattice parameter of a =.9 Å (c.f. Fig. S). Bond lengths and adsorption heights (with respect to the surface averaged Pt atoms heights) are measured between centers of the atoms and are given in Å. Paired numbers refer to the distances to hydrogen atoms in the FeH cases. In order to get more information about the formation of Fe-H complexes on the Pt surface, we simulated the surface system with ab-initio methods. The geometries, magnetic moments and hybridization functions were calculated within density-functional theory (DFT) (VASP package) [] with the projector augmented waves basis sets (PAW) [, 5] and the generalized gradient approximation (GGA) [6] to the exchange-correlation potential. The plane-wave cutoff was fixed to ev and the supercell Brillouin zone was sampled using 8x8x k-meshes. The Pt() surface was constructed using the lattice parameter for bulk Pt (a =.9 Å) [7]. The modelled slab includes 6 layers of x supercells of the Pt() surface separated by 5 layers of vacuum. One Fe impurity atom per supercell (i.e. concentration. monolayers) was placed at an hcp or fcc hollow site on top of the slab and surrounded by different hydrogen complexes. These structures were then relaxed until the forces in the cell were less than. ev/å. During the relaxations, the lowermost Pt layers were fixed to their bulk positions and the volume as well as shape of the supercell were kept constant. Our calculations reveal various relaxed configurations of atomic hydrogen adsorbed near the Fe adatoms as visualized in Fig. S. Structural details (bond lengths and adsorption heights) 6 5 Macmillan Publishers Limited. All rights reserved

7 of the Fe hcp, Fe fcc, and the different FeH hcp, FeH fcc and FeH hcp, FeH fcc configurations are summarized in Table SI. There are no significant structural differences between complexes based on Fe hcp and Fe fcc. Fig. S. Different structures of Fe hcp, FeH hcp, and FeH hcp complexes on Pt(). (Left) side view; (right) top view. The Fe adatoms are depicted in magenta, H atom in blue and Pt gray. From the 6 Pt layers of the slab, only the three uppermost layers are shown for clarity. Different adsorption sites of H are illustrated. (a) on top of the Fe adatom, (b) beside Fe, on top of a neighboring Pt atom, and (c) beneath Fe, where H occupies a pore between the surface and the sub-surface layer of Pt. The adsorption geometries we obtain for single Fe adatoms on Pt() are in good agreement with previous investigations [7, 8]. We now focus on the hydrogenated Fe adatoms and compare them to the experimental STM topographies. If hydrogen occupies the side position (b, Fig. S), the threefold rotational symmetry of the Pt() surface is broken which differs from our STM observations. Furthermore, the side adsorption of hydrogen leads to the smallest height of all Fe adatom complexes under investigation, as can be seen from Table SI. STM, however, detects a height increase of almost Å upon hydrogenation. For these two reasons, realization of the side configuration (b, Fig. S) for FeH hcp appears unlikely. The most pronounced change in the height of the Fe complex is found for the top configuration (c.f. Table SI). Apart from atop and side adsorption, the third possible FeH configuration is that hydrogen resides under the Fe impurity in a tetrahedral space inside the Pt slab, i.e. in the first interlayer (c, Fig. S). Relaxation of H into this tetrahedral space is facilitated by local distortions of the Pt lattice. Also here, the threefold symmetry is preserved. Symmetry-wise H on top and beneath Fe would be in line with our STM observations. Comparing the hydrogen induced cluster height changes in theory and experiment, adsorption of hydrogen on top of Fe 7 5 Macmillan Publishers Limited. All rights reserved

