16136829, 2021, 35, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/smll.202102753 by Readcube (Labtiva Inc.), Wiley Online Library on [15/12/2022]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License Research Article www.small-journal.com Tuning the Magnetic Anisotropy of Lanthanides on a Metal Substrate by Metal–Organic Coordination Sofia O. Parreiras,* Daniel Moreno, Borja Cirera, Miguel A. Valbuena, José I. Urgel, Markos Paradinas, Mirco Panighel, Fernando Ajejas, Miguel A. Niño, José M. Gallego, Manuel Valvidares, Pierluigi Gargiani, Wolfgang Kuch, José I. Martínez, Aitor Mugarza, Julio Camarero, Rodolfo Miranda, Paolo Perna,* and David Écija* 1. Introduction Taming the magnetic anisotropy of lanthanides through coordination environments is crucial to take advantage of the lanthanides properties in Lanthanide metals are nowadays ubiqui- tous in technology, being used in diverse thermally robust nanomaterials. In this work, the electronic and magnetic fields including alloys, permanent mag- properties of Dy-carboxylate metal–organic networks on Cu(111) based on nets, optical fibers, luminescent devices an eightfold coordination between Dy and ditopic linkers are inspected. This and probes, high-temperature super- surface science study based on scanning probe microscopy and X-ray magnetic conductors, and catalysts.[1–3] In addi- circular dichroism, complemented with density functional theory and multiplet tion, recent findings have highlighted the potential of lanthanides in single atom calculations, reveals that the magnetic anisotropy landscape of the system is magnetism.[4,5] Fundamental requirements complex. Surface-supported metal–organic coordination is able to induce a for a single atom magnet are: i) a doubly change in the orientation of the easy magnetization axis of the Dy coordinative degenerate ground state with a high mag- centers as compared to isolated Dy atoms and Dy clusters, and significantly netic moment and ii) protection from increases the magnetic anisotropy. Surprisingly, Dy atoms coordinated in the scattering with electrons/phonons of the metallosupramolecular networks display a nearly in-plane easy magnetization substrate and from quantum tunneling, which ensures the bistability of the ground axis despite the out-of-plane symmetry axis of the coordinative molecular state.[6] In quantum systems the stability lattice. Multiplet calculations highlight the decisive role of the metal–organic of the magnetic moment is determined by coordination, revealing that the tilted orientation is the result of a very delicate the energy difference between the bistable balance between the interaction of Dy with O atoms and the precise geometry ground state and the first excited state.[6] of the crystal field. This study opens new avenues to tailor the magnetic A large separation between these states protects the system against quantum fluc- anisotropy and magnetic moments of lanthanide elements on surfaces. tuations. For lanthanides, the intrinsic Dr. S. O. Parreiras, D. Moreno, Dr. B. Cirera, Dr. M. A. Valbuena, Dr. J. M. Gallego, Dr. J. I. Martínez Dr. J. I. Urgel, Dr. F. Ajejas, Dr. M. A. Niño, Dr. J. M. Gallego, Instituto de Ciencia de Materiales de Madrid (ICMM-CSIC) Prof. J. Camarero, Prof. R. Miranda, Dr. P. Perna, Prof. D. Écija Cantoblanco, Madrid 28049, Spain Instituto Madrileño de Estudios Avanzados en Nanociencia Dr. M. Valvidares, Dr. P. Gargiani (IMDEA Nanoscience) ALBA Synchrotron Light Source Madrid 28049, Spain Barcelona 08290, Spain E-mail: sofia.oliveira@imdea.org; paolo.perna@imdea.org; Prof. W. Kuch david.ecija@imdea.org Institut für Experimentalphysik Dr. M. A. Valbuena, Dr. M. Paradinas, Dr. M. Panighel, Prof. A. Mugarza Freie Universität Berlin Catalan Institute of Nanoscience and Nanotechnology (ICN2) Arnimallee 14, 14195 Berlin, Germany CSIC and The Barcelona Institute of Science and Technology Prof. A. Mugarza Campus UAB, Bellaterra, Barcelona 08193, Spain Institució Catalana de Recerca i Estudis Avançats (ICREA) The ORCID identification number(s) for the author(s) of this article Barcelona 08010, Spain can be found under https://doi.org/10.1002/smll.202102753. Prof. J. Camarero, Prof. R. Miranda © 2021 The Authors. Small published by Wiley-VCH GmbH. This is an Departamento de Física de la Materia Condensada and Condensed open access article under the terms of the C ­ reative Commons Attribu- Matter Physics Center (IFIMAC) tion-NonCommercial License, which permits use, distribution and repro- Universidad Autónoma de Madrid duction in any medium, provided the original work is properly cited and Cantoblanco, Madrid 28049, Spain is not used for commercial purposes. DOI: 10.1002/smll.202102753 Small 2021, 17, 2102753 2102753 (1 of 11) © 2021 The Authors. Small published by Wiley-VCH GmbH 16136829, 2021, 35, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/smll.202102753 by Readcube (Labtiva Inc.), Wiley Online Library on [15/12/2022]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License www.advancedsciencenews.com www.small-journal.com spin–orbit interaction leads to a large energy splitting between dichroism (XNLD), and X-ray magnetic circular dichroism the quantum states. Furthermore, the strong localization of the (XMCD), and complemented by density functional theory (DFT) 4f states reduces the hybridization with the surface, increasing calculations, we reveal the electronic and magnetic properties the spin lifetimes,[6–8] which is crucial, since a long magnetic of these Dy-carboxylate networks. On the one hand, our calcula- relaxation time is mandatory for technological applications.[4] tions show a metal–organic bond that is predominantly ionic, In this context, the stabilization of magnetic remanence in though a certain degree of covalence between dysprosium and single holmium (Ho) atoms on MgO(100)/Ag(100) surfaces, the carboxylate moieties is observed by scanning tunneling with relaxation times up to 1500 s at 10 K, confirmed the fea- spectroscopy (STS). On the other hand, such coordination sibility of using lanthanides as single atom magnets.[4] The scheme results in a change of the easy axis of magnetization of subsequent demonstration of electrical reading and writing of the Dy mononuclear center, which upon coordination is aligned single magnetic atoms by means of electron spin resonance nearly parallel to the surface, in opposition to the original out- has experimentally proven that their use for magnetic storage is of-plane easy axis reported for isolated dysprosium atoms on the possible.[5] However, the low thermal stability, below the boiling same Cu(111) surface.[21] Notably, there is a large increment of point of nitrogen, of single standing atoms due to their high the magnetic anisotropy of Dy and a reorientation of the ani- diffusion on surfaces avoids their use in practical applications. sotropy axis when compared to individual and non-coordinated A tentative chemical strategy to increase their thermal stability Dy atoms, which is rationalized as a consequence of the com- could be the coordination of mononuclear lanthanide atoms in bined effect of the interaction with the negative charges of the metal–organic networks. Notably, regarding single atom mag- oxygen atoms and the coordination symmetry of the molecular netism, lanthanides offer additional advantages over other ele- CF. Thus, it is feasible to tune the magnetic anisotropy of lan- ments. In 4f elements, the spin–orbit coupling (SOC) is larger thanide centers on surfaces by metal–organic coordination. than the crystal field (CF), which might result in higher ani- sotropies.