Moiré Tuning of Spin Excitations: Individual Fe Atoms on ${\mathrm{MoS}}_2/\mathrm{Au}(111)$

Magnetic adatoms on properly designed surfaces constitute exquisite systems for addressing, controlling, and manipulating single quantum spins. Here, we show that monolayers of ${\mathrm{MoS}}_2$ on a Au(111) surface provide a versatile platform for controllably tuning the coupling between adatom spins and substrate electrons. Even for equivalent adsorption sites with respect to the atomic ${\mathrm{MoS}}_2$ lattice, we observe that Fe adatoms exhibit behaviors ranging from pure spin excitations, characteristic of negligible exchange and dominant single-ion anisotropy, to a fully developed Kondo resonance, indicating strong exchange and negligible single-ion anisotropy. This tunability emerges from a moiré structure of ${\mathrm{MoS}}_2$ on Au(111) in conjunction with pronounced many-body renormalizations. We also find striking spectral variations in the immediate vicinity of the Fe atoms, which we explain by quantum interference reflecting the formation of Fe-S hybrid states despite the nominally inert nature of the substrate. Our work establishes monolayer ${\mathrm{MoS}}_2$ as a tuning layer for adjusting the quantum spin properties over an extraordinarily broad parameter range. The considerable variability can be exploited for quantum spin manipulations.

Figure 1

(a) STM image of ${\mathrm{MoS}}_2$ on Au(111) with a small number of iron atoms. ($V=50\mathrm{mV}$, $I=100\mathrm{pA}$). (b) Atomic-resolution topography of a clean ${\mathrm{MoS}}_2$ island. ($V=5\mathrm{mV}$, $I=42\mathrm{nA}$). (c) Close-up of individual Fe atoms on a ${\mathrm{MoS}}_2$ island. At low bias voltages, most atoms appear triangular. ($V=50\mathrm{mV}$, $I=100\mathrm{pA}$).

Figure 2

$dI/dV$ spectra at the center above Fe adatoms (blue) in different moiré environments as indicated by the STM topographies in the insets (scale bars are 1 nm, crosses mark the location of the spectra). The Fe atoms are located on islands with different orientations with respect to the Au(111) lattice [18]. Correspondingly, the triangles point in opposite directions. Fits are shown as black dashed lines. The spectrum in (a) can be reproduced by symmetric Fermi-Dirac functions. The spectra in (b)–(d) exhibit additional cusps on top of the inelastic steps. These spectra are fitted within a perturbative approach in the exchange interaction [26]. Spectrum (e) was fitted using a Frota line shape with an additional Lorentz peak. In (f), the spin excitation gap has closed, resulting in a fully developed Frota line shape. For fit parameters see Ref. [19]. Spectra recorded at $V=10\mathrm{mV}$, $I=1\mathrm{nA}$, lock-in frequency $f=911\mathrm{Hz}$ and modulation $V_{\mathrm{rms}}=50\mu \mathrm{V}$.

Figure 3

(a) STM topography of an Fe atom located on a moiré minimum. (b),(c) STM topographies (blue-yellow, background) with superimposed $dI/dV$ signal at the indicated bias voltage (black-white dots, scale below panels) extracted from a densely spaced grid of spectra. (d) $dI/dV$ spectra on the center [indicated by blue cross in (a)] and vertex [indicated with a purple cross in (a)]. Fits (black) as described in [26] with $J\rho =-0.13$, $U=-0.14$, $D=2.75\mathrm{mV}$ (center) and $J\rho =-0.13$, $U=-0.78$, $D=2.74\mathrm{mV}$ (vertex). (e) $dI/dV$ spectra (orange) recorded across the Fe-S complex along the orange line in (f) and fits (black) where $J\rho$ was kept constant in all fits, while $U$ and the transmittivity of the junctions were adjusted. Values of $U$ are shown in the Supplemental Material [19]. Spectra are offset for clarity. (f) STM topography (blue-yellow, background) with superimposed values of the potential scattering parameter $U$ (black-white dots, scale below panel) extracted from fits of a grid of spectra. (g) STM topography with superimposed $dI/dV$ signal at the indicated bias voltage extracted from a grid of spectra. (h) $dI/dV$ spectra over a larger energy range at the same positions as in (b). Spectra in (b)–(f) recorded at $V=10\mathrm{mV}$, $I=1\mathrm{nA}$ and tip retracted by 20 pm, lock-in frequency $f=911\mathrm{Hz}$ and modulation $V_{\mathrm{rms}}=50\mu \mathrm{V}$; spectra in (g) and (h) at $V=10\mathrm{mV}$, $I=20\mathrm{pA}$ and tip retracted by 20 pm, lock-in modulation $V_{\mathrm{rms}}=1\mathrm{mV}$. Grids were analyzed using SpectraFox [33].