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Atomic-scale spin sensing with a single molecule at the apex of a scanning tunneling microscope

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Science  01 Nov 2019:
Vol. 366, Issue 6465, pp. 623-627
DOI: 10.1126/science.aax8222

Single molecules sense spin

Imaging surface magnetism, and, in particular, spin excitations of adsorbed molecules or films, is challenging. Verlhac et al. demonstrate spin-sensing capability by using the magnetic exchange interaction between a surface sample and the spin-excited states of a nickelocene molecule attached to a scanning tunneling microscope tip. The spatial dependence of the exchange field at the atomic scale enabled imaging of magnetic corrugation with atomic-scale lateral resolution for iron atoms and small islands of cobalt atoms absorbed on nonmagnetic copper surfaces.

Science, this issue p. 623

Abstract

Recent advances in scanning probe techniques rely on the chemical functionalization of the probe-tip termination by a single molecule. The success of this approach opens the prospect of introducing spin sensitivity through functionalization by a magnetic molecule. We used a nickelocene-terminated tip (Nc-tip), which offered the possibility of producing spin excitations on the tip apex of a scanning tunneling microscope (STM). When the Nc-tip was 100 picometers away from point contact with a surface-supported object, magnetic effects could be probed through changes in the spin excitation spectrum of nickelocene. We used this detection scheme to simultaneously determine the exchange field and the spin polarization of iron atoms and cobalt films on a copper surface with atomic-scale resolution.

In conventional scanning tunneling microscopy (STM), the magnetic ground state of an isolated atom or molecule is inferred by collecting spin-related fingerprints in the conductance measured with a metallic tip. Isolated atoms or molecules can also serve as spin detectors when controllably moved on the surface with the help of the tip within their local magnetic environment. The magnetic ground state can change in the presence of a magnetic coupling. Exchange- and surface-mediated Ruderman–Kittel–Kasuya–Yosida interactions have been spatially mapped in this way by monitoring the zero-bias peak in the differential conductance (dI/dV) associated with the Kondo effect (14), tunneling magnetoresistance (57), and spin excitation spectra and spin relaxation times (812). Recently, dipolar and hyperfine interactions have also been observed through electrically driven spin resonances (13, 14).

A well-calibrated sensor attached to the tip apex would allow the tip to be freely positioned above a surface target. This detection scheme eliminates surface-mediated interactions and benefits from the vertical-displacement sensitivity of the STM as the sensor-target distance is no longer imposed by the surface corrugation. Probing a magnetic exchange interaction across a vacuum gap is experimentally demanding (1521) because scanning probe techniques suffer from poor structural and magnetic characterization of the tip apex. To overcome these limitations, we introduced spin sensitivity by functionalizing the tip apex with a single magnetic molecule. Such a strategy has proven successful for collecting chemical and structural information on surface-supported atoms and molecules otherwise inaccessible with a metallic tip (2227). We used a tip decorated by a spin S = 1 nickelocene molecule (Fig. 1A) (28, 29), which comprises an Ni atom sandwiched between two C5H5 cyclopentadienyl (Cp) rings and we accurately capture the junction geometry by comparison with first-principles calculations.

Fig. 1 Spin excitation spectra above the Cu surface and a single Fe atom.

(A) Schematic view of the tunnel junction. Atom colors: Cu, orange; C, gray; H, white; Ni, green; Fe, red. (B) d2I/dV2 spectra acquired above a surface atom of Cu(100) at a distance between z = 133 and z = 80 pm. The solid red line is a fit based on a dynamical scattering model (12) and yielded an axial magnetic anisotropy of D = 3.5 meV, a coupling between the localized Nc spin and the tip electrons of J0ρ0 = –0.08, and a spin-conserving potential scattering of U = 0.02. Inset: Image of Nc on Cu(100) acquired with a copper-coated tip apex (V = 20 mV, I = 100 pA, size: 2 nm by 22nm). (C) Image of Fe atoms on Cu(100) (V = –15 mV, I = 30 pA, size: 5 nm by 5 nm) and corresponding line profile of one atom (inset) revealing the presence of a tilted Nc at the tip apex. The tilt angle θ was estimated through the height difference between the left and right protrusion of the line profile. (D) d2I/dV2 spectra acquired with the tip positioned above the high-intensity side of the ring-shaped Fe atom. Tip distances z < 80 pm resulted in the transfer of Nc atop the Fe atom (figs. S1B and S1C). (E) Peak and dip energy positions extracted from the spectra of (D). The color scale flanking the panel corresponds to the d2I/dV2 amplitudes and is given in units of G0/V. For clarity, the spectra in (B) and (D) were shifted vertically from one another by 5 × G0/V, where G0 = 2e2/h, the quantum of conductance.

