Single molecule magnets and single spin centres can be individually addressed when coupled to contacts forming an electrical junction. To control and engineer the magnetism of quantum devices, it is necessary to quantify how the structural and chemical environment of the junction affects the spin centre. Metrics such as coordination number or symmetry provide a simple method to quantify the local environment, but neglect the many-body interactions of an impurity spin coupled to contacts. Here, we utilize a highly corrugated hexagonal boron nitride monolayer to mediate the coupling between a cobalt spin in CoHx (x=1,2) complexes and the metal contact. While hydrogen controls the total effective spin, the corrugation smoothly tunes the Kondo exchange interaction between the spin and the underlying metal. Using scanning tunnelling microscopy and spectroscopy together with numerical simulations, we quantitatively demonstrate how the Kondo exchange interaction mimics chemical tailoring and changes the magnetic anisotropy.
Magnetic anisotropy defines the stability of a spin in a preferred direction1,2,3. For adatoms on surfaces, the low coordination number and changes in hybridization can lead to dramatic enhancement of magnetic anisotropy2,3,4,5. Surface adsorption site and the presence of hydrogen has been shown to alter the magnetic anisotropy of adatoms on bare and graphene covered Pt(111)6,7,8. Furthermore, the exchange interaction and strain has been invoked for 3d adatoms on Cu2N islands where the adatom position on the island affects the observed magnetic anisotropy9,10. Studies on single molecule magnets (SMMs) containing 3d or 4f spin centres have revealed that chemical changes to the ligands surrounding the spin affect the magnetic anisotropy11,12,13. However, the most important factor for maintaining magnetic anisotropy in SMMs is a low coordination environment and a high axial symmetry3,14,15.
Magnetic anisotropy is not guaranteed in SMMs or single spin centres on coupling to contacts9,16. The spin interacts with the electron bath through the exchange interaction leading to a finite state lifetime and the decay of quantum coherence17,18. Additionally, the scattering of the spin with the electron bath results in an energy renormalization of the spin’s eigenstate energy levels, similar to the case of a damped harmonic oscillator17. In practice, this leads to a net reduction of the magnetic anisotropy, pushing the system closer to a Kondo state. At the heart of the Kondo effect are spin-flip scattering processes between localized states at the impurity spin and delocalized states in the bulk conduction band, resulting in the formation of a correlated quantum state19. The Kondo regime is reached when the magnetic moment of the impurity spin is screened by the electron bath, with the exchange interaction defining the relevant energy scale, the Kondo temperature (TK). High-spin systems with a total spin S>½ have the potential for both magnetic anisotropy and the Kondo effect20,21. Thus, the Kondo exchange interaction with the electron bath can force the impurity spin into a competing Kondo state, where antiferromagnetic coupling with the reservoir reduces or even quenches the magnetic moment. The outcome of this competition can be determined in local transport measurements, but few quantitative measures of this competition exist.
Here, we study CoHx complexes coupled to a spatially varying template, the hexagonal boron nitride (h-BN) moiré on Rh(111), to observe, model and quantify how the environment influences magnetic anisotropy. The h-BN monolayer, a wide bandgap two-dimensional material, decouples and mediates the interactions between CoHx and the underlying Rh metal while lattice mismatch leads to a spatial corrugation resulting in an enlarged unit cell with 3.2 nm periodicity corresponding to 13 BN units on top of 12 Rh atoms22,23. The local adsorption configuration of CoHx on the h-BN is conserved across the moiré unit cell, with the large number of inequivalent adsorption sites allowing us to explore how hybridization affects magnetic anisotropy. To complement our experimental observations, we model transport through the CoHx complexes using Hamiltonians that incorporate magnetic anisotropy as well as coupling to the environment. This is accomplished by parameterizing the environment through use of a dimensionless coupling constant −Jρ0, describing the strength of the Kondo exchange interaction, −J, between the localized spin and the electron density ρ0 of the substrate near the Fermi level.
STM topography and local spectroscopy
Figure 1a shows a representative scanning tunnelling microscopy (STM) topograph of the h-BN/Rh(111) moiré with isolated CoHx (x=1,2) complexes, line profiles across the h-BN indicate CoHx can adsorb at multiple positions within the moiré (Fig. 1b)24. On these CoHx complexes we measure the differential conductance (dI/dV) against the applied bias voltage V between tip and sample at low-temperature (T=1.4 K) and zero magnetic field (B=0 T, details see Methods section). The spectra can be divided into two broad classes: a sharp peak centred at zero bias or two symmetric steps of increasing conductance at well-defined threshold energies (Fig. 1d). The peak at zero bias is consistent with a spin-½ Kondo resonance while the steps correspond to the onset of inelastic excitations from the magnetic ground state to excited states. The observation of two steps hints at a spin-1 system with zero field splitting. The two lower spectra (Fig. 1d; red and blue curves) are measured on CoH at different parts of the moiré and share the same characteristics but the step positions vary.