8 seems most likely. In the following, we assume top adsorption of H in the FeH complex. We also analyzed adsorption of two hydrogen atoms near one Fe impurity (c.f. Table SI). On the basis of the same symmetry and height arguments as above, we find that the FeH configuration with one hydrogen above (a-position) and one beneath Fe (c-position) appears most likely. hcp fcc Fe FeH FeH Fe FeH FeH H position b a c b-b a-b a-c a a-c Fe d Total cell Table S II: Magnetic moments calculated for selected Fe-H configurations. Labels correspond to the structures defined in Fig. S. All magnetic moments are given in µ B. The total cell magnetization depends on the size of the considered Pt slab. To understand the impact of hydrogen on the magnetism of the Fe adatom, we calculated the magnetic properties of the systems in the DFT electronic ground state as summarized in Table S II. We find only rather small changes of the total Fe d-shell magnetic moments upon hydrogenation. All values are around. µ B with differences between Fe hcp and Fe fcc on the order of. µ B, which is consistent with previous calculations []. The main change upon adsorption of H concerns the induced magnetizations in Pt as can be seen from the total cell magnetizations. These changes in magnetization point towards significant changes in the hybridization of the Fe d-shell electrons with the substrate upon hydrogenation, which will be discussed below. ANDERSON IMPURITY MODELS OF FE hcp, FEH hcp AND FEH hcp ON PT () In order to study the electronic structure of Fe hcp, FeH hcp and FeH hcp on Pt() including dynamic electron correlation effects, we consider the multi-orbital Anderson impurity model (AIM) [9]. This model includes the competing effects of local multi-orbital Coulomb interactions, hybridization between the adatom d-electrons and the metallic environment of the substrate, crystal fields, and spin-orbit coupling (SOC). Thereby, the multi-orbital AIM is capable of describing transition metal impurity systems, from the atomic limit of weak hybridization to the limit of strong hybridization and the Hund s impurity regime in between []. The Hamiltonian 8 5 Macmillan Publishers Limited. All rights reserved

9 reads with the local impurity part H loc = mσ + ϵ d d mσd mσ + mm m m σσ H = H bath + H loc (6) and the bath as well as bath-impurity coupling H bath = kmσ mm σσ ( CF + ξl s + B z (s z + l z )) σσ mm d mσd m σ (7) U mm m m dmσd m σ d m σ d m σ ϵ km c kmσ c kmσ + kmm σ Here, d mσ adds an electron to an impurity d-orbital and c kmσ ( ) [V dk ] mm c kmσ d m σ + h.c.. (8) adds an electron in the bath. The indices m and σ label the orbital and spin, respectively. The model takes into account the Coulomb interaction U in the Fe-d orbitals, the crystal field CF, spin-orbit coupling (SOC) ξ, and a magnetic field B z perpendicular to the Pt () surface. ϵ d is an average impurity d-level energy and ϵ km is a bath orbital energy. Both, the crystal field matrix CF and the SOC, ξ =.65 ev, are derived from our DFT calculations []. The Coulomb interaction U mm m m is constructed using the Slater parameters F = U Coulomb, F = (/.65)J Hund, F =.65F assuming the form of a fully spherically symmetric atom [, ], where the parameters U Coulomb = F =. ev and J Hund =. ev are used. This interaction, as illustrated in Fig. of the main text, includes Hubbard U-type terms which tend to reduce charge fluctuations as well as Hund s exchange J Hund, which facilitates the formation of local spin- and orbital moments. The bath electrons are treated as non-interacting in this model and can be integrated out in an effective action / Green s function formulation []. Then, the coupling between impurity d-orbitals and their metallic environment is summarized in the hybridization function mm (ϵ) = [V dk ] m m [V dk] m m, (9) ϵ + i + ϵ km km where + is a positive infinitesimal number. Using the projector formalism of Ref. [], mm (ϵ) can be directly extracted from the DFT calculations. In line with Ref. [], we extract mm (ϵ) from non spin-polarized GGA calculations and we assume mm (ϵ) m (ϵ)δ mm in orbital indices. 9 to be diagonal 5 Macmillan Publishers Limited. All rights reserved