[8,9] Furthermore, the CF acts as a perturbation of the SOC and can be tailored to increase the anisotropy by choosing 2. Results and Discussion an appropriate coordination environment,[7,10] though so far such finding has not been demonstrated for surface-confined The sublimation of TDA and TPA species (see atomic models metal–organic networks embedding lanthanides. at Figure 1a,e) on a Cu(111) surface, held at 373 K to steer dif- Contemporarily to the development of lanthanide science fusion of the linkers and deprotonation of the functional and technology, supramolecular chemistry on surfaces, mostly groups,[13,14] followed by Dy deposition, leads to the formation employing transition metals, has allowed the design of inter- of coordinated Dy-carboxylate metal–organic networks (see facial metal–organic complexes and architectures.[11,12] Only Figure 1b,f). These self-assembly patterns can only be designed recently, surface-confined lanthanide-directed architectures on a substrate, since the role of the surface is critical, imposing have been reported,[3,13–18] exhibiting the affinity of lanthanides the growth in 2D. Dy centers are imaged as voids due to the to coordinate with carbonitrile, carboxylic, and terpyridine tip conditions in the scanning tunneling microscopy (STM) functional groups.[19] These findings afforded the formation experiments, similarly as observed for Gd-TDA networks.[14] of lanthanide-directed networks on surfaces, which might be Such networks are stabilized by an eightfold DyO coordina- used to study the promising properties of f-block elements for tive interaction, featuring internodal distances of 20.5(5) Å for nanomagnetism in an ordered and thermally stable coordina- TDA and 11.8(5) Å for TPA, as previously reported.[13] tion environment. Hereby, carboxylate-directed networks were Figure 1c,g shows DFT-optimized models for Dy-TDA and recently reported to be stable up to 360 K.[14] Dy-TPA interfacial architectures, respectively. The resulting In a previous work, we have observed by X-ray photoelectron optimized structure reveals that Dy atoms lie on hollow sites spectroscopy (XPS) a +3 oxidation state for dysprosium (Dy) for both lattices. The linkers are bonded to the Dy atoms via atoms coordinated with linkers equipped with terminal carboxy- the carboxylate terminal groups, which alternate the torsional late functional groups, namely p-terphenyl-4,4′-dicarboxylic acid angle within the same molecule, as previously observed for (TDA) and benzene-1,4-dicarboxylic acid (TPA), on Cu(111).[13] Gd-TDA networks on Cu(111).[14] The bonding energy per TDA With an odd number of electrons, Dy3+ is a Kramers ion with a (TPA) molecule to the Dy/Cu surface is ≈9.84 eV (10.47 eV), doubly degenerate ground state,[7] fulfilling one of the prerequi- which has two main contributions. On the one hand, the inter- sites for single atom magnets. In this case, the magnetic anisot- action of each molecule with the metal surface is ≈1.25 eV per ropy can be increased by a proper ligand field.[7,20] For TDA and TDA molecule and 1.1 eV per TPA. On the other hand, ≈2.15 eV TPA, the planar structure of the networks combined with the accounts for each DyO bond per TDA molecule (and 2.34 eV eightfold coordination of the Dy atoms with the oxygen atoms per TPA), in agreement with the expected value for a bond of of the carboxylic groups is expected to result in a compressed a predominant ionic nature. In the case of the TDA network, square antiprism CF, similar to that of the {Pc(OEt)8}2Dy com- the DyO bonding energy is ≈0.2 eV lower than for the TPA plex, where a large magnetic remanence is observed.[20] case, see Section III, Supporting Information, for comprehen- Here we report the formation of metal–organic networks sive discussion. on Cu(111) based on Dy employing the two above-mentioned The coordination structures calculated by DFT resemble a molecular species, TDA and TPA, in order to tailor the inter- distorted square antiprism (D4d symmetry) with the symmetry nodal distance while keeping a similar coordination environ- axis parallel to the surface normal. This structure was analyzed ment. Based on a scanning probe microscopy study, combined by a continuous shape measurement (CShMs),[22] as described with X-ray absorption spectroscopy (XAS), X-ray natural linear in Section IV, Supporting Information, to determine the Small 2021, 17, 2102753 2102753 (2 of 11) © 2021 The Authors. Small published by Wiley-VCH GmbH 16136829, 2021, 35, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/smll.202102753 by Readcube (Labtiva Inc.), Wiley Online Library on [15/12/2022]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License www.advancedsciencenews.com www.small-journal.com Figure 1. On-surface design of Dy-carboxylate metal–organic networks on Cu(111). a–d) Dy-TDA on Cu(111): a) Atomic model of TDA molecule where C, H, and O atoms are represented by black, white, and red balls, respectively. The indicated distance is measured between the terminal oxygen atoms. b) STM image with atomistic model superimposed. Scanning parameters: Vb = −0.80 V and I = 150 pA, T = 4 K, scale bar: 1.0 nm. c) Pictorial views of the DFT-optimized network. d) 3D and top views of the DyO coordination polyhedron. e–h) Dy-TPA on Cu(111): e) Atomic model of TPA molecule where C, H, and O atoms are represented by black, white, and red balls, respectively. The indicated distance is measured between the terminal oxygen atoms. f) STM image with atomistic model superimposed. Scanning parameters: Vb = −1.10 V and I = 170 pA, T = 300 K, scale bar: 1.0 nm. g) Pictorial views of the DFT-optimized network. h) 3D and top views of the DyO coordination polyhedron. deviation from an ideal eightfold polyhedra. Of all symmetries resonance is found at negative bias. A comparison with DFT allowed in the simulations, D4d comes closest (see Table S1, simulations (Figure 2c,d) confirms our assignment of the Supporting Information, and related discussion, note that C4 unoccupied orbitals. The calculated projected density of states is not included in the software), but with still relatively large displays a LUMO resonance for the uncoordinated species CShMs values. This indicates that the real shapes diverge sig- (Figure 2d) that is shifted toward higher energies for the coor- nificantly from ideal D4d symmetry. As expected, the antiprism dinated one, in qualitative agreement with the experimental is compressed in the vertical axis for both TDA and TPA lattices results. The shift between the LUMO states upon coordination (Figure 1d,h). There is an additional distortion regarding the toward higher energies is visually and numerically indicated relative rotation between the two squares that deviates from in Figure 2c,d and is attributed to a change on