Statistical analysis of electron-induced switching of a spin-crossover complex

TL;DR

This work addresses how tunneling electrons induce spin-state switching in a single Fe(II) SCO complex on Ag(111) and what molecular orbitals are involved. By analyzing waiting-time distributions from extensive STM time traces, the authors develop a four-state master-equation model that includes neutral and transiently charged spin states, yielding effective two-state switching rates and estimating the energies of participating molecular orbitals. The fits reveal orbital energies around $ε_L ≈ 1.105$ eV and $ε_H ≈ 1.100$ eV, consistent with, or slightly above, DFT predictions, and demonstrate that transient charging governs the switching; ab initio results support the involvement of a LUMO-related state near 0.7–1.15 eV. The model also predicts that electron-induced switching should be enhanced by reducing molecule–substrate coupling, for instance via an ultrathin insulating layer, providing design guidelines for SCO-based molecular devices.

Abstract

Spin-crossover complexes exhibit two stable configurations with distinct spin states. The investigation of these molecules using low-temperature scanning tunneling microscopy has opened new perspectives for understanding the associated switching mechanisms at the single-molecule level. While the role of tunneling electrons in driving the spin-state switching has been clearly evidenced, the underlying microscopic mechanism is not completely understood. In this study, we investigate the electron-induced switching of [Fe(H$_2$B(pz)(pypz))$_2$] (pz = pyrazole, pypz = pyridylpyrazole) adsorbed on Ag(111). The current time traces show transitions between two current levels corresponding to the two spin states. We extract switching rates from these traces by analyzing waiting-time distributions. Their sample-voltage dependence can be explained within a simple model in which the switching is triggered by a transient charging of the molecule. The comparison between experimental data and theoretical modeling provides estimates for the energies of the lowest unoccupied molecular orbitals, which were so far experimentally inaccessible. Overall, our approach offers new insights into the electron-induced switching mechanism and predicts enhanced switching rates upon electronic decoupling of the molecule from the metallic substrate, for example by introducing an ultrathin insulating layer.

Figures (8)

• Figure 1: (a) Scheme of the experiment with a single molecule in the tunneling gap of a STM. (b) Exemplary time series of the tunneling current (black dots) measured across a switchable complex. The state with higher (lower) tunneling current represents the $H$ ($L$) state. This time trace was measured with a sample voltage of $\qty{1}{V}$. The red line is a guide to better visualize the states of the complex along with transitions between those states, for which a statistical analysis is performed.
• Figure 2: Example of waiting-time distributions (dots) using a binning of 0.25 s displayed in a logarithmic plot. The corresponding time trace was recorded with a sample voltage of $V=\qty{1}{V}$ leading to tunneling currents of $I_{\text{T},L}=\qty{2.87}{pA}$ and $I_{\text{T},H}=\qty{3.90}{pA}$ in the $L$ and $H$ states, respectively. The solid lines are linear fits of the logarithms of the WTD, effectively describing an exponential time decay with a decay constant of $(1.19\pm 0.07)\,\text{s}^{-1}$ for the $L\rightarrow H$ and $(3.33\pm 0.18)\,\text{s}^{-1}$ for the $H\rightarrow L$ transition. Note that the uncertainties are the ones given by the fitting routine. The colored areas illustrate the impact of those uncertainties.
• Figure 3: Switching yields $Y_{ L\to H}$ and $Y_{ H\to L}$ as a function of the sample voltage $V$. The uncertainty bars are determined from Eq. \ref{['UncertaintyYield']}. The solid lines are fits of the switching yields using Eq. \ref{['FitfunktionArctan']}footnote1 for both switching directions separately, as described in section \ref{['chap:2state']}. The fit parameters are provided in Appendix \ref{['app:fits']}.
• Figure 4: Scheme of the electronic transport from the tip to the substrate via a molecular orbital at an energy $\epsilon$. The difference of the chemical potentials between the tip and the substrate is adjusted with the sample voltage $V$. The electronic coupling between the molecule and the substrate $\Gamma_\text{sub}$ is assumed to be significantly larger than that between the tip and the molecule $\Gamma_\text{tip}$, a general situation for STM experiments. The transmission through the molecular state (depicted in red) has a Breit-Wigner form with the width essentially determined by the electronic coupling to the substrate $\Gamma_\text{sub}$.
• Figure 5: Fraction of the current via the molecular orbital $I_{\text{mol}}/I_\text{T}$ as a function of the sample voltage $V$ for different parameters (a) $\Gamma_{\text{sub}}/\hbar$, (b) $\alpha$, and (c) $\varepsilon$. Note that these plots assume a constant-current measurement mode, where the tip-substrate distance is adjusted to maintain $I_T$ constant. In each plot all constant parameters are set to $\Gamma_{\text{sub}}/\hbar = 10^{13}$ s$^{-1}$, $\alpha = 1$ V$^{-1}$, and $\varepsilon = 1$ eV which corresponds to the blue curves.