10 -ImΔ(ω) (ev) ReΔ(ω) (ev) Fe E E A Fe E E A FeH FeH FeH FeH ω (ev) ω (ev) ω (ev) Fig. S. Imaginary (top) and real (bottom) part of m (ϵ) for the three Fe hcp complexes (solid lines). The orbitals are denoted according to their symmetry. A refers to the d z r orbital of Fe. E and E denote two different sets of two-fold degenerate eigenstates of the crystal field transforming according to the E irreducible representation of C v. E and E are superpositions of the d xz, d yz, d x y, and d xy orbitals. For Im m (ϵ) the corresponding Fe fcc data (dashed lines) reveal the same trend of increasing hybridization of the d z r orbital upon hydrogenation as in the Fehcp cases. For the relaxed Fe hcp, FeH hcp, and FeH hcp adatom configurations, we obtain the hybridization functions resolved by the orbitals A, E, and E, where A refers to the d z r orbital, and E and E are superpositions of the d xz, d yz, d x y, and d xy orbitals. These are shown in Fig. S. Their imaginary part, Im (ϵ), quantifies the impurity-bath coupling as function of quasiparticle energy ϵ. In all cases, we find a sizable hybridization of the Fe d-orbitals in the energy range of the Pt d- bands, which exceeds typical hybridizations of adatoms on noble metal surfaces by up to a factor of 5. [5, 6] The most significant effect of hydrogenation is an increase of the hybridization of the A-orbital of FeH hcp and FeH hcp as compared to Fe hcp. The same trend is observed for the corresponding Fe fcc cases. The A-orbital (i.e. d z r) is directly oriented towards the additional hydrogen atoms. The increase in hybridization of the A-orbital will generally broaden the DOS in this orbital and thus reduce the polarizability of the formation of in-plane orbital moments. 5 Macmillan Publishers Limited. All rights reserved

11 The enhanced A-orbital hybridization is thus expected to support the experimentally observed out-of-plane orientation of the magnetic easy direction upon hydrogenation. Quantum Monte Carlo simulations: Charge fluctuations, self-energies and quasi-particle scattering We performed interaction expansion continuous time Quantum Monte Carlo (CT-QMC) [7, 8] calculations using a segment algorithm [9] to solve the AIM numerically in the temperature range 96 K< T < 58 K, i.e. for inverse temperatures ev > β = /k B T > ev. In these calculations we considered the density-density part of the Coulomb matrix, Eq. 7, and neglected spin-orbit coupling. The results were cross-checked for selected occupation numbers n of 6., 6.5 and 7. for Fe hcp with calculations based on the TRIQS solver [], where we employed the full Coulomb matrix of Eq. 7. d-orbital occupation n(µ) (el.) µ (ev).6.5 µ= (ev) µ= (ev) n (el.) probability rate of electronic states Fig. S 5. d-orbital occupation n for Fe hcp as function of chemical potential µ (left) and valence histograms for selected values of µ (right), as obtained from the QMC simulations. Error-bars visualize the amount of valence fluctuations n n in the Fe d-orbitals. The QMC calculations yield the impurity Fe d-orbital occupation n as a function of the local chemical potential µ, as shown for Fe hcp in Fig. S5. The results for FeH hcp and FeH hcp are similar to Fe hcp (c.f. Fig. a of the main text). We find that the impurity occupation varies smoothly with µ which demonstrates that the impurity is far away from the atomic (A) limit. Apart from the region near n = 5, there are sizeable charge fluctuations basically for all chemical potentials µ. Our DFT calculations suggest an Fe d-shell occupancy of n 6. The charge fluctuations 5 Macmillan Publishers Limited. All rights reserved

