Transfering spin into an extended $\pi$ orbital of a large molecule

By means of low-temperature scanning tunneling microscopy (STM) and spectroscopy (STS), we have investigated the adsorption of single Au atoms on a PTCDA monolayer physisorbed on the Au(111) surface. A chemical reaction between the Au atom and the PTCDA molecule leads to the formation of a radical that has an unpaired electron in its highest occupied orbital. This orbital is a $\pi$ orbital that extends over the whole Au-PTCDA complex. Because of the large Coulomb repulsion in this orbital, the unpaired electron generates a local moment when the molecule is adsorbed on the Au(111) surface. We demonstrate the formation of the radical and the existence of the local moment after adsorption by observing a zero-bias differential conductance peak that originates from the Kondo effect. By temperature dependent measurements of the zero-bias differential conductance, we determine the Kondo temperature to be $T_{\mathrm{K}}=(38\pm 8)\mathrm{K}$. For the theoretical description of the properties of the Au-PTCDA complex we use a hierarchy of methods, ranging from density functional theory (DFT) including a van der Waals correction to many-body perturbation theory (MBPT) and the numerical renormalization group (NRG) approach. Regarding the high-energy orbital spectrum, we obtain an excellent agreement with experiments by both spin-polarized DFT/MBPT and NRG. Moreover, the NRG provides an accurate description of the low-energy excitation spectrum of the spin degree of freedom, predicting a Kondo temperature very close to the experimental value. This is achieved by a detailed analysis of the universality of various definitions of $T_{\mathrm{K}}$ and by taking into account the full energy dependence of the coupling function between the molecule-metal complex and the metallic substrate.

Figure 1

Constant current STM image $(200\AA \times 200\AA )$ after deposition of single Au atoms on a PTCDA monolayer on Au(111) (bias voltage $V=50\mathrm{m}\mathrm{V}$, tunneling current $I=2.8\times {10}^{-11}\mathrm{A})$. In the insets the two observed types of Au-PTCDA complexes are shown.

Figure 2

$dI/dV\left(V\right)$ spectra acquired over the center of type 1 (top) and type 2 (bottom) Au-PTCDA complexes. For clarity, the spectrum of type 1 is shifted by $+0.5\text{nS}$ (bias voltage and tunneling current at the stabilization point $V=500\mathrm{m}\mathrm{V}$ and $I=4.0\times {10}^{-11}\mathrm{A}$, lock-in modulation amplitude $5\mathrm{m}\mathrm{V}$ at $713.3\mathrm{Hz})$.

Figure 3

$dI/dV\left(V\right)$ spectra acquired over the center of different type 2 complexes (bias voltage and tunneling current at the stabilization point $V=$ $360\mathrm{m}\mathrm{V}$ and $I=2.5\times {10}^{-11}\mathrm{A},z$-offset = +1.$0\AA$, lock-in modulation amplitude $1\mathrm{m}\mathrm{V}$ at $5981\mathrm{Hz})$. The spectra are vertically displaced for clarity.

Figure 4

(a) Experimentally determined centres of type 1 (blue) and type 2 (red) Au atoms in the PTCDA unit cell on Au(111). The white, grey, and red circles indicate hydrogen, carbon, and oxygen atoms of PTCDA. The golden spheres denote the positions of the Au atoms in the topmost layer of the Au surface, assuming a commensurate arrangement of the molecules. (b) Potential energy surface (in eV) for an Au atom adsorbed on a PTCDA freestanding monolayer.

Figure 5

Theoretical constant current STM images of (a) Au on PTCDA/Au(111) and (b) Au on PTCDA/Au(111) with an additional hydrogen molecule adsorbed on the Au atom. The green circle denotes the position of the Au atom, the pink circles the positions of the hydrogen atoms. The tip height is given in angstrom. The insets below show the structure of the corresponding complexes.

Figure 6

Constant current STM image $(710\AA \times 710\AA )$ taken after hydrogen decontamination of the low-temperature STM (bias voltage $V=$ $316\mathrm{m}\mathrm{V}$, tunneling current $I=2.5\times {10}^{-11}\mathrm{A})$. As highlighted in the inset, only type 1 Au-PTCDA complexes are observed.

Figure 7

(a) FWHM of the differential conductance peak at zero bias, measured at different temperatures. Data points include measurements with different tips and on different Au-PTCDA complexes of type 1. Note that the FWHM after deconvolution to correct for broadening due to finite temperature and modulation amplitude are plotted. (b) $dI/dV\left(V\right)$ conductance (as measured, not deconvoluted) of one type 1 Au-PTCDA at $T\approx$ $5\mathrm{K}$. (c) Peak heights of the differential conductance peak at zero bias, measured at different temperatures. All data points were measured with the same tip on the same Au-PTCDA complex. (d) $dI/dV\left(V\right)$ conductance of the same radical as in (c) at specific temperatures. (b) and (d) Bias voltage and tunneling current at the stabilization point $V=$ $316\mathrm{m}\mathrm{V}$ and $I=$ $2.5\times {10}^{-11}\mathrm{A},z$ offset = +1.$0\AA$, lock-in modulation amplitude $1\mathrm{m}\mathrm{V}$ at $6100\mathrm{Hz}$.

Figure 8

Wave functions of PTCDA (left) and Au-PTCDA (right) for orbitals around $E_F$ calculated within LDA. Green indicates the positive isosurface, red the negative one.

Figure 9

Projected density of states of a commensurate PTCDA monolayer adsorbed on Au(111) with two PTCDA molecules in the unit cell. The PDOS was obtained within the LDA (dashed blue, vertically shifted for clarity) and the LDA+$GdW$ (black). The energies are given relative to the Fermi level of the Au(111) substrate.

Figure 10

Projected density of states for the PTCDA molecule and the Au-PTCDA complex in the monolayer, adsorbed on Au(111). The PDOS was evaluated from LDA+$GdW$ energies. The projection on the states of the Au-PTCDA complex is shown in shades of red (solid), while projections on the PTCDA molecule are shown in shades of blue (dashed). The yellow curve marks the projection on the states of the Au atom (6s and 6p) only. In addition the wave functions of some of the involved levels are plotted in corresponding colors. The energies are given relative to the Fermi level of the Au(111) substrate.

Figure 11

Projected density of states of the LUMO+Au orbital from an unpolarized LDA+$GdW$ calculation (black) in comparison to the spin-polarized LSDA+$GdW$ result (red dashed) of Fig. 10. In addition, the LDA+$GdW$+NRG result is included $(T=0\text{K}$ and $U=1.2\text{eV}$, see Sec. 3d).

Figure 12

The full energy-dependent hybridization function $\Gamma \left(E\right)$ obtained from the LDA+$GdW$ PDOS. $\Gamma \left(E\right)$ is independent of the Coulomb interaction $U$ and therefore always the same for every NRG calculation in which an energy-dependent hybridization function is used.

Figure 13

Results of the NRG calculations based on the LDA+$GdW$ for the Au-PTCDA complex on Au(111). (a) Spectra for three different values $U=1.1,1.2,1.3\text{eV}$ and $T=5\text{K}$. The Kondo temperature is increasing with decreasing $U$. (b) Spectra for different temperatures for $U=1.2\text{eV}$. (c) The temperature dependent differential conductance for different interactions $U$ as a universal function of $T/T_{\mathrm{K}}^{\text{zbc}}$. (d) Zero-temperature spectra for the interactions $U=1.1$ and $1.3\text{eV}$ and their Fano fits to extract the FWHM. For more details see main text.