Precise Control of Local Spin States in an Adsorbed Magnetic

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Surfaces, Interfaces, and Catalysis; Physical Properties of Nanomaterials and Materials

Precise control of local spin states in adsorbed magnetic molecule with STM tip: Theoretical insights from first-principles based simulation xiaoli Wang, Longqing Yang, LvZhou Ye, Xiao Zheng, and YiJing Yan J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.8b00808 • Publication Date (Web): 24 Apr 2018 Downloaded from http://pubs.acs.org on April 24, 2018

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The Journal of Physical Chemistry Letters

Precise Control of Local Spin States in Adsorbed Magnetic Molecule with STM Tip: Theoretical Insights from First-Principles Based Simulation Xiaoli Wang,† Longqing Yang,† LvZhou Ye,† Xiao Zheng,∗,† and YiJing Yan¶ Hefei National Laboratory for Physical Sciences at the Microscale & Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China, Guizhou Provincial Key Laboratory of Computational Nano-Material Science, Institute of Applied Physics, Guizhou Normal College, Guiyang, Guizhou 550018, China, and Hefei National Laboratory for Physical Sciences at the Microscale & iChEM, University of Science and Technology of China, Hefei, Anhui 230026, China E-mail: [email protected]

∗ To

whom correspondence should be addressed National Laboratory for Physical Sciences at the Microscale & Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China ‡ Guizhou Provincial Key Laboratory of Computational Nano-Material Science, Institute of Applied Physics, Guizhou Normal College, Guiyang, Guizhou 550018, China ¶ Hefei National Laboratory for Physical Sciences at the Microscale & iChEM, University of Science and Technology of China, Hefei, Anhui 230026, China † Hefei

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Abstract The precise tuning of local spin states in adsorbed organometallic molecules by a mechanically controlled scanning tunneling microscope (STM) tip has become a focus of recent experiments. However, the underlying mechanisms remain somewhat unclear. We investigate theoretically the STM-tip control of local spin states in a single iron(II) porphyrin molecule adsorbed on the Pb(111) substrate. A combined density functional theory and hierarchical equations of motion approach is employed to simulate the tip tuning process, in conjunction with the complete active space self-consistent field method for an accurate computation of magnetic anisotropy. Our first-principles based simulation accurately reproduces the tuning of magnetic anisotropy realized in experiment. Moreover, we elucidate the evolution of geometric and electronic structures of the composite junction, and disclose the delicate competition between the Kondo resonance and local spin excitation. The understanding and insight provided by the first-principles based simulation may help to realize more fascinating quantum-state manipulations.

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Motivated by the rapid advancement of quantum computing 1,2 and quantum information processing technologies, 3,4 nanoscopic materials that have potential applications for electronic or spintronic quantum devices have received wide interest. Organometallic molecules with magnetic transition metal (TM) atoms have become a promising candidate, 5–9 because the spin-unpaired d electrons on the TM atoms give rise to well-defined spin qubits. For practical purposes, it is highly desirable that the physical properties of these magnetic molecular complexes could be tuned in a controllable manner. In particular, it is crucial to achieve the precise manipulation of the local spin states in these organometallic complexes. In experiments, an organometallic molecule is often adsorbed onto a metal substrate in a scanning tunneling microscope (STM) setup, 5–7 or sandwiched between two electrodes to form a mechanical controlled break junction (MCBJ). 8,9 Various physical and chemical approaches have been devised to measure and tune the local spin states in organometallic complexes. These have included the modification of ligand shell, 10,11 the chemical doping, 12–14 the application of electric fields, 15–18 the variation of substrate material 19,20 or adsorption site, 6,21,22 and the attachment of small molecules. 23–26 In particular, applying mechanical forces to change the local geometry around the magnetic TM atom has offered a feasible way to realize a precise, continuous and on-demand control of local spin states. 7,8,27–30 Recently, the competition between spin excitation and Kondo resonance 31,32 in adsorbed magnetic molecules has become a focus of experimental efforts. 8,33–35 While the former is largely caused by the spin-orbit coupling (SOC), the latter originates from the screening of local spin moment by the spins of itinerant electrons. 36 For instance, Parks et al. have measured the differential conductance (dI/dV ) spectra of a Co(tpy–SH)2 molecule embedded in an MCBJ. 8 They have demonstrated that, by stretching the molecule in the axial direction, the Kondo conductance peak gets split by the enhancing magnetic anisotropy (MA) induced by the SOC. Moreover, Heinrich et al. have used an STM tip as a probe to measure and tune the magnitude of MA of adsorbed ironoctaethylporphyrin (FeOEP) molecules. 28 By moving the tip closer towards the substrate, they have achieved a continuous tuning of MA with a high precision of sub-meV. In particular, they

