Microscopic origin of the quantum-size-effect modulation of the Kondo temperature of MnPc molecules on Pb(111) thin films: density-of-states versus exchange-coupling mechanisms

Fu et al. [Phys. Rev. Lett. 99, 256601 (2007)] showed by scanning tunneling spectroscopy that the Kondo temperature $T_K$ of individual manganese phthalocyanine (MnPc) molecules adsorbed on Pb(111) islands grown on Si(111) oscillates with the Pb film thickness with a period of two monolayers, ranging from about 23 K at 15 monolayers to 419 K at 17 monolayers, and attributed this to the modulation of the host density of states at the Fermi level by quantum-well states. The source left open the microscopic decomposition of this modulation: how much reflects the density-of-states variation and how much any thickness or adsorption-geometry dependence of the exchange coupling $J$; whether the anomalous $T_K$ maximum at 17 ML (where a quantum-well state crosses the Fermi level) is a genuine additional enhancement or an artifact; and the origin of a small zero-bias conductance dip seen both on MnPc and on bare oxidized Pb regions. A later film-only ab initio analysis found $J\approx 0.32$ eV and no thickness dependence between 11 and 18 monolayers, but excluded the 17 ML data point, reported a one-monolayer shift between computed and measured oscillations, and explicitly asked for further experiments; a counterexample (Co adatoms on Pb islands, where adsorption locally destroys the quantum-well states and $T_K$ hardly varies) shows the mechanism is impurity-dependent. The decomposition, the 17 ML anomaly, and the origin of the dip have not been settled in the literature, so the problem remains open.

Background

The Kondo effect is the many-body screening of a localized magnetic moment by conduction electrons of a nonmagnetic host; below a characteristic Kondo temperature $T_K$ the coupling becomes nonperturbative and a narrow many-body resonance (the Kondo resonance) appears in the impurity spectral function pinned to the host Fermi energy $E_F$. In scanning tunneling spectroscopy (STS, measuring the differential conductance $dI/dV$ versus bias), the resonance appears as a zero-bias peak, often with an asymmetric Fano lineshape because tunneling into the impurity interferes with direct tunneling into the host; Fu et al. fitted their spectra with the Doniach–Šunjić spectral function, whose width $\Gamma_K$ is proportional to $T_K$. For a single magnetic impurity coupled to a metal, perturbation theory gives $T_K\sim A\,\exp[-1/(\rho J)]$, where $\rho$ is the host density of states (DOS) at $E_F$ and $J$ is the antiferromagnetic exchange coupling between the impurity spin and host electrons; because of the exponential, small changes in $\rho J$ produce large changes in $T_K$. Manganese phthalocyanine (MnPc) is a flat organic molecule whose central Mn ion carries a local spin; first-principles density-functional calculations reported by Fu et al. (using the Vienna Ab initio Simulation Package, VASP) indicate that MnPc adsorbs on Pb(111) with the Mn ion on a top site (directly above a surface Pb atom), that the total molecular magnetic moment is reduced from about $3\,\mu_B$ (Bohr magnetons) for the free molecule to about $1\,\mu_B$ on the surface, mainly through strong hybridization of the Mn $d_{z^{2}}$ orbital with the Pb $p_z$ orbital beneath, and that the moment residing in the Mn $d_{xy}$ orbital is largely preserved because that orbital hybridizes only weakly with the substrate. Pb(111) films a few to tens of monolayers (ML) thick grown on Si(111) host quantum-well states (QWS): electronic states confined perpendicular to the film, formed when the film thickness matches standing-wave conditions for the Pb $6p_z$-like electrons. As the thickness changes layer by layer, QWS peaks sweep through $E_F$ and periodically modulate the DOS there (for this system with a 2 ML period and, as reported for the Fu et al. data, fractional changes of order ten percent). Fu, Ji, Chen, Ma, Wu, Wang, Duan, Qiu, Sun, Zhang, Jia, and Xue [Phys. Rev. Lett. 99, 256601 (2007)] used this to manipulate the Kondo effect of a single molecule: measuring $T_K$ of individual MnPc molecules on Pb islands of different thickness, they observed the oscillation described above, verified the Kondo attribution by the disappearance of the resonance when the molecule was decoupled by an oxidized Pb (PbO) patch and by linear Zeeman splitting in magnetic field, and argued that the QWS-induced DOS modulation quantitatively accounts for the $T_K$ variation. They also noted unresolved issues: the possible role of thickness-dependent changes in $J$ (expected to be less affected by QWS, with the caveat that a QWS crossing $E_F$, for example near 17 ML, might enhance $T_K$ further), and a small dip at zero bias observed both on MnPc and on bare oxidized Pb regions whose origin was not understood. Related single-impurity experiments in other confined geometries (Co adatoms on Cu films on Co/Cu(100), where $T_K$ varies between 60 K and 134 K across spacer thicknesses, and Co adatoms on Pb/Si(111) islands, where adsorption locally destroys the QWS and $T_K$ is nearly thickness-independent) show that whether quantum confinement controls $T_K$ depends sensitively on the impurity and geometry. The general open question is therefore a quantitative, microscopic account of which factor—host DOS or impurity–host exchange coupling—sets $T_K$ in a quantum-confined metallic film, for the specific MnPc/Pb(111)/Si(111) system in which the effect was demonstrated.

Problem Statement

Give a quantitative, microscopic account of the quantum-size-effect modulation of the Kondo temperature of individual MnPc molecules adsorbed on Pb(111) islands grown on Si(111), as observed by Fu et al. [Phys. Rev. Lett. 99, 256601 (2007)]: determine how the observed oscillation of $T_K$ with Pb film thickness (period 2 ML; minimum 23 K at 15 ML, maximum 419 K at 17 ML) decomposes into (a) the modulation of the host density of states $\rho(E_F)$ by the thickness-dependent quantum-well states and (b) any thickness- or adsorption-geometry-dependence of the exchange coupling $J$ (equivalently, the impurity-host hybridization) in the relation $T_K\sim A\exp[-1/(\rho J)]$. Concretely: (1) determine $J$ microscopically for this system, with the adsorbed molecule included, as a function of film thickness and adsorption geometry, and establish whether $J$ is effectively constant (as the one existing film-only ab initio analysis by Schwingenschlögl and Shelykh [Phys. Rev. B 80, 033101 (2009)] suggests) or varies, in particular at 17 ML; (2) clarify whether the anomalous $T_K$ maximum at 17 ML, where a quantum-well state crosses $E_F$, is a genuine additional enhancement beyond the DOS mechanism or an experimental artifact, and resolve the approximately one-monolayer shift between computed DOS oscillations and measured $T_K$; and (3) identify the origin of the small dip at zero bias observed in $dI/dV$ spectra both on MnPc molecules and on bare oxidized Pb (PbO) regions, distinguishing residual electronic-structure features from experimental artifacts. The scientific target is a validated microscopic account that predicts $T_K$ as a function of host thickness and adsorption geometry for a magnetic molecule on a quantum-confined metallic film, with all observed zero-bias spectral features attributed: a quantitatively consistent joint experimental and ab initio description of this system that goes beyond a repetition of the DOS-modulation argument.

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