Article www.acsnano.org Slow Magnetic Relaxation of Dy Adatoms with In-Plane Magnetic Anisotropy on a Two- Dimensional Electron Gas Valerio Bellini, Stefano Rusponi, Jindřich Kolorenč, Sanjoy K. Mahatha, Miguel Angel Valbuena, Luca Persichetti, Marina Pivetta, Boris V. Sorokin, Darius Merk, Sébastien Reynaud, Dante Sblendorio, Sebastian Stepanow, Corneliu Nistor, Pierluigi Gargiani, Davide Betto, Aitor Mugarza, Pietro Gambardella, Harald Brune, Carlo Carbone, and Alessandro Barla* Cite This: ACS Nano 2022, 16, 11182−11193 Read Online ACCESS Metrics & More Article Recommendations * sı Supporting Information ABSTRACT: We report on the magnetic properties of Dy atoms adsorbed on the (001) surface of SrTiO3. X-ray magnetic circular dichroism reveals slow relaxation of the Dy magnetization on a time scale of about 800 s at 2.5 K, unusually associated with an easy-plane magnetic anisotropy. We attribute these properties to Dy atoms occupying hollow adsorption sites on the TiO2-terminated surface. Conversely, Ho atoms adsorbed on the same surface show paramagnetic behavior down to 2.5 K. With the help of atomic multiplet simulations and first-principles calculations, we establish that Dy populates also the top-O and bridge sites on the coexisting SrO-terminated surface. A simple magnetization relaxation model predicts these two sites to have an even longer magnetization lifetime than the hollow site. Moreover, the adsorption of Dy on the insulating SrTiO3 crystal leads, regardless of the surface termination, to the formation of a spin-polarized two- dimensional electron gas of Ti 3dxy character, together with an antiferromagnetic Dy−Ti coupling. Our findings support the feasibility of tuning the magnetic properties of the rare-earth atoms by acting on the substrate electronic gas with electric fields. KEYWORDS: slow magnetic relaxation, single atom magnets, X-ray magnetic circular dichroism, density functional theory, perovskite oxides T he study of the interaction between a magnetic impurity and a nonmagnetic host is of fundamental interest, as the hybridization between the two determines the electronic and magnetic properties of the system, including its anisotropy. The magnetism of transition- extraordinary stability, like in the case of lanthanide-based single-molecule magnets,26−28 results from a symmetry- protected magnetic ground state, achieved through a strongly axial crystal field interaction, and the decoupling of the RE spin metal atoms on surfaces has been an active field of research for from the underlying metal through the MgO layers, preventing almost 20 years,1−9 while investigations of the magnetic spin reversal due to scattering with electrons and phonons.21 In properties of rare-earth (RE) individual atoms are more comparison, under identical adsorption conditions on a MgO recent.10−22 The latter studies have recently led to the discovery layer, transition-metal single atoms show a large magnetic of single atom magnets (SAMs), based on either Ho or Dy anisotropy but magnetization lifetime in the range of milli- atoms deposited on MgO/Ag(100)21,22 or Dy atoms on a graphene/Ir(111) substrate.14 These systems confirmed seconds.5,6,29 previous expectations that long magnetic relaxation times could be reached with strongly axial chemical bonds leading to Received: April 25, 2022 uniaxial magnetic anisotropy.21,23 In the case of Ho/MgO/ Accepted: June 23, 2022 Ag(100), it was found that a single Ho atom is able to keep its Published: June 30, 2022 magnetization for at least tens of minutes at temperatures up to 35 K.21,24,25 For Dy/MgO/Ag(100), the stability of the magnetization at T ≤ 15 K extends to several days.22 This © 2022 The Authors. Published by American Chemical Society https://doi.org/10.1021/acsnano.2c04048 11182 ACS Nano 2022, 16, 11182−11193 ACS Nano www.acsnano.org Article Figure 1. (a) Experimental magnetization cycle recorded by following the magnetic field dependence of the XMCD peak at the Dy M5 edge [see black arrow in panel (c)], at T = 2.5 K, dB/dt = 33.3 mT/s, θ = 60°, ΘDy = 0.004 ML (corresponding to a surface density of 0.026 Dy atoms/nm2). (b) Experimental magnetization relaxation curve (dots) and corresponding exponential fit (line), recorded at B = 0.375 T [see black arrow in panel (a)] after saturation at B = 5 T (Dy M5 edge, θ = 60°, T = 2.5 K, ΘDy = 0.029 ML). (c) Normalized XMCD spectra measured for magnetic field applied in the out-of-plane direction (θ = 0°) and predominantly in the STO(001) plane (θ = 60°), at the Dy M5 edge with T = 2.5 K, B = 5 T, ΘDy = 0.004 ML. (d,f) Sketches of the atomic structures and (e,g) corresponding electronic band structures for: (d,e) the plain STO substrate and (f,g) Dy adatoms (ΘDy = 0.25 ML) at the hollow site on the TiO2 terminated surface (spin up channel only). Although in the latter case only the top two STO atomic layers are visualized in the sketch for space reasons, the bands were calculated using the same 2 × 2 STO slab sketched in panel (d). In panels (e) and (g), the orbital projection on the Ti-dxy character is highlighted, for the surface Ti layer only, by filled red circles whose size is proportional to its contribution at each eigenvalue. Note that the experimental data were acquired on Dy adsorbed on Nb:STO(001), while calculations are for a pure STO(001) cell. In Ho/MgO/Ag(100), direct manipulation of the spin of the band gap of 3.25 eV,40 its surface can host a high-mobility two- Ho atoms (i.e., read and write) with a scanning tunneling dimensional electron gas (2DEG).41−45 The density of carriers microscope (STM) tip was demonstrated,24,30,31 highlighting within this surface can be controlled either via the application of the potential of these systems for information storage. a gate voltage46 or through exposure to intense ultraviolet Alternative routes to the control of the magnetic state of the radiation.43,47,48 Both methods can be effective in controlling lanthanide atoms may be achieved through their interaction the scattering rate between the conduction electrons of the with the substrate. These span from structural modifications substrate and the localized magnetic moments of the lanthanide that can lead to local variations of the crystal field potential atom, thus offering a potential way to control the reversal of the impacting the charge and magnetic anisotropy of the rare-earth rare-earth spins. atoms, to electronic modifications, such as variations of the In this context, we have studied the structural, electronic, and surface electron density influencing the spin reversal rate of the magnetic properties of Dy atoms adsorbed onto STO(001) lanthanide atoms. surfaces. We have found that Dy impurities are preferentially A potential candidate as a support for rare-earth SAMs, located at four-fold