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have employed a superconducting tip and substrate to completely suppress the Kondo resonances, and hence greatly extend the lifetimes of SOC-induced spin excitations. 37 Very recently, Hiraoka et al. have performed a similar STM-tip control on an adsorbed FePc molecule. 29 By varying the position of the tip, they have realized the crossover between the Kondo-dominant regime and the SOC-dominant regime. These works have paved the way for the development of more sophisticated quantum-state control techniques. Despite the exciting progress, it has remained unclear on what leads to the variation of local observable (such as the MA) under the tip control. Since it is difficult to extract further details from the experiments, theoretical studies become a valuable means to shed light on the underlying mechanisms. However, the adsorbed magnetic complex presents a formidable challenge for theoretical investigations. Regarding an STM-tip control experiment, the main difficulties are (i) the system of interest is a composite of the organometallic molecule, the bulk substrate, and the STM tip. 30,38 Atomistic simulations would thus require a comprehensive and accurate description for the complex interactions among all the component parts. (ii) The low-energy d-band excitations at the TM center, including the Kondo resonance and the local spin excitation, are of strong static correlation (or multi-reference) nature. However, conventional density functional theory (DFT) methods could not characterize such strongly correlated states properly. 39–41 (iii) To make a direct comparison to experimental measurements, simulations need to be done for nonequilibrium situations, so as to evaluate the pertinent response properties (such as the dI/dV spectra) under realistic experimental conditions. Because of the above difficulties, previous theoretical works focused either on DFT calculations for geometric and band structures, 30,38,42 or on model Hamiltonian calculations for unravelling electron correlation effects. 43–45 To bridge the gap between these two types of studies and thus achieve a first-principles based simulation for the control of local spin states, we have combined the DFT methods with a hierarchical equations of motion (HEOM) method, 46–53 which enables an accurate and efficient characterization of equilibrium and nonequilibrium properties of quantum impurity systems. The DFT+HEOM approach has been applied to investigate the local spin states

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and associated Kondo phenomena in a series of adsorbed or embedded organometallic molecules, including d-CoPc/Au(111), 54 FePc/Au(111), 55 few-layer CoPc/Au(111), 56 and Au–Co(tpy–S)2 – Au composites. 57 In this Letter, we employ the DFT+HEOM approach to reexamine the STM-tip control experiment on an adsorbed FeOEP molecule accomplished by Heinrich and co-workers. 28 The physical origins of the variation in MA magnitude and the concomitant effects of Kondo resonance and spin excitation will be elucidated. Figure 1(a) depicts the FeOEP molecule of our interest, which is a tetra-coordinated iron porphyrin complex with eight ethyl groups attached to the porphyrin macrocycle. When the FeOEP is adsorbed on the surface of a superconducting substrate, the inert organic groups of the molecule separate the central Fe ion from the superconducting environment, and hence the magnetic interaction between the molecular spin and the superconductor is negligibly small. 37 A structural model for the tip/FeOEP/Pb(111) composite is established to mimic the experimental setup; see Figure 1(b) and (c) for the top and side views. The bulk Pb substrate is represented by three atomic layers with each containing 70 atoms, while the tip is modeled by a pyramidal cluster with three Pb atoms at the bottom layer. Note that the shape of the tip has a nontrivial influence on the local electronic structure of the molecule. 58 A sharp tip with a single-atom apex would couple too strongly to the Fe center of the molecule, and the resulting MA deviates too much from the experimental values; see section S5 in Supporting Information. Therefore, a blunt tip with a three-atom apex is adopted instead. The periodic boundary condition is imposed, with a sufficiently large vertical spacing adopted to avoid unwanted interactions among periodic images. Our first-principles based simulation for the continuous STM-tip control process proceeds as follows. Initially the FeOEP molecule is adsorbed onto the substrate, and their structures are fully relaxed, while the tip is placed far away from the substrate with a vertical distance of z0 = 1110 pm. Then the tip is moved towards the substrate with small incremental steps. The smallest incremental step adopted is 0.05 Å. In each step, the geometries of the two bottom layers of substrate and the two top layers of tip are fixed to sustain the stability of the overall structural model, while the positions of all other atoms are optimized to determine the variation of local geometry around the