the adsorption the 45° of the perfect square antiprism case. The twist angles geometry of the molecular species, which becomes flatter upon of the two diagonals are 31° and 34° (22° and 28°) for the TDA coordination (see Figures S5 and S6, Supporting Information). (TPA) networks. Taking into account these distortions the coor- The constant current dI/dV map displays the shape of the dination symmetry is actually C4. LUMO (Figure 2f), which consists of two lobes at the rims of Next, we have inspected the electronic properties of the the molecular backbone that are more intense for molecules Dy-TDA metal–organic network by means of STS, comple- in one direction of the network than in another, probably due mented with DFT calculations. To this aim we acquired point to the different registry with the substrate. Notably, spectra spectra on the bare substrate, uncoordinated isolated species acquired on top of the lanthanide centers also display a reso- (see explanation in Section I and Figure S1, Supporting Infor- nance at similar energies as the LUMO observed for the coor- mation), mononuclear Dy centers and coordinated molecules, dinated molecular species, as depicted in the dI/dV spectrum as illustrated in Figure 2a,b. A STS spectrum measures the (Figure 2a) and in the constant current map acquired at 1.6 eV dI/dV signal as a function of bias voltage, which provides infor- (Figure 2f). This resonance is more intense in the molecular mation on the local density of states of the sample, both at backbone and decays toward the metal center. Such finding the occupied (negative bias) and unoccupied regions (positive might reveal a partial covalent nature of the coordinative Dy- bias), where zero bias voltage corresponds to the Fermi level. carboxylate interaction.[23,24] At this stage, it is worth to point An intense resonance is found at 1.2 eV for the uncoordinated out that the metal–organic coordination based on a lantha- species (purple curve), whereas the coordinated one (red curve) nide bond is universally considered to be predominantly ionic, features a strong peak at 1.7 eV, both of them assigned to the due to the internal location of the f-valence electrons, though lowest unoccupied molecular orbital (LUMO) of the uncoor- there is always a certain degree of covalence,[2,19] which is dinated and coordinated species, respectively. No discernible clearly observed here for the Dy-TDA network. Our insights are Small 2021, 17, 2102753 2102753 (3 of 11) © 2021 The Authors. Small published by Wiley-VCH GmbH 16136829, 2021, 35, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/smll.202102753 by Readcube (Labtiva Inc.), Wiley Online Library on [15/12/2022]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License www.advancedsciencenews.com www.small-journal.com Figure 2. Electronic structure of Dy-TDA networks on Cu(111). a) STS spectra taken at coordinated TDA (red), Dy center (blue), non-coordinated TDA (purple) and Cu substrate (green). b) High-resolution STM image showing a coordinated TDA network (lower part) and non-coordinated molecules (upper part) with crosses indicating the positions where the STS spectra were taken. Scanning parameters: Vb = −0.70 V and I = 80 pA, T = 4 K, scale bar: 3.0 nm. c,d) Computed density of states projected onto the TDA molecule for c) non-coordinated and d) Dy-coordinated TDA/Cu(111) interfaces. e) Reference STM image for the dI/dV map. Scanning parameters: Vb = −0.20 V and I = 80 pA, T = 4 K scale bar: 1.0 nm. f) Constant-current dI/dV map taken at 1.60 V, showing the LUMO resonance, with a superimposed atomistic model, scale bar: 1.0 nm. g) 3D charge–density difference plot with the structural model of Dy-TDA on the Cu(111) surface superimposed. h) Top view DFT equilibrium geometry and i) isosurface corresponding to the spatially distributed 3D charge–density difference plot (with isovalues of 0.001 a.u.). Green isosurfaces represent charge depletion and red isosurfaces indicate charge accumulation. corroborated by the calculated charge density difference plots the Dy M4,5-edges at grazing (70°) and normal (0°) incidences. (see Figure 2g–i and Section III, Supporting Information, for The spectra are presented after the subtraction of the Cu back- detailed analysis). The plots illustrate the difference between ground, however XLND and XMCD spectra can be obtained the electron charge density of the interacting system and those directly from the raw data before the background subtraction of its non-interacting counterparts. Positive values (blue, red) (see Figure S4, Supporting Information). The temperature (T) indicate charge accumulation, highlighting the charge gained of the experiments was 6 K (see the discussion of the fit of by the carboxylate moieties. Negative values (green) represent magnetization curves in Section V, Supporting Information, for charge depletion, and are an indication of a bond dominated more details). For Dy centers on Dy-TDA and Dy-TPA networks by ionic interactions, in agreement with XPS data of the same multiplet calculations are presented together with the experi- network, recently published by us,[13] and in analogy to Gd-TDA mental data and will be discussed latter. networks on Cu(111).[14] By analyzing the peak structure of the M5-edge, the oxida- Next, we have focused our attention on the effect of mole- tion state can be determined. The higher intensity of the third cular coordination on the electronic and magnetic properties of peak at 1289 eV in the XAS spectra of Dy clusters and Dy-TDA Dy atoms by performing XAS, XNLD, and XMCD experiments. networks (Figure 3a,b) is a fingerprint of a trivalent state.[21,25] XAS measures the X-ray absorption as a function of the inci- Results found in the literature for isolated Dy atoms adsorbed dent energy, giving information on the geometric and electronic on Cu(111) indicate a divalent configuration,[21] and, thus, coor- structure of the samples. This technique is element specific, dination with TDA changes the Dy oxidation state from +2 to allowing the identification of the chemical composition and the +3, as typically encountered in bulk coordination chemistry.[26] oxidation state. XNLD employs linearly polarized X-rays, pro- The change of the oxidation state for the clusters when com- viding fingerprints of the anisotropy of the electronic orbitals, pared to isolated atoms is attributed to the metallic bonds whereas XMCD makes use of circular polarization, being the between the Dy atoms, as also happens for bulk compounds. workhorse technique for inspecting the magnetic properties Figure 3a,b shows XNLD spectra of Dy clusters and Dy of the samples. Samples of Dy clusters, Dy-TDA, and Dy-TPA centers on the Dy-TDA networks, respectively. XNLD was networks on Cu(111) were measured, maintaining a similar Dy calculated as the difference between absorption spectra with coverage, equivalent to ≈0.01 monolayer. In addition, we com- linear vertical and horizontal polarizations (μV − μH) at a low pared our results to recent analogous experiments performed magnetic field (0.01 T). The linear dichroism observed in Dy for isolated Dy atoms on Cu(111).