We prepared the nickelocene-terminated tip (Nc-tip) with atomic control. We first performed soft tip–surface indentations into our pristine working surfaces, either Cu(100) or Cu(111) (30), to ensure a monoatomically sharp Cu apex. Nickelocene was then imaged as a ring (inset in Fig. 1B); the molecule adsorbed on copper with one Cp bound to the surface and the other exposed to vacuum (31). After transferring the Nc molecule from the surface to the tip [details of the molecule transfer to the tip can be found in (29)], the Nc-tip was characterized by spectral features found in the second derivative, d2I/dV2, of the current I with respect to the bias V measured at a set of constant distances z between tip and the pristine Cu(100) surface (Fig. 1B). We calibrated z by performing controlled tip contacts to the surface tracking the current I and defining z = 0 as the distance where the transition from the tunneling to contact regime occurs [see fig. S1 and accompanying discussion in the supplementary materials (30)].

The spectra varied with z only in amplitude and were dominated by a peak at positive V and a dip at negative V at energies symmetric to zero. These peaks and dips correspond to inelastic tunneling events in which tunneling electrons excite the Nc from its magnetic ground state M = 0, with M as the magnetic quantum number projected onto the axis perpendicular to the rings of the molecule, to one of the two degenerate excited states M = ±1. These states are at a higher energy D = 3.5 ± 0.1 meV relative to the ground state (28), where D is the axial magnetic anisotropy (Eq. 2). The inelastic conductance was nearly one order of magnitude greater than the elastic conductance [see fig. S2 and accompanying discussion in the supplementary materials (30)], highlighting that the spin of Nc was well preserved from scattering events with itinerant electrons of the metal (28, 32). This response is notable, differentiating Nc from other single atoms or molecules, which instead require a thin, insulating spacer between them and the metal surface (8, 33, 34) or a superconductor (35) to preserve their quantum nature.

We used the Nc-tip to probe surface magnetism through changes in the spin excitation spectrum. We initially probed a single magnetic Fe atom adsorbed on Cu(100) (Fig. 1A). Iron atoms on the surface (30) protruded by 115 pm and were imaged with the Nc-tip as rings with an asymmetric apparent height (Fig. 1C). The structure observed in the image reflected the presence of Nc on the tip apex and resulted from the tilted adsorption geometry of the molecule. Indeed, density functional theory (DFT) calculations showed that Nc bonded to the tip-apex atom through two C atoms of the Cp ring (29). The tilt angle was estimated through the line profile of the Fe atom (inset of Fig. 1C), which revealed that the tips used were typically at angles ~<15° relative to the surface normal.

A set of d2I/dV2 spectra recorded at different z heights above the Fe atom (Fig. 1D) showed that, at z = 133 pm, the spectrum was indistinguishable from the one acquired above the bare Cu(100) (Fig. 1B). In this low-energy range, Fe was spectroscopically dark, i.e., its contribution to the spin excitation spectrum was negligible, due to the strong screening and broadening effects (7). However, for smaller z heights, we observed a splitting of the peak and the dip that became increasingly stronger as z decreased (Fig. 1E). The average position of the spin-split peaks and dips varied at most by 0.2 meV with distance (dashed line in Fig. 1E).

We tested several Nc-tips with tilt angles ranging from 5° to 15°, and all showed similar behavior—the distances for a given splitting changed only by ±10 pm. Apart from the splitting, we also observed a marked intensity asymmetry of the split spectral features. Although the amplitudes of the positive peak and negative dip were identical for the Nc-tip probed against the bare surface (Fig. 1B), at positive bias, the energetically lower excitation had higher peak amplitude than the energetically higher excitation, whereas at negative bias, the dips showed opposite behavior compared with the peaks.