hollow sites of the TiO2-terminated surface, allowing for the active control of both their structural and with a 4f9 configuration and a strong in-plane magnetic electronic properties, is the cubic perovskite dielectric oxide anisotropy. However, under the experimental conditions of SrTiO3 (STO). This is a paradigmatic example of a quantum this study, a significant minority of Dy adatoms adsorb at sites paraelectric material, where paraelectricity down to temper- of the coexisting SrO termination. Dy atoms at the TiO2- atures in the mK range is the result of the competition between terminated surface are found to be SAMs, characterized by an ferroelectricity, quantum fluctuations, and structural distor- open magnetization cycle and spin relaxation times of the order tions.32−37 Paraelectricity in STO is intimately coupled with the of at least 800 s at 2.5 K. This was unexpected since this atomic giant piezoelectric effect observed at cryogenic temper- species is characterized by an easy-plane magnetic anisotropy atures.38,39 These properties make STO a rich playground to [i.e., there is no unique magnetic quantization axis in the study the effect of electric-field-induced changes of the local STO(001) plane]. Finally, we find a significantly long-ranged crystalline environment on the magnetic properties of the antiferromagnetic coupling between Dy and Ti, related to the lanthanide atoms. Moreover, whereas bulk STO has a large formation of a 2DEG at the STO surface upon Dy adsorption. 11183 https://doi.org/10.1021/acsnano.2c04048 ACS Nano 2022, 16, 11182−11193 ACS Nano www.acsnano.org Article Figure 2. X-ray absorption spectra and magnetization curves of Dy atoms on a Nb:STO(001) surface (ΘDy = 0.037 ML). (a) XAS, XMCD, and XLD spectra measured at the Dy M4,5 edges and T = 2.5 K. The XAS and XMCD were recorded at B = 5 T, and the XLD was recorded at grazing incidence (θ = 60°). (b) XAS, XMCD, and XLD simulated by means of atomic multiplet calculations based on a point-charge model for the Dy crystal field, with the proportions between Dy species discussed in the text. (c) Experimental magnetization cycles (Dy M5 edge, T = 2.5 K, dB/dt = 33.3 mT/s) at normal (θ = 0°) and grazing (θ = 60°) incidence and corresponding simulated cycles at thermodynamical equilibrium based on the atomic multiplet model, with the proportions between Dy species discussed in the text. The experimental curves are normalized to the corresponding simulated curves at B = 6 T. Dark symbols are used for the downward magnetic field ramps (i.e., from positive to negative field), while light symbols are used for the upward field ramps. (d) Experimental magnetization cycles (θ = 60°, dB/dt = 33.3 mT/s) at various temperatures and corresponding simulated equilibrium curves based on the atomic multiplet model. RESULTS AND DISCUSSION coverage dependence of the Dy magnetic properties). By following the decay of the XMCD amplitude as a function of The electronic and magnetic properties of Dy adatoms on the time at a given magnetic field, after saturation at B = 5 T, we STO(001) surface were studied experimentally by polarization- find the largest value of the magnetic lifetime τ of the Dy atoms dependent X-ray absorption spectroscopy (XAS) at the M4,5 at B = 0.375 T, where τ = 800 ± 200 s, as shown in Figure 1b. edges, in particular by making use of X-ray magnetic circular Moreover (see Figure 1c), dilute Dy atoms show an in-plane dichroism (XMCD) and X-ray linear dichroism (XLD). The magnetic anisotropy, as indicated by the larger XMCD high sensitivity of these spatially averaging techniques allows amplitude (relative to the XAS peak) at the M5 absorption measuring the properties of surface spins down to the edge when the magnetic field is applied close to the STO(001) noninteracting limit. Such a high magnetic dilution is achieved plane (θ = 60°), as compared to the out-of-plane direction (θ = by depositing minute amounts of magnetic atoms at cryogenic 0°). Very similar results are obtained for Dy adsorbed on the temperatures, thus preventing their diffusion and consequent (001) surface of pure (i.e., without Nb doping) STO (see aggregation, and ensures that the magnetic properties are those Supporting Information for a comparison between pure and of individual atoms, as demonstrated by comparison with Nb-doped STO), indicating that the extra conductivity single-atom scanning probe investigations on similar sys- achieved through Nb doping does not shorten the magnet- tems.14,21,24,30,31,49 The experimental investigations were ization relaxation times. Dy/STO(001) can therefore be complemented by atomic multiplet simulations and first- classified as a SAM, but unlike the previously reported cases principles calculations based on the density functional theory of RE SAMs,14,21,22,50 all showing strong out-of-plane magnetic (DFT) (see Methods for a description of experimental and anisotropy, here the Dy atoms have in-plane magnetic theoretical techniques). As depicted in Figure 1a, Dy atoms anisotropy. Contrary to Dy, Ho single atoms show purely adsorbed with very low density on the clean and ordered paramagnetic behavior down to T = 2.5 K, despite a magnetic Nb:STO(001) surface (see Methods for the sample preparation anisotropy similar to that of Dy (see Supporting Information procedure) show slow relaxation of the Dy magnetization, for the Ho/STO magnetic properties). resulting in an open magnetization cycle at a temperature T = The recorded value of τ for Dy/STO(001) is comparable to 2.5 K for magnetic fields up to B ≃ ±3 T. We observe a similar that previously reported for Dy/graphene/Ir(111).14 Indeed, opening of the magnetization cycle in a wide range of Dy our DFT calculations indicate that the STO substrate, whose surface concentrations, up to ΘDy = 0.037 ML, and temper- atomic structure is sketched in Figure 1d, shares some features atures up to T = 6 K, while the opening is considerably reduced with such graphene/metal substrates. The (001) surface of starting at ΘDy = 0.145 ML (see Supporting Information for the bare, stoichiometric STO is an insulator as depicted in Figure 11184 https://doi.org/10.1021/acsnano.2c04048 ACS Nano 2022, 16, 11182−11193 ACS Nano www.acsnano.org Article Figure 3. (a) Sketches of the six possible adsorption sites on TiO2 and SrO terminated STO(001) surfaces. The STO(001) single crystals used in the experiments are oriented as in the sketch, and both the magnetic field and the X-rays are always aligned within the xz plane. For the TiO2/top-O and SrO/bridge sites, with two-fold point symmetry, two inequivalent orientations are indicated. These are inequivalent with respect to the direction of magnetic field and X-rays. (b) Spin majority (↑) orbitally projected electronic band structure in the [−1 eV, +1 eV] energy range around the Fermi level for a Dy adatom at the TiO2/hollow adsorption site. The size of the red circles is proportional to the sp and d contribution to each eigenvalue. Spin-polarized LDOS projected on the (c) s and f and (d) p and d orbitals of a Dy adatom at the TiO2/ hollow adsorption site. For p and d orbitals, the projection is carried out for each orbital symmetry separately. In the inset of panel (c), a close- up view of the spin-density isosurface at the Dy site is shown (isovalue of 10−3 e−/Å3). Yellow and cyan colors are associated with an excess of spin up and down electrons, respectively. 