State identification and tunable Kondo effect of MnPc on Ag(001)

We present a detailed investigation of spectroscopic features located at the central metal ion of MnPc (where Pc represents phthalocyanine) on Ag(001) by means of scanning tunneling spectroscopy (STS) and first-principles theory. STS data taken close to the Fermi level reveal an asymmetric feature that cannot be fitted with a single Fano function representing a one-channel Kondo effect. Instead, our data indicate the existence of a second superimposed feature. Two potential physical origins, a second Kondo channel related to the $d_{xz/yz}$ orbitals, and a spectral feature of the $d_{z^2}$ orbital itself, are discussed. A systematic experimental and theoretical comparison of MnPc with CoPc and FePc indicates that the second feature observed on MnPc is caused by the $d_{z^2}$ orbital. This conclusion is corroborated by STM-induced dehydrogenation experiments on FePc and MnPc which in both cases result in a gradual shift towards more positive binding energies and a narrowing of the Kondo resonance. Theoretical analysis reveals that the latter is caused by the reduced hybridization between the $d$ orbital and the substrate. Spatially resolved differential conductivity maps taken close to the respective peak positions show that the intensity of both features is highest over the central Mn ion, thereby providing further evidence against a second Kondo channel originating from the $d_{xz/yz}$ orbital of the central Mn ion.

Figure 1

Point spectrum measured with the STM tip positioned over the central metal ion of MnPc (black squares, repeated in the upper panel of each section of this figure) fitted with different functions (stabilization value $U=0.5$ V, $I=10$ nA): (a) a single Fano profile for modeling a single Kondo system, (b) two Fano profiles for modeling a double Kondo system, and (c) a Fano profile with a Gaussian peak superimposed for modeling a single Kondo system and a superimposed orbital state. The deviation between the different fitting functions and the measured data is shown in the lower panel (gray squares). While the single Fano profile shows significant deviations from the data, the quality of the fit is greatly improved for the other two models.

Figure 2

(a), (b) Constant-current topographs of MnPc, FePc, and CoPc on Ag(001) (scan parameters $U=+200\mathrm{mV},I=1\mathrm{nA}$). (c) Overview spectra of MnPc, FePc, and CoPc taken at the central metal ion of the molecule (stabilization value $U=-1\mathrm{V},I=1\mathrm{nA}$). The $dI/dU=0$ intensity for each spectrum is indicated by a colored dashed line. (d) $\mathrm{DFT}+\mathrm{PLO}$ spectra for CoPc, FePc, and MnPc showing the level shift of $d_{z^2}$ and $d_{xz/yz}$ orbitals.

Figure 3

Comparison of the spatial distributions of the two effects close to the Fermi energy: (a) Topography and (b), (c) $dI/dU$ maps of a MnPc molecule measured at the voltages indicated (taken from a full spectroscopy data set, stabilization parameters $U=200$ mV, $I=1$ nA). (d) Radial average of these $dI/dU$ maps (data points) compared to a line cut through the square of the calculated Wannier orbitals at 1.5 Å above the molecule for the $d_{z^2}$-like orbital (blue) and for the $d_{xz/yz}$-like orbitals (green) along the respective arm of the molecule where they do not vanish.

Figure 4

Dehydrogenation series of FePc: (a)–(d) Topographic images of the intact and the partly dehydrogenated molecules. The increment between two contour lines is 15 pm (scan parameters $U=+0.2$ V, $I=1$ nA). The dehydrogenated arms can be identified by the deflection of the arms and the resulting charge depletion on the substrate, indicated by the dark area. (e) Series of tunneling spectra (stabilization value $U=-1.0$ V, $I=1$ nA) measured on the molecules shown in (a)–(d). A gradual shift of the peak corresponding to the $d_{z^2}$ orbital towards the Fermi level can be observed, as marked by colored dashed lines.

Figure 5

(a) Calculated geometries for the complete MnPc molecule on Ag(001) and for successive dehydrogenation steps with two, four, and eight of the outer hydrogens atoms removed. (b),(c) Charge density of MnPc on Ag(001) integrated over an energy range of $\pm 200$ meV around the Fermi energy, cut along the center of one arm of the molecule for the complete molecule (b) and for the molecule with two outer hydrogens removed (c). The outer surface of the density is an isosurface at $5\times {10}^{-6}e/a_0^3$ ($a_0$ denoting the Bohr radius), while the color-coded section is cyan-magenta-yellow with yellow being the most saturated at $0.01e/a_0^3$ descending to cyan at $5\times {10}^{-6}e/a_0^3$. The outer isosurface has been highlighted with a black line to increase visibility. The observed decrease of the charge density in the vicinity of the dehydrogenated arms [compare the left arm of the molecule in (b) and (c)] is in accordance with the reduction of the apparent height observed in the STM topography (cf. Fig. 4).

Figure 6

Local spectral functions as obtained from $\mathrm{DFT}+\mathrm{PLO}$ calculations of the $d_{z^2}$ (left panel) as well as the $d_{xz/yz}$ orbitals (right) for (a) FePc and (b) MnPc, respectively. In both cases a shift of the orbitals towards positive energies is observed. Since the four fold symmetry of $d_{xz/yz}$ orbitals is broken for the $-2\mathrm{H}$ and $-4\mathrm{H}$ structures, an average is shown.

Figure 7

Dehydrogenation series of MnPc: (a)–(d) Topographic images of the intact and the partly dehydrogenated molecules, where the distance between two contour lines is 15 pm (scan parameters $U=+0.2$ V, $I=1$ nA). (e) The spectroscopy data (black dots) are fitted by a superposition (red) of a Gaussian (blue) and a Fano (green) profile (stabilization value $U=0.2$ V, $I=1$ nA). With progressing dehydrogenation a reduction of the Kondo temperature from $T_{\text{K}}=(135\pm 25)\mathrm{K}$ down to $T_{\text{K}}=(43\pm 5)\mathrm{K}$ is observed. The peak positions of the superimposed state are marked by colored dashed lines.

Figure 8

Decomposition of the local eigenstates contributing to the partition function during the CT-QMC imaginary-time evolution (in %) by (a) total charge and (b) total spin of the state. Numbers missing to make up 100% are due to minor contributions of other states. The most probable local contributions remain unaltered during the dehydrogenation series and are shown pictorially in (c).

Figure 9

$\mathrm{DFT}+\mathrm{CT}-\mathrm{QMC}$ spectrum of the $d_{z^2}$ orbital for the intact MnPc molecule as well as the $-4\mathrm{H}$ molecule on Ag(001). The calculations were performed at $\beta =200{\text{eV}}^{-1}\approx 58$ K. The curves are labeled by the ratio of the calculated temperature to the experimental Kondo temperature. In both cases, below the Kondo peak, or below its precursor slightly above the Fermi level for the $-4\mathrm{H}$ case, we find a small broad peak, which could be the origin of the superimposed feature seen in the STM measurements.