The splitting and asymmetry of the line shape observed above Fe have a magnetic origin. To rationalize these observations, we assigned the z-axis as the out-of-surface direction neglecting the small tilt of the molecule and used a spin Hamiltonian that includes the magnetic anisotropy of the Nc molecule and of the Fe atom on copper (DFe) (7, 36):H=DS^z2+DFeS^z,Fe2JS^zS^z,Fe(1)where J is an Ising-like exchange coupling restraining the Nc-Fe magnetic interaction along the z-axis [see fig. S3 and accompanying discussion in the supplementary materials (30)]. Within this framework, the ground state of the combined system is a doublet G = 0,⇑ and 0,⇓, where the energetically lowest states of the Fe spin are noted as ⇑ and ⇓. The exchange interaction lifts the degeneracy between the two excited doublets AP (antiparallel) and P (parallel) of the coupled spin system and causes the line shape to split apart. As the exchange interaction is antiferromagnetic (J < 0, see below) and the Fe is spectroscopically dark, the lowest excited-state doublet is AP = –1,⇑ and +1,⇓ and corresponds to an antiferromagnetic configuration where the Fe spin is anti-aligned with the Nc spin. The higher excited-state doublet corresponds to the ferromagnetic configuration, P = +1,⇑ and –1,⇓. Note that for this derivation, neither the spin magnitude of the Fe atom nor the sign of DFe has to be explicitly set so long as the ground state is a doublet.

To simplify the discussion, it is preferable to express the spin Hamiltonian of Eq. 1 with an effective Zeeman term consisting of the gyromagnetic factor (g), the Bohr magnetron (μB), and the exchange field (B) produced by the Fe atom and acting along the z-axis of the Nc molecule:H^=DS^z2gμBBS^z(2)This expression has the advantage of providing a common framework for describing the spin systems investigated in the present study. Within mean-field theory, B = JSFe〉/gμB, where 〈SFe〉 is the effective spin of Fe on the Cu(100) surface. In the following, for clarity, we restrain the analysis to a ⇓ Fe spin without loss of generality [see fig. S4 and accompanying discussion in the supplementary materials (30)]. Within this viewpoint, the exchange field causes a Zeeman splitting of the line shape into the two excited states +1 and –1 of Nc that are located at low and high energy, respectively. The bias asymmetry in the peaks and dips reflects instead a spin imbalance in the tunneling current (10, 21, 3739). This mechanism is illustrated in Fig. 2, A and B, and is qualitatively similar to conventional spin-polarized STM (5) and, more generally, to spin valves or to Kondo systems coupled to magnetic electrodes (4, 19, 40, 41).

Fig. 2 Inelastic tunneling and magnetic coupling measured above an Fe atom.

(A) and (B) show the mechanism leading to the bias asymmetry in the d2I/dV2 spectra acquired above Fe. (A) At negative bias, inelastic electrons tunneled from the spin-up states of the Fe atom to the spin-down states of the Nc-tip with transmission proportional to T, leading to a dip in the d2I/dV2 spectrum. At positive bias, the junction polarity was reversed and inelastic electrons tunneled from the spin-up states of the Nc-tip to the spin-down states of the Fe atom with transmission proportional to T, leading to a peak in the d2I/dV2 spectrum. During the tunneling process, the electrons excited Nc from its ground to its first excited state. The weaker amplitude for the dip compared with the peak reflects the difference in the transmission (TT). (B) Same mechanism as (A) but for inelastic tunnel electrons exciting Nc from its ground state to its second excited state. (C) Exchange field B and (D) spin-asymmetry η extracted from the spectra of Fig. 1D using Eq. 2. (E) DFT-calculated configuration of the tunnel junction for a distance of 100 pm with isosurface of the spin density (antiferromagnetic coupling).

As illustrated in Fig. 2A, the excitation of Nc from the ground state to its first excited state +1 requires a change in spin angular momentum of δM = +1. Because the total angular momentum must be conserved, it can only be induced by electrons that compensated for this moment by flipping their spin direction during the tunneling process from ↑ to ↓. At negative bias, the tunneling process may be viewed as a ↑ electron hopping from the substrate into the molecular orbital with transmission T, whereas a ↓ electron is emitted from the molecular orbital toward the tip. At positive bias, the tunneling direction reverses and the transmission from tip to sample is T. The relative height of the dip at low negative voltage (h) compared with the peak at low positive voltage (h+) yields a quantitative measure of the spin asymmetry η = (h+h)/(h+ + h), with h ∝ T and h+ ∝ T. The excitation of Nc from the ground state to its second excited state –1 requires instead electrons starting in a ↓ state and ending in a ↑ state (Fig. 2B), resulting in a spin asymmetry of –η.