[21] clusters reveals the anisotropy of 4f orbitals. The Dy-TDA net- Figure 3 displays XAS, XNLD, and XMCD spectra of Dy clus- work presents a slightly higher dichroic signal when compared ters and Dy centers on Dy-TDA and Dy-TPA networks taken at to Dy clusters as a result of the CF generated by the molecular Small 2021, 17, 2102753 2102753 (4 of 11) © 2021 The Authors. Small published by Wiley-VCH GmbH 16136829, 2021, 35, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/smll.202102753 by Readcube (Labtiva Inc.), Wiley Online Library on [15/12/2022]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License www.advancedsciencenews.com www.small-journal.com Figure 3. XAS, XNLD, and XMCD spectra of Dy clusters, Dy-TDA, and Dy-TPA networks on Cu(111). a–c) XAS spectra acquired with vertical (μV, black/grey spectra) and horizontal (μH, orange/yellow) linearly polarized light and XNLD (μV − μH, green) taken at Dy M5-edge at grazing (70°) incidence for: a) Dy clusters, b) Dy-TDA networks, and c) Dy-TPA networks (B = 0.01 T, T = 6 K). d–f) XAS spectra acquired with positive (μ+, purple) and negative (μ−, brown) circularly polarized light and XMCD (μ− − μ+) taken at Dy M4,5-edges at normal (0°, red) and grazing (70°, blue) incidences for: d) Dy clusters, e) Dy-TDA networks, and f) Dy-TPA networks (B = 6 T, T = 6 K). For Dy-TDA and Dy-TPA networks multiplet calculations are presented together with the experimental data. network. These results were compared with XNLD spectra of isotropic, having a very small magnetic anisotropy with an DyPc2 double-decker magnets,[27] which can be considered as out-of-plane easy axis.[21] However, the intensity of the XMCD metal–organic sandwiches of Dy with a +3 oxidation state and a signal of Dy clusters on Cu(111) for grazing incidence is larger D4d coordination symmetry.[28] Surprisingly, such double-decker than for normal incidence (Figure 3d) revealing a change of compounds show a XNLD spectrum inverted when compared the anisotropy axis, which proves that it is possible to tune the to the Dy-TDA network. Even if in our case the symmetry is magnetic anisotropy of Dy by adjacent metallic bonds, as found C4 instead of D4d, the symmetry axis has the same orientation for other lanthanide elements.[29] and a similar XNLD would be expected. The inverted orienta- In order to exploit such magnetic anisotropy, Dy-directed tion indicates that for Dy-TDA networks the effective CF acting metal–organic architectures are ideal candidates because their on the Dy atoms does not follow the coordination symmetry mononuclear configuration imposes a specific CF to the lantha- axis. A further comparison with Dy3+ ions in the dysprosium- nide sphere. In fact, XMCD experiments of surface-supported tris(1,1,1-trifluoro-4-(2-thienyl)-2,4-butanedionate) (Dy(tta)3) Dy-TDA networks show a drastic increase of the difference complex on Au(111)[10] also confirms that the alignment of the between grazing and normal XMCD intensity of Dy (Figure 3e). Dy 4f orbitals in the Dy-TDA network is close to the surface Sum rules[30,31] were used to calculate the projections of the plane (see the Experimental Section for more details). magnetic moments at the experimental conditions of 6 T and Concerning the magnetic properties, isolated Dy atoms a temperature of 6 K (see Experimental Section) and the results on Cu(111) at 2.5 K have been recently reported to be almost for grazing (70°) and normal (0°) incidences are presented in Small 2021, 17, 2102753 2102753 (5 of 11) © 2021 The Authors. Small published by Wiley-VCH GmbH 16136829, 2021, 35, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/smll.202102753 by Readcube (Labtiva Inc.), Wiley Online Library on [15/12/2022]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License www.advancedsciencenews.com www.small-journal.com Table 1. Expectation values at the experimental temperature and at 6 T field of orbital (〈Lz〉), spin (〈Sz〉) and total (〈Jz〉) moments, total magnetic moment (MT), and moment anisotropy (ΔMT) obtained from XMCD sum rules for normal (0°) and grazing (70°) incidences for Dy clusters on Cu(111) and Dy centers on Dy-TDA and Dy-TPA networks on Cu(111). Dy clusters on Cu(111) Dy centers on TDA network Dy centers on TPA network Dy single atoms on Cu(111)[21] Incidence angle [°] 0 70 0 70 0 70 0 60 〈Lz〉 [ћ] 1.19 (12) 1.87 (19) 1.36 (14) 2.35 (24) 1.00 (10) 2.77 (28) 4.7 (2) 4.4 (2) 〈Sz〉 [ћ] 0.65 (6) 0.86 (9) 0.44 (4) 1.14 (11) 0.60 (6) 1.18 (11) 1.6 (1) 1.5 (0) 〈Jz〉 [ћ] 1.84 (18) 2.73 (27) 1.80 (18) 3.49 (35) 1.60 (16) 3.95 (40) 6.3 (2) 5.9 (2) MT [μB] 2.49 (25) 3.59 (36) 2.24 (22) 4.63 (46) 2.20 (22) 5.13 (51) 7.9 (2) 7.4 (2) ΔMT [μB] 1.10 (61) 2.39 (68) 2.93 (73) 0.5 (3) Table 1. We define the moment anisotropy ΔMT as the differ- averaged) easy axis onto the grazing incidence direction of the ence between grazing and normal magnetic moments meas- X-rays compared to the case of normal incidence. ured at 6 T and 6 K (Δ MT = MT (70°) − MT(0°)). Data for Dy2+ Importantly, the very similar slope of the experimental M(H) single atoms on Cu(111) from reference [21], measured at 6.8 T curves for normal and grazing incidences together with the and 2.5 K, is also presented for comparison. significant difference in the XMCD signal at 6 T can neither Here it is worth mentioning that lanthanides show a high be modeled by an in-plane easy-axis anisotropy nor by an easy- SOC and their electronic and magnetic properties are described plane anisotropy in the surface plane. In both cases the curva- by the quantum numbers J and Jz. On surfaces, Dy3+ shows a ture in the hard-axis direction, for normal incidence, would be remarkably high orbital moment, as observed for other rare- inconsistent with the experimental observation. Both results, earths[6,21] and contrary to 3d metals.[35] Importantly, the orbital however, can be explained by an oblique orientation of the moment is not quenched by the ligand field, being of the same quantization axis of the Dy ions. order of magnitude than the spin moment. As can be seen As mentioned before, in the discussion of Figure 3a,b, the in Table 1, both orbital and spin moments differ strongly for XNLD spectra show an intensity asymmetry compatible with normal and grazing incidences. When comparing the moment 4f orbitals aligned parallel to the surface. However, it is not anisotropies (ΔMT) of Dy clusters on Cu(111) and Dy centers possible to determine if they are lying totally in-plane or are in Dy-TDA networks, the latter is 2.2 times greater, due to the in a tilted orientation close to the surface. Considering this cooperative effect of the CF. Furthermore, the high moment tilted orientation of the anisotropy axis it is possible that the 4f anisotropy of Dy-TDA can be clearly observed when comparing orbitals have also an oblique orientation following the quantiza- XMCD spectra acquired at 0° and 70° incidences, and the tion axis. 〈Jz〉 evaluated for grazing incidence is more than twice larger In the case of the clusters, the fitted angle of 65.0° between than for normal incidence (Figure 3e). In the case of isolated the quantization axis and the surface normal is attributed to Dy2+ atoms adsorbed on Cu(111), the difference between the the averaging of Dy atoms with distinct anisotropy orienta- spectra measured at 0° and 60° is negligible, and the resulting tions, since Dy was deposited at room temperature and diffused moments are very close, with a difference ≈7%.