1e. Oxygen atoms at the TiO2 terminated surface layer are In order to rationalize our findings, we first analyze the XAS, responsible for the inverted parabolic band that reaches the XMCD, and XLD spectra of Dy adatoms deposited on the Fermi level at the Γ point. On the other hand, it is well-known (001) surface of Nb:STO. Figure 2a displays the M4,5 XAS (top that oxygen vacancies act as charge donors and lead to the panel) characteristic for the Dy coverage range up to ΘDy = formation of a 2DEG at the STO surface.42,43 Here, we show 0.037 ML. At the M4,5 edges, transitions from a 3d10 4fn state to that also the presence of Dy adatoms on the stoichiometric a 3d9 4fn+1 state are mainly excited, allowing one to probe the STO(001) surface, sketched in Figure 1f, leads to an electron electronic and magnetic configuration of the rare-earth 4f shell. doping, resulting in the partial filling of conduction bands. This The spectral line shape of the XAS and XMCD (middle panel) effect is shown in Figure 1g, which depicts the spin up/majority is typical for a 4f shell occupation n = 9.15 Thus, adsorption at channel bands (similar bands and projections are found in the the STO(001) leads to a decrease of one electron in the spin down/minority channel) for a calculation based on a 2 × 2 occupation of this shell, characterized by n = 10 for Dy atoms in cell, corresponding to a Dy concentration ΘDy = 0.25 ML. the gas phase. The in-plane magnetic anisotropy, related to the However, comparable results were obtained for a 4 × 4 cell larger XMCD amplitude at grazing than at normal incidence, (discussed later in Figure 6d), corresponding to ΘDy = 0.06 ML, suggests that the ground state of individual Dy atoms on very close to the coverage range used during the XMCD experiments. Moreover, although we depict here the case of the STO(001) is characterized by a low value of the projection of hollow adsorption site on the TiO2 termination (the different the total angular momentum J = 15/2 along the z-axis sites/terminations will be discussed at a later stage), the surface [corresponding to the (001) axis of the STO lattice]. The metallization occurs regardless of the crystal termination. It spectral shape of the XLD (bottom panel of Figure 2a) at the involves bands with predominant Ti 3dxy character, related to M5 edge is characterized by a large positive feature (blue arrow surface Ti atoms in the case of a TiO2 termination, as shown in in the graph) followed, at higher energy, by a negative feature Figure 1g, and to subsurface Ti atoms in the case of a SrO- (red arrow). Such an XLD is characteristic for Dy when the 4f terminated crystal (see Supporting Information for the depth- charge distribution is mostly pointing in the direction dependence of this metallic state). Thus, our calculations show perpendicular to the STO surface.51 Due to the oblate character that, independently of the adsorption site, Dy deposition will of the Dy(4f9) free-ion electron density, this charge distribution lead to the formation of a 2DEG, reminiscent of what was corresponds to a 4f magnetic moment pointing within the STO previously observed at the oxygen-deficient STO surface. surface plane, consistently with the XMCD result. 11185 https://doi.org/10.1021/acsnano.2c04048 ACS Nano 2022, 16, 11182−11193 ACS Nano www.acsnano.org Article Table 1. Total Energies (in eV) and Occupations (n) of the orbitals of spd character is sizable. However, the magnetic 4f Orbitals of the Six Stable Adsorption Sites for Dy on TiO2 polarization of each of these shells is very low, with spin and SrO Terminationsa moments below 0.1 μB. Figure 3b shows the contributions to the band structure close to the Fermi level of majority spin sp Termination Adsorption Site Energy (eV) n (e−) and d Dy orbitals, while in Figure 3c,d, the spin-dependent local TiO2 hollow +0.00 9.00 density of states (LDOS) is plotted for spdf Dy orbitals, for the top-O +2.61 9.39 case of the TiO2/hollow site (for p and d orbitals, the symmetry top-Ti +3.22 9.71 dependence is also given). The spatial localization of spd SrO top-O +2.34 (+0.00) 9.38 electrons on the Dy atoms is clearly evidenced by the bridge +2.95 (+0.61) 9.04 nondispersive character of the partially occupied band close top-Sr +4.87 (+2.53) 9.37 to EF. Indeed, inspection of the projected electronic density of a The values are relative to the energy of the TiO2/hollow site. In the states shown in Figure 3c,d reveals the presence of a localized case of the SrO termination, the energies in brackets are relative to the band at the Fermi level, with high spin polarization and mixed SrO/top-O site. 6s−6pz−5dz2 character. This can be nicely visualized in real space by plotting the spin-density isosurface around the Dy ion, In view of the quantitative interpretation of the experimental as shown in the inset of Figure 3c. Its anisotropic shape with a XAS, XMCD and XLD, we have established by DFT the most vertically elongated spatial extension, going well beyond the Dy stable adsorption configurations on both TiO2 and SrO crystal atomic position, cannot be accounted for only by the anisotropy terminations and the corresponding occupation of 4f and of the well localized 4f shell. The larger spatial extension of 5dz2 valence (6s, 6p, and 5d) orbitals. Since our simulation cell (see and especially of 6pz orbitals in the z direction, compared to Figure 1c) hosts both terminations simultaneously, we can that of the 4f shell, suggests assigning the spin cloud above the compare the total energies of all six high-symmetry adsorption Dy atom to these orbitals. An anisotropic contribution from the sites, sketched in Figure 3a. The total energies are tabulated in 6s shell may also arise, due to the hybridization between this Table 1. The most stable adsorption configuration is found to and the other valence orbitals. be the hollow site of the TiO2 termination (Dyhollow atoms), Having established the most likely occupied adsorption sites where Dy has a four-fold coordination to its O nearest and the presence of a charge and spin cloud localized above the neighbors. This is followed in energy by the top-O site at the Dy atoms on hollow