12 and the smooth variation of n with µ found in this region are characteristic of Hund s impurity systems []. ImΣ(iω) (ev) Fe FeH FeH A E E iω (ev).5.5 iω (ev).5.5 iω (ev) Fig. S 6. Imaginary parts of the orbitally-resolved self-energies ImΣ as a function of the Matsubara frequency iω n for temperatures of T = 9 K (β = ev ) (dark) and T = 65 K (β = 7 ev ) (light). Results for Fe hcp, FeH hcp, and FeH hcp are shown. The insets show close up views of ImΣ(iω n ) in vicinity of zero Mastubara frequency and include also results for the temperature T = 96 K (β = ev, very light). The Fe d-shell occupancy is n = 6 in all cases. Fig. S6 shows the orbitally-resolved imaginary parts of impurity self-energies for Fe hcp, FeH hcp, and FeH hcp. For the temperatures under consideration, all ImΣ(iω n ) curves extrapolate to finite values Γ as iω. Γ has the meaning of a low energy quasi-particle scattering rate, which tends to zero according to Γ T in a Fermi liquid. In our calculations Γ appears merely independent of the temperature. This non-fermi liquid behavior is a hallmark of Hund s metals [, ] and Hund s impurity systems []. Taken together, the impurity self-energies and the chemical potential dependence of the impurity occupancies clearly corroborate the Hund s impurity character of all impurity systems under investigation here. Hydrogenation turns out to affect the self-energy of the A-orbital (d z r) most strongly, which is in line with the hybridization of this orbital changing most strongly upon hydrogenation (c.f. Fig. S). For FeH hcp and FeH hcp we find an increase in Im Σ(iω n ) for iω n in the A-orbital, which is in clear contrast to Fe hcp. Naively, one might expect that this signals atomic behavior in the A-orbital of FeH hcp and FeH hcp. That is, however, not the case here, since the 5 Macmillan Publishers Limited. All rights reserved

13 A-orbitals of FeH hcp and FeH hcp indeed show enhanced hybridization close to the Fermi level. The increase in Im Σ(iω n ) rather signals strong quasi-particle scattering at low energies, which facilitates higher Kondo temperatures, as discussed in the main text. Exact diagonalization of impurity models of Fe hcp and FeH hcp on Pt(): low energy many body level structure The exact diagonalization (ED) of the impurity model, Eq. 6, allows us to study the influence of hydrogenation on the low energy many body level structure of Fe on Pt(), taking into account spin-orbit coupling (SOC) and Coulomb interaction induced electron correlations. The main approximation in the ED calculations is the discretization of the electronic bath, where we assume one bath site per impurity spin-orbital. As this approximation hinders a quantitative analysis, we illustrate the qualitative evolution of the low energy level structure with the examples of Fe hcp and FeH hcp. Given that the hydrogen induced increasing hybridization of the Fe d z r-orbitals is universal for all clusters under investigation (c.f. Fig. S), we expect that the conclusions drawn below transfer in a qualitatively similar manner to the other clusters. The bath parameters were determined from the DFT derived Fe d hybridization functions [ (ϵ)] σ σ mm. We used the diagonal matrix elements of in the spin and orbital m = (E, E, A) basis. Here, E refers to the {d xz, d yz } orbitals, E to the {d x y, d xy} orbitals, and A to the {d z r} orbital. The integrated hybridization functions in a region of ev around the Fermi level were used to determine the hopping parameters according to π[v dk ] m = / ev / ev Im [ (ϵ)] mmdϵ. The resulting bath couplings for Fe hcp and FeH hcp on Pt () are in given in Tab. SIII. For the bath energies, we choose ϵ km =, i.e. we assume that the bath orbitals are directly at the Fermi level. We adjust the chemical potential to obtain impurity occupancies n 6. The lowest many body eigenstates of the resulting impurity models were obtained with the Lanczos method. With this choice of model parameters, the impurity model (i.e. bath and impurity) is filled with electrons in the ground state and we find impurity spin (S) expectation values S S(S+) of S.. for both Fe hcp and FeH hcp in the ground state as well as in the first few excited states. The evolution of the many body level structure with external magnetic field perpendicular to the surface (B z ) is shown in Fig. S7. In both cases we find a singlet ground state which is followed by triplet states approx. ev higher in energy. This finding is independent of the presence of SOC. The fact that we have a singlet ground state (followed by a triplet of excited 5 Macmillan Publishers Limited. All rights reserved