The spin-polarized nature of the transmission reflects a delicate balance between the spin dependence of the Nc-Fe hybridization and of the density of states (DOS) of both tip and substrate. Neglecting the small tilt angle of Nc relative to the quantization axis z, the Nc-tip DOS is instead unpolarized as the M = 0 ground state of Nc leads to a projected moment 〈mz〉 = 0. As a consequence, the spin polarization of the transmission reflects the polarization of the DOS of the substrate weighted by the spin-dependent Fe hybridization with the π orbitals of Nc [see fig. S6 and accompanying discussion in the supplementary materials (30)].

The fit to the line shape using Eq. 2 and a dynamical scattering model (solid red lines in Fig. 1D) (10, 12) was highly satisfactory and provided quantitative values of the spin-asymmetry η and the exchange-field B exerted by the Fe atom onto the Nc molecule assuming a gyromagnetic factor of g = 1.89 (42). The exchange field was an exponential function of z (Fig. 2C), allowing us to exclude a magnetic dipolar interaction. Assuming an exponential decay of the form exp – z/λ, we found a decay length λ = 34 ± 2 pm, consistent with other tip-induced exchange interactions (17, 18, 21, 42). Different Nc-tips showed similar decay constants [see fig. S5 in the supplementary materials (30)]. Using our DFT-computed effective spin of 〈SFe〉 ≈ 1.7, the exchange coupling was |J| ≈ 0.9 meV at the shortest probed Fe-Nc distances, typical for a tip-adsorbate exchange interaction across a vacuum gap (19, 20). Details regarding the DFT calculations can be found in the supplementary materials (30). The magnetic anisotropy D, which corresponds to the average position of the spin-split peaks and dips, remained constant with z (Fig. 1E). This result indicated that the intramolecular structure of Nc was preserved on the tip apex (28, 43).

For the data presented in Fig. 1D, we found a spin asymmetry of η = 32% at the highest fields measured (Fig. 2D). The data collected on an ensemble of different Nc-tips on different Fe atoms yielded a lower average value of η = 23% [see fig. S5 in the supplementary materials (30)]. The observed spin asymmetry is in agreement with the spin polarization found for electrons inelastically tunneling between an Fe-terminated tip and the quantized states of single adsorbates (18, 21).

The sign of the exchange interaction between a magnetic atom and a magnetic tip apex is determined by the competition of direct and indirect interactions and may vary with tip-to-atom distance (44). To gain insight into the exchange coupling between the Nc-tip and Fe atom, we computed with DFT the exchange energy defined as Eex = EPEAP at various Nc-Fe distances by fully relaxing the junction geometry; EP (EAP) is the total energy of the junction with the spin directions of Nc and Fe in parallel (antiparallel) alignment. To facilitate the comparison with the experimental findings, we took z = 0 as the center-to-center distance between the closest carbon atom of Nc and the Fe atom, which is ~250 pm. The exchange interaction favored an antiparallel alignment of the two spins (Fig. 2E)—the junction geometry remained constant up to 50 pm, at which distance a chemical bond started to form between Fe and Nc [see fig. S1 in the supplementary materials (30)]. The energy difference between antiparallel and parallel alignment is 13 meV at 120 pm, whereas no difference could be evidenced above 300 pm. The antiferromagnetic coupling was short ranged and attributed to the direct hybridization of the Fe orbitals with the frontier molecular orbitals of Nc.

We extended the proof of concept for the Nc-tip to a collection of atoms by investigating a prototypical ferromagnetic surface consisting of a nanoscale Co island grown on Cu(111) (Fig. 3A) (4548). The islands are triangular-like and two layers high with typical lateral extensions ≥10 nm for the Co coverage used (30). They possess at low temperature an out-of-plane magnetization perpendicular to the Cu surface (inset of Fig. 3A) (46, 49, 50). Unlike the Fe atom, the Co spin is fixed and we assume it to be ⇑ without loss of generality. We found that Nc adsorbed preferentially on Co, either on top of the nanoislands or on the bottom edge of the island as described for other molecules (51). Nc-tips were routinely prepared by transferring a molecule from the edge of the island to the Cu-tip apex. Given the low molecular coverage, large pristine areas of Co could be found on the sample.

Fig. 3 Spin excitation spectra above a cobalt surface.