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Fe center. All the geometry optimizations and band structure calculations for the tip/FeOEP/Pb(111) composite junction are performed by using DFT methods implemented in the Vienna ab initio simulation package (VASP). 59–61 The generalized gradient approximation (GGA) developed by Perdew, Burke, and Ernzerhof (PBE) 62,63 is used for the exchange-correlation functional. The Grimme’s empirical correction method 64,65 for dispersive interactions is used, and a Hubbard-like +U correction 66–72 is adopted to improve the electronic structure calculation by reducing the delocalization error associated with the density functional approximation (DFA). 41,73,74 In particular, we set Ueff = 2 eV, which is the difference between the fundamental gap and the derivative gap 75,76 of the FeOEP molecule calculated with the PBE functional; see section S2 in Supporting Information. The superconducting states in the Pb substrate and tip create only a small band gap of about 1.4 meV around the Fermi energy, 37 and hence their influence on the junction geometry and the molecular spin are expected to be rather small. Therefore, these superconducting states are not included in our simulation. Accurate computation of MA is challenging for an adsorbed organometallic molecule, because the surrounding environment has a nontrivial influence on the magnitude of MA by modifying the crystal ligand field. It is known that the conventional DFT methods perform rather poorly on the prediction of MA, 57,77,78 because the popular DFAs suffer severely from the static correlation error. 39,73,79,80 We thus adopt a hybrid approach to evaluate the MA of the composite junction during the tip control process. We first use the complete active space self-consistent field (CASSCF) method 81–83 implemented in the ORCA program 84–86 to compute the MA of an isolated FeOEP molecule. Since the spin-unpair electrons locate mostly on the Fe center, the CASSCF calculation should well capture the multi-reference nature of the MA, 87,88 provided that the Fe d-orbitals are all included within the active space. We then use the DFT method to assess the influence of surrounding environment by comparing the MA of the tip/FeOEP/Pb(111) composite to that of an

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isolated FeOEP molecule. For instance, the axial MA is calculated via ( ) DFT DFT D = DCASSCF + D − D FeOEP . FeOEP tip/FeOEP/Pb(111)

(1)

DCASSCF FeOEP has an almost constant value around 10.9 meV throughout the tip control process; while the parenthesized term varies in the range of −2.0 to 0.3 meV, which reflects the influence of the changing environment induced by the mechanically controlled tip. The in-plane MA has a much smaller magnitude than D, and is thus not considered in this work. Figure 2(a) compares the calculated axial MA with the experimental data reported in Ref. 28. The two curves agree remarkably with each other, with a rather minor deviation (less than 0.3 meV) between them. As the tip approaches towards the substrate, the magnitude of D first increases slowly and then decreases rapidly, with a small kink appearing at ∆z = −200 pm. The quantitative agreement between the experimental and computational results is achieved because (i) in simulation a reasonable structure model is chosen, and the geometry relaxation is conducted carefully with sufficiently small incremental steps; (ii) the DFT calculations are performed carefully with the dispersive interactions accurately accounted for, and the delocalization error of the PBE functional gets minimized by the Hubbard-like +U correction with the carefully chosen value of Ueff ; (iii) and the multi-reference nature of the MA is captured by the CASSCF calculation through Eq. (1). The experimental measurement terminated at ∆z = −330 pm, where the composite was reported to “become instable”. 28 In contrast, the calculation could proceed further, and the resulting D is found to increase again after reaching a minimum at ∆z = −350 pm. To disclose the physical origins of the varying D, in Figure 2(b) we show the change of distances from the Fe atom (and its neighboring atoms) to the substrate surface, while Figure 2(c) exhibits the evolution of the d-orbitals at the Fe center. Based on the lineshape of the calculated D versus ∆z curve, we partition the whole tip control process into four regions (regions I–IV); see Figure 2. In the following we will elaborate on the geometric and electronic structure changes of the FeOEP molecule in each region, as well as their influence on the axial MA.