sites, we have simulated the XAS, XMCD, SrO termination (Dytop atoms), where Dy is axially coordinated and XLD of Dy adatoms on the STO(001) surface by atomic to the underlying O atom, and its Sr next nearest neighbors lead multiplet calculations performed with the Quanty code53 (see to a four-fold symmetry. Since the method used for the Methods and Supporting Information for details about the preparation of clean STO(001) surfaces in vacuum is known to atomic multiplet calculations). The system Hamiltonian yield coexisting TiO2 and SrO terminations,52 it is instructive to includes Coulomb, spin−orbit, Zeeman, and crystal-field analyze the relative stability of the different sites on the two (CF) interactions acting on the 4f shell only. Figure 2b shows terminations separately. Based on the results of Table 1, on the our best simulations, which reproduce very well the TiO2 surface, the energy differences between hollow and top- experimental data shown in the corresponding panels of Figure O/top-Ti sites are so big (more than 2.5 eV) that we expect the 2a. Our simulations, based on the combination of spectra Dy adatoms to easily diffuse to the most stable four-fold hollow characteristic for different adsorption sites, indicate that (66 ± site, irrespective of where the atoms land at deposition. 5)% of the Dy adatoms occupy Dyhollow sites, (20 ± 2)% occupy Therefore, a single site is expected on this termination. On SrO bridge sites, equally distributed among Dybr‑Ox and Dybr‑Oy terraces, top-O and bridge sites are close in energy (the species, and (14 ± 2)% are in Dytop sites. Thus, we confirm that difference is only 0.6 eV), whereas the top-Sr site is significantly TiO2 and SrO terminations coexist, with relative abundances of higher in energy (2.5 eV), compared to the top-O site. In such a (66 ± 5)% and (34 ± 5)%, respectively. The relative case, there might be diffusion barriers between the top-O and abundances of Dy atoms at top-O and bridge sites on the the bridge sites, which cannot be overcome at our low SrO termination, (41 ± 6)% and (59 ± 6)%, respectively, deposition temperature, whereas diffusion from top-Sr to the suggest that atoms landing on top-Sr sites diffuse with other sites is likely to have no barrier. On this termination, we approximately the same probability to either of those sites. thus expect occupation of both top-O and bridge sites. On the Indeed, from the statistics of impact sites (there are two bridge bridge site, Dy has a two-fold coordination with its O nearest sites, one top-O and one top-Sr site per SrO unit cell) and in the neighbors and Sr next nearest neighbors. In each SrO unit cell, case of equal diffusion probability from top-Sr to top-O and there are two bridge sites with perpendicular projections in the bridge, we infer relative abundances for these sites of 37.5% and xy plane of the O−Dy−O bond, as sketched in Figure 3a. This 62.5%, respectively, in agreement with the experimental values. projection is aligned along x for one bridge site and along y for The coexistence of Dy atoms at top-O and bridge sites of the the other bridge site. In our experiments, the external magnetic SrO termination is similar to the case of rare-earth adatoms on field is always applied in the xz plane, thus making Dy atoms at the MgO surface (which is isostructural to the SrO termination the two bridge sites inequivalent. We thus label as Dybr‑Ox Dy discussed here), where adsorption at both top-O and bridge atoms at bridge sites with O−Dy−O bond projection along x sites was experimentally observed by STM.22,50,54 The and Dybr‑Oy those at sites with O−Dy−O bond projection along equilibrium magnetization cycles calculated by atomic multiplet y. Concerning the electronic configuration, Dy atoms at TiO2/ calculations capture very well both the angular dependence of hollow sites are found to have n = 9 electrons in the 4f shell. the experimental magnetization cycles, as shown in Figure 2c, The same holds for the SrO/bridge site, while a small departure and their temperature dependence up to T = 15 K, as depicted from the 4f9 configuration is observed for all other sites, except in Figure 2d. At 15 K, the cycle is closed, indicating that, at this for TiO2/top-Ti, where the occupation is closer to 4f10. We find temperature, magnetic relaxation is faster than the measure- that for all adsorption sites the occupation of the valence ment time, which is of the order of 10 s. 11186 https://doi.org/10.1021/acsnano.2c04048 ACS Nano 2022, 16, 11182−11193 ACS Nano www.acsnano.org Article Figure 4. (a) Calculated adsorption configuration of the three sites at the origin of the simulated XAS, XMCD, and XLD spectra. The Dy atom and the first two coordination shells are shown. (b) Corresponding calculated energy scheme of the ground-state atomic J multiplet of Dy atoms, as obtained by diagonalization of the Hamiltonian defined for the atomic multiplet calculations, in a small magnetic field B = 1 μT applied along different high-symmetry directions (left column: z, middle column: x, right column: either y or xy). The small magnetic field is applied in order to define the quantization axis for each diagram. Based on the atomic multiplet calculations, we can establish Dy br Ox(y) = ± 0.778 |Jx(y) = 15/2 the 4f quantum level schemes and the ground-state wave 0.550 |Jx(y) = 11/2 functions for Dy in the three adsorption configurations used in 0.262 |Jx(y) = 7/2 our simulations, which are depicted in Figure 4a. Dytop has a strong out-of-plane anisotropy, with a ground-state charac- 0.099 |Jx(y) = 3/2 terized by the maximum value of the total angular momentum J 0.044 |Jx(y) = ± 1/2 along the z direction, perpendicular to the STO(001) surface 0.029 |Jx(y) = ± 5/2 (see top panel of Figure 4b). The ground-state wave function is 0.030 |Jx(y) = ± 9/2 Dy top = 1.000 Jz = 15/2 0.030 |Jx(y) = ± 13/2 corresponding to a pure doublet, extremely well isolated from the first excited state (ΔE = 84.2 meV), and with a total barrier with a first excited state at ΔE = 11.3 meV and a total barrier height of 270 meV. On the other hand, the two-fold C2v height of 266 meV. Finally, on the hollow site of the TiO2 symmetry of the bridge site leads to a strong in-plane uniaxial termination, the maximum projection of J lies within the anisotropy. The maximum projection of J for Dybr‑Ox atoms is STO(001) plane, independent of the direction (bottom panel along the x direction (see middle panel of Figure 4b), while it is of Figure 4b). This suggests an easy-plane type anisotropy, with along the y direction for Dybr‑Oy atoms (not shown). Along the respective easy axes, the ground state wave function for these the hard axis perpendicular to the STO surface. In the plane, the two species is ground state of the Dy 4f9 configuration is 