Making closed-shell lead phthalocyanine paramagnetic on Pb(100)

Lead phthalocyanine (PbPc), a nonplanar molecule, is studied on Pb(100) by scanning tunneling spectroscopy. A rigid shift of the molecular orbitals is found between molecules with the central Pb ion pointing toward $(\mathrm{PbPc}\downarrow )$ or away from $(\mathrm{PbPc}\uparrow )$ the substrate and is understood from the interaction between the molecules and their image charges. Within the superconducting energy gap, Yu-Shiba-Rusinov (YSR) resonances are observed for $\mathrm{PbPc}\uparrow$ molecules in islands, indicating the presence of a magnetic moment. Such bound states are not present on $\mathrm{PbPc}\downarrow$ molecules, nor on isolated $\mathrm{PbPc}\uparrow$ or molecules that have lost the Pb ion during deposition $\left({\mathrm{H}}_0\mathrm{Pc}\right)$. The YSR energies vary depending on the orientation and type of the molecular neighbors. We analyze the role of the out-of-plane electrostatic dipole moment of PbPc.

Figure 1

Topographs of submonolayer coverages of PbPc on Pb(100). (a), (b) Images from two separate experimental runs. The PbPc molecules assemble into ordered islands. In addition, isolated ${\mathrm{H}}_0\mathrm{Pc}$ molecules are found. Squares in black, light blue, and red indicate examples of $\mathrm{PbPc}\uparrow$, $\mathrm{PbPc}\downarrow$, and ${\mathrm{H}}_0\mathrm{Pc}$ molecules, respectively. In the upper-left and lower-left parts of (a), two molecular domains are discernible. Imaging parameters: (a) $I=200\mathrm{pA}$, $V=-10\mathrm{mV}$; (b) $I=100\mathrm{pA}$, $V=100\mathrm{mV}$.

Figure 2

Topographs with molecular outlines indicated. (a), (b) Domains A and B. Black, light blue, and red lines show $\mathrm{PbPc}\uparrow$, $\mathrm{PbPc}\downarrow$, and ${\mathrm{H}}_0\mathrm{Pc}$ molecules. In domain A, the orientations of all molecules are fairly similar, while nearest neighbors are rotated by $\approx {20}^{\circ }$ with respect to each other in domain B. Imaging parameters: $I=100\mathrm{pA}$, $V=6\mathrm{mV}$ in (a) and $-6\mathrm{mV}$ in (b).

Figure 3

Adsorption geometry of PbPc on Pb(100). (a) Models of domains A and B. The square Pb(100) mesh is indicated by gray lines. Phthalocyanine molecules with different orientations are displayed as colored crosses. The molecules are arranged in a $\left[\begin{array}{cc}5& 3\\ -3& 5\end{array}\right]$ superstructure with two molecules per unit cell and occupy atop positions. (b) Molecular models of the orientations, which are described by the angles (arrows) enclosed between a molecular lobe and a $\langle 110\rangle$ direction. (c) Histogram of observed angles from 32 B1, 33 B2, 45 A1, and 45 A2 molecules. The scatter is partially due to measurement uncertainty ($\approx \pm 2^{\circ }$). In a few cases, e.g., $>{60}^{\circ }$, the molecular orientation does not fall in any of the four classes.

Figure 4

$dI/dV$ spectra measured at constant $I=76\mathrm{pA}$ with the tip placed above (a) $\mathrm{PbPc}\uparrow$, (b) $\mathrm{PbPc}\downarrow$, and (c) ${\mathrm{H}}_0\mathrm{Pc}$ molecules inside a domain-A island. Data at positive and negative $V$ were measured separately, starting at $V=\pm 100\mathrm{mV}$. A voltage modulation $V_M=14.1$ ${\mathrm{mV}}_{\mathrm{PP}}$ was used. A reference spectrum taken on the Pb(100) substrate has been subtracted from each data set. Arrows indicate major resonances that we attribute to molecular orbitals.