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In the region I, the tip is overall distant from the FeOEP. As the tip is displaced from ∆z = 0 to −200 pm, the axial MA has a rather minor increase of 0.32 meV (both in experiment and in simulation). Since the molecular geometry and the positions of Fe d-orbitals remain almost intact in region I [see Figure 2(b) and (c)], the minor increase in D is likely related to the slightly enhanced dispersive interaction between the tip and the molecule; see Figure S7 in Supporting Information. It is worth pointing out that, with a loosely coupled tip, the Fe atom locates distinctly below the molecular plane; see Figure 2(c). The out-of-plane position of Fe atom originates from the couplings between the Fe d-orbitals and the substrate states; see Figure 3(a) and related discussions. At the end of region I, a small kink appears in the D versus ∆z curve, which indicates that the molecular structure starts to deform under the force exerted by the approaching tip; see Figure 2(b). In the region II, the magnitude of D reduces rapidly as the tip is displaced from ∆z = −200 to −350 pm. The approaching tip gradually pulls the Fe center upward away from the substrate. Subject to the pulling force, the central part of the FeOEP molecule suddenly “jumps” towards the tip at ∆z = −330 pm, as indicated by the abrupt change in the distances from the Fe and surrounding atoms to the substrate surface; see Figure 2(b). Interestingly, the experimental measurement terminated exactly at ∆z = −330 pm; see Figure 2(a). Our simulation thus provides a direct evidence for the geometric instability observed in experiment. 28 Nevertheless, if such an instability could be overcome (say, by moving the tip extremely slowly), one will observe a further decrease in D until it reaches a minimum of 8.96 meV at ∆z = −350 pm, where the FeOEP molecule becomes almost planar. The reduced magnitude of D is clearly associated with a higher crystal-field symmetry at the Fe center. In the region III, the calculated D increases again from its minimum value as the tip displacement varies from ∆z = −350 to −420 pm. There, the composite junction becomes more compact, and the FeOEP molecule is subject to strong dispersive forces exerted by both the tip and the substrate. The resultant force pushes the molecule closer to the substrate surface. In particular, the Fe atom again locates below the molecular plane, and thus the lowered crystal-field symmetry leads

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to the rising of D. The calculated D exhibits a sharp increase at ∆z = −420 pm where the tip enters the region IV. Apart from the geometric variation, the sharp increase in D is mainly caused by the change in ground-state electronic structure. Specifically, at this point the degeneracy between the two dπ orbitals (dxz and dyz ) is broken, and the relative positions of the dxy and dz2 orbitals are reversed. Consequently, while the adsorbed FeOEP remains in the local S = 1 state, the local electron configuration undergoes the change from (dxy )1.8 (dz2 )1.7 (dπ )2 to (dxy )1.8 (dz2 )1.3 (dπ )2.4 ; see the inset of Figure 2(c) and Table S2 in Supporting Information. The above analysis provides an unambiguous interpretation of the continuous tuning of MA by the mechanically controlled STM tip. The delicate changes in the geometric and electronic structures disclosed by the first-principles simulation also enable us to investigate the evolution of Kondo resonance under the tip control. Throughout the tip control process the spin density of electrons is found to locate primarily on the Fe center. The local spin moment originates from the dπ orbitals in the regions I–III, and from the dπ and dz2 orbitals in the region IV, respectively. The intensity of Kondo resonance depends critically on the strength of couplings between the spin-unpaired d electrons and the conduction electrons in the substrate/tip. To explore the variation of these coupling strengths, in Figure 3 we show the Kohn–Sham orbitals that have the main character of Fe d-orbitals as well as the maximum hybridization with substrate states. From the spatial distribution of the orbitals, it is obvious that the d electrons couple most strongly to the substrate states in the region IV, where the composite junction has a most compact geometry; see Figure 3(c). In contrast, the coupling is much weaker when the tip is positioned at the boundary between the regions II and III; see Figure 3(b). At this point, the Fe atom is pulled upward by the tip and forms a planar molecule, and the axial MA reaches its minimum value. It could thus be inferred that, as the tip approaches towards the substrate, the Kondo screening effect is at first weakened by the increased Fe-to-substrate distance, and then substantially enhanced with the Fe atom being pushed back towards the substrate.

