Spin-state engineering of single titanium adsorbates on ultrathin magnesium oxide

Domain: physics
Published: 2026-01-16
Editorial outcome: minor_revision

Abstract
Single atomic adsorbates on ultrathin insulating films provide a promising route towards building bottom-up quantum architectures based on atomically identical yet individually addressable spin qubits on solid surfaces. A key challenge in engineering quantum-coherent spin nanostructures lies in understanding and controlling the spin state of individual adsorbates. In this work, we investigate single titanium (Ti) atoms adsorbed on MgO/Ag(100) surfaces using a combined scanning tunneling microscopy and electron spin resonance. Our measurements reveal two distinct spin states, S = 1/2 and S = 1, depending on the local adsorption site and the thickness of the MgO film. Density functional theory calculations suggest a Ti+ configuration for the Ti adsorbates with approximately 3 electrons in the 4s and 3d valence shells. Using multi-orbital magnetic multiplet calculations the site dependence of the spin can be rationalized as a charge redistribution between spin-polarizing and depolarizing orbitals. These findings underscore the potential of surface-supported single atoms as spin qubits with tunable spin and charge states, enabling atom-by-atom control in the realization of a versatile quantum platform on surfaces.

Introduction
Positioning individual atoms using the tip of a scanning tunneling microscope (STM) has paved the way for the bottom-up fabrication of tailored nanostructures on surfaces with atomic precision1. Subsequent achievements have highlighted the potential of single atoms on surfaces as basic building blocks for constructing nanoscale devices with diverse charge and spin functionalities, exploiting the atomic precision of STM2,3. By choosing an appropriate substrate, it is possible to tune the properties of atomic spins4–6, particularly given the subatomic scale of magnetic phenomena7.

The implementation of electron spin resonance (ESR) in STM experiments has pushed the spectroscopic energy resolution to an extraordinary limit of ~10 neV, and has enabled the coherent manipulation of individual spin states since the first unequivocal continuous-wave ESR spectra were obtained from iron (Fe) single adsorbates on two-monolayer (2ML) magnesium oxide (MgO) films grown on a silver substrate8–11.

Atoms or molecules hosting an electronic spin S = 1/2, when coupled to a magnetic field, serve as natural two-level systems and are promising candidates for building solid-surface quantum platforms composed of identical but individually addressable qubits12–14. ESR-STM studies on a variety of S = 1/2 systems, including titanium (Ti)15, iron (II) phthalocyanine (FePc)16,17, alkali dimers and pairs on MgO18, molecular radicals19,20, and bis(phthalocyaninato)terbium(III) on sodium chloride (NaCl)21, have demonstrated the suitability of single-spin adsorbates for quantum-coherent experiments at the atomic scale. In particular, Ti atoms on MgO have enabled the realization of advanced ESR control protocols, including universal single-qubit gates, a two-qubit gate13,22, and the observation of the free coherent evolution of entangled spins23.

Despite these advances, the practical implementation of atomic spin qubits in quantum technologies remains challenging. This is largely due to the complex interplay between adsorbates and substrates, which can induce deviations from free-atom configurations both in charge and spin states-and may result in reduced coherence times. A detailed understanding of the physical and chemical environment of single atoms on surfaces is therefore essential for the controlled realization of scalable quantum-coherent nanostructures.

The charge and spin states of individual adsorbates can differ substantially from their isolated counterparts, due to mechanisms such as charge transfer, ligand-field effects, or chemical reactions during deposition. For instance, Ti atoms expected to have S = 1 in the gas phase have been reported to exhibit S = 1/2 on MgO/Ag(100), an observation previously attributed to hydrogen capture from residual gas11,15,24,25. Similarly, FePc has been observed to change its spin state from S = 1 to S = 1/2 due to electron transfer from the Ag substrate16,17. A systematic understanding of how the substrate modifies the electronic configuration of adsorbates is thus a prerequisite for designing robust atomic-scale quantum systems.

The first studies of Ti adsorbates on MgO/Ag(100) concluded that Ti could not explain the experimental evidence showing a spin-1/2 system and proposed the formation of a TiH species15. These conclusions were based on density-functional-theory (DFT) calculations in which Ti adatoms were modeled on free-standing MgO layers, without including the metallic Ag(100) substrate present in the experiments. The calculations yielded a spin S = 1/2 for adsorbed TiH and S = 1 for bare Ti, independent of the adsorption site. Consequently, later studies of Ti on MgO/Ag(100) adopted the assumption of TiH formation to explain their experimental data15,24,25. In the present work, we show that DFT descriptions of Ti adsorbates are highly sensitive to the delicate balance between charge transfer and electronic correlations. Nevertheless, DFT robustly confirms that Ti can have S = 1/2 and S = 1 when adsorbed on MgO/Ag(100) depending on the adsorption site and MgO thickness.

In this work, we combine scanning tunneling spectroscopy (STS), ESR, DFT, and magnetic multiplet calculations to investigate the spin and charge states of Ti atoms adsorbed on MgO films of two and three monolayers (MgO(2) and MgO(3)) grown on Ag(100). We find that the spin state of the adsorbate depends sensitively on both the local adsorption geometry and the MgO thickness. Specifically, Ti exhibits a spin S = 1/2 when adsorbed on both oxygen-atop (O-atop) and O-O bridge sites of MgO(2), and on bridge sites of MgO(3). In contrast, on O-atop sites of MgO(3) we find a spin S > 1/2, identified via remote-spin ESR, STS, and multiplet calculations. Atom manipulation confirms robust and reversible switching between these distinct spin states and adsorption geometries. Our DFT calculations support a consistent Ti+ oxidation state primarily governed by the lowering of the work function by the MgO layer. The Ti spin can be rationalized as a charge redistribution between spin-polarizing and depolarizing orbitals that we model by 4s23d1 and 4s13d2 configurations in our magnetic multiplet calculations. These findings indicate that the interaction with the adsorption site, rather than chemical doping or hydrogenation, is the principal mechanism for spin variability, providing new avenues for the quantum engineering of surface-supported spin qubits.

Results
Experiment

STM images and STS spectra. The sample was prepared by depositing Ti and Fe atoms with a submonolayer coverage (<1%) onto defect-free MgO films grown on a clean Ag(100) substrate (see “Methods” and Supplementary Section 1). Figure 1A presents an STM topography of the sample surface, which includes regions of MgO(2), MgO(3), and bare Ag. Well-isolated atomic adsorbates are observed throughout all regions.

High-resolution STM images on MgO(2) (Fig. 1B) reveal two distinct Ti adsorption geometries: one atop surface oxygen atoms (Ti(2)O), and one bridging two adjacent oxygen atoms (Ti(2)B), consistent with earlier reports26,27. Similarly, on MgO(3) (Fig. 1C), two Ti species are also identified. The bridge-site configuration (Ti(3)B) appears with considerable abundance and shows STS characteristics closely resembling those of Ti(2)B. In contrast, the oxygen-atop configuration (Ti(3)O) displays a much larger apparent height in STM images and distinct spectroscopic features (Fig. 1E), which are discussed in detail below. A third, minor O-atop variant, similar to Ti(2)O, was also occasionally observed on MgO(3) but accounted for less than 0.1% of the total Ti adsorbate population. This minority species is not considered further (see Fig. S2).

To probe the electronic properties of the four dominant Ti configurations identified in STM (Fig. 1B, C), we performed STS measurements (Fig. 1D, E). The spectra acquired for Ti adsorbates on MgO(2) exhibit features in agreement with previous studies15,23,28. Likewise, Ti(3)B exhibits an early identical spectral profile to Ti(2)B, characterized by a smooth, monotonic conductance curve and a step-like feature at zero bias (marked by a cyan triangle), attributed to spin polarization of the STM tip27,29. In contrast, Ti(3)O exhibits a pronounced inelastic tunneling (IET) signature at ±18 meV (orange arrows in the inset), symmetrically positioned about Vb = 0. This feature indicates a zero-field splitting and the presence of a sizable magnetic anisotropy energy (MAE),30 consistent with a spin state S > 1/2. DFT and multiplet calculations for Ti(3)O confirm that this state corresponds to a magnetic ground state with spin S = 1 (see the theory section below).

ESR spectra. ESR measurements of the Ti adsorbates provided direct insight into their spin states (Fig. 2A). Three species—Ti(2)O, Ti(2)B, and Ti(3)B—exhibit ESR resonances (red, blue, and cyan traces, respectively) within the frequency range expected for Zeeman splitting under an applied magnetic field of ~0.6 T and an effective g-factor of ~2, consistent with a spin angular momentum of S = 1/2 15,27. The assignment of S = 1/2 for Ti(3)B is further supported by the close resemblance between its dI/dV spectrum (Fig. 1D, blue) and that of Ti(2)B (Fig. 1E, cyan).

In contrast, Ti(3)O does not display any ESR resonance within the same frequency window (orange trace in Fig. 2A), indicating a fundamentally different spin configuration. Coupled with the IET-like steps observed in its dI/dV spectrum at ±18 meV (Fig. 1E), this suggests a spin state with S > 1/2 and significant magnetic anisotropy, warranting further investigation.