[21] Thus, the forming clusters, bulkier than their metallosupramolecular moment anisotropy of Dy3+ centers in Dy-TDA networks is architecture counterparts. much higher than for Dy2+ isolated atoms. Figure 4d presents XAS and XMCD spectra of Dy centers Figure 4a,b displays magnetization curves of Dy clusters on Dy-TDA networks taken at a temperature of 6 K at the Dy and Dy-TDA calculated by evaluating the variation of the M4,5-edges for incidence angles ranging from 0° (normal) to XMCD signal of the highest peak of the M5-edge with the 80°. The experimental angle dependence was compared with applied magnetic field. The curves were fitted to the model models for the easy axis oriented in-plane, out-of-plane, and in described in the Experimental Section. During the fits, the a tilted angle of 71.2° from the normal as obtained from the value of anisotropy energy (D) was going to high negative fitting of the magnetization curves. Figure 4e presents the values (minus infinity), indicating strong easy-axis anisot- experimental data of the angular variation of the integrated M5 ropy, which at the temperature and for the fields used in the XMCD signal and maximum intensity together with the theo- experiment means that the system is basically modeled by retical models. It is clear that the experimental data does not an effective spin-1/2 system, with only the ground-state dou- follow the expected behavior for in-plane nor for out-of-plane blet being significantly occupied. Additionally, fit deviation anisotropy, being closer to the tilted model. data indicates that a wider range of D values is tolerated by It is important to point out that the magnetic moments pre- Dy clusters suggesting that the molecular networks may have sented in Table 1 correspond to the projections of the moments larger anisotropy energy than the clusters (see Figure S9, Sup- on the incidence directions (0° and 70°) at 6 T and a tem- porting Information). The similar slope of the curves obtained perature of 6 K. To determine the saturation values, it would at grazing and normal incidences for all samples can be repro- be necessary to measure aligning the beam to the quantiza- duced by easy axes tilted by 73°–65° away from the surface tion axis. However, the networks grow in domains, and given normal. The higher XMCD signal for grazing incidence is the relationship between the network unit cell and the sur- then explained by the larger projection of this (azimuthally face high-symmetry directions, there is a total of six possible Small 2021, 17, 2102753 2102753 (6 of 11) © 2021 The Authors. Small published by Wiley-VCH GmbH 16136829, 2021, 35, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/smll.202102753 by Readcube (Labtiva Inc.), Wiley Online Library on [15/12/2022]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License www.advancedsciencenews.com www.small-journal.com Figure 4. Magnetization curves of Dy clusters, Dy-TDA and Dy-TPA networks on Cu(111) and angle dependence of Dy-TDA integrated XMCD. a–c) Magnetization curves acquired by measuring the intensity of the XMCD signal at the M5-edge at the highest peak for: a) Dy clusters, b) Dy-TDA network, and c) Dy-TPA network (T = 6 K). The curves were fitted according to the model described in the SI (T = 6 K). In the y scale 1 corresponds to a full alignment of a not-azimuthally-rotated Dy magnetization with the X-ray incidence. d) XAS-TEY + ( µ + µ− 2 ) and XMCD (μ− − μ+) spectra taken at the Dy M4,5-edges at incidence angles (θ) ranging from 0° (normal) to 80° (grazing) for Dy centers on Dy-TDA networks on Cu(111) (B = 6 T, T = 6 K). e) Angle dependence data for the Dy-TDA network. Dark yellow dots are the maximum intensity of the M5-edge, wine dots are the integrated M5 XMCD signal. The lines are some theoretical models with the easy axes oriented at distinct angles (θ) with respect to the surface plane. The simulated curves are the projection of the expectation value of the magnetization on the light incidence direction at 6 T. It was assumed that they are proportional to the maximum XMCD as well as the integrated XMCD. Both, theoretical curves and experimental data, were normalized so that 1 correspond to the maximum intensity. orientational domains. Experimentally, what is measured is an is the [Na{Dy(DOTA)(H2O)}]·4H2O salt (Dy-DOTA), which pre- average over these six domains and the system will never be sents a decker plane formed by oxygen atoms apically capped totally saturated. Nevertheless, it is possible to have an estimate with a water molecule. In this salt, the anisotropy orientation is of the saturation values when dividing the moments in Table 1 not linked to the symmetry axis of the coordination polyhedron, by the intensities of the simulated magnetization curves at 6 T but nearly orthogonal to it, that is, almost perpendicular to the presented in Figure 4a–c. one observed for double-deckers.[32,34] Moreover, theoretical The explanation for the origin of the tilted easy axis of mag- calculations for the salt showed that small structural changes, netization is not trivial. As discussed previously, the CF imposed such as the rotation or removal of the water molecule, leads to on Dy centers by the TDA network leads to a compressed and abrupt changes on the magnetic anisotropy. Dy-TDA networks distorted square antiprism coordination polyhedron. The on Cu(111) behave magnetically in a way more similar to Dy- square antiprism is the coordination environment of double- DOTA than to double-deckers, with the easy axis of magnetiza- decker magnets,[28] which display out-of-plane anisotropies,[27,33] tion oriented in a small angle close to the surface plane. following the D4d symmetry axis. However, the anisotropy To better understand this orientation of the easy axis we have in lanthanide systems is very complex and can be drastically performed a series of multiplet calculations using the MultiX altered by minor changes in the coordination environment.[32] A code.