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In the experiment conducted by Heinrich et al., the Kondo resonances are completely quenched by the superconducting gap created in the substrate and tip, so that the measurement and tuning of the MA could be achieved at a high-precision level. 37 It is however interesting to learn how the Kondo resonance will compete with the spin excitation under the same tip control, if a temperature higher than the superconducting transition temperature (TC ) is adopted. To elucidate this issue and to shed some light on the experiment, we construct a two-orbital Anderson impurity model 89,90 to describe the spin-unpaired d electrons and the surrounding environment. The impurity Hamiltonian assumes the form of

Himp =

∑

ν =1,2

εν (nˆ ν ↑ + nˆ ν ↓ ) +Uν nˆ ν ↑ nˆ ν ↓ + DSˆz2 .

(2)

Here, nˆ νσ is the electron number operator for spin-σ electron on the ν th orbital (σ =↑ or ↓), εν is the orbital energy, Uν is the electron-electron interaction strength, and Sˆz is the z-component of the total spin operator. The substrate (s) and the tip (t) are treated as noninteracting electron reservoirs, Wα2 2. 2 α ) +Wα

which are characterized by the hybridization functions Γνα (ε ) = ∆να (ε −Ω

Here, ∆να is the

effective coupling strength between the ν th orbital and the α th reservoir (α = s or t), and Ωα (Wα ) is the band center (width) of the α th reservoir. With the DFT+HEOM approach, the energetic parameters including εν , Uν , ∆να , Ωα and Wα are extracted from the results of DFT calculations. 54,91,92 In particular, Ωα is set to the chemical potential of α th reservoir, and ∆να is determined by comparing the PDOS of the Fe d-orbitals with and without the coupled substrate/tip. The magnitude of MA assumes the averaged value of D = 0.01 eV. The temperature is set to T = 0.001 eV ≃ 11.6 K, higher than the TC of lead. The dI/dV spectra of the Anderson impurity model are computed by using the HEOM method implemented in the HEOM–QUICK program. 51 A recently developed low-frequency logarithmic discretization scheme is employed to assist the construction of the hierarchy. 52 In relation to Figure 3, we focus on two situations: (i) the tip pulls the Fe atom upward so that the Kondo correlation is weakened; and (ii) the tip pushes the Fe atom close to the substrate so that the Kondo screen-

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ing effect is enhanced. The calculated dI/dV spectra corresponding to these two situations are displayed in Figure 4(a) and (b), respectively. In Figure 4(a) the dI/dV spectrum (red curve) exhibits a three-peak structure — the main peak at zero bias is a characteristic signature of the Kondo resonance, while the side peaks at V = ±D indicate the presence of inelastic excitations between local spin states. 33–35 The attribution of peaks is verified by taking D = 0, with which the side peaks are absent from the resulting spectrum (gray curve). It is thus inferred that, even with the Kondo screening weakened by the enlarged Fe-to-substrate distance, the remaining Kondo correlation still has a prominent influence on the dI/dV spectra. Therefore, external means (such as the superconducting reservoirs) are needed to completely suppress the Kondo resonance for realizing the precise measurement and tuning of D. On the other hand, the dI/dV spectrum (red curve) depicted in Figure 4(b) resolves only a single Kondo peak, and there are no signs of side peaks at V = ±D. Instead, the finite D only makes the Kondo peak lower and broader. This clearly indicates that the strong Kondo resonance overwhelms the inelastic excitation, and thus its feature becomes dominant in the conductance spectrum. To summarize, by using the combined DFT+HEOM approach, we achieve a first-principles based simulation on the tuning of local spin states in the adsorbed FeOEP molecule by a mechanically controlled STM tip. Our simulation accurately reproduces the observed variation of the magnetic anisotropy, and predicts the possible extension of the experiment. Moreover, we elucidate the changes of the geometric and electronic structures of the composite junction throughout the tip control process, and disclose the competition between the Kondo resonance and the local spin excitation. This work demonstrates that the first-principles based simulation could provide useful insights for the cutting-edge experiments, and thus may help to realize more fascinating quantum-state manipulations of potential quantum-device applications.