14 Table SIII. Orbital (m) dependent values of crystal field CF (ev) and impurity-bath coupling [V dk ] mm (ev) as obtained from DFT for Fe hcp and FeH hcp on Pt (). E E A Fe on Pt () CF [V dk ] mm..9. FeH on Pt () CF [V dk ] mm...8 a. Fe b. FeH E (ev) E (ev) B (ev) B (ev) Fig. S7. Evolution of the lowest energy many body levels with external out-of-plane magnetic fields (B z ) for the models of Fe hcp (a) and FeH hcp (b) on Pt (). The many-body energy eigenvalues of the full system containing bath and impurity are shown. The insets show a close up view of the lowest energy excited triplet state. states) for an impurity spin magnetic moment on the order of S.. shows that the local impurity moment is screened by the bath electrons. For an exact solution of the impurity problem, the singlet-triplet splitting energy is on the order of the Kondo temperature. This energy scale is largely exaggerated in the model at hand in comparison to the experimental finding due to the bath discretization. The main effect of SOC is that it can lift the degeneracy of the excited state triplet, where the splitting depends on the presence of additional hydrogen atoms near the Fe impurities. It is 5 Macmillan Publishers Limited. All rights reserved

15 very small for Fe hcp, but on the order of a few mev for FeH hcp. The experimentally observed tendency that hydrogenation favors an out-of-plane magnetic easy axis is reproduced in this model. Since the effective Kondo scale is strongly overestimated in the ED model and due to the fact that the induced magnetic moment in the Pt substrate is partially neglected in the model at hand, the ED model does not allow for a quantitative analysis of the competition between Kondo screening and magnetic anisotropy. On qualitative grounds, the ED results demonstrate, however, that the impurity spin can be screened by the conduction electrons and that the low energy many body level structure (and thereby the magnetic anisotropy) of the Fe impurity systems is sensitive to hydrogenation. [] F. Natterer, F. Patthey, and H. Brune, Surface Science 65, 8 (). [] D. M. Eigler and E. K. Schweizer, Nature, 5 (99). [] A. A. Khajetoorians, T. Schlenk, B. Schweflinghaus, M. dos Santos Dias, M. Steinbrecher, M. Bouhassoune, S. Lounis, J. Wiebe, and R. Wiesendanger, Phys. Rev. Lett., 57 (). [] B. Chilian, A. A. Khajetoorians, S. Lounis, A. T. Costa, D. L. Mills, J. Wiebe, and R. Wiesendanger, Phys. Rev. B 8, (). [5] H. Prüser, M. Wenderoth, P. Dargel, A. Wiesmann, R. Peters, T. Pruschke, and R. Ulbrich, Nature Phys. 7, 75 (). [6] R. Žitko, Phys. Rev. B 8, 956 (). [7] V. Madhavan, W. Chen, T. Jamneala, M. F. Crommie, and N. S. Wingreen, Science 8, 567 (998). [8] K. Nagaoka, T. Jamneala, M. Grobis, and M. F. Crommie, Phys. Rev. Lett. 88, 775 (). [9] Y.-H. Zhang, S. Kahle, T. Herden, C. Stroh, M. Mayor, U. Schlickum, M. Ternes, P. Wahl, and K. Kern, Nature Comm., 7 (). [] R. H. Wallis and A. F. G. Wyatt, Journal of Physics C: Solid State Physics 7, 9 (97). [] A. Hurley, N. Baadji, and S. Sanvito, Phys. Rev. B 8, 55 (). [] T. A. Costi, Phys. Rev. Lett. 85, 5 (). [] G. Kresse and J. Hafner, J. Phys. Cond. Matter 6, 85 (99). [] P. E. Blöchl, Phys. Rev. B 5, 795 (99). 5 5 Macmillan Publishers Limited. All rights reserved

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