Adsorption site and magnetic moments by DFT
We employ density functional theory (DFT) to correlate the magnetic properties of CoHx with the local adsorption configuration. Our calculations (see Methods section, Supplementary Fig. 1 and Supplementary Note 1) show that adsorption in the BN hexagon, that is, hollow site, is preferable for bare Co. The addition of hydrogen shifts the preferred adsorption site to N, with the hollow site adsorption energy consistently higher. For CoH complexes the preferred hydrogen position was found to be either exactly on top of Co or tilted towards the nearest B atom (Fig. 2a). An important consequence of the N adsorption site is the linear crystal field acting on the cobalt (that is, N–Co–H) removing the fivefold degeneracy of the d-levels (Fig. 2b).
In Fig. 2c the spin-resolved, symmetry decomposed local density of states of CoH and CoH2 adsorbed in the h-BN valley are plotted. The atomic d-levels are exchange-split roughly 1.2 eV due to the intrinsic Stoner exchange giving a bare Co adatom a magnetic moment of 2.2 Bohr magnetons (μB). Formation of CoH leads to hybridization of the H sp orbitals and the Co orbitals, slightly reducing the magnetic moment to 2.0 μB, equivalent to a 3d8 configuration (Fig. 2b). The second hydrogen changes the picture significantly, with the sp-d hybridization sufficient to bring the Co d-levels closer together, reducing the magnetic moment to 1.2 μB resulting in a 3d9 configuration. Addition of a third hydrogen results in a complete quenching of the magnetic moment. Therefore, from the combination of our spectroscopic observations and DFT calculations we identify CoH as an effective spin-1 and CoH2 as spin-½ system.
Figure 2d,e shows the spin density distribution for CoH in a N adsorption configuration at two high-symmetry points of the moiré. The strong vertical bond between Co and N leads to an effective spin-polarization along this axis and can be expected to provide the system with out-of-plane magnetic anisotropy. The hydrogen is not rigidly pinned to the cobalt and tilting of the hydrogen combined with the underlying lattice mismatch reduces the C3v symmetry and introduces small shifts in the dxz, dyz levels producing a non-negligible in-plane component of the anisotropy.
Local spectroscopy in magnetic fields
To model the experimentally observed tunnelling spectra and to determine the magnetic anisotropy we use a phenomenological spin Hamiltonian including the Zeeman energy and magnetic anisotropy:
with g as the gyromagnetic factor, the magnetic field, the total spin operator, and D and E as the axial and transverse magnetic anisotropy9,10,25,26,27. Transport through the junction is calculated using a Kondo-like interaction between the tunnelling electrons and the localized spin system, with as the standard Pauli matrices. We account for scattering up to third order in the matrix elements by considering additional exchange processes between the localized spin and substrate electrons of the form28,29 (Supplementary Fig. 2, Supplementary Note 2):
to confirm the magnetic origin of the spectroscopic features in CoH and CoH2, we measure the differential conductance at magnetic fields up to 14 T normal to the surface. Figure 3c shows experimental spectra taken over one CoH2 complex and Fig. 3d the model calculations for the Kondo resonance. Applying an external magnetic field introduces Zeeman splitting to the spin–½ system (Fig. 3a). At low magnetic fields, 2.5 T, the peak broadens and the differential conductance of the resonance is reduced. Increasing the field to 5 T, a clear splitting of the Kondo resonance is observed. For the highest fields, the degeneracy of the spin-½ state is effectively lifted, resulting in a strong reduction of the Kondo resonance and the appearance of an inelastic excitation gap. We can reproduce the peak and its splitting by our perturbative model (Fig. 3d) even though at high fields the peak-like conductance is weaker in the experimental data than expected from the model calculation. This indicates that the Kondo temperature of the system lies close to the base temperature of our experiment29.
Increasing the external magnetic field has two effects on the spin-1 CoH; Zeeman splitting separates the steps and the ratio between inner and outer conductance step height decreases (Fig. 3g). At zero field, the ground and first excited states are a superposition of mz= |+1〉 and |−1〉 states, applying a magnetic field reduces the spin mixing and leads towards a |+1〉 ground and |−1〉 excited state. This accounts for the reduction of the inner step with increased magnetic field, as the transition between ground and first excited state becomes less probable because it would require a change in mz of two. Reverting to a purely second order simulation, large deviations are observed at both steps, evidence that coupling of the spin to the substrate conduction electron bath must be considered (Fig. 3h, dashed line). The experimental data fits excellently when including third order terms, that is, assuming a finite −Jρ0, an out-of-plane anisotropy axis and g=2.2±0.2.
