Figure 1

Schematic situation: (a) Electrode tunnel-coupled to a transition-metal-organic complex. Charging of the complex by a tunnel process deforms the outer part of the ligand cage without strongly affecting the direct coordination sphere of the metal ion and thereby the ligand-field splitting. We assume that the extra electron is localized mainly on the cage. Electrons tunnel onto the ion through the tails of the molecular state centered on the ion, which includes admixtures of the outer shell electronic states. Therefore the main effect of the charging is the modulation of the tunnel barrier between the ion-centered states and electrode. (b) Occupation of the two $e$-type orbitals (orbital splitting $\delta$) discussed in the text in order of increasing many-particle energy going from left to right: $0,\delta -I,\delta ,2\delta$, where $I$ is the exchange energy.Reuse & Permissions

Figure 2

Two types of phonon-assisted Kondo cotunneling processes. (a) Virtual phonon absorption initiates a $S\mathrm{\text{−}}T$ transition, Kondo processes take place in an intermediate triplet state, and the phonon is emitted in the end. (b) Every spin-flip process in the intermediate triplet state is accompanied by a two-phonon process. Points and crosses denote spin-flip process in the $S\mathrm{\text{−}}T$ and $T\mathrm{\text{−}}T$ channels, $t_{i,f}$ are initial and final times, and $t_1,\dots ,t_n$ denote the intermediate cotunneling acts.Reuse & Permissions

Figure 3

(a) Bare exchange vertices $J_{S,R}$; (b) single-phonon correction $j_R$ to the vertex $J_R$; (c) two-phonon correction $j_S$ to the vertex $J_S$; (d),(e) renormalized vertices ${\gamma }_{1,2}$ corresponding to the processes illustrated by Figs. 2a, 2b, respectively.Reuse & Permissions