[36] These simulations reveal that the anisotropy is the recently reported system with a similar coordination symmetry result of a delicate balance between different contributions. Small 2021, 17, 2102753 2102753 (7 of 11) © 2021 The Authors. Small published by Wiley-VCH GmbH 16136829, 2021, 35, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/smll.202102753 by Readcube (Labtiva Inc.), Wiley Online Library on [15/12/2022]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License www.advancedsciencenews.com www.small-journal.com On one side, the symmetry axis of the coordination polyhe- that the Dy 4f orbitals in Dy-TPA networks also display a sym- dron favors an out-of-plane orientation. On the other side, the metry axis close to the plane (Figure 3c) and the effective CF is interaction of the negative charges of the oxygen atoms with the even larger than in the Dy-TDA counterparts (Figure 3b). This positive charge of the Dy3+ ion changes the charge distribution, increase is attributed to the small differences in the coordina- favoring an in-plane orientation. The balancing of these two tion symmetry between both networks, which should also influ- opposite contributions results in a tilted easy axis. For a per- ence the magnetic properties. fect square antiprism, the effect of the charge interaction is Magnetic moments of Dy-TPA calculated from sum rules stronger than the coordination symmetry and the in-plane com- show larger moment anisotropy (ΔMT in Table 1), being ponent is larger (see Figure S10, Supporting Information). The 2.7 times greater than the moment anisotropy of Dy clusters orientation of the magnetic anisotropy and the angle depend- and 1.2 times greater than that of Dy-TDA networks (note the ence of XMCD spectra depend on the precise geometry of the importance of the error bar for a rigorous comparison). Such CF. The effect of distortions from the ideal D4d symmetry on increase in moment anisotropy can be a consequence of the the XNLD and XMCD spectra is described in Section VI, Sup- differences in the coordination antiprism, since minor varia- porting Information, (see Figures S11–S13, Supporting Infor- tions in the coordination geometry can lead to major changes mation, and related discussion). in the magnetic moments. The fitting of the magnetization A comparison between XAS, XNLD, and XMCD simula- curves (Figure 4c) again indicates an anisotropy energy in the tions and measurements for Dy-TDA networks is shown in maximum negative limit (see Table S2, Supporting Informa- Figure 3b,e. Although a perfect fit between experiment and tion). The changes in the magnetization curves for the different simulation was not achieved due to the difficulty of repro- systems are due to the reorientation of the easy axis, not to any ducing the exact coordination symmetry of the real molecular change in the anisotropy energy. For Dy-TPA, the easy axis of CF, there is a reasonable qualitative agreement: the peak struc- magnetization is oriented at a smaller angle when compared ture of XAS, the sign of the XNLD and the larger intensity of to Dy-TDA, closer to the surface plane, 72.9° from the surface XMCD for grazing incidence are well reproduced. Notably, we normal. The smaller tilting angle of the easy axis is attributed to have also explored the impact of the substrate on the magnetic differences in the geometry of the CF, as predicted by DFT and properties, not finding significant contributions. The role of the multiplet calculations. The coordination polyhedron of Dy-TPA Cu(111) support is to fix the coordination geometry, but beyond has a lower compression and a higher twist angle between the that important structural contribution, the magnetic properties oxygen planes than that of Dy-TDA. According to multiplet cal- are determined by the lanthanide-ligand field interactions (see culations, both changes contribute to increase the difference Figure S15, Supporting Information). between grazing and normal XMCD intensity (see Figures S12 Despite the changes in XMCD intensity with coordination, and S13, Supporting Information, and related discussion). the magnetization curves still present a paramagnetic behavior, A comparison between simulations and experimental XAS, with no opening of the hysteresis loop and no remanence. In XNLD and XMCD spectra for Dy-TPA is shown in Figure 3c,f. principle, a Dy3+ Kramers ion with J = 15/2 would imply 8 fea- Similar to Dy-TDA, there is a good qualitative agreement with sible doubly degenerate |Jz| states, being an excellent candidate the experimental results and the role of the Cu(111) substrate is for measuring magnetic remanence, that is, behaving as single negligible (see Figure S16, Supporting Information). atom magnet.[4,5] The absence of single atom magnet behavior Although the magnetization curves still exhibit a paramag- can be tentatively explained by distinct factors: the interaction netic behavior, the change of the molecular linker improved of the Dy atoms i) with the metallic substrate via conduction the magnetic properties. The high magnetic anisotropy is pre- electrons and phonon modes or ii) with the molecules via served and the projected magnetic moments are even larger, phonons could destabilize the magnetic moments;[21,37–39] as can be seen in Table 1. Our findings demonstrate that these iii) the magnetic relaxation time could be smaller than the Dy-directed metal–organic networks are very robust and suit- measuring time, which would avoid the observation of the able for tuning the magnetic anisotropy of lanthanides and, magnetic remanence.[25] thus, opening avenues in the development of single atom mag- In an attempt to see the influence of the internodal dis- netism. A promising approach to further advance and stabilize tance on the magnetic properties of the network, we engi- the magnetic remanence is the insertion of decoupling layers neered a Dy-TPA metal–organic coordination network on between the substrate and the molecular network. Graphene, Cu(111) where the distance between Dy centers is ≈50% MgO, and other insulating layers have been demonstrated to shorter than in the Dy-TDA network, but featuring the same be effective on decoupling lanthanides from metallic sub- coordination environment. On one hand, the reduction of the strates.[4,41,42] Graphene was also used to decouple Co metal– length of the molecular precursor has been investigated as a organic networks from an iridium substrate.[23,43] Furthermore, route to reduce the vibrational excitations and limit phonon long relaxation times have been observed for Dy single atoms interactions, which could help to stabilize the magnetic rema- adsorbed on graphene/Ir(111),[37] revealing a promising sub- nence. On the other hand, it is necessary to know if there strate for the preparation of coordinated Dy networks. is any coupling between the lanthanide centers, which could be pernicious for stabilizing a single atom magnet, but very relevant for engineering lanthanide-based metal–organic 3. Conclusion ferromagnets.[40] By performing XAS, it is found that the oxidation state of Dy In summary, we have studied the electronic and magnetic prop- in the Dy-TPA network is again +3 (Figure 3c). XNLD reveals erties of Dy-carboxylate metal–organic networks on Cu(111) Small 2021, 17, 2102753 2102753 (8 of 11) © 2021 The Authors. Small published by Wiley-VCH GmbH 16136829, 2021, 35, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/smll.202102753 by Readcube (Labtiva Inc.), Wiley Online Library on [15/12/2022]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License www.advancedsciencenews.com www.small-journal.com using two ditopic linkers, TDA and TPA, featuring distinct by STM experiments carried out with an Aarhus-150 VT-STM at internodal distances, but a similar coordination environment. room temperature, where large domains of coordinated network in Regarding the electronic properties, the coordination is coexistence with uncoordinated molecules were observed. Notably the absence of Dy clusters was also corroborated. Figure S3, Supporting dominated by ionic interactions with a minority covalent com- Information, presents large scale images of the Dy-TDA network. The ponent. Dysprosium coordinative