Electron spin secluded inside a bottom-up assembled standing metal-molecule nanostructure

Artificial nanostructures, fabricated by placing atoms or molecules as building blocks in well-defined positions, are a powerful platform in which quantum effects can be studied and exploited. In particular, they offer the opportunity to reduce the electronic interaction between large aromatic molecules and the underlying metallic substrate, if the manipulation capabilities of scanning tunneling microscopy to lift the molecule into an upright geometry on a pedestal of two metal atoms are used. Here, we report a strategy to study this interaction by investigating the Kondo effect. Measurements at millikelvin temperatures and in magnetic fields reveal that this bottom-up assembled standing metal-molecule nanostructure has an $S=1/2$ spin which is screened by substrate electrons, resulting in a Kondo temperature of only $291\pm 13$ mK. We extract its Landé $g$ factor and its exchange coupling $J\rho$ to the substrate, using a third-order perturbation theory in the weak-coupling and high-field regimes. We also show that the interaction between the scanning tunneling microscope tip and the molecule can tune the exchange coupling.

Figure 1

(a) Schematic view of a standing PTCDA $+$ 2Ag nanostructure on the Ag(111) surface, including the STM tip above the molecule. The bar shows the tunneling current $I_T$ measured above the standing nanostructure at constant height. The white, gray, and red spheres indicate hydrogen, carbon, and oxygen atoms, respectively, of PTCDA. (b) Constant-height STM image above a standing nanostructure recorded at a tip height of $z\simeq 17.5$ Å above the surface. The bias voltage was $V=-50$ mV. The white cross marks the location where the $dI/dV$ conductance spectra were measured. The molecular plane is indicated by the dashed orange line. (c) $dI/dV$ conductance spectrum (blue) on a standing metal-molecule nanostructure measured at $T=30$ mK and $B=0$ T ($I_T=45$ pA, $V=-1$ mV, $V_{\mathrm{mod}}=50$ $\mu \mathrm{V}$). The red curve shows the fit based on the Frota function (see text for details). The spectrum is shown in units of the conductance quantum $G_0=\frac{2e}{h}$.

Figure 2

(a) and (b) $dI/dV$ spectra (blue) on a standing metal-molecule nanostructure, measured at different $B$ fields at $T=40\text{–}50$ mK [set points in (a) were $I_T=100$ pA, $V=-1$ mV, $V_{\mathrm{mod}}=20$ $\mu \mathrm{V}$, and set points in (b) were $I_T=100$ pA, $V=-10$ mV, $V_{\mathrm{mod}}=100$ $\mu \mathrm{V}$]. In (a), the $B$ field was changed in steps of 20 mT. The orange curves in (b) show the fits based on perturbation theory (see text for details). The spectra are vertically displaced by multiples of $3.0\times {10}^{-4}{G}_0$ with respect to the spectrum measured at 0.2 T in (a) and by multiples of $1.0\times {10}^{-4}{G}_0$ with respect to the spectrum measured at 7 T in (b) for clarity. (c) and (d) The Zeeman splitting $\mathrm{\Delta }$ extracted from the $dI/dV$ spectra as a function of $B$. The gray dashed curve in (c) serves as a guide for the eye. The red line in (d) shows the linear fit for the Zeeman splitting.

Figure 3

(a) Coupling strength $J\rho$ as extracted from the fits in Fig. 2 as a function of $B$ field. (b) $dI/dV$ spectra (blue) on a standing metal-molecule nanostructure, measured at different temperatures in an external field $B=7$ T ($I_T=100$ pA, $V=-10$ mV, $V_{\mathrm{mod}}=100$ $\mu \mathrm{V}$). The orange curves show the fits based on perturbation theory (see text for details). The spectra are vertically displaced by multiples of $1.0\times {10}^{-4}{G}_0$ with respect to the spectrum at 41 mK for clarity. (c) Coupling strength $J\rho$ as extracted from the fits as a function of temperature. The dashed blue line indicates the Kondo energy scale $T_K$ as determined from the $B$-field data of Fig. 2. (d) Landé $g$ factor estimated from the fits in (b) (black) and the effective $g$ factor $g_{\mathrm{eff}}$ after taking into account renormalization effects due to the exchange interaction (red). The red line illustrates a linear fit, and the red shaded area illustrates the corresponding confidence interval.

Figure 4

Coupling strength $J\rho$ as extracted from the fits of $dI/dV$ spectra on a standing metal-molecule nanostructure that were measured for different set-point conductances at $T=40\text{–}50$ mK and an external field of $B=7$ T. The tip was initially stabilized at $I_T=100$ pA and $V=-6$ mV and then moved up by 1 Å in steps of 0.1 Å. The gray dashed curve serves as a guide for the eye. Insets show schematically how the PTCDA molecule is pulled up by the tip.

Figure 5

$dI/dV$ conductance spectra on a standing metal-molecule nanostructure (blue) and on the Ag(111) surface (black) measured at $T=40\text{–}50$ mK ($V_{\mathrm{mod}}=20$ $\mu \mathrm{V}$). The tip was stabilized at $I_T=100$ pA and $V=-1$ mV. The spectrum on the standing nanostructure corresponds to the spectrum in Fig. 2 at $B=80$ mT.

Figure 6

$d^{2}I/d{V}^2$ spectra (blue) on a standing metal-molecule nanostructure after applying a second-order Savitzky-Golay filter to the $dI/dV$ spectra and calculating the numerical derivative. These data correspond to the $dI/dV$ spectra in Fig. 2. The red (orange) dashed curves illustrate the Gaussian fits to the peaks at positive (negative) bias voltage. The spectra are vertically displaced for clarity.