(A) Cobalt island on Cu(111) decorated with Nc molecules (V = –50 mV, I = 20 pA, size: 25 nm by 25 nm). The white lines highlight the presence of Nc. The white square corresponds to the area investigated in (B) and (F). Inset: Schematic view of an Nc-tip above a cobalt island. The arrow indicates the out-of-plane magnetization of the island. Atom colors: Co, gray; Cu, orange. (B) Constant-height image acquired in the center of the island at z = 80 pm with V = –1 mV (size: 1 nm by 1 nm). The color scale indicates the value of the tunnel current and the corresponding B, which is estimated using the exchange coupling of the two spectra in (E). (C) d2I/dV2 spectra acquired with the tip positioned above a Co atom of the island. The tip was moved from z = 150 pm to z = 70 pm. For clarity, the spectra are displaced vertically from one another by 5 × 10–3 G0/mV. The solid red line is a fit based on a dynamical scattering model. Unlike the fits of Fig. 1D, to correctly capture the line shape, we allowed the tunneling electrons to produce out-of-equilibrium state populations (10) in Nc by solving the dynamical rate equations of the tunneling process (12). (D) Exchange field B extracted from the spectra of (C) using Eq. 2. (E) d2I/dV2 spectra acquired at z = 80 pm above a top site [red dot in (B)] and above a hollow site [blue dot in (B)]. (F) Ratio between the tunnel current above a top site and the tunnel current above a hollow site. (G) Constant-height image of the same area in (B) also acquired at z = 80 pm, but with lower tunnel bias (–5 mV).

In Fig. 3B, we present a typical constant-height image acquired in a small area located in the center of a Co island (white square in Fig. 3A) at a bias V = –1 mV, which is very close to the Fermi energy. The Co atoms of the island can be readily visualized with the Nc-tip, whereas this resolution is lost above nonmagnetic Cu(111) [see fig. S7A in the supplementary materials (30)]. This difference points to the magnetic origin of the contrast. At z = 150 pm above the Co surface, the spin excitation spectrum (Fig. 3C) was similar to the spectra of Fig. 1B, which indicated that the island was spectroscopically dark. However, upon vertically approaching a Co atom in the cobalt island, the peak and dip in the d2I/dV2 spectrum progressively split apart. Using the spin Hamiltonian of Eq. 2 and g = 1.89, we found that the exchange field varied exponentially and reached values as high as 26 T at the shortest distances explored (z = 70 pm; Fig. 3D). The decay length was λ = 50 ± 5 pm. Consistent with the exponential decay of the exchange field, we found that the image corrugation increased when decreasing z [see fig. S7B in the supplementary materials (30)].

The exchange field originates mostly by direct orbital overlap and corresponds to an exchange coupling of |J| ≈ 3.2 meV taking our DFT-computed value of 〈SCo〉 ≈ 0.9 for the effective spin of a Co atom. The spectra showed weak spin asymmetry (η = 5 to 15%) and changed in sign at the island rim [see fig. S8 in the supplementary materials (30)], in agreement with spin-polarized STM measurements (46, 47, 5052). The spin polarization found is lower compared with STM measurements carried out with a superconducting tip (53), suggesting a π-orbital influence on the transmission T, as evidenced in other molecular tips (54, 55).

To clarify the observed atomic resolution in the constant-height images taken at bias voltages near the Fermi energy, we compare in Fig. 3E two spectra, one with the Nc-tip positioned above a Co atom (designated hereafter as a top site of the surface; red dot in Fig. 3B) and the other with the Nc-tip above a hollow site of the surface (blue dot in Fig. 3B). As shown in the figure, the exchange field varied among the two sites and with it the position of the low-energy excitation peak and dip. These moved toward zero bias when the exchange field increased, shifting instead toward e|V| = D when the exchange field decreased.

The shift of the low-energy peak (dip) translated into a variation of the tunneling current I by working at biases sufficiently low. In particular, at |V| = 1 mV and z = 80 pm, inelastic excitation to the first excited state was possible only when the Nc-tip was placed above the top site; above the hollow site, this channel was closed. The ratio of Itop/Ihollow ≈ 3 (Fig. 3F) produced a contrast in the constant-height image. At increased absolute bias (|V| > 5 mV), Itop/Ihollow was reduced to 1.25, which led to a loss of contrast in the constant-height image (Fig. 3G). At first approximation, the low-bias image shown in Fig. 3B reflected the spatial dependence of the exchange field at the atomic scale [for completeness, fig. S7, C and D, in the supplementary materials (30) presents a low-bias constant-current image]. Alternatively, it could also be possible to plot the exchange field from the spectra as a function of position at the expense of considerably increasing the acquisition time of the image.