Acknowledgement Support from the Ministry of Science and Technology of China (Grants Nos. 2016YFA0400900 and 2016YFA0200600), the National Natural Science Foundation of China (Grant Nos. 21573202 11



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and 21633006), the Fundamental Research Funds for the Central Universities (Grant No. 2340000074), and the SuperComputing Center of USTC is gratefully acknowledged.

Supporting Information Available Further details on the electronic structure calculations, the computation of magnetic anisotropy, as well as the Anderson impurity model and HEOM calculations are provided in the Supporting Information.

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(b)

(a)

(c)

0

Figure 1. (a) An isolated FeOEP molecule. Blue and brown circles highlight the nitrogen and carbon atoms on the ligand, respectively. (b) Top view of the tip/FeOEP/Pb(111) system. The Fe atom is adsorbed at the hollow site of Pb surface. (c) Side view of the tip/FeOEP/Pb(111) system. Left and right panels display the system geometries when the tip is away from and near to the FeOEP molecule, respectively. The initial tip-to-substrate distance is z0 = 1110 pm.

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STM-tip displacement

Figure 2. (a) Calculated axial MA of the tip/FeOEP/Pb(111) composite versus the tip displacement (∆z). The experimental data 28 are also shown for a direct comparison. Since the initial tip-tosubstrate distance is unknown in experiment, we shift the experimental curve horizontally (but not vertically) until reaching an overall best match to the calculated curve. (b) Variation of the distances from the Fe atom (and its neighboring N and C atoms) to the substrate surface. (c) Variation of the energies of Fe d-orbitals under the tip control (only majority-spin orbitals are shown). The orbital energies are determined from the calculated projected density of states (PDOS) on the Fe atom; see section S3 in Supporting Information. The Fermi energy EF is set to zero. The inset diagram depicts the population of electrons on the Fe d-orbitals before and after ∆z = −420 pm. The fractional electron occupations on the dxz and dz2 orbitals are indicated by hollow arrows. 23 ACS Paragon Plus Environment


(a)

(b)

(c)

Figure 3. Contour plot of the Kohn–Sham orbitals that have the main character of dπ (left) or dz2 (right) orbital on the Fe center and the maximum hybridization with substrate states. The tip displacement is (a) ∆z = 0, (b) ∆z = −350 pm, and (c) ∆z = −450 pm, respectively. The isosurfaces of ±0.016 a.u. are shaded in red and blue, respectively.

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Figure 4. Calculated dI/dV versus V spectra for the Anderson impurity models corresponding to the composite junction at (a) ∆z = −350 pm and (b) ∆z = −450 pm. The values of the energetic parameters are (in units of eV): (a) ε1 = ε2 = −3.2, U1 = U2 = 5.0, Ws = Wt = 5.0, ∆1s = ∆2s = 0.04, and ∆1t = ∆2t = 0.02. Here, the orbitals 1 and 2 represent the Fe dyz and dxz orbitals, respectively. (b) ε1 = −3.2, ε2 = −2.6, U1 = 5.0, U2 = 4.5, Ws = Wt = 5.0, ∆1s = 0.13, ∆2s = 0.33, ∆1t = 0.12 and ∆2t = 0.16. Here, orbital–1 represents the dyz orbital, while orbital–2 stands for a combination of dxz and dz2 orbitals, as they together possess one spin-unpaired electron; see section S3 in Supporting Information for more details. The temperature is T = 0.001 eV. The inset of (b) depicts the energy diagram of the local spin states on the Fe center.

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Precise Control of Local Spin States in an Adsorbed Magnetic

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