To probe the magnetic anisotropy of Ti(3)O, we analyzed its interaction with a neighboring spin. In this approach, the target spin (Ti(3)O) couples to an nearby probe spin with S = 1/2 (Ti(3)B), and the anisotropy of the target is inferred from angular variations in the ESR spectrum of the probe31,32. The Ti(3)B–Ti(3)O pair was assembled by lateral manipulation using the STM tip (“dragging”; see Fig. 3C), with a separation of 0.72 nm as denoted in Fig. 2B.

The ESR spectrum acquired on the Ti(3)B in this pair (Fig. 2C) exhibits a clear peak splitting Δf arising from spin-spin interaction, modeled as J S · S. The angular dependence of Δf with respect to the orientation of the external magnetic field θext (Fig. 3D) follows a cos(θext) trend31, consistent with uniaxial out-of-plane anisotropy of the Ti(3)O spin. Given that the Ti(3)B spin aligns with the external field direction, the sinusoidal modulation of Δf(θext) provides strong evidence for a spin angular momentum S > 1/2 in Ti(3)O. The observation of two sinusoidal branches further suggests bistability in the spin orientation of Ti(3)O, with preferred alignment along two collinear directions, which in turn defines the pair of resonance frequencies observed in the ESR spectrum (see up and down arrows in Fig. 3C).

Control of adsorption sites. When adsorbed on MgO(2), Ti atoms exhibit relatively short spin lifetimes and coherence times, most likely limited by substrate-induced spin scattering in the absence of tunneling electrons33. Consequently, Ti atoms adsorbed on thicker insulating layers such as MgO(3) may exhibit significantly enhanced coherence, owing to the reduced electronic coupling to the underlying Ag substrate, which suppresses backscattering of free electrons33. In this context, achieving precise control over Ti atom positioning on MgO(3) is essential for constructing artificial spin structures with optimized quantum coherence. To this end, we employ two complementary atom manipulation techniques to reposition Ti atoms on MgO(3), as illustrated in Fig. 3 (see Supplementary Section 2 for technical details).

The first method consists of picking up a Ti(3)O atom with the STM tip and dropping it off at a new location, as shown schematically in Fig. 3A. This approach is suitable for long-distance repositioning, typically resulting in a Ti(3)O species within a MgO(3) domain. Interestingly, when the atom is dropped onto a MgO(2) region, the resulting species at the surface (see Fig. 3B) confirms the established S = 1/2 spin state. Based on the experimental evidence, this observation, together with the absence of ESR signal (Fig. 2A), support that a Ti atom adsorbes with different spin-dependent electronic structures depending on the thickness of the MgO layer.

The second method enables short-distance repositioning by inducing lateral hopping of the Ti atom between neighboring lattice sites using voltage pulses applied to the STM junction, as depicted in Fig. 3C (“dragging”). By fine-tuning the lateral tip displacement xhop, vertical approach zhop, and pulse amplitude Vhop, we achieve controlled atomic movement over half the O-O lattice spacing on the MgO surface (see sequential STM images in Fig. 3D). This manipulation protocol enables precise construction of multi-atom assemblies, including the Ti(3)B–Ti(3)O pair discussed in Fig. 2B. Notably, the hopping process is reversible, allowing the Ti atom to switch between two distinct adsorption sites. As demonstrated in Figs. 1E and 2A, this transition induces a corresponding change in the atom’s spin, which is either S > 1/2 or S = 1/2, depending on whether the atom occupies an O-atop or bridge site. This strongly suggests that the spin state of Ti is governed by its local bonding environment and can be reversibly switched via site-selective manipulation.

Theory

In order to rationalize the experimental findings concerning the spin state of adsorbed Ti, we have studied its electronic structure in different environments, including the presence of H. In general, H-adsorption has been suggested to occur in experimental conditions under ultrahigh vacuum and low temperatures for Ti adsorbates15. Indeed, our DFT calculations show that Ti can readily form stable hydride species when adsorbed on the MgO/Ag(100) surface, see the Supplementary Section 3. Among the considered configurations, TiH emerges as the thermodynamically favored species under hydrogen-rich conditions, as determined by comparing Gibbs free energies referenced to gas-phase H2. The formation of TiH is found to be unstable, typically leading to spontaneous H desorption.

TiH has a reduced thermodynamic phase space and can only be formed for a small range of hydrogen chemical potentials. Under low concentration of hydrogen, bare Ti will be stabilized depending on the source of hydrogen that fixes the hydrogen chemical potential. This is further supported by the experimental observation that Ti adatoms can slowly degrade over time and sporadically become spectroscopically dark no longer exhibiting any ESR features. We tentatively assign this latter behavior to a degradation process related to slow hydrogen adsorption that happens on the scale of months, hopefully to be confirmed by a more systematic study.

Under ultra-low temperature and ultrahigh vacuum experimental conditions, Ti atoms are likely found on the surface. A comparison of the theoretically obtained magnetic structures of the TiH species indicates that the bare Ti adsorbate is compatible with the experimental data, while TiH does not reproduce the observed behavior (see the Supplementary Section 3, for details).

Our calculations give us access to the adsorption energies, which can be tentatively compared to the relative abundance of adsorbate on the atop and bridge sites. In our experiments, the prevalence of the bridge site on two monolayers is changed to the atop site on three monolayers. This behavior is reproduced by the chemisorption energy of the Ti adsorbate (Supplementary Section 3).

In the following, we analyze in detail the electronic structure of Ti atoms on MgO(2) and MgO(3).

Ti on MgO/Ag(100): electronic configuration. Our DFT calculations reveal distinct behavior depending on the adsorption site of Ti (O-atop vs. O-bridge), whereas the influence of MgO thickness (MgO(2) vs. MgO(3)) is confirmed by the established S = 1/2 and S = 1 spin states. In all cases, we find a charged Ti+ configuration, resulting from charge transfer to the substrate, facilitated by the reduced work function due to the MgO overlayer.

In all cases, charge analysis indicates that Ti adsorbed on MgO/Ag(100) retains approximately three valence electrons (see Table 1). While the non-integer values arise from the intrinsic ambiguity in decomposing the DFT total charge density into orbital contributions, the net charge consistently supports a Ti+ oxidation state.

As shown in Table 1, the total 3d occupation lies consistently in the range of d2.3–d2.45, with the 4s orbitals slightly less than singly occupied. Despite the similar total electron count, the magnetic moments differ significantly: O-atop configurations yield magnetic moments of ~2.3 μB, while bridge-site configurations exhibit reduced moments as low as 0.87 μB on MgO(2). This disparity arises not from charge transfer but from spin depolarization within the occupied states.

Figure 4 displays the projected density of states (PDOS) for Ti adsorbed on MgO/Ag(100). O-atop adsorption (Fig. 4A, B) shows two occupied d-orbitals around −1 eV, which yield a magnetic moment close to 2 μB (Table 1) for both MgO thicknesses. The 4s orbital plays only a minor role; instead, two d-orbitals in the majority-spin channel are occupied, resulting in an effective spin S = 1. This finding aligns well with the experimental results for MgO(3), but differs for MgO(2), where ESR indicates an S = 1/2 configuration.

In bridge-site geometries (Fig. 4C, D), the d-orbitals appear at approximately −1 eV below the Fermi level. Depolarizing contributions appear near the Fermi level. These results are consistent with a d2.3 configuration of Table 1 with a magnetic moment close to S = 1/2.

To further elucidate the observed spin states and particularly the contrasting behavior of Ti on O-atop sites of MgO(2) versus MgO(3), we performed multiplet calculations assuming three valence electrons in the s and d shells. In this model, the 4s orbital acts as a depolarizing channel, mimicking the enhanced hybridization and spin screening expected for bridge-site adsorption. This approach enables us to capture the delicate interplay between orbital configuration and spin state, as explored in the next section.

Multiplet calculations. We performed multiplet calculations to understand the DFT results and explore their experimental consequences on STS and ESR data (Figs. 1E and 2A). Following the methodology of ref. 34, we first determined the relaxed ground-state geometry of the Ti(3)O adsorbate via DFT calculations (Fig. 5A, B). We then generate a local basis set through wannierization, which then serves as input for the multiplet calculation. DFT suggests that the three valence electrons of Ti are in a 3d24s1 configuration. Here, sd hybridization to the 4s orbital plays the role of the depolarizing hybridization found in the above DFT calculations, with the 3d orbitals contain the magnetic properties of the Ti atom. By systematically varying the 4s-3d orbitals splitting Δsd, the multiplet calculations reveal a crossover between the configurations 3d14s2 and 3d24s1 around Δsd ≈ 1.2 eV (Fig. 5C).