To confirm the magnetic origin of the contrast, we computed with DFT the exchange energy Eex = EPEAP by varying the distance between the Nc-tip and the Co surface (surface spin density is presented in Fig. 4A). Three locations were investigated, corresponding to an Nc-tip laterally positioned above the surface with its Ni atom centered above a top, hollow, or bridge site of the surface (inset of Fig. 4B). Just before the contact formation between Nc and the surface, which is the distance interval explored in the experiment, the exchange energy was markedly different between these sites (Fig. 4B) because the local character of the d electrons starts imprinting a lateral corrugation to the interaction. The exchange field can then be expected to change when moving the Nc-tip above the surface, in qualitative agreement with our experimental findings of Fig. 3B. We stress that for a quantitative comparison, which is beyond the scope of the present study, the noncollinearity among magnetic moments of Co and Nc should be taken into account.

Fig. 4 Computed exchange interaction between Nc and Co.

(A) Isosurface of the spin density for a Co bilayer. Spin-down (↓) and spin-up (↑) densities are plotted in red (–0.003 Å–3) and blue (+0.003 Å–3), respectively. The unit cell is indicated by a black line and Co atoms are in gray. Spin-up d electrons are mainly located on the Co atoms, whereas spin-down sp electrons are dispersive in nature (45, 47, 50). The Co atoms had a magnetic moment of 1.76 μB, which was mainly carried by the d orbitals (d: 1.81 μB, p: –0.04 μB, s: –0.01 μB). The spatial confinement of sp electrons within the island (45, 47, 50) was not accounted for. (B) Difference in exchange energy (|ΔEex|) between the top and the hollow positions (red) and between the top and bridge positions (black). The energy difference was computed as a function of tip distance to the Co surface. The filled red area indicates the contact regime where the Nc molecule is covalently bond to the surface. Inset: Junction geometry used in the DFT calculations defining the top, hollow, and bridge site. Atom colors: Co, gray; Cu, orange. Experimentally, the difference in exchange energy between the top and hollow sites is 2 meV when z = 80 pm (see peak/dip splittings in Fig. 3E).

The spin excitation spectrum of an Nc molecule attached to the apex of an STM tip can be used to probe the magnetism of an adsorbate and of a surface with atomic-scale resolution. Magnetic information is gathered through the simultaneous measurement of the exchange field across the vacuum gap, as in pioneering magnetic exchange-force microscopy experiments (15, 56), and of the sample spin polarization at the Fermi level. Unlike conventional spin-polarized STM, the sample spin polarization is determined with minimal influence of the probe on the system owing to the well-characterized Nc-tip apex. A large variety of magnetic systems can be investigated, ranging from systems having resolvable magnetic quantum states (28, 42) to systems having a magnetic moment but nonresolvable quantum states (as shown here). The latter could include single atoms and organometallic molecules on magnetic surfaces or surfaces with complex magnetic structures. The visualization of complex spin textures should benefit from an external magnetic field, making it possible to experimentally determine the sign of the magnetic exchange interaction (20, 42). Minor drawbacks of the technique are the tip-related patterns in the images, which can be corrected given tip-status knowledge, and the possible back action by the Nc-tip on the sample.

Supplementary Materials

science.sciencemag.org/content/366/6465/623/suppl/DC1

Materials and Methods

Supplementary Text

Figs. S1 to S8

References (5767)

References and Notes

  1. See supplementary materials for more details.
Acknowledgments: Funding: L.L. acknowledges support by the Agence Nationale de la Recherche (grant nos. ANR-13-BS10-0016, ANR-15-CE09-0017, ANR-11-LABX-0058 NIE, and ANR-10-LABX-0026 CSC). M.T. acknowledges support by the Heisenberg Program (grant no. TE 833/2-1) of the German Research Foundation. N.L. acknowledges support by the Spanish MICINN (grant no. RTI2018-097895-B-C44). N.L. and R.R. acknowledge support by the EU H2020 FET open project MeMo (grant no. 766864). L.L. acknowledges F. Scheurer and V. Speisser for technical assistance. We have used VESTA to plot geometrical structures and isosurfaces (https://jp-minerals.org/vesta/en/download.html). Author contributions: Experiments were performed by B.V., N.B., L.G., M.O., and L.L. and calculations were performed by P.A., R.R., M.-L.B., M.T., and N.L. Competing interests: The authors declare no competing financial interests. Data and materials availability: All data are available in the main text or the supplementary materials.
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