centers feature a +3 oxidation same preparation procedure was also followed for Dy-TPA networks, state, underlining that it is feasible to tailor the oxidation state guaranteeing that all Dy atoms are coordinated. of lanthanides on surfaces by metal–organic coordination. For XAS, XNLD, and XMCD measurements were performed at the both networks, the symmetry axis of Dy 4f orbitals is close to BOREAS beamline of the ALBA synchrotron light source, Spain. The the surface. experiments have been done in total electron yield (TEY) mode with a 90% circularly polarized beam and magnetic fields up to 6 T. The nominal Concerning magnetism, the easy axis of magnetization was temperature was 2 K, however, as is discussed in Section V, Supporting found to be lying nearly in-plane, despite the out-of-plane orien- Information, the fitting of the magnetization curves indicates that the tation of the coordination symmetry axis. Such a finding high- real temperature is higher, ≈6 K. For a matter of clarity, only the fitting lights the complexity of the magnetism of lanthanide systems temperature is indicated in the main text. XNLD is the difference between on surfaces, which can be drastically affected by small structural spectra measured with vertical and horizontal polarizations (μV − μH). changes due to molecular coordination and by interaction with The spectra were measured at 0.01 T and normalized at the Dy M5-edge the charges of coordination linkers. The magnetic properties are the result of a delicate balance between the interaction of ( 1 2 ) of isotropic spectra: Iso XNLD = µV + µH . XAS spectra were obtained 3 3 from the average of the spectra measured with two circular polarizations Dy3+ with the negative charges of oxygen atoms and the precise geometry of the CF. Subtle changes in the coordination sym- ( ) µ + + µ − . XMCD is the difference between negative and positive 2 metry of Dy-TPA when compared to Dy-TDA lead to a change polarizations (μ− − μ+). XAS and XMCD spectra were normalized by the in the tilting angle of the anisotropy axis, which is slightly smaller for Dy-TPA. Dy3+ centers in Dy-TDA and Dy-TPA net- Dy M5-edge of average absorption spectra: Ave XAS = + ( µ + µ− 2 ) . works have stronger magnetic anisotropies than isolated Dy2+ Figure S4, Supporting Information, shows XAS and XMCD spectra of the Dy-TDA network on Cu(111) taken at the Dy M4,5-edges acquired atoms and higher magnetic moments than Dy2+ atoms or Dy3+ with positive (μ+) and negative (μ−) circularly polarized light. The figure clusters. However, it was not possible to observe any magnetic presents the raw data before background subtraction (Figure S4a, remanence, which is attributed to either short spin relaxa- Supporting Information) as also the normalized spectra after background tion time or scattering with conduction electrons and phonon subtraction (Figure S4b, Supporting Information). The XMCD spectrum modes arising from the molecular or metallic environment. in Figure S4a, Supporting Information, was obtained by the difference Since we show that it is feasible to tame the magnetic between XAS spectra with negative and positive polarization before the background subtraction. STM was used to provide information on anisotropy of lanthanides by coordinative protocols, we the morphology of the metal–organic network as well as to calibrate the propose to grow such metal–organic architectures on non- coverage. conductive layers or ultra-thin film insulators as a paradigm to When comparing XNLD spectra with results found in the literature, stabilize the magnetic remanence by reducing the interaction it is necessary to take into account how the spectra were defined. with the substrate. In this quest, networks should be carefully Studniarek et al.[27] defined the XNLD as (μV − μH), which allows designed to allow enough internodal distances to prevent cou- a direct comparison with our spectra. On the other side, in the pling of lanthanide centers. work of Stoll et al.[10] it is defined as ( µ 25° − µ 90° ); considering that μθ = [cos (θ)]2 ·μV + [sin (θ)]2·μH (see supplementary note 6 of ref. [44]), this implies that ( µ 25° − µ 90° ) = 0.18 · ( µH − µV ) . As only the spectral shapes are being compared, not the intensities, the proportionality 4. Experimental Section factor is not relevant and it is only necessary to invert the spectra to have (μV − μH) and compare with our XLND results. After the inversion, our Experimental Methods: The Cu(111) substrate was prepared by cycles spectra have the same orientation as the Dy3+ ions in the dysprosium- of sputtering (Ar+, 800 eV) and annealing (723 K, 10 min). TDA and TPA tris(1,1,1-trifluoro-4-(2-thienyl)-2,4-butanedionate) (Dy(tta)3) complex molecules (purchased from Sigma-Aldrich) were deposited by organic on Au(111), where the symmetry axis of 4f orbitals is lying in-plane. molecular deposition from Knudsen cells (Kentax evaporator) on the As discussed in the main text, for our systems it is possible that clean Cu surface (see Figure S2, Supporting Information) heated to the symmetry axis is the same as the anisotropy quantization axis, 373 K. Next, Dy was deposited by e-beam evaporation from a metal rod presenting a tilted orientation close to the plane, but it is not possible to (Omicron 3-cell evaporator) with the substrate still maintained at 373 K. determine undoubtedly this orientation. The XNLD spectra only indicate Dy clusters were prepared by the deposition of an amount of Dy similar that the symmetry axis is closer to the surface plane. to the one used in the networks (≈0.01 monolayer) directly on the clean Expectation values of orbital 〈LZ〉 and effective spin 〈Szeff〉 = 〈Sz〉 + Cu surface at room temperature (300 K). All the experiments were carried 3〈Tz〉 moments in units of ћ were calculated using sum rules[30,31] with out in situ in UHV chambers with base pressures below 5 × 10−10 mbar. the quantum numbers c = 2 and l = 3, and the number of holes nH = STM experiments were done in two different systems. TPA networks 5 for Dy3+.[45] The spin moment 〈Sz〉 was separated from the dipole were measured with an Aarhus-150 VT-STM at room temperature. TDA Tz contribution 〈Tz〉 assuming the theoretical value = −0.053 for networks were analyzed in an Omicron LT-STM at 4 K. In both cases, Sz the images were taken using tungsten tips and measured in constant Dy . The total magnetic moment per atom was also calculated in μB, 3+ [46] current mode. dI/dV spectroscopy was acquired by stabilizing the tip, MT = 2〈Sz〉 + 〈Lz〉. The moment anisotropy of MT is defined in this work opening the feed-back loop, applying a Vbias ramp with a modulation of as the difference between the projections of the magnetic moments on 10 meV and recording the dI/dV signal with a lock-in amplifier. the incidence direction at grazing and normal incidences in a field of 6 T For the synchrotron experiments the samples were prepared with and a temperature of 6 K, ΔMT = MT (70°) − MT(0°). an excess of molecules to ensure that all Dy atoms are coordinated Theoretical Framework and Computational Details: Ab initio calculations with molecules and no magnetic signal is arising from Dy clusters for structural optimization and electronic structure properties have and/or uncoordinated single atoms. Such behavior was checked been carried out by DFT as implemented in the plane-wave QUANTUM Small 2021, 17, 2102753 2102753 (9 of 11) © 2021 The Authors. Small published by Wiley-VCH GmbH 16136829, 2021, 35, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/smll.202102753 by Readcube (Labtiva Inc.), Wiley Online Library on [15/12/2022]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License www.advancedsciencenews.com www.small-journal.com ESPRESSO simulation package.