Since the DFT electronic structure suggests a 3d24s1 configuration for both Ti(2)O and Ti(3)O we assume that these systems are near the crossover regime. Most likely DFT does not accurately predict Δsd for MgO(2), due to limitations in capturing the Ti intra-atomic correlations in the presence of external hybridization and lower symmetry. We find that in all systems that show S = 1/2 behavior in the experiment DFT predicts a small 3d-4s level split and only in 3ML O-top (S > 1/2) shows a significantly increased level separation (see Fig. S6), responsible for stabilizing the 3d2 configuration. Remarkably, a single adjustable parameter-Δsd-is sufficient to reproduce all experimentally observed spin states on MgO(2) and MgO(3) without invoking additional charge transfer or a hydrogen adsorption/desorption mechanisms. In the following we use Δsd to select either a 3d1 or 3d2 configuration for MgO(2) and MgO(3) for the oxygen atop adsorption site, respectively. We calculate differential conductance spectra and find good agreement between simulations and experiments. In particular, the calculated dI/dV spectrum for the 3d1 configuration of MgO(2) (Fig. 5D) qualitatively reproduces the features observed in Fig. 3B, including the crystal-field-induced excitation from the ground-state doublet, which is known to be sensitive to tip-adsorbate distance. Likewise, for the 3d2 configuration on MgO(3), the simulated spectrum in Fig. 5E aligns with the experimental excitation near 20 mV (cf. Fig. 3B).

Finally, we note that the work functions of MgO(2) and MgO(3) are nearly identical35 (see also Fig. S5), which should enable electron transfer from Ti to the Ag substrate for both cases, stabilizing a Ti+ state in good agreement with the above DFT results.

Methods
Experimental

The methods employed in the experiments mainly involved the preparation of the sample, including cleanliness and Ti deposition. This is a critical stage to have reproducible data. The second important methodology is the actual measurement of ESR on the single atoms used in this work.

Sample preparation. An atomically clean Ag(100) substrate was prepared through repeated cycles of Ar+ sputtering and thermal annealing. MgO films were grown on the Ag substrate at 580 K by evaporating Mg in an O atmosphere of 1.1 × 10−6 Torr. Fe and Ti atoms were deposited on the MgO surface at <100 K, by precooling the sample holder in the STM state of liquid helium temperature. The STM tip was fabricated by mechanically cutting a Pt/Ir wire (0.25 mm diameter), and its apex was spin-polarized by picking up Fe atoms from the MgO surface. The tip’s spin polarization was calibrated using the asymmetry of the differential conductance (dI/dV) across the zero bias in STS spectra measured from the Ti adsorbates on the oxygen-atop sites of MgO.

Single-atom ESR experiments. STS and ESR measurements were performed on Ti adsorbates on the surfaces of both two- and three-monolayer-thick MgO layers in an ultrahigh-vacuum (UHV) chamber (base pressure <10−10 mbar) using a 3He-cooled STM (Unisoku, USM1300) at T=0.4 K, equipped with two-axis superconducting magnets and high-frequency transmission cables. The ESR measurements were conducted using a commercial RF signal generator (Agilent E8257D), with the RF signal combined with a DC bias voltage through a bias tee (SigaTek, SB15D2). To read out the spin-polarized current in the ESR of the spins, a commercial current preamplifier (Femto, SPECS) followed by a lock-in amplifier (SR860, Stanford Research) was used. The RF signals were modulated at 95 Hz, with the modulation signal sent to the lock-in amplifier as a reference. The bias voltage Vb refers to the sample voltage while the tip is grounded. The STM constant-current feedback loop was set to open and low gain during the STS and ESR measurements, respectively.

Theoretical

The methods used for our theoretical analysis involve the calculation of highly correlated electronic structure to account for the atomic structure using the Mutliplet method, together with general DFT calculations that take into account the interactions between the different parts of this study involving surfaces and atoms. Finally, an important part of the work has been devoted to rationalizing the energetics behind the presence of H. This has been achieved by Gibbs free energy studies.

Multiplet calculations and Wannier basis construction. The multiplet calculations were performed within a Wannier-function framework following ref. 34. The Wannierization was carried out starting from a non-spin-polarized GGA calculation, using the same computational parameters described above. An 11 × 11 × 1 k-point grid was employed, with projections onto the Ti s and d manifolds and the O p manifold.

The resulting Wannier functions associated with the Ti 3d orbitals are highly localized, with a quadratic spread of Ω2 ≈ 1 Å2, whereas the Ti 4s Wannier function is more spatially extended, with Ω2 ≈ 3 Å2. The resulting basis set comprises six Ti-derived states (one 4s and five 3d) together with projections onto the O 2p states. This choice allows us to analyze the orbital level alignment and, in particular, the energetic splitting between the Ti s and d states for different adsorption geometries.

The on-site energies extracted from the Wannier Hamiltonian are shown in Fig. S6 for the four adsorption configurations considered. For the MgO(2) atop and bridge configurations, as well as for the MgO(3) bridge configuration, the on-site levels exhibit a similar structure characterized by a small s–d energy splitting. These three configurations are therefore expected to host a single unpaired electron on the Ti atom, consistent with the experimentally observed S = 1/2 behavior. In contrast, for the MgO(3) atop configuration the Ti 3d levels are significantly lowered in energy, stabilizing a 3d2 electronic configuration. This electronic structure naturally leads to a higher-spin ground state, in agreement with the experimentally observed S > 1/2 behavior.

Density functional theory calculations. DFT calculations have been performed using the plane-wave codes Quantum Espresso36–38 and VASP39,40. In addition to the PBE exchange and correlation functional, the calculations used an empirical Hubbard U correction41 in order to improve the description of localized 3d electrons. The chosen value, U−J=2.0 eV, is in agreement with thorough VASP DFT calculations42. Van der Waals (VdW) interactions were described by the semi-empirical dispersion-forces correction D343. The calculations were performed using the projector augmented-wave method (PAW)44 to treat the electron-atom potential. We used complementary calculations of the same system using VASP since it has been shown in literature45 that the ground state for Ti on MgO/Ag was hard to uniquely identify. Our additional calculations confirm the fundamental ground state properties of Ti on MgO/Ag, however, they also show subtle differences with respect to energy splitting of the 4s and 3d states as well as different polarizations close to the Fermi level. This indicates that there is a dependence on the ground state solution on the pseudopotentials since all other factors (e.g., the dispersion correction) were kept consistent across different codes. For the adsorbed species, we need at least a 3 × 3 unit cell of oxygen atoms to converge the calculations with respect to cell size in order to reproduce single adsorbates. We have used four layers of Ag(100) that are critical to obtain results closer to the experiment.