Correlation between coupling and magnetic anisotropy
Evaluation of >30 CoH complexes (Fig. 4a) shows no sharp distribution of the anisotropy parameters D and E. A transition of the main anisotropy axis into the surface plane occurs when 3E>|D|, therefore we have only considered complexes with a clear out-of-plane anisotropy determined by the criterion (|D|)/(3E)>1.5; a representative spectrum with in-plane anisotropy is shown in Supplementary Fig. 3. By considering the values of −Jρ0 from our fits, we observe a correlation between the magnetic anisotropy and coupling with the substrate, −Jρ0. The red branch in Fig. 4a shows that as the substrate coupling increases, the axial magnetic anisotropy decreases. These results are in line with predictions that increased coupling shifts energy levels. The solid red line shows the best fit to our data and follows the trend D=D0(1−α(Jρ0)2), where α is a constant describing the bandwidth of the Kondo exchange interaction. The shaded red region accounts for the possible range of α by considering an effective bandwidth of ω0=0.4–1.2 eV (see Supplementary Information). For 0.1<−Jρ0<0.2 the variation in magnetic anisotropy fits exceptionally well, but for small values of −Jρ0, some spread in the axial anisotropy is observed. These fluctuations are not accounted for in our model and indicate that for small −Jρ0 additional factors such as strain or defects may contribute to the magnetic anisotropy. While the axial anisotropy shows clear dispersion, the transverse anisotropy is essentially constant (Fig. 4a, blue).
Figure 4b shows the influence of −Jρ0 on the tunnelling spectra calculated using a Bloch-Redfield approach to incorporate virtual correlations between the ground and excited states due to the coupling with the dissipative spin bath in the substrate assuming a flat density of states and an effective bandwidth of ω0=1 eV (Supplementary Fig. 4, Supplementary Note 3)9,17,18. As −Jρ0 is increased, virtual correlations lead to renormalization and reduce the level splitting. This is observed experimentally as a reduction of the axial magnetic anisotropy. Furthermore, higher order scattering processes in the tunnelling influence the conductance leading to an enhanced shoulder at the outer energy step that changes the contours of the spectrum (Supplementary Fig. 5). The symmetric peaks shift towards zero bias as −Jρ0 increases indicating that correlations drive the anisotropic spin-1 system closer to the Kondo state. Figure 4c schematically depicts the observed trend, when the spin is weakly coupled to the conduction electrons the magnetic anisotropy is stabilized. Increasing the exchange interaction introduces correlations between the excited spin states and the conduction electrons, leading to a net reduction in the magnetic anisotropy (Fig. 4d).
In conclusion, our results show that the Kondo exchange interaction modulates the magnetic anisotropy of single spin CoH complexes. The role of exchange was quantitatively determined by exploiting the corrugated h-BN moiré structure. In conjunction with third order perturbation theory simulations, we extracted the precise values of the spin coupling to the environment and its influence on the magnetic anisotropy. Kondo exchange must be considered an additional degree of freedom—beyond local symmetry, coordination number and spin state—for spins connected to contacts. This parameter is non-local and therefore expected to be discernable at surfaces, in junctions and perhaps in bulk SMM materials.
The Rh (111) surface was prepared by multiple cycles of argon ion sputtering and annealing to 1100 K. On the final annealing cycle borazine (B3N3H6) was introduced at a pressure of 1.2 × 10−6 mbar for 2 min resulting in a monolayer h-BN film. Cobalt was deposited onto a cold, ∼20 K, h-BN surface via an electron beam evaporator. Hydrogen is the predominant component of the residual gas background and is responsible for the formation of the cobalt hydride complexes30,31.
Scanning tunnelling experiments were performed on a home-built STM/AFM in ultra-high vacuum with a base temperature of 1.4 K and magnetic fields up to 14 T. All spectroscopic (dI/dV) measurements presented were obtained with an external lock-in amplifier and a modulation voltage of 0.2 mV applied to the bias voltage at a frequency of 799 Hz. The tunnelling set point before the feedback loop was disabled was V=−15 mV and I=500 pA. Given the distinct spectroscopic fingerprints, that is, steps or peaks, we used spectroscopy to sort our data as either spin-1 or spin-½. In conjunction with the DFT calculations, we assign the spin-½ species as CoH2 and spin-1 species as CoH. For measurements on the same adatoms in different external magnetic fields the tip was retracted while the field was ramped and allowed to settle for maximum stability. Supplementary Fig. 6 shows a bare Co adatom spectrum. Supplementary Fig. 7 shows an error analysis. Supplementary Fig. 8 shows a set point dependence.
Density functional calculations
First principles calculations have been carried out in the framework of the DFT as implemented in the Vienna Ab-initio Simulation Package (VASP) code32,33. We use the projector augmented-wave technique34 where the exchange and correlation were treated with the gradient-corrected PBE functional as formalized by Perdew, Burke and Ernzerhof35. Hubbard U and J values were taken from self-consistent calculations and fitting to experiments to be U−J=3 eV (refs 36, 37, 38). Full details are presented as Supplementary Note 1, Supplementary Fig. 1 and Supplementary Tables 1 and 2.
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P.J. acknowledges support from the Alexander von Humboldt Foundation. T.H., M.M. and M.T. acknowledge support by the SFB 767. O.B. and V.S. acknowledge support by the SFB 762.
The authors declare no competing financial interests.
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Jacobson, P., Herden, T., Muenks, M. et al. Quantum engineering of spin and anisotropy in magnetic molecular junctions. Nat Commun 6, 8536 (2015). https://doi.org/10.1038/ncomms9536
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