[47] One-electron wave-functions were No. EFA 194/16 TNSI); and “Severo Ochoa” Programme for Centres of expanded in a plane-waves basis with energy cutoffs of 500 and 600 eV Excellence in R&D (grants SEV-2016-0686, and SEV-2017-0706). for the kinetic energy and the electronic density, respectively. Exchange and correlation have been computed in the revised generalized gradient corrected approximation PBESol.[48,49] Kresse–Joubert projector augmented wave pseudopotentials[50] have been adopted to model the Conflict of Interest ion–electron interaction for all the involved atoms (H, C, O, Cu, and Dy) in order to include the SOC effect and a potential non-collinearity The authors declare no conflict of interest. of spins. Besides, 20 valence electrons have been accounted for the Dy atom in order to check the role of the lanthanide 4f10 electrons in the subtle interfacial chemistry. In all the calculations, Brillouin zones have been sampled using optimal Monkhorst–Pack grids (2 × 2 × 1) during Data Availability Statement structural relaxation and 4 × 4 × 1 for the electronic calculation).[51] A Research data are not shared. perturbative van der Waals (vdW) correction, with an empirical vdW R-6 correction, was used to add dispersive forces to conventional density functionals (DFT+D3).[52] Atomic relaxations were carried out using a conjugate gradient minimization scheme until the maximum force on Keywords any atom was lower than 0.02 eV Å−1. The Fermi level was smeared out using the Methfessel–Paxton approach[53] with a Gaussian width of lanthanides, magnetic anisotropy, metal–organic networks, single atom 0.01 eV, and all energies were extrapolated to T = 0 K. Self-consistency magnetism, X-ray magnetic circular dichroism in the electron density was converged to a precision in the total energy better than 10−6 eV. Received: May 11, 2021 Theoretical Fit of Magnetization Curves: The theoretical model uses a Revised: June 25, 2021 simple spin Hamiltonian with uniaxial zero-field splitting characterized   Published online: July 18, 2021 by the axial zero-field splitting parameter D: H = µ B g J B ⋅ J + DJ z2 , where we use J = 15/2 and the Landau g factor gJ = 4/3 for the nine 4f electrons of Dy3+. To simulate the field-dependent XMCD we neglect the dipole term of the magnetic moment, Tz, which is expected to be [1] S. V. Eliseeva, J. -C. G. Bünzli, New J. Chem. 2011, 35, 1165. small for Dy[46] and populate the eigenstates of H thermally according [2] J. -C. G. Bünzli, J. Coord. Chem. 2014, 67, 3706. to the temperature T. The quantization axis is oriented under a fixed [3] D. Écija, J. I. Urgel, A. P. Seitsonen, W. Auwärter, J. V. Barth, Acc. polar angle θ defined with respect to the surface normal. To account Chem. Res. 2018, 51, 365. for random azimuthal orientations of the structures on the surface, [4] F. Donati, S. Rusponi, S. Stepanow, C. Wäckerlin, A. Singha, we perform an azimuthal averaging over all orientations of the easy axis rotated around the surface normal for the same polar angle theta. L. Persichetti, R. Baltic, K. Diller, F. Patthey, E. Fernandes, J. Dreiser, Details of the procedure are described in reference [10]. Ž. Šljivančanin, K. Kummer, C. Nistor, P. Gambardella, H. Brune, Multiplet Calculations: The calculations have been done using the Science 2016, 352, 318. MultiX code,[36] for a Dy3+ ion with 3d104f9 ground state, a temperature [5] F. D. Natterer, K. Yang, W. Paul, P. Willke, T. Choi, T. Greber, of 6 K (as determined by the fitting of magnetization curves), and A. J. Heinrich, C. P. Lutz, Nature 2017, 543, 226. magnetic fields of 6 T for XMCD and 0.01 T for XNLD. The Hartree–Fock [6] F. Donati, A. Singha, S. Stepanow, C. Wäckerlin, J. Dreiser, parameters where rescaled by factors of 0.96 for the SOC and 0.80 for P. Gambardella, S. Rusponi, H. Brune, Phys. Rev. Lett. 2014, 113, the Coulomb interaction and a core–hole broadening of 0.5 eV was used 237201. to reproduce the experimental resolution. The CF was simulated using [7] J. D. Rinehart, J. R. Long, Chem. Sci. 2011, 2, 2078. point charges, that is, the coordinates and charges of the neighboring [8] T. Schuh, T. Miyamachi, S. Gerstl, M. Geilhufe, M. Hoffmann, atoms were used to simulate their interaction with Dy. S. Ostanin, W. Hergert, A. Ernst, W. Wulfhekel, Nano Lett. 2012, 12, 4805. [9] S. T. Liddle, J. van Slageren, Chem. Soc. Rev. 2015, 44, 6655. [10] P. Stoll, M. Bernien, D. Rolf, F. Nickel, Q. Xu, C. Hartmann, Supporting Information T. R. Umbach, J. Kopprasch, J. N. Ladenthin, E. Schierle, Supporting Information is available from the Wiley Online Library or E. Weschke, C. Czekelius, W. Kuch, K. J. Franke, Phys. Rev. B 2016, from the author. 94, 224426. [11] J. V. Barth, Annu. Rev. Phys. Chem. 2007, 58, 375. [12] L. Dong, Z. Gao, N. Lin, Prog. Surf. Sci. 2016, 91, 101. [13] B. Cirera, L. Dordevic, R. Otero, J. M. Gallego, D. Bonifazi, Acknowledgements R. Miranda, D. Ecija, Chem. Commun. 2016, 52, 11227. [14] J. I. Urgel, B. Cirera, Y. Wang, W. Auwärter, R. Otero, J. M. Gallego, The authors acknowledge Johannes V. Barth, Willi Auwärter and Koen M. Alcamí, S. Klyatskaya, M. Ruben, F. Martín, R. Miranda, D. Ecija, Lauwaet for fruitful discussions. The ALBA synchrotron is acknowledged J. V. Barth, Small 2015, 11, 6358. for providing beam time at BOREAS beamline (proposal number [15] J. I. Urgel, D. Ecija, W. Auwärter, D. Stassen, D. Bonifazi, J. V. Barth, 2015091454). This project has received funding from the European Research Council (ERC, grant 766555) and Marie Sklodowska-Curie Angew. Chem., Int. Ed. 2015, 54, 6163. Actions (MSCA, project 894924) under the European Union’s Horizon [16] D. Écija, J. I. Urgel, A. C. Papageorgiou, S. Joshi, W. Auwärter, 2020 research and innovation programme. This work has been financed A. P. Seitsonen, S. Klyatskaya, M. Ruben, S. Fischer, by the Spanish Ministerio de Economía, Industria y Competitividad S. Vijayaraghavan, J. Reichert, J. V. Barth, Proc. Natl. Acad. Sci. U. S. (projects FIS2016-78591-C3-1-R, RTI2018-097895-B-C42, MAT2016- A. 2013, 110, 6678. 78293-C6-2-R, MAT2017-85089-C2-1-R, and PID2019-107338RB-C65); the [17] J. I. Urgel, D. Écija, G. Lyu, R. Zhang, C. -A. Palma, W. Auwärter, Comunidad de Madrid (Projects S2013/MIT-2850, P2018/NMT4321, and N. Lin, J. V. Barth, Nat. Chem. 2016, 8, 657. S2018/NMT-4367); the European Regional Development Fund (ERDF) [18] G. Lyu, Q. Zhang, J. I. Urgel, G. Kuang, W. Auwärter, D. Ecija, under the program Interreg V-A España-Francia-Andorra (Contract J. V. Barth, N. Lin, Chem. Commun. 2016, 52, 1618. Small 2021, 17, 2102753 2102753 (10 of 11) © 2021 The Authors. 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