Gibbs free energy stability calculations. The relative stability of different hydrogenated adsorbates is assessed using the Gibbs free energy,
G=H−TS, (1)
where H is the enthalpy and TS the entropic contribution. Under the experimental conditions considered here, the relative prevalence of competing adsorption configurations is determined by their Gibbs free energies46. In practice, the evaluation of G is based on total energies obtained from first-principles calculations, with a key ingredient being the chemical potential of the hydrogen reservoir. Hydrogen is assumed to be supplied in its molecular form, H2, which is energetically favorable at the experimental temperature (~0.4 K). The chemical potential per hydrogen atom, μH, is therefore defined as one half of the dissociation energy of an isolated H2 molecule,
μH = E[H2] = 1/2 E(diss)[H2], (2)
with the energy reference taken as gas-phase H2. Alternative hydrogen sources, denoted Hnew, are incorporated through their chemical potential relative to atomic hydrogen in the gas phase,
Δμ = E[Hnew] − E[H], (3)
The incremental chemical potential associated with adding one hydrogen atom to a TiHx adsorbate is computed as
μx = E[TiHx] − (E[TiHx−1] + E[H]), (4)
which corresponds to the binding energy of a hydrogen atom in the TiHx complex. Here, E[TiHx] denotes the total energy of TiHx adsorbed on MgO/Ag(100), and E[H] is the reference energy per hydrogen atom. Within this framework, the change in Gibbs free energy associated with the adsorption of x hydrogen atoms on Ti is given by
ΔG(Δμ) = xμx − xΔμ. (5)
At the experimental temperature (~0.4 K), additional free-energy contributions arising from molecular rotations, vibrational entropy, configurational entropy, and vapor-pressure effects are negligible compared to chemical bond energies and are therefore omitted. Consequently, evaluating ΔG(Δμ) as a function of the hydrogen chemical potential provides a direct criterion for the relative thermodynamic stability of different TiHx species.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The manuscript reports combined experimental and theoretical investigations of Ti atoms adsorbed on 2 and 3 layers of\nMgO on Ag(100). From STM images the Ti atoms present two different adsorptions sites (atop of O atom and bridge site\nbetween two O atoms). Electron spin resonance and scanning tunneling spectroscopy measurements revealed a spin S = ½\nfor Ti atoms adsorbed on 2 layers of MgO and on bridge site of the 3 layers of MgO while a spin S = 1 is observed for the\natop O site of the 3 layers of MgO. The adsorption site can be manipulated with atomic precision by the STM tip.\nExperiments and calculations indicate that the measured spin values are compatible with pristine adsorbed Ti atoms and do\nnot require hydrogenation of the Ti atoms as previously suggested.\nThe experimental results clearly validate the spin values of the different systems combining two different spectroscopic\nmethods (STS and ESR). The manipulation of the spin by atomic manipulation is well evidenced from the experimental\nobservations. The novel interpretation of pristine rather than hydrogenated Ti atoms is compatible with the combined\nexperimental and calculated results.\nInvestigations of spin properties of single atoms on thicker decoupling layer are highly interesting due to the possible\nincreased spin lifetimes and coherence times, which are desirable for the realization of quantum coherent spin structures.\nMost important are the different spin values depending on the adsorption site of the Ti atoms on the 3 layers of MgO and their\nreversible switching using atomic manipulation. These observations may paved a way to the fabrication of desired\narchitectures of spin assemblies with tunable spin values.\nFinally the new interpretation involving pristine rather than hydrogenated Ti atoms is also important for future (and maybe\npast) experiments. Accurate description of the electronic structure of the single atoms is mandatory to the interpretation of\nmore complex systems.\nThe manuscript is clearly written and the results are presented and discussed in relation to previous works which are\nreferenced appropriately.\nI think that the manuscript deserves a publication in Nature Communications but needs to be improved taking in\nconsideration the following remarks.\n1. My main remarks concern the discussions regarding the multiplet calculations which should be extended (Section III B):\nDFT reveal that the s-d splitting increases with the MgO thickness. What is the reason for this observation?\nWhy does the crossover from 3d1 4s2 to 3d2 4s1 occurs for such large value of Δsd (1.2 eV)? Intuitively one could expect all\nelectrons in 3d state for such large splitting.\nThe authors say that the DFT electronic structure is approximated by a 3d2 4s1 configuration for both species. However they\nshow that simulated dI/dV for the 3d1 4s2 configuration reproduces the experimental observation of Ti_O on 2 layer of MgO.\nThis is confusing and should be clarified.\nThey also say that the DFT calculated s-d splitting may be slightly overestimated for 2 layer of MgO. However the value of\n0.2 eV would be in agreement with a 3d1 4s2 configuration, I do not see why it is overestimated.\n2. The DFT calculations reveal a spin S = ½ for bridge site with a 3d2 4s1 configuration. Could a similar mechanism as for\nthe atop O site on 2 layer of MgO (transition from 3d2 4s1 to 3d1 4s2) explain these value of the spin for the bridge site? How\nlarge are the s-d splitting for these sites?\n3. The apparent heights of Ti atoms is reversed between bridge and atop sites when going from 2 to 3 layers of MgO. Can\nthe authors provide any explanation for this observation?\n4. dI/dV spectra of Tio on the 3 layer of MgO exhibit a dip at V = 0. What is the origin of this electronic feature?\n5. Page 6, bottom of top paragraph: it is said that the assignment of a spin S = 1 to Tio on 3 layer of MgO is in agreement with\nthe configuration expected for a neutral Ti atom in vacuum. I do not see why the neutral atomic configuration would be\nexpected, in particular since calculations reveal a Ti+ state for all adsorbed Ti atom.\n6. In many figures the legends and labels are rather small and difficult to read.", "reviewer_2": "The manuscript of Phark et al. reports on a combined experimental-theoretical study of Spin-State Engineering of Single\nTitanium Adsorbates on Ultrathin Magnesium Oxide. The topic is highly relevant for an atomic scale engineering of spin\nqubits for the realization of various quantum platforms on material surfaces, and a very nice example of Ti ions on MgO/Ag\nsubstrate are reported. The conducted research is of a very high quality, and the STM/STS and STM-ESR experimental\nresults of a controlled creation of different spin states of Ti atoms are well supported and explained by DFT calculations.\nTwo experimental atom manipulation techniques for long- and short-range repositioning are also reported in detail. The\nmanuscript is well written, though some clarifications/improvements will be needed. The reported new knowledge on the\ndependence of the spin states depending on the local adsorption site and oxide film thickness will be highly relevant for\nthe design of future artificial spin systems with atomic precision. I recommend the manuscript for publication in Nature\nCommunications after a minor revision considering the following points:\n1. A considerable part of the theoretical results addresses the effect of TiH_x adsorbates in the search for agreement with the\nexperimental findings, but this aspect of the role of hydrogen is not clearly motivated in the Introduction and throughout the\nmanuscript. From the current literature it is evident that it is an important problem, but the manuscript should better motivate\nthis aspect, in my view. It is also somewhat unfortunate to introduce the description and discussion of the hydrogen-related\nresults with the 1st sentence in III. Theory with \"Such a reversible change of spin states is unlikely to be the result of\nselective adsorption or desorption of atomic hydrogen (H).\" An explicit indication of why it is still studied in much detail in the\nfollowing part would be a crucial improvement.\n2. Considering the significant numerical differences in the obtained results by using Quantum Espresso (QE) and VASP\nsoftwares, which are reported and discussed in detail in the Supplementary Information (SI, Table VII), it is not completely\nclear how and why the results of Table I were chosen. Moreover, there is an inconsistency between Tables I and VII, please\ncorrect them. It is also reported that all numerical parameters for QE and VASP calculations are identical (except the\ndifferences in the implementations in the two codes), but the reported k-sampling is still different: 3x3x1 for VASP and 4x4x1 for QE, please reformulate your statements accordingly. Overall, the discussion about the compatibility of the QE and VASP\nresults is confusing in its present state. What do we learn from this?\n3. In Section III.A it is claimed that \"... single Ti atom in a positively charged Ti+ configuration, resulting from charge transfer\nto the Ag substrate ...\". However, there is no direct evidence provided for the negative charge transferred to the Ag substrate.\nThis should be provided by analyzing the difference of Bader charges before and after adsorbing Ti on the MgO/Ag (\\Delta Q\n= Q_{Ti+MgOAg} - Q_{Ti} - Q_{MgOAg} and its change on the Ag substrate). The reduced electron work function with\nincreasing MgO thickness is nicely demonstrated experimentally. Instead of referring to [54], was this not demonstrated by\nthe performed DFT calculations? Please report the calculated work functions.\n4. To enrich the context of the manuscript considering the charge and spin states of individual atoms on surfaces I\nrecommend the inclusion of the following references into the Introduction:\n- https://doi.org/10.1103/PhysRevLett.127.236801 , where a nice experimental example of the effect of the local adsorption\ngeometry on the spin states of Fe atoms are presented on a Moiré structure platform.\n- https://doi.org/10.1088/1361-6528/aaf6dc , where the theoretical limits of SPM subatomic resolution in relation to the\ncharge/spin states and Hubbard U parameter of a Co atom on an oxide surface are investigated.\n5. Although in Section VII.A in the SI it is stated that \"In the following, we present DFT total energy calculations of TiHx ...\",\nthere are no actual total energies reported for the gas phase TiHx in section VII.B (SI).\n6. Fig. S2 is not referred to in the SI text and there is no description of it except its caption, is it intentional?\n7. Some references in the manuscript to the Supplementary Information (SI) are too general, and should be made explicit to\nthe particular sections in the SI.\n8. Please correct typos throughout the SI, for example \"The trend with MgO thickness is also nicely recover\" (recovered),\n\"results points\" (results point), \"Bader surface\" (not Bader volume?), \"The d orbitals result in highly localized Wannier\nfunctions (quadratic spread \\Omega^2\\approx 1 \\AA^2), whilst the s-orbital is more diffuse (\\Omega^2\\approx 3 \\AA)\"\n(Angstrom or squared-Angstrom? Should be consistent).\nKrisztián Palotás", "reviewer_3": "The manuscript covers the results in an orderly fashion and it presents evidence explaining the intriguing nature of the spin-\nstates of Ti adatoms on MgO ultrathin films. The literature on the system of Ti adatoms deposited on 2 monolayers (ML) of\nMgO ultrathin films grown on Ag(100) has assumed that Ti adatoms become hydrogenated in ultrahigh vacuum immediately\nafter deposition, thus becoming TiH molecules. In the early publication, “Engineering the Eigenstates of Coupled Spin-½\nAtoms on a Surface” by Kai Yang et al. in 2017, this hypothesis was supported by the following rationale, theoretical\npredictions and experimental observations:\n- Tunneling spectroscopy revealed S=½ characteristics on Ti adatoms deposited on 2ML MgO, namely a zero-bias Kondo\nresonance.\n- In disagreement, DFT calculations predicted a S=1 for Ti adatoms on 2ML MgO.\n- It is well known that hydrogen is a predominant component of the residual gas in ultrahigh vacuum. Moreover, a high\naffinity of Ti for hydrogen has been experimentally observed in the system of Ti adatoms on hexagonal boron nitride.\n- In agreement, DFT calculations predicted a S=½ for hydrogenated Ti adatoms on 2ML MgO.\nWhether the Ti adatoms on 2ML MgO were really getting immediately hydrogenated in ultrahigh vacuum has never been put\ninto question in the past 8 years. This manuscript submitted by Soo-hyon Phark unveils this mystery while playing for the first\ntime with the parameter of thickness (or amount of layers) of the MgO ultrathin film.\nFind my questions and minor comments below.\n1. In the Experiment section - STM and STS spectra, page 4, paragraph 2, line 8: “This feature indicates a zero-field\nsplitting…”. Can the authors comment on why such a signature of +-18 meV is associated with a sizable magnetic\nanisotropy energy and/or include a reference?\n2. In the Experiment section - ESR spectra, page 5, third paragraph, in Fig.2C, it is written that the angle of the external\nmagnetic field is 20° and the splitting seems to be approximately 1.5 GHz. However, when we look at Fig.2D, the lowest\ndata point seems to be around 30-40° and the plotted splitting is 6 GHz. Am I misunderstanding something? If so, this may\nneed some clarification in the text.\n3. In the Experiment section - Control of adsorption sites, page 6, first paragraph:\n3.1 The authors state very confidently that after dropping a Ti atom into a MgO(2) region it becomes ESR-active and refer to\nFig.3B. However, in Fig.3B, they present STM topographies and tunneling spectra corresponding to the Ti atom before and\nafter the manipulation. If the Ti atom does become ESR-active, I would expect them to present STM-ESR data in the main\ntext or in the supplementary materials. Otherwise, I suggest changing the text and clarify that this is an assumption based on\nboth the STM contrast and the spectroscopic features.\n3.2 Then, in the last sentence, the authors suggest that their observation supports the assignment of a spin S=1 to the Ti (3).\nO\nCan the authors develop more on why exactly S=1 and not S>1/2? and how the observations from the atom manipulation\nreflect this?\n4. In the Theory section, page 7, paragraph 1: The authors mention that there has been an experimental observation of Ti\nadatoms slowly degrading over time becoming spectroscopically dark and not exhibiting ESR features. Can the authors\nprovide a reference or explicitly comment if this is based on an anecdote?\n5. Some references are repeated: 12 and 19, 6 and 24, and 16 and 34."}, "author_response": "Nicolás Lorente\nCentro de Física de Materiales, CSIC-EHU,\nSan Sebastián, Spain\nnicolas.lorente@ehu.eus Tph: +34-66575327\nSan Sebastián, 13 Novembre 2025\nResponses to the Reviewers' comments of the manuscript NCOMMS-25-59896:\nReviewer #1 (Remarks to the Author):\nThe manuscript reports combined experimental and theoretical investigations of Ti atoms adsorbed\non 2 and 3 layers of MgO on Ag(100). From STM images the Ti atoms present two different\nadsorption sites (atop of O atom and bridge site between two O atoms). Electron spin resonance and\nscanning tunneling spectroscopy measurements revealed a spin S = ½ for Ti atoms adsorbed on 2\nlayers of MgO and on bridge site of the 3 layers of MgO while a spin S = 1 is observed for the atop O\nsite of the 3 layers of MgO. The adsorption site can be manipulated with atomic precision by the STM\ntip. Experiments and calculations indicate that the measured spin values are compatible with pristine\nadsorbed Ti atoms and do not require hydrogenation of the Ti atoms as previously suggested.\nThe experimental results clearly validate the spin values of the different systems combining two\ndifferent spectroscopic methods (STS and ESR). The manipulation of the spin by atomic manipulation\nis well evidenced from the experimental observations. The novel interpretation of pristine rather than\nhydrogenated Ti atoms is compatible with the combined experimental and calculated results.\nInvestigations of spin properties of single atoms on thicker decoupling layer are highly interesting due\nto the possible increased spin lifetimes and coherence times, which are desirable for the realization of\nquantum coherent spin structures.\nMost important are the different spin values depending on the adsorption site of the Ti atoms on the 3\nlayers of MgO and their reversible switching using atomic manipulation. These observations may\npaved a way to the fabrication of desired architectures of spin assemblies with tunable spin values.\nFinally the new interpretation involving pristine rather than hydrogenated Ti atoms is also important\nfor future (and maybe past) experiments. Accurate description of the electronic structure of the single\natoms is mandatory to the interpretation of more complex systems.\nThe manuscript is clearly written and the results are presented and discussed in relation to previous\nworks which are referenced appropriately.\nI think that the manuscript deserves a publication in Nature Communications but needs to be\nimproved taking in consideration the following remarks.\n1\n>> We are pleased the reviewer finds this work to be suitable for publication in Nature\nCommunications. Below, we address all points raised by the reviewer.\n1. My main remarks concern the discussions regarding the multiplet calculations which should be\nextended (Section III B):\n1.1 DFT reveals that the s-d splitting increases with the MgO thickness. What is the reason for this\nobservation?\n>> This is a very interesting question. The contributing factors are not easy to disentangle from DFT\ncalculations, in particular due to the fact that we anticipate that the absolute value of the splitting is\nnot correct due to significant underestimation of the correlation by standard DFT exchange-correlation\nfunctionals. We can identify two differences in the systems:\n(i) the increased stiffness of the MgO will lead to less distortion of the MgO layer which subsequently\nleads to a change in the local adsorption geometry, and\n(ii) the increased thickness of the MgO should lead to better decoupling of the Ti from the Ag\nconduction electrons.\nIndeed, for 3 ML we observe a shorter Ti-O bond-length d= 1.82 Ang vs d= 1.89 Ang. This results in a\ndecrease of hybridization between the Ti:4s and O:2pz orbitals and a slight increase in the Ti:dz2 and\nO:pz. As a consequence, the dz2 orbital energy is lowered, which stabilizes the d2 configuration.\nBased on this, it seems that the change in adsorption height results in a change of on-site energies\nand hybridizations but future comparative DFT studies might be necessary to disentangle the\ninfluence of XC functional, vdW correction etc on this observation.\nTo incorporate this information we have made the following changes:\nWe have added a figure in the SI that discusses the trends in the splitting from a Wannier basis (Fig.\nS6).\nIn the main text we added the following to the discussion on page 9:\nWe find that in all systems that show S = 1/2 behavior in the experiment DFT predicts a small 3d-4s\nlevel split and only in 3 ML O-top (S > 1/2) shows a significantly increased level separation (see Fig.\nS6), responsible for stabilizing the 3d2 configuration\n1.2 Why does the crossover from 3d1 4s2 to 3d2 4s1 occur for such a large value of Δsd (1.2 eV)?\n>> This is a consequence of the particular values for electron-electron repulsion (Udd~6 eV close to\ngas phase calculations of 3d transition metals) and crystal field splitting as well as the magnitude of\nthe spin-orbit coupling. Without crystal field and degenerate 3d levels one would indeed expect the s\nshell to be completely empty at much smaller values of the s-d splitting as the referee noted. Since\nwe are looking for a “global solution” of the multiplet calculation that can explain the experiment for\nthe values of SOC, CF and Udd this value of \\Delta_{sd} corresponds to the transition point for the\ntwo configurations.\nChanges made:\nIn the SI we clarified the parameters and how they were chosen:\nFor Ti$^+$ in vacuum atomic calculations using the Cowan code suggest that $U_{dd}=17$ eV, $\n\\zeta=0.000555$ Ha, $\\langle r^2\\rangle$ = 2.712 and $\\langle r^4\\rangle$= 17.17 (atomic units). We\nfind optimized values for the multiplet calculations as $U_{dd}=12$ eV, $\\zeta=0.0006$ Ha $\\langle\nr^2\\rangle$ = 3.1 and $\\langle r^4\\rangle$= 12.9, which are all close to gas phase values. The\nscaling for SOC and CF were chosen to reproduce the remaining features of the experiment, namely\nthe 100 meV excitation for Ti O-atop on MgO$^{(2)}$ and the 20 meV excitation for Ti O-atop on\nMgO$^{(3)}$.\n1.3 The authors say that the DFT electronic structure is approximated by a 3d2 4s1 configuration for\nboth species. However they show that simulated dI/dV for the 3d1 4s2 configuration reproduces the\nexperimental observation of Ti_O on 2 layers of MgO. This is confusing and should be clarified.\n>> We apologize that this was poorly explained in the first version of the manuscript. Based on our\nexperience, Ti on Ag/MgO is a particularly tricky system compared to other 3d transition metals such\nas Fe. Ti on Ag/MgO on the plain GGA-PBE level seems to prefer a 3d2 4s1 configuration (the DFT\noccupations of the shells are however not integer and can only be assigned approximately to the\nelectron configuration). The reason for this could be physical, for example a multi-configurational\nground state. A final experimental determination would require complementary measurements such\nas X-ray magnetic circular dichroism (XMCD), which are currently not available for this system.\nThe following changes have been made:\nWe have revised the relevant section in the main text to explain how \\Delta_{sd} can be used to\nselect a 3d1 or 3d2 configuration of the 3d shell and why DFT for MgO^(2) most likely gives the\nwrong configuration. On page 9 we added:\noxygen atop adsorption site, respectively. We calculate differential conductance spectra and find\ngood agreement between simulations and experiments.\n1.4 They also say that the DFT calculated s-d splitting may be slightly overestimated for 2 layer of\nMgO. However the value of 0.2 eV would be in agreement with a 3d1 4s2 configuration, I do not see\nwhy it is overestimated.\n>> The reviewer is correct and the sentence is misleading. It should have said underestimate which\nwe have fixed in the revised manuscript.\n2. The DFT calculations reveal a spin S = ½ for bridge site with a 3d2 4s1 configuration. Could a\nsimilar mechanism as for the atop O site on 2 layer of MgO (transition from 3d2 4s1 to 3d1 4s2)\nexplain these value of the spin for the bridge site? How large are the s-d splitting for these sites?\n>> This is indeed an important point; for the two adsorption sites (top, bridge) and the two layer\nthicknesses (2 and 3 ML) only one (3 ML top) shows a behavior different from the other 3. The bridge\nsites and 2 ML top consistently show “S=½” behavior. We therefore expect these three systems to\nshare a common level scheme and the third, 3 ML top, to be different. Indeed, our calculations for all\n4 systems show this behavior. For 2 ML top and 2 and 3 ML bridges the s-d splitting is minimal,\nindicating that the DFT solution is close to a transition between 3d2 4s1 <-> 3d1 4s2. Only for the\n3ML top system the splitting is significantly larger and stabilizes a 3d2 solution.\nThe following changes have been made:\nWe have added the extended level plot of all 4 systems to the supplement in Fig. S6 and referred to it\nin the main text.\n3. The apparent heights of Ti atoms are reversed between bridge and atop sites when going from 2 to\n3 layers of MgO. Can the authors provide any explanation for this observation?\n>> This is in part due to the imaging conditions in our experiments. Whilst we can discuss the\ngeneral understanding of STM apparent height below, we are unfortunately not able to give a\nquantitative discussion on the specific cases since we don’t have a complete dataset obtained in\nconstant current (CC) mode.\nIn the CC-STM, apparent height is a spatial collection of the tip height (z ) with the tunneling current\ntip\nfeedback ON. This adjusts z to maintain the same tunneling current in the scanning, resulting in an\ntip\nequi-tunneling-conductance contour above the sample surface, i.e., z – z ∼ ln(σ /σ ), where σ\ntip tip,0 tun tun,0 tun\n4\n= I /V . The Bardeen’s approach together with the Tersoff–Hamann approximation leads to a STM\ntun bias\neVbias\ntunneling current I ∼ ∫ DOS (E +E)dE. Thus, together with the above relationship between z\ntun sample F tip\n0\nand σ , z strongly depends on the detailed features of the DOS (E) in the energy range of 0 to\ntun tip sample\nV . Below we show in Fig. R1 an example for V -dependence of STM apparent height measured\nbias bias\non TiB(2) and TiO(2). The apparent height of the TiO(2) shows a dramatic increase as the bias\nincreases above 100 mV while the TiB(2) doesn’t show any notable dependence. We tentatively\nunderstand this as follows. As shown in Fig. 1D, the differential conductance dI/dV of TiO(2) suddenly\njumps up at V ~ ±90 mV, which stems from an opening of inelastic tunneling channels. Below the |\nV |, the dI/dV of TiO(2) is smaller than that of TiB(2), hence the smaller I . The STM feedback\nth\nth tun\nelectronics pushes down the tip to keep the same σ , resulting in the lower z (lower STM apparent\ntun tip\nheight; Fig. R1A). As the bias increases across the V , the dramatic increase of the dI/dV, hence the\nth\ntunneling conductance I/V does, pushes the tip up due to the same mechanism of the feedback\ncircuit. On the other hand, the dI/dV of TiB(2) has a relatively smooth dependence on V , leading to\nbias\nan almost constant apparent height throughout the V range compared to the TiO(2).\nbias\nWe can apply the similar analogy also to the case of MgO(3) requested by the referee. A quantitative\nunderstanding needs a special and systematic experiment, such as a comparison of STS intensity on\nboth species with a constant z relative to the sample surface.\ntip\nsurface at 5 tip bias voltages (I = 10 pA). (F) Height profiles measured across a TiB(2) and a TiO(2) along the\ntun\nlines depicted in the images. Note that the apparent height of the TiO(2) showed a dramatic increase as the\nbias increases while the TiB(2) doesn’t show any notable bias dependence.\n4. dI/dV spectra of Tio on the 3-layer of MgO exhibit a dip at V = 0. What is the origin of this electronic\nfeature?\n>> We understand the low energy (|V | ≤ 10 mV) feature stemming from the electronic states of the\nb\ntip. Additional Explanation: Differential conductance (dI/dV) signal in a STS measurement is a product\nof sample DOS and tip DOS. The low energy electronic states of the atomic species in this study, Fe\nand Ti on MgO, don’t show any specific features in their STS spectra when measured using a non-\nmagnetic tip. The dI/dV feature at |V | ≤ 10 mV is strongly dependent on the choice of the probing tip,\nb\nwhich can be confirmed by performing STS on a bare MgO surface. For the atoms shown in Fig. 1,\nwe did not obtain a spectra on a bare MgO. Instead, we show in Fig. R2 below a set of spectra\nmeasured on MgO(3), Fe(3), and TiO(3) using a different tip to compare their low energy features and\ndiscuss their resemblance. It is therefore unrelated to the adsorbate in this case Ti O-atop on 3 ML\nMgO.\nconditions (V = 15 mV, I = 150 pA). The spectra for Fe and TiO are shifted up by 1.5 and 3 pA/mV,\nset set\nrespectively, for clarity. Note that the low energy features of all 3 spectra resemble, implying that the features\noriginate from either tip’s or bare MgO’s electronic states.\n5. Page 6, bottom of top paragraph: it is said that the assignment of a spin S = 1 to Tio on 3 layer of\nMgO is in agreement with the configuration expected for a neutral Ti atom in vacuum. I do not see\nwhy the neutral atomic configuration would be expected, in particular since calculations reveal a Ti+\nstate for all adsorbed Ti atom.\n>> We agree with the referee. S = 1 of TiO(3) doesn’t necessarily mean that it should be in the same\nelectronic configuration of a Ti in vacuum state. We modified the corresponding text.\n6. In many figures the legends and labels are rather small and difficult to read.\n>> We thank the referee for this careful advice. We updated the figures to be more legible.\nReviewer #2 (Remarks to the Author):\nThe manuscript of Phark et al. reports on a combined experimental-theoretical study of Spin-State\nEngineering of Single Titanium Adsorbates on Ultrathin Magnesium Oxide. The topic is highly\nrelevant for an atomic scale engineering of spin qubits for the realization of various quantum\nplatforms on material surfaces, and a very nice example of Ti ions on MgO/Ag substrate are reported.\nThe conducted research is of a very high quality, and the STM/STS and STM-ESR experimental\nresults of a controlled creation of different spin states of Ti atoms are well supported and explained by\nDFT calculations. Two experimental atom manipulation techniques for long- and short-range\nrepositioning are also reported in detail. The manuscript is well written, though some\nclarifications/improvements will be needed. The reported new knowledge on the dependence of the\nspin states depending on the local adsorption site and oxide film thickness will be highly relevant for\nthe design of future artificial spin systems with atomic precision. I recommend the manuscript for\npublication in Nature Communications after a minor revision considering the following points:\n7\n1. A considerable part of the theoretical results addresses the effect of TiH_x adsorbates in the\nsearch for agreement with the experimental findings, but this aspect of the role of hydrogen is not\nclearly motivated in the Introduction and throughout the manuscript. From the current literature it is\nevident that it is an important problem, but the manuscript should better motivate this aspect, in my\nview. It is also somewhat unfortunate to introduce the description and discussion of the hydrogen-\nrelated results with the 1st sentence in III. Theory with \"Such a reversible change of spin states is\nunlikely to be the result of selective adsorption or desorption of atomic hydrogen (H).\" An explicit\nindication of why it is still studied in much detail in the following part would be a crucial improvement.\n>> We have added a paragraph to motivate our work from the point of view of the presence or not of\nTiH in agreement with present literature. The new paragraph is the sixth paragraph of the new\nintroduction.