Figure 5

Image potential of (a) $\mathrm{PbPc}\uparrow$ and (b) $\mathrm{PbPc}\downarrow$ molecules calculated from the Mulliken charges from gas-phase DFT calculations. The image plane used is indicated by a dashed line. The molecules are represented by black dots at the projected atomic positions and a gray area representing constant LUMO density. Colored contour lines range from – 500 (blue) to 500 meV (red) in increments of 50 meV. $V_{im}=0$ is further marked using black dotted lines. Negatively charged nitrogen atoms of the molecular macrocycle are accompanied by positive image charges that lower the LUMO energy. For $\mathrm{PbPc}\downarrow$, the downshift is largely compensated by the negative image charge of the central Pb ion.

Figure 6

(a), (c) $dI/dV$ spectra of $\mathrm{PbPc}\uparrow$, isolated (blue curves) and inside an ordered island (red curves). In (a), a spectrum of the Pb(100) substrate was subtracted for background correction. The resonances at low voltages in (a) are attributed to the LUMO. They are located at 140 mV for the isolated molecule and at 30 mV for the molecule inside an island. Additional resonances at higher voltages are likely due to vibronic excitations. The low-bias spectra in (c) show the coherence peaks of the Pb substrate on the isolated molecule. In contrast, the spectrum measured inside an island exhibits resonances with different heights at $\approx \pm 2.05\mathrm{mV}$, i.e., inside the superconductor gap. The small features at $\approx \pm 0.57\mathrm{mV}$ are replicas of these peaks due to tunneling of thermally excited electrons or holes. Temperature of the tip and the sample: 2.21 K. (b) Spatial map of the LUMO peak height at $V=135\mathrm{mV}$ of an isolated $\mathrm{PbPc}\uparrow$ molecule. The map was generated from a $32\times 32$ grid of $I\left(V\right)$ spectra by numerical derivation, background subtraction, and low-pass filtering. The data are normalized to the normal-state conductance $G_N$, which was determined from the constant differential conductance at $V<-3.5\mathrm{mV}$. (d) Map of the normalized YSR peak height ($V=2.35\mathrm{mV}$) of a $\mathrm{PbPc}\uparrow$ molecule inside an ordered island, generated from a $16\times 16$ grid. Tip position frozen at (a) $V=1\mathrm{V}$, $I=100\mathrm{pA}$ with a voltage modulation of $V_M=14.1$ ${\mathrm{mV}}_{\mathrm{PP}}$, and (c) $V=6\mathrm{mV}$, $I=100\mathrm{pA}$, $V_M=113\mu {\mathrm{V}}_{\mathrm{PP}}$.

Figure 7

$dI/dV$ spectra of $\mathrm{PbPc}\uparrow$ molecules. (a) No YSR states are observed on isolated $\mathrm{PbPc}\uparrow$ molecules. (b)–(e) YSR signatures of molecule classes A1 – B2. The spectrum in (e) is scaled with a factor of 0.33. All spectra were measured with the tip position frozen at $V=6\mathrm{mV}$ and $I=100\mathrm{pA}$ with $V_M=113\mu {\mathrm{V}}_{\mathrm{PP}}.$ The parameters ${\tilde{E}}_P$ and ${\chi }^{*}$ are discussed in the main text.

Figure 8

${\tilde{E}}_P$ vs ${\chi }^{*}$ from many $\mathrm{PbPc}\uparrow$ molecules. Data from two STM instruments, denoted 1 and 2, are shown. Different molecular configurations are indicated by colors. Molecules of groups A1, A2, B1, and B2 were only considered when they were completely surrounded by neighbor molecules. Data points from molecules at the edges of ordered islands are labeled “Other.” The spectra underlying the data points with filled symbols and arrows are shown in Fig. 7.

Figure 9

(a) Topograph of a domain-A island ($V=2.6\mathrm{mV}$ and $I=50\mathrm{pA}$). (b) $dI/dV$ map measured simultaneously with the topograph. Increased (decreased) conductance is shown in yellow and red (blue). White corresponds to the differential conductance of the substrate. YSR states reduce the differential conductance at the voltage used and thus appear blue. Negative differential conductance (purple spots) is occasionally observed. The outlines of some molecules (classes A1 and A2, in red and black, respectively) are indicated for easier comparison of the maps.

Figure 10

Parametrization of the peak energy. Data from A1 $\mathrm{PbPc}\uparrow$ molecules and isolated $\mathrm{PbPc}\uparrow$ molecules are shown. The black line indicates a fit according to Eq. (1).