11187 https://doi.org/10.1021/acsnano.2c04048 ACS Nano 2022, 16, 11182−11193 ACS Nano www.acsnano.org Article Figure 5. (a) Experimental magnetization relaxation time τexp of Dy atoms as a function of external magnetic field B (ΘDy = 0.029 ML, T = 2.5K, θ = 60°). (b) Intrinsic relaxation time τ calculated with the model described in the text for Dyhollow, Dytop, and Dybr‑Ox atoms (T = 2.5K, θ = 60°). Dy hollow = ±0.683 |Jx = 15/2 Based on the magnetic field dependence of the electronic levels obtained by our multiplet simulations, we have calculated 0.223 |Jx = 11/2 the magnetic field dependence of the intrinsic relaxation time τ with a spin−lattice relaxation model, including direct and 0.297 |Jx = 7/2 Orbach-type scattering mechanisms, based on Fermi’s golden ±0.386 |Jx = 3/2 rule and the Hamiltonian proposed by Fort et al.,55 which involves transitions with ΔJz = ±1, ±2. A Debye model was +0.365 |Jx = ± 1/2 used for the low-energy phonon spectrum. Spin-electron scattering was included based on the theory by Delgado and ±0.248 |Jx = ± 5/2 Fernández-Rossier,56 involving transitions between states with +0.132 |Jx = ± 9/2 ΔJz = 0, ±1 (see Supporting Information for a detailed description of the magnetic relaxation model). We neglected 0.131 |Jx = ± 13/2 the coupling with the spin of the Dy spd shells,49 due to their vanishing spin polarization. The spin−lattice and spin−electron Even in this case, the ground doublet is well isolated from the scattering cross sections were adjusted so as to match the values first excited state (ΔE = 11.9 meV), while the total barrier of τexp in the magnetic field range 0.375 ≤ B ≤ 1 T, taking into height amounts to 109 meV. account that τexp is related to τ by the expression τ−1 exp = τ −1 + −1 Figure 5a shows the magnetic field dependence of the τsec, where τsec is a contribution to the experimental relaxation magnetization relaxation time τexp as recorded under low time arising from secondary electrons generated in the X-ray photon flux conditions (see Methods for the procedure used to absorption process (see Supporting Information for an measure τexp and for the definition of “low flux” conditions). As evaluation of τsec). The calculation for Dyhollow, shown as a B is decreased from 1 to 0.375 T, τexp more than doubles, continuous blue line in Figure 5b, relates the decay of τ with reaching a maximum value of 800 ± 200 s. At lower magnetic increasing field beyond 0.3 T with an enhanced probability of fields, however, τexp falls rapidly reaching a value of about 200 s spin−phonon scattering (see Figure S8a of the Supporting at B = 125 mT. In order to determine which Dy species are Information for the decomposition of τ into a spin−phonon responsible for the observed field dependence of τexp, we note and a spin−electron contribution). The field dependence of the that, as shown in Figure 1b, at B = 0.375 T, the decrease of the lifetime for magnetic fields B < 0.3 T is not captured by our magnetization over time from its initial to its equilibrium value simplified model, which does not include Raman scattering is of the order of 20%. In our grazing incidence geometry, mechanisms and local phonon modes. The drop of τexp at small Dyhollow atoms account for (69 ± 5)% of the total magnetization, fields may in fact originate in a two-phonon Raman mechanism while Dybr‑Ox for (16 ± 2)%, Dytop for (14 ± 2)%, and Dybr‑Oy similar to that found for Ho/MgO.25 We estimate that quantum for only about 1%. Assuming that a Dy species retains its tunneling due to the coupling of the 4f magnetic moment with saturation magnetization, while the magnetic field is quickly the nuclear spin may be significant only for selected values of ramped from 5 T down to 0.375 T without exposing the sample the magnetic field, in the range B ≲ 40 mT, thus it cannot to the X-ray beam and based on the equilibrium magnetization explain the field dependence of τ in our investigated field range curves calculated for each species (see Supporting Informa- (see Figure S8b of the Supporting Information for the effect of tion), we expect a maximum decrease over time at 0.375 T of | the coupling between 4f moment and nuclear spin in the field M(0.375 T) − M(5 T)|/M(5 T) = 42% if the decay of M is due range of the experiment). For comparison, assuming identical to Dyhollow atoms, 8% in the case of Dytop, 6% for Dybr‑Ox, and spin−lattice and spin−electron cross sections for all adsorption about 1% in the case of Dybr‑Oy. In reality, due to its intrinsic sites, we can estimate the magnetic field dependence of τ for finite lifetime, the magnetization partially relaxes already during Dybr‑Ox and Dytop. These are also shown in Figure 5b. Dytop the field ramp, so that the actual decrease of the magnetization shows values of τ which are orders of magnitude greater than over time at B = 0.375 T will be lower than the above estimate. those of Dyhollow. Indeed, the ground state of Dytop, an almost We can thus conclude that the observed magnetization pure doublet with |Jz| = 15/2, is expected to be particularly relaxation at θ = 60° is likely related to the Dyhollow atoms. stable against spin−electron and spin−phonon scattering, even 11188 https://doi.org/10.1021/acsnano.2c04048 ACS Nano 2022, 16, 11182−11193 ACS Nano www.acsnano.org Article Figure 6. (a) Ti XAS (top panel) and XMCD (middle panel) spectra, with the corresponding XMCD integral (bottom panel) recorded at the L2,3 edges with T = 2.5 K, B = 5 T, and θ = 60°, before and after deposition of Dy (ΘDy = 0.035 ML) on the clean Nb:SrTiO3(001) surface. (b) Comparison between the magnetic field dependence of the Ti 3d orbital magnetic moment mL (red dots) and the Dy total 4f moment (blue squares and line), both normalized at their corresponding values at B = 5 T. (c) Spin density isosurface of Dy/STO (Dyhollow sites, 4 × 4 cell corresponding to ΘDy = 0.06 ML, GGA, isovalue of 10−3 e−/Å3), highlighting the magnetic polarization of Ti induced by Dy. Yellow and cyan colors are associated with an excess of spin up and down electrons, respectively. (d) Spin-resolved electronic band structures (top: spin-up, bottom: spin-down) for Dy adatoms (ΘDy = 0.06 ML) at the hollow site of the TiO2 terminated surface. The orbital projection on the Ti-dxy character is highlighted by filled red circles (whose size is proportional to its contribution at each eigenvalue) for the surface Ti layer and by filled blue circles for the first subsurface Ti layer. The spin splitting at the Γ point amounts to 22 meV. when projected at θ = 60°. In fact, the adsorption geometry of adsorption sites of Dy on STO(001) have stable magnetization Dytop is identical to that of both Dy and Ho on the top-O site of on time scales of at least a few hundreds of seconds. It is MgO. These show stable magnetization over time scales of interesting that, although the Dytop site with its out-of-plane hours or days (only limited by the time scales of the magnetic anisotropy appears to be by far the most stable, the measurements), in a wide range of fields (up to at least 7 T easy-plane configuration of Dyhollow and the easy-axis in-plane for Dy and 8 T for Ho) and temperatures (up to at least 15 K configuration of Dybr‑Ox may also lead to slow magnetic for Dy and 40 K for Ho).21,22,24 Dytop on SrO-terminated STO, relaxation. together with its analogues on MgO, can be regarded as an Stimulated by the finding of a Dy-adsorption-induced approximate realization of a RE-O dimer, whose magnetization metallization of the STO substrate, we have investigated the was predicted to be extremely stable by means of quantum influence of the Dy deposition on the magnetic properties of chemistry calculations.23,57 We anticipate even longer intrinsic the STO surface. Figure 6a shows the XAS (top panel) and the lifetimes for Dytop when the magnetic field is applied corresponding XMCD (middle panel) recorded at the Ti L2,3 perpendicular to the STO(001) surface, due to the strong edges before and after deposition of 0.035 ML of Dy on out-of-plane anisotropy of this species. However, our magnet- Nb:STO(001). Prior to Dy deposition, the Ti XAS has the ization cycles are recorded under X-ray flux conditions which typical features of the 3d0 configuration.58 Moreover, Ti shows severely limit the lifetime, especially at θ = 0°, where the density a small XMCD, with a positive integral (bottom panel). The of the incident photon flux, twice as high as at θ = 60°, leads to a XMCD amplitude at the most prominent peak of the L3 edge higher density of secondary electrons and thus a lower value of amounts to only about 0.6% of the corresponding edge jump. τsec by a factor of 4 (eq S7 of the Supporting Information). This is very similar to the XMCD previously found at the Under these conditions, we measure τexp = 160 ± 24 s at θ = 60° LaAlO3/SrTiO3 interface, on O2-annealed samples with a and we expect τexp ≲ 50 s at θ = 0°, fully limited by τsec (which is minimal amount of oxygen vacancies.58 Nominally Ti is in a considerably lower than the value reported for Ho/MgO).25 tetravalent oxidation state, corresponding to a 3d0 configuration Thus, we barely see an opening of the magnetization loop at with no magnetic moment. However, covalence in the bond normal incidence, as shown in Figure 2c. On the other hand, between Ti 3d and O 2p electrons leads to an actual 3d(0+δ) Dybr‑Ox shows a 1 order of magnitude longer lifetime than occupation (where the value of δ depends on the degree of Dyhollow at low magnetic fields, but a much faster decay at high covalence), which can be associated with a small paramagnetic fields. Our qualitative comparison suggests that all considered moment. A finite contribution to δ may also come from a small 11189 https://doi.org/10.1021/acsnano.2c04048 ACS Nano 2022, 16, 11182−11193 ACS Nano www.acsnano.org Article concentration of oxygen vacancies which may form at the 2DEG of Ti 3dxy character at the Dy/STO interface offers surface during the sample preparation procedure or by promising ways for the electrical manipulation of the Dy irradiation with the X-rays. Although the magneto-optical magnetism. Besides tuning the density of carriers of the 2DEG, sum rules59,60 cannot be applied to determine the spin magnetic modifying the STO lattice through its piezoelectricity or moment at the Ti L2,3 edges, due to mixing of the L2 with the L3 exploiting the substrate magnetic moments induced by the intensity,61 we can extract an orbital magnetic moment mL = fluctuating charge dipoles near the STO ferroelectric quantum −⟨Lz⟩ = −0.003 ± 0.001 μB (assuming a vanishing δ and thus critical point,62 one can envisage injecting/extracting a spin- 10 holes in the 3d shell). Its negative sign suggests that, polarized electrical current in/from the surface or subsurface according to Hund’s rules, the Ti spin magnetic moment is TiO2 layer to “write/read” the Dy magnetization. aligned parallel to the applied magnetic field. The extremely small magnitude of the orbital moment supports that δ ≪ 1. METHODS After Dy deposition, the Ti XAS shows only minor variations, with a small decrease of the intensity of the sharp peaks and a Clean and ordered SrTiO3(001) surfaces were prepared by cycles of Ar+ sputtering and annealing in O2 atmosphere (partial pressure of p = consequent increase of the valleys between them. This indicates 2−5 × 10−6mbar) at a temperature of 923 K on commercial SrTiO3 that, at least locally around the Dy impurities, the Ti 3d orbital single crystals, either pure or doped with 1% at. Nb (the latter are occupation δ slightly increases, thus confirming that the Dy referred to as Nb:STO in the manuscript). Nb:STO crystals were deposition actually dopes the STO(001) surface even in the preferentially used, as their enhanced electrical conductivity compared case of Nb-doped STO crystals. The XMCD, on the other to that of pure STO led to a higher signal-to-noise ratio of the XMCD hand, shows no significant change of magnitude, but its sign and measurements in the surface-sensitive total-electron-yield mode. The that of its integral are reversed. This implies that the Ti spin ordered surfaces exhibited sharp 1 × 1 LEED patterns (see Supporting moment aligns antiparallel to the Dy spin moment, suggesting Information), i.e., they were unreconstructed. Dy was evaporated, from the onset of an antiferromagnetic coupling between the two. thoroughly degassed rods or lumps in tungsten crucibles, onto SrTiO3(001) kept at T ≤ 6K, in order to prevent surface diffusion, and Indeed, Figure 6b shows that the magnitude of the Ti XMCD p ≤ 1 × 10−10mbar. The Dy coverage is expressed in monolayers (ML) integral (proportional to the Ti orbital moment), normalized at relative to the SrTiO3(001) surface, where 1 ML is defined as 1 Dy its value at B = 5 T follows closely the normalized Dy atom per SrTiO3(001) unit cell (lattice parameter a = 0.3905 nm), magnetization curve. Thus, our experimental results are fully corresponding to a surface density of 6.56 atoms/nm2. The coverage consistent with the first-principles calculated spin-density calibration based on the Dy XAS integral is obtained by comparison isosurface sketched in Figure 6c. Here, the opposite spin with previous investigations on Sm/graphene/Cu(111) (where STM polarization of Ti with respect to Dy extends for several atomic and XAS were combined on the same sample) after proper rescaling of distances, especially across Ti layers, and is maximal within the the different absorption coefficients and lattice parameters of the Ti subsurface layer, where Ti exhibits the highest spin magnetic substrates and the number of holes of the rare-earth atoms. moment mS = −0.06 μB/Ti atom, as compared to mS = −0.03 The XMCD experiments were carried out at the EPFL/PSI X- Treme beamline63 of the Swiss Light Source (data taken at 2.5 and 15 μB/Ti atom in the surface layer (note that these are the K), at the BOREAS beamline64 of the ALBA synchrotron radiation moments of the Ti atoms which, in each layer, are closest to the facility (data taken at 5 K), and at the ID32 beamline65 of the Dy atom). This finding correlates with the fact that the largest European Synchrotron Radiation Facility (data not shown in the electron doping is found for the Ti-dxy orbitals of the subsurface manuscript). The measurements were performed in the total-electron- layer, whose bands are shown as blue circles in Figure 6d, while yield mode at temperatures in the range 2.5−15 K, and magnetic fields the Ti-dxy bands of the surface layer (red circles) remain well up to 9 T, applied parallel to the X-ray beam. The energy resolution of above the Fermi level. We conclude that Dy induces a sizable the X-ray beam at the Dy M4,5 edges was of the order of at least 250 spin polarization of the Ti atoms, which extends beyond the meV, the photon flux was of the order of 2 × 1010 photons/s, and both nearest-neighbor positions, suggesting that long-range Ti−Ti linear and circular X-rays were polarized to a degree close to 100%. The background-subtracted Dy M4,5 edge XAS [(I+ + I−)/2, where I+ correlations may be active even at the extremely low Dy surface and I−are the XAS spectra recorded with right and left circularly densities under study, likely due to the formation of the 2DEG polarized X-rays, respectively], as shown in Figure 2a, is obtained by within a couple of atomic layers at the Dy/STO interface. subtracting the X-ray absorption spectra of the bare SrTiO3(001) crystals, taken prior to Dy evaporation, from those of Dy/SrTiO3(001) CONCLUSIONS recorded under identical conditions, and then subtracting step In conclusion, we have observed that Dy atoms adsorbed on the functions at the two edges. The XMCD is then calculated as I− − I+. SrTiO3(001) surface show slow relaxation of the magnetization The XLD is defined as IV − IH, where IV and IH are the XAS spectra recorded with vertically and horizontally linearly polarized X-rays. at temperatures T ≤ 6 K in an extended range of magnetic fields With reference to the sample orientation, as shown in Figures 3 and 4, up to about 3 T. A careful comparison between experimental the vertical linear polarization lies along the y axis, which corresponds results, first-principles calculations, and a simple spin−lattice to the sample rotation axis in our experiments, while the horizontal relaxation model allows us to attribute our observations to Dy linear polarization lies within the xz plane. The magnetic field atoms adsorbed at the hollow site of the TiO2 termination. dependence of the magnetization relaxation time τ was recorded by These are characterized by an occupation of the 4f shell with 9 saturating the Dy magnetization at a field of +5 T, then ramping the electrons and a strong easy-plane magnetic anisotropy, which field to its target value at a speed of 33.3 mT/s and without X-rays on results from the combined effect of the equatorial O and Ti the sample, and finally recording the time dependence of the XMCD ligands and a top charge due to strongly anisotropic, partially magnitude, which is fitted by a single exponential function. DFT calculations were performed by means of the augmented-plane occupied Dy spd orbitals. The lifetime of the magnetic state, of wave + local orbital method, as implemented in the Wien2K code,66,67 the order of a few hundred seconds, is mainly limited by without including spin−orbit coupling. The in-plane STO lattice transitions between the two states of the ground-state doublet. constant was fixed to the experimental value at T = 300 K, a = 0.3905 In this geometry, Dy atoms induce a sizable spin polarization at nm. The generalized-gradient approximation (GGA) of the exchange the Ti atoms, whose magnetic moments couple antiferromag- and correlation functional was considered for the structural character- netically with those of Dy. The formation of a spin-polarized ization. Atomic relaxations of the coordinates of the Dy adatom and of 11190 https://doi.org/10.1021/acsnano.2c04048 ACS Nano 2022, 16, 11182−11193 ACS Nano www.acsnano.org Article the upper substrate layer atoms, carried out within the GGA Jindřich Kolorenč − Institute of Physics (FZU), Czech functional,68 were allowed until residual forces were <1 meV/au. Academy of Sciences, CZ-182 21 Prague, Czech Republic The electronic structure analysis reported in the main text was Sanjoy K. Mahatha − Istituto di Struttura della Materia obtained by using an on-site version of the hybrid B3LYP functional,69 (ISM), Consiglio Nazionale delle Ricerche (CNR), I-34149 while, for testing purposes, an on-site Hubbard correction term (as implemented in the DFT+U method) on the f orbitals of Dy (U = 7 Trieste, Italy; School of Physics and Materials Science, Thapar eV, J = 0.82 eV) was also considered. The former approach was found Institute of Engineering and Technology, Patiala 147004, to describe the valence configuration of the Dy ions better, and a India; orcid.org/0000-0002-5394-6911 comparison between the two methods is given in the Supporting Miguel Angel Valbuena − Catalan Institute of Nanoscience Information. Within the on-site B3LYP approach, a calculated and Nanotechnology (ICN2), CSIC and BIST, Campus electronic gap for STO bulk of 2.3 eV was found, to be compared UAB, E-08193 Barcelona, Spain; Instituto Madrileño de with an experimental value of 3.25 eV.40 Further details on the Estudios Avanzados en Nanociencia (IMDEA Nanoscience), simulation cell are given in the Supporting Information. E-28049 Madrid, Spain; orcid.org/0000-0002-0585- Atomic multiplet calculations were performed with the Quanty 5636 multielectron code,53 partially using the Crispy graphical interface,70 and used to simulate the temperature and magnetic field dependence Luca Persichetti − Department of Materials, ETH Zurich, CH- of XAS, XMCD, XLD, and magnetization cycles. The Hamiltonian for 8093 Zurich, Switzerland; Dipartimento di Fisica, Università the multiplet calculations includes electron−electron interactions, di Roma “Tor Vergata”, I-00133 Roma, Italy; orcid.org/ spin−orbit coupling, Zeeman energy due to the external magnetic 0000-0001-6578-254X field, and the crystal field potential acting on the Dy 4f shell. The Marina Pivetta − Institute of Physics, Ecole Polytechnique electron−electron interactions (in terms of Slater−Condon integrals) Fédérale de Lausanne (EPFL), CH-1015 Lausanne, as well as the spin−orbit coupling values were computed using Switzerland; orcid.org/0000-0001-5330-8648 Cowan’s atomic structure code. The Slater integrals were reduced to Boris V. Sorokin − Institute of Physics, Ecole Polytechnique 66% of their atomic value in order to account for the screening due to Fédérale de Lausanne (EPFL), CH-1015 Lausanne, surface electrons. The crystal field potential was calculated, for each adsorption site, by using an electrostatic point charge model, based on Switzerland; orcid.org/0000-0002-4950-5654 the optimized adsorption geometry and the Bader charges of the Dy Darius Merk − Institute of Physics, Ecole Polytechnique neighbors, as obtained by our first-principles calculations (see Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Supporting Information for charge values and positions and the Switzerland corresponding crystal field parameters in Wybourne notation). The Sébastien Reynaud − Institute of Physics, Ecole Polytechnique final state Hamiltonian includes the presence of the core hole. Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland ASSOCIATED CONTENT Dante Sblendorio − Institute of Physics, Ecole Polytechnique * sı Supporting Information Fédérale de Lausanne (EPFL), CH-1015 Lausanne, The Supporting Information is available free of charge at Switzerland https://pubs.acs.org/doi/10.1021/acsnano.2c04048. Sebastian Stepanow − Department of Materials, ETH Zurich, CH-8093 Zurich, Switzerland; orcid.org/0000-0002- Complementary experimental data: STO(001) crystals 4090-6574 characterization; Comparison between Nb-doped and Corneliu Nistor − Department of Materials, ETH Zurich, CH- pure SrTiO3; Coverage dependence of XAS, XMCD and 8093 Zurich, Switzerland magnetization cycles; XAS, XMCD, XLD and magnet- Pierluigi Gargiani − ALBA Synchrotron Light Source, E- ization cycles of Ho/STO(001). DFT calculations: 08290 Cerdanyola del Vallès, Spain; orcid.org/0000- further details on the DFT simulation cell and the 0002-6649-0538 methodology; Comparison GGA+U vs on-site B3LYP; Davide Betto − European Synchrotron Radiation Facility, F- Spin and orbital projected band structures: 2DEG at the 38043 Grenoble, France STO surface; Details about the atomic multiplet Aitor Mugarza − Catalan Institute of Nanoscience and calculations: Point charges and crystal field parameters; Nanotechnology (ICN2), CSIC and BIST, Campus UAB, E- Simulated XAS, XMCD, and magnetization cycles for 08193 Barcelona, Spain; Institució Catalana de Recerca i each adsorption site; Details about the calculation of the Estudis Avançats (ICREA), Barcelona E-08010, Spain; magnetization relaxation time τ: theoretical model; orcid.org/0000-0002-2698-885X Estimate of the secondary electrons contribution to the Pietro Gambardella − Department of Materials, ETH Zurich, value of the relaxation time (PDF) CH-8093 Zurich, Switzerland Harald Brune − Institute of Physics, Ecole Polytechnique AUTHOR INFORMATION Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Corresponding Author Switzerland; orcid.org/0000-0003-4459-3111 Carlo Carbone − Istituto di Struttura della Materia (ISM), Alessandro Barla − Istituto di Struttura della Materia (ISM), Consiglio Nazionale delle Ricerche (CNR), I-34149 Trieste, Consiglio Nazionale delle Ricerche (CNR), I-34149 Trieste, Italy Italy; orcid.org/0000-0002-5632-4915; Email: alessandro.barla@trieste.ism.cnr.it Complete contact information is available at: https://pubs.acs.org/10.1021/acsnano.2c04048 Authors Valerio Bellini − S3-Istituto di Nanoscienze-CNR, I-41125 Modena, Italy Notes Stefano Rusponi − Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland; orcid.org/0000-0002-8494-5532 The authors declare no competing financial interest. 11191 https://doi.org/10.1021/acsnano.2c04048 ACS Nano 2022, 16, 11182−11193 ACS Nano www.acsnano.org Article ACKNOWLEDGMENTS (11) Miyamachi, T.; Schuh, T.; Märkl, T.; Bresch, C.; Balashov, T.; Stöhr, A.; Karlewski, C.; André, S.; Marthaler, M.; Hoffmann, M.; et al. Computation time at CINECA supercomputing centers is Stabilizing the Magnetic Moment of Single Holmium Atoms by gratefully acknowledged. The X-ray absorption measurements Symmetry. Nature 2013, 503, 242−246. were performed on the EPFL/PSI X-Treme beamline at the (12) Donati, F.; Singha, A.; Stepanow, S.; Wäckerlin, C.; Dreiser, J.; Swiss Light Source, Paul Scherrer Institut, Villigen, Switzerland, Gambardella, P.; Rusponi, S.; Brune, H. Magnetism of Ho and Er at the BOREAS beamline of the Alba Synchrotron Radiation Atoms on Close-Packed Metal Surfaces. Phys. Rev. Lett. 2014, 113, Facility, Cerdanyola del Vallés, Spain, and at the ID32 beamline 237201. of the European Synchrotron Radiation Facility, Grenoble, (13) Steinbrecher, M.; Sonntag, A.; Dias, M. d. S.; Bouhassoune, M.; France. We acknowldege funding from the National Research Lounis, S.; Wiebe, J.; Wiesendanger, R.; Khajetoorians, A. A. Absence Council (CNR) within the CNR/CAS Cooperative Pro- of a Spin-Signature from a Single Ho Adatom as Probed by Spin- gramme project "Advanced characterization methods for the Sensitive Tunneling. Nat. Commun. 2016, 7, 10454. (14) Baltic, R.; Pivetta, M.; Donati, F.; Wäckerlin, C.; Singha, A.; study of rare-earth single-ion magnets on oxide substrates", Dreiser, J.; Rusponi, S.; Brune, H. Superlattice of Single Atom Magnets from the Czech Academy of Sciences (Mobility Plus Project on Graphene. Nano Lett. 2016, 16, 7610−7615. No. CNR-19-03), and from the Swiss National Science (15) Singha, A.; Baltic, R.; Donati, F.; Wäckerlin, C.; Dreiser, J.; Foundation (200020_176932 and 200021_175941). ICN2 Persichetti, L.; Stepanow, S.; Gambardella, P.; Rusponi, S.; Brune, H. was funded by the CERCA Programme/Generalitat de 4f Occupancy and Magnetism of Rare-Earth Atoms Adsorbed on Catalunya and supported by the Spanish Ministry of Economy Metal Substrates. Phys. Rev. B 2017, 96, 224418. and Competitiveness, MINECO (grant nos. SEV-2017-0706 (16) Baltic, R.; Donati, F.; Singha, A.; Wäckerlin, C.; Dreiser, J.; and PID2019-107338RB-C65/AEI/10.13039/ Delley, B.; Pivetta, M.; Rusponi, S.; Brune, H. Magnetic Properties of 501100011033). IMDEA Nanociencia acknowledges support Single Rare-Earth Atoms on Graphene/Ir(111). Phys. Rev. B 2018, 98, from the Severo Ochoa Programme for Centres of Excellence in 024412. R&D (MINECO, grant SEV-2016-0686). We acknowledge P. (17) Kozub, A. L.; Shick, A. B.; Máca, F.; Kolorenč, J.; Lichtenstein, A. I. Electronic Structure and Magnetism of Samarium and Orgiani (CNR-SPIN) for the loan of some of the Nb-doped Neodymium Adatoms on Free-Standing Graphene. Phys. Rev. B STO single crystals used in these studies and M. Retegan 2016, 94, 125113. (ESRF) for assistance with the use of Crispy and Quanty. (18) Shick, A. B.; Shapiro, D. S.; Kolorenč, J.; Lichtenstein, A. I. 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