\nIn agreement with the above comment by the Referee, we have replaced the sentence of III. Theory:\n“Such a reversible change of spin states is unlikely to be the result of selective adsorption or\ndesorption of atomic hydrogen (H).” by “In order to rationalize the experimental findings concerning\nthe spin state of adsorbed Ti, we have studied its electronic structure in different environments,\nincluding the presence of H.”\n2. Considering the significant numerical differences in the obtained results by using Quantum\nEspresso (QE) and VASP softwares, which are reported and discussed in detail in the Supplementary\nInformation (SI, Table VII), it is not completely clear how and why the results of Table I were chosen.\nMoreover, there is an inconsistency between Tables I and VII, please correct them. It is also reported\nthat all numerical parameters for QE and VASP calculations are identical (except the\ndifferences in the implementations in the two codes), but the reported k-sampling is still different: 3x3x1 for VASP\nand 4x4x1 for QE, please reformulate your statements accordingly. Overall, the discussion about\nthe compatibility of the QE and VASP results is confusing in its present state. What do we learn from\nthis?\n>> We apologize for the confusion. We did not intend to claim that the parameters used in the\ncalculation are identical (since different pseudopotentials are used for example which require different\nconverged cutoff values) but that the results are converged to the same level. We have now corrected\nthe values in Table I from the main text and the present Table VI of the SI (previous VII of the\ncombined document).\nWe have written now that the results are “qualitatively similar yielding the same physical picture”,\nwhich is what we intended to show. The reason to use QE and VASP stems from the difficulty in\ntrying to reproduce the experimental behavior between adsorption site and atomic spin. Our\n8\ncalculations permit us to confirm that the present level of DFT consistently gives the same result and\nit is not the result of a particular choice of pseudopotential or code implementation.\nWe have modified the statement in the SI:\nWe performed calculations in both codes to ensure that the results are not strongly dependent on the\nchoice of the pseudopotential or specific implementation. Both codes give a coherent picture with\nsmall numerical deviations contributing to show the reliability of our results.\n3. In Section III.A it is claimed that \"... single Ti atom in a positively charged Ti+ configuration,\nresulting from charge transfer to the Ag substrate ...\". However, there is no direct evidence provided\nfor the negative charge transferred to the Ag substrate. This should be provided by analyzing the\ndifference of Bader charges before and after adsorbing Ti on the MgO/Ag (\\Delta Q = Q_{Ti+MgOAg}\n- Q_{Ti} - Q_{MgOAg} and its change on the Ag substrate).\n>> We agree with the Referee. We have now added a discussion showing the total charge balance in\nthe TI adsorption in section V of the SI, showing the transfer of charge to the substrate. We also\nclarified in the main text that the charge transfers most likely partially into the MgO and partially into\nthe Ag/MgO interface (“the substrate”).\nThe following changes have been made:\nWe have added a table, Table VII, to the present-version supplement that shows that the integrated\ncharge on the Ti indicates that it is in good approximation Ti+. We have added Figure S5 which\nshows the charge difference. The corresponding text reads:\nWe estimate the charge transfer by integrating the charge of the whole system (ρAg+MgO+Ti) and\nsubtracting the charge of the substrate and adatom (ρAg+MgO + ρTi). The resulting charge-\ndifference plot indicates that most of the charge goes into the local bonding environment and the Ag-\nMgO interface, see Fig. S5 (B). The Lowdin net charge loss for Ti is listed in Tab. VII\nThe reduced electron work function with increasing MgO thickness is nicely demonstrated\nexperimentally. Instead of referring to [54], was this not demonstrated by the performed DFT\ncalculations? Please report the calculated work functions.\n>> We agree with the Referee.\nWe have added the values of the calculated work functions in Figure S5 in the SI.\n4. To enrich the context of the manuscript considering the charge and spin states of individual atoms\non surfaces I recommend the inclusion of the following references into the Introduction:\n- https://doi.org/10.1103/PhysRevLett.127.236801 , where a nice experimental example of the effect\nof the local adsorption geometry on the spin states of Fe atoms are presented on a Moiré structure\nplatform.\n- https://doi.org/10.1088/1361-6528/aaf6dc , where the theoretical limits of SPM subatomic resolution\nin relation to the charge/spin states and Hubbard U parameter of a Co atom on an oxide surface are\ninvestigated.\n>> We thank the Referee for letting us know about these references. We have added these two\nreferences with a citing sentence, to the first paragraph of the introduction.\n5. Although in Section VII.A in the SI it is stated that \"In the following, we present DFT total energy\ncalculations of TiHx ...\", there are no actual total energies reported for the gas phase TiHx in section\nVII.B (SI).\n>> We apologize for the unintended omission. We have added the deprotonation energies of the\ndifferent molecules and discussed their stability.\nThe following changes have been made:\nIn section III.B of the SI, we say:\nIn this way, we can expect a spin $S=3/2$ for TiH since the H will close one shell and three will be left\nhalf-occupied. \\corr{Indeed, we find that TiH has a magnetic moment of 3 $\\mu_B$ gaining 0.5 eV in\nthe Ti-H bond.} For TiH$_2$ we find a spin $S=1$ for the same reason but now with 2 H atoms.\n\\corr{Correspondingly, the computed magnetic moment is 2.0 $\\mu_B$ and adding 2H reduces the\nenergy by 1.2 eV.} TiH$_3$ is then a spin $S=1/2$, \\corr{as confirmed by the computed magnetic\nmoment of 1 $\\mu_B$, and an energy stabilization of 1.7 eV} and TiH$_4$ (titanium tetrahydride) is a\nclosed-shell tetrahedral molecule \\corr{with zero magnetic moment and an energy stabilization of 2.3\neV}. Thus, of all these molecules, TiH$_4$ is the most stable one, followed by TiH$_2$.\n6. Fig. S2 is not referred to in the SI text and there is no description of it except its caption, is it\nintentional?\n>> We thank the referee for this valuable advice.\nSupplementary Information with explicit reference to Fig. S2.\n7. Some references in the manuscript to the Supplementary Information (SI) are too general, and\nshould be made explicit to the particular sections in the SI.\n>> We have added a reference to the particular section when referred to in the main text.\n8. Please correct typos throughout the SI, for example \"The trend with MgO thickness is also nicely\nrecover\" (recovered), \"results points\" (results point), \"Bader surface\" (not Bader volume?), \"The d\norbitals result in highly localized Wannier functions (quadratic spread \\Omega^2\\approx 1 \\AA^2),\nwhilst the s-orbital is more diffuse (\\Omega^2\\approx 3 \\AA)\" (Angstrom or squared-Angstrom?\nShould be consistent).\n>> We thank the referee, we hope to have addressed all typos in the SI now.\nReviewer #3 (Remarks to the Author):\nThe manuscript covers the results in an orderly fashion and it presents evidence explaining the\nintriguing nature of the spin-states of Ti adatoms on MgO ultrathin films. The literature on the system\nof Ti adatoms deposited on 2 monolayers (ML) of MgO ultrathin films grown on Ag(100) has assumed\nthat Ti adatoms become hydrogenated in ultrahigh vacuum immediately after deposition, thus\nbecoming TiH molecules. In the early publication, “Engineering the Eigenstates of Coupled Spin-½\nAtoms on a Surface” by Kai Yang et al. in 2017, this hypothesis was supported by the following\nrationale, theoretical predictions and experimental observations:\n- Tunneling spectroscopy revealed S=½ characteristics on Ti adatoms deposited on 2ML MgO,\nnamely a zero-bias Kondo resonance.\n- In disagreement, DFT calculations predicted a S=1 for Ti adatoms on 2ML MgO.\n11\n- It is well known that hydrogen is a predominant component of the residual gas in ultrahigh vacuum.\nMoreover, a high affinity of Ti for hydrogen has been experimentally observed in the system of Ti\nadatoms on hexagonal boron nitride.\n- In agreement, DFT calculations predicted a S=½ for hydrogenated Ti adatoms on 2ML MgO.\nWhether the Ti adatoms on 2ML MgO were really getting immediately hydrogenated in ultrahigh\nvacuum has never been put into question in the past 8 years. This manuscript submitted by Soo-hyon\nPhark unveils this mystery while playing for the first time with the parameter of thickness (or amount\nof layers) of the MgO ultrathin film.\nFind my questions and minor comments below.\n1. In the Experiment section - STM and STS spectra, page 4, paragraph 2, line 8: “This feature\nindicates a zero-field splitting…”. Can the authors comment on why such a signature of +-18 meV is\nassociated with a sizable magnetic anisotropy energy and/or include a reference?\n>> Sharp jumps of differential conductance signals in STS spectra have been attributed to the\nopening/closing of inelastic tunneling channels, mostly involving either phonon [Stipe et al. Science\n280, 1732-1735 (1998)] or spin [Heinrich et al. 306, 466-469 (2004)] excitations. This type of\nexperimental technique has been standardized in STM with “inelastic tunneling spectroscopy (IETS).\nSpin-IETS using a STM is thoroughly reviewed in a S. Loth’s paper [New J. Phys. 12, 125021 (2010)],\nwhere one finds 2 representative cases. One is IETS on a spin of no (negligible) magnetic anisotropy\nenergy (MAE), e.g., Ti on 2ML-MgO/Ag (S = 1/2) [Yang et al. Phys. Rev. Lett. 122, 227203 (2019)]\nand Mn on CuN (S = 5/2) [Loth et al. Nat. Phys. 6, 340-344 (2010)]. This case allows IETS\naccompanying only spin excitations between the states, split by Zeeman energy under a magnetic\nfield. The resultant STS spectrum shows across the zero-bias a square-shaped gap-like feature,\noriginating from the Zeeman energy difference between the two states relevant to the spin excitation.\nThe other is IETS on a spin of sizable magnetic anisotropy energy (i.e., E >> E , only available\nMAE Zeeman\nfor a spin of S > 1/2), e.g., Fe on 2ML-MgO/Ag (S = 2) or Fe on CuN (S = 2), which easily splits the\nenergies of different |m | by > 1 meV. This case allows IETS corresponding to spin excitations\nS\nbetween the states, split by MAE, at a rather higher energy, and can be distinguished from that of the\nZeeman energy splitting at a nominal magnetic field (e.g., a few Tesla) which is < 1 meV, e.g., ~0.1\nmeV for S = 1/2 at 1 Tesla. One well-known example is the feature at |V | = 14 meV in the spectrum\nb\nof Fe/MgO [Baumann et al. Phys. Rev. Lett. 115, 237202 (2015)], as also shown in the reply to the\ncomment 4 of the referee #1. We believe that a sharp jump at |V | = 18 meV in our spectrum of TiO(3)\nb\nalso stems from a similar origin.\nThe following changes have been made:\nWe added a reference (Loth et al. New J. Phys. 12, 125021 (2010)) in the text for this aspect.\n12\n2. In the Experiment section - ESR spectra, page 5, third paragraph, in Fig.2C, it is written that the\nangle of the external magnetic field is 20° and the splitting seems to be approximately 1.5 GHz.\nHowever, when we look at Fig.2D, the lowest data point seems to be around 30-40° and the plotted\nsplitting is 6 GHz. Am I misunderstanding something? If so, this may need some clarification in the\ntext.\n>> We thank the referee for finding this fault. The polar angle of the magnetic field is defined and\nused in a conventional spherical coordinate system as in Fig. 2d. However, we made a mistake of\nusing the machine-specific measure of the polar angle, from the in-plane direction, in Fig. 2c. Thus\nthe θ = 20 degrees in Fig. 2c corresponds to 70 degrees in Fig. 2d.\nWe correct this, and it is properly denoted in the revised manuscript.\n3. In the Experiment section - Control of adsorption sites, page 6, first paragraph:\n3.1 The authors state very confidently that after dropping a Ti atom into a MgO(2) region it becomes\nESR-active and refer to Fig.3B. However, in Fig.3B, they present STM topographies and tunneling\nspectra corresponding to the Ti atom before and after the manipulation. If the Ti atom does become\nESR-active, I would expect them to present STM-ESR data in the main text or in the supplementary\nmaterials. Otherwise, I suggest changing the text and clarify that this is an assumption based on\nboth the STM contrast and the spectroscopic features.\n>> We thank the referee. We want to clarify by first mentioning that the ESR signal for S = 1/2 is well-\nknown characteristics of both TiO(2) and TiB(2). Based on previous literature results either specific\nSTS features or directly measured ESR signals can be used to characterize the spin-dependent\nelectronic configurations of the two species. Hence, we didn’t obtain an ESR spectrum from the\natoms after moving them from MgO(3) to MgO(2) as STS signatures can confirm that the species has\nthe expected spin state.\nTo avoid confusion on this specific part, we have modified the text in the revised manuscript.\nThe revised text now reads:\nInterestingly, when the atom is dropped onto a MgO(2) region, the resulting species are either Ti(2)O\nor Ti(2)B , as confirmed by both STM contrast and STS features (see Fig. 3B for Ti(2)O ). Given the\nwell-established S = 1/2 character of Ti adsorbates on MgO(2) using ESR,[8, 16, 36] this observation,\ntogether with the absence of ESR signal (Fig. 2A), supports that a Ti atom adsorbes with different\nspin-dependent electronic structures depending on the thickness of the MgO layer.\n3.2 Then, in the last sentence, the authors suggest that their observation supports the assignment of\n13\na spin S=1 to the Ti (3).\nO\nCan the authors develop more on why exactly S=1 and not S>1/2? and how the observations from the atom manipulation\nreflect this?\n>> We agree with the referee. Experimental data just revealed that TiO(3) is not in S = 1/2, i.e., S >\n1/2. Our theoretical studies, both DFT and Multiplet calculations, support S = 1 is the most probable\nspin state of TiO(3).\nWe correct it by specifying S > 1/2 in the corresponding text.\n4. In the Theory section, page 7, paragraph 1: The authors mention that there has been an\nexperimental observation of Ti adatoms slowly degrading over time becoming spectroscopically dark\nand not exhibiting ESR features. Can the authors provide a reference or explicitly comment if this is\nbased on an anecdote?\n>> Unfortunately this is so far mostly anecdotal observation in our own lab and we are not aware of\nany systematic study (for example controlled H2 exposure). Below we show a comparison of STM\nand STS data taken from 2 O-atop Ti atoms on MgO(2). Both alpha and beta showed the exactly\nsame features in STM/S and ESR a day before this measurement, showing a single ESR peak at ~16\nGHz at B = 0.65 T and implying S = 1/2. Beta underwent a spontaneous change into a dark spot,\next\nwhich we suspect is hydrogenation, leading to a totally different STS and no ESR signal.\nUnfortunately, due to the randomness of the process that leads to a spectroscopically dark Ti we do\nnot currently have a systematic dataset, however we can provide a comparison of two species in\nfigure R3 below for the referee.\nalpha and beta (V = 50 mV, I = 10 pA). (B–C) STS data measured on alpha and beta (V = 30 mV, I =\nbias tun set set\n300 pA). Both alpha and beta showed the exact same features in both STM/S and ESR a day before this\nmeasurement. The beta suddenly changed into a dark spot at the same position, and it didn’t show ESR with a\ntotally different STS.\nWe have also slightly modified the main text to emphasize that this is an infrequent observation in our\nexperiments currently lacking a systematic study.\nThe relevant section now reads:\nThis is further supported by the experimental observation that Ti adatoms can slowly degrade\nover time and sporadically become spectroscopically dark no longer exhibiting any ESR\nfeatures. We tentatively assign this latter behavior to a degradation process related to slow\nhydrogen adsorption that happens on the scale of months, hopefully to be confirmed by a\nmore systematic study.\n5. Some references are repeated: 12 and 19, 6 and 24, and 16 and 34.\n>> We thank the referee for finding these mistakes.\nWe have removed redundancies in the references in the revised manuscript.\nWe are very pleased by the very positive comments of the three reviewers that we paste below for your\nconvenience.\nYours Sincerely,\nNicolás Lorente on behalf of all authors.\nREVIEWERS' COMMENTS\nReviewer #1 (Remarks to the Author):\nAs stated in my first report the manuscript reports on the atomic manipulation of adsorption site and\nspin state of single Ti atoms using STM/ESR measurements and theoretical calculations. Combined\nwith the use of a thicker oxyde layer, mandatory for increased spin lifetimes and coherence times, this\nwork may paved a way toward the realization of quantum coherent spin structures with desired\narchitectures of spin assemblies and tunable spin values. It also gives a new explanation to the observed\nspin values without involving the formation of TiH_n complexes as previously reported.\nThe revised manuscript and supplementary material have been modified accordingly to my requests in\nthe first report. In particular the discussion regarding the multiplet calculations has been extended. It\nnow gives a better picture regarding the origin of the distinct spin state of Ti_O adsorbed on the 3\nlayers of MgO compared to the other adsorption sites (Ti_B on 3 layer of MgO and Ti_O and Ti_B on\n2 layers of MgO).\nThe manuscript is clearly written and the results are presented and discussed in relation to previous\nworks which are referenced appropriately.\nI think that the manuscript is now suitable for a publication in Nature Communications.\nReviewer #2 (Remarks to the Author):\nIn my opinion the Authors properly addressed all points raised by the three Reviewers, provided\nconvincing replies, and improved their manuscript considerably following the comments. Given the\nsignificant experimental-theoretical results and their insightful discussion, which is relevant for a wide\nreadership, I'm happy to recommend the manuscript for publication in Nature Communications, and\ncongratulations on this nice piece of work.\nKrisztián Palotás\nReviewer #3 (Remarks to the Author):\nThanks for considering my commments and suggestions."}, {"round": 2, "reviewer_comments": {"reviewer_1": "As stated in my first report the manuscript reports on the atomic manipulation of adsorption site and spin state of single Ti\natoms using STM/ESR measurements and theoretical calculations. Combined with the use of a thicker oxyde layer,\nmandatory for increased spin lifetimes and coherence times, this work may paved a way toward the realization of quantum\ncoherent spin structures with desired architectures of spin assemblies and tunable spin values. It also gives a new\nexplanation to the observed spin values without involving the formation of TiH_n complexes as previously reported.\nThe revised manuscript and supplementary material have been modified accordingly to my requests in the first report.\nIn particular the discussion regarding the multiplet calculations has been extended. It now gives a better picture regarding the\norigin of the distinct spin state of Ti_O adsorbed on the 3 layers of MgO compared to the other adsorption sites (Ti_B on 3\nlayer of MgO and Ti_O and Ti_B on 2 layers of MgO).\nThe manuscript is clearly written and the results are presented and discussed in relation to previous works which are\nreferenced appropriately.\nI think that the manuscript is now suitable for a publication in Nature Communications.", "reviewer_2": "In my opinion the Authors properly addressed all points raised by the three Reviewers, provided convincing replies, and\nimproved their manuscript considerably following the comments. Given the significant experimental-theoretical results and\ntheir insightful discussion, which is relevant for a wide readership, I'm happy to recommend the manuscript for publication in\nNature Communications, and congratulations on this nice piece of work.\nKrisztián Palotás", "reviewer_3": "Thanks for considering my commments and suggestions